id	sid	tid	token	lemma	pos
ejpam-6262	1	1	european	european	PROPN
ejpam-6262	1	2	journal	journal	PROPN
ejpam-6262	1	3	of	of	ADP
ejpam-6262	1	4	pure	pure	ADJ
ejpam-6262	1	5	and	and	CCONJ
ejpam-6262	1	6	applied	applied	ADJ
ejpam-6262	1	7	mathematics	mathematic	NOUN
ejpam-6262	1	8	2025	2025	NUM
ejpam-6262	1	9	,	,	PUNCT
ejpam-6262	1	10	vol	vol	NOUN
ejpam-6262	1	11	.	.	PROPN
ejpam-6262	1	12	18	18	NUM
ejpam-6262	1	13	,	,	PUNCT
ejpam-6262	1	14	issue	issue	NOUN
ejpam-6262	1	15	3	3	NUM
ejpam-6262	1	16	,	,	PUNCT
ejpam-6262	1	17	article	article	NOUN
ejpam-6262	1	18	number	number	NOUN
ejpam-6262	1	19	6262	6262	NUM
ejpam-6262	1	20	issn	issn	PROPN
ejpam-6262	1	21	1307	1307	NUM
ejpam-6262	1	22	-	-	SYM
ejpam-6262	1	23	5543	5543	NUM
ejpam-6262	1	24	–	–	PUNCT
ejpam-6262	2	1	ejpam.com	ejpam.com	X
ejpam-6262	2	2	published	publish	VERB
ejpam-6262	2	3	by	by	ADP
ejpam-6262	2	4	new	new	PROPN
ejpam-6262	2	5	york	york	PROPN
ejpam-6262	2	6	business	business	PROPN
ejpam-6262	2	7	global	global	ADJ
ejpam-6262	2	8	derivative	derivative	ADJ
ejpam-6262	2	9	-	-	PUNCT
ejpam-6262	2	10	free	free	ADJ
ejpam-6262	2	11	method	method	NOUN
ejpam-6262	2	12	for	for	ADP
ejpam-6262	2	13	nonlinear	nonlinear	ADJ
ejpam-6262	2	14	systems	system	NOUN
ejpam-6262	2	15	with	with	ADP
ejpam-6262	2	16	some	some	DET
ejpam-6262	2	17	real	real	ADJ
ejpam-6262	2	18	-	-	PUNCT
ejpam-6262	2	19	life	life	NOUN
ejpam-6262	2	20	applications	application	NOUN
ejpam-6262	2	21	yanal	yanal	PROPN
ejpam-6262	2	22	al	al	PROPN
ejpam-6262	2	23	-	-	PUNCT
ejpam-6262	2	24	shorman1,∗	shorman1,∗	NOUN
ejpam-6262	2	25	,	,	PUNCT
ejpam-6262	2	26	abdullah	abdullah	PROPN
ejpam-6262	2	27	alsoboh2	alsoboh2	PROPN
ejpam-6262	2	28	,	,	PUNCT
ejpam-6262	2	29	obadah	obadah	PROPN
ejpam-6262	2	30	said	say	VERB
ejpam-6262	2	31	solaiman1	solaiman1	PROPN
ejpam-6262	2	32	,	,	PUNCT
ejpam-6262	2	33	ishak	ishak	VERB
ejpam-6262	2	34	hashim1,3	hashim1,3	PROPN
ejpam-6262	2	35	1	1	NUM
ejpam-6262	2	36	school	school	NOUN
ejpam-6262	2	37	of	of	ADP
ejpam-6262	2	38	mathematical	mathematical	ADJ
ejpam-6262	2	39	sciences	science	NOUN
ejpam-6262	2	40	,	,	PUNCT
ejpam-6262	2	41	faculty	faculty	NOUN
ejpam-6262	2	42	of	of	ADP
ejpam-6262	2	43	science	science	PROPN
ejpam-6262	2	44	&	&	CCONJ
ejpam-6262	2	45	technology	technology	PROPN
ejpam-6262	2	46	,	,	PUNCT
ejpam-6262	2	47	universiti	universiti	PROPN
ejpam-6262	2	48	kebangsaan	kebangsaan	PROPN
ejpam-6262	2	49	malaysia	malaysia	PROPN
ejpam-6262	2	50	,	,	PUNCT
ejpam-6262	2	51	43600	43600	NUM
ejpam-6262	2	52	bangi	bangi	PROPN
ejpam-6262	2	53	,	,	PUNCT
ejpam-6262	2	54	selangor	selangor	PROPN
ejpam-6262	2	55	,	,	PUNCT
ejpam-6262	2	56	malaysia	malaysia	PROPN
ejpam-6262	2	57	2	2	NUM
ejpam-6262	2	58	department	department	NOUN
ejpam-6262	2	59	of	of	ADP
ejpam-6262	2	60	basic	basic	ADJ
ejpam-6262	2	61	and	and	CCONJ
ejpam-6262	2	62	applied	applied	ADJ
ejpam-6262	2	63	sciences	science	NOUN
ejpam-6262	2	64	,	,	PUNCT
ejpam-6262	2	65	college	college	NOUN
ejpam-6262	2	66	of	of	ADP
ejpam-6262	2	67	applied	apply	VERB
ejpam-6262	2	68	and	and	CCONJ
ejpam-6262	2	69	health	health	NOUN
ejpam-6262	2	70	sciences	science	NOUN
ejpam-6262	2	71	,	,	PUNCT
ejpam-6262	2	72	a’sharqiyah	a’sharqiyah	PROPN
ejpam-6262	2	73	university	university	NOUN
ejpam-6262	2	74	,	,	PUNCT
ejpam-6262	3	1	post	post	PROPN
ejpam-6262	3	2	box	box	PROPN
ejpam-6262	3	3	no	no	INTJ
ejpam-6262	3	4	.	.	PROPN
ejpam-6262	3	5	42	42	NUM
ejpam-6262	3	6	,	,	PUNCT
ejpam-6262	3	7	post	post	VERB
ejpam-6262	3	8	code	code	NOUN
ejpam-6262	3	9	no	no	INTJ
ejpam-6262	3	10	.	.	PROPN
ejpam-6262	3	11	400	400	NUM
ejpam-6262	3	12	,	,	PUNCT
ejpam-6262	3	13	ibra	ibra	NOUN
ejpam-6262	3	14	,	,	PUNCT
ejpam-6262	3	15	sultanate	sultanate	NOUN
ejpam-6262	3	16	of	of	ADP
ejpam-6262	3	17	oman	oman	PROPN
ejpam-6262	3	18	3	3	NUM
ejpam-6262	3	19	nonlinear	nonlinear	ADJ
ejpam-6262	3	20	dynamics	dynamic	NOUN
ejpam-6262	3	21	research	research	NOUN
ejpam-6262	3	22	center	center	NOUN
ejpam-6262	3	23	(	(	PUNCT
ejpam-6262	3	24	ndrc	ndrc	PROPN
ejpam-6262	3	25	)	)	PUNCT
ejpam-6262	3	26	,	,	PUNCT
ejpam-6262	3	27	ajman	ajman	PROPN
ejpam-6262	3	28	university	university	PROPN
ejpam-6262	3	29	,	,	PUNCT
ejpam-6262	3	30	ajman	ajman	PROPN
ejpam-6262	3	31	,	,	PUNCT
ejpam-6262	3	32	p.o	p.o	PROPN
ejpam-6262	3	33	.	.	PROPN
ejpam-6262	3	34	box	box	PROPN
ejpam-6262	3	35	346	346	NUM
ejpam-6262	3	36	,	,	PUNCT
ejpam-6262	3	37	united	united	PROPN
ejpam-6262	3	38	arab	arab	PROPN
ejpam-6262	3	39	emirates	emirates	PROPN
ejpam-6262	3	40	abstract	abstract	PROPN
ejpam-6262	3	41	.	.	PUNCT
ejpam-6262	4	1	this	this	DET
ejpam-6262	4	2	study	study	NOUN
ejpam-6262	4	3	implements	implement	VERB
ejpam-6262	4	4	a	a	DET
ejpam-6262	4	5	very	very	ADV
ejpam-6262	4	6	effective	effective	ADJ
ejpam-6262	4	7	derivative	derivative	ADJ
ejpam-6262	4	8	-	-	PUNCT
ejpam-6262	4	9	free	free	ADJ
ejpam-6262	4	10	approach	approach	NOUN
ejpam-6262	4	11	for	for	ADP
ejpam-6262	4	12	root	root	NOUN
ejpam-6262	4	13	determination	determination	NOUN
ejpam-6262	4	14	in	in	ADP
ejpam-6262	4	15	the	the	DET
ejpam-6262	4	16	context	context	NOUN
ejpam-6262	4	17	of	of	ADP
ejpam-6262	4	18	nonlinear	nonlinear	ADJ
ejpam-6262	4	19	equations	equation	NOUN
ejpam-6262	4	20	.	.	PUNCT
ejpam-6262	5	1	the	the	DET
ejpam-6262	5	2	use	use	NOUN
ejpam-6262	5	3	of	of	ADP
ejpam-6262	5	4	homeier	homeier	PROPN
ejpam-6262	5	5	’s	’s	PART
ejpam-6262	5	6	third	third	ADJ
ejpam-6262	5	7	-	-	PUNCT
ejpam-6262	5	8	order	order	NOUN
ejpam-6262	5	9	technique	technique	NOUN
ejpam-6262	5	10	,	,	PUNCT
ejpam-6262	5	11	which	which	PRON
ejpam-6262	5	12	is	be	AUX
ejpam-6262	5	13	based	base	VERB
ejpam-6262	5	14	on	on	ADP
ejpam-6262	5	15	the	the	DET
ejpam-6262	5	16	application	application	NOUN
ejpam-6262	5	17	of	of	ADP
ejpam-6262	5	18	newton	newton	PROPN
ejpam-6262	5	19	’s	’s	PART
ejpam-6262	5	20	theorem	theorem	VERB
ejpam-6262	5	21	to	to	ADP
ejpam-6262	5	22	the	the	DET
ejpam-6262	5	23	inverse	inverse	NOUN
ejpam-6262	5	24	function	function	NOUN
ejpam-6262	5	25	,	,	PUNCT
ejpam-6262	5	26	as	as	ADV
ejpam-6262	5	27	well	well	ADV
ejpam-6262	5	28	as	as	ADP
ejpam-6262	5	29	the	the	DET
ejpam-6262	5	30	development	development	NOUN
ejpam-6262	5	31	of	of	ADP
ejpam-6262	5	32	a	a	DET
ejpam-6262	5	33	new	new	ADJ
ejpam-6262	5	34	category	category	NOUN
ejpam-6262	5	35	of	of	ADP
ejpam-6262	5	36	newton	newton	PROPN
ejpam-6262	5	37	-	-	PUNCT
ejpam-6262	5	38	type	type	NOUN
ejpam-6262	5	39	procedures	procedure	NOUN
ejpam-6262	5	40	that	that	PRON
ejpam-6262	5	41	exhibit	exhibit	VERB
ejpam-6262	5	42	cubic	cubic	ADJ
ejpam-6262	5	43	convergence	convergence	NOUN
ejpam-6262	5	44	,	,	PUNCT
ejpam-6262	5	45	is	be	AUX
ejpam-6262	5	46	the	the	DET
ejpam-6262	5	47	basis	basis	NOUN
ejpam-6262	5	48	of	of	ADP
ejpam-6262	5	49	this	this	DET
ejpam-6262	5	50	study	study	NOUN
ejpam-6262	5	51	.	.	PUNCT
ejpam-6262	6	1	a	a	DET
ejpam-6262	6	2	variety	variety	NOUN
ejpam-6262	6	3	of	of	ADP
ejpam-6262	6	4	non	non	ADJ
ejpam-6262	6	5	-	-	ADJ
ejpam-6262	6	6	linear	linear	ADJ
ejpam-6262	6	7	problems	problem	NOUN
ejpam-6262	6	8	,	,	PUNCT
ejpam-6262	6	9	such	such	ADJ
ejpam-6262	6	10	as	as	ADP
ejpam-6262	6	11	non	non	ADJ
ejpam-6262	6	12	-	-	ADJ
ejpam-6262	6	13	linear	linear	ADJ
ejpam-6262	6	14	equations	equation	NOUN
ejpam-6262	6	15	and	and	CCONJ
ejpam-6262	6	16	non	non	ADJ
ejpam-6262	6	17	-	-	ADJ
ejpam-6262	6	18	linear	linear	ADJ
ejpam-6262	6	19	systems	system	NOUN
ejpam-6262	6	20	of	of	ADP
ejpam-6262	6	21	equations	equation	NOUN
ejpam-6262	6	22	,	,	PUNCT
ejpam-6262	6	23	have	have	AUX
ejpam-6262	6	24	been	be	AUX
ejpam-6262	6	25	examined	examine	VERB
ejpam-6262	6	26	to	to	PART
ejpam-6262	6	27	examine	examine	VERB
ejpam-6262	6	28	the	the	DET
ejpam-6262	6	29	efficacy	efficacy	NOUN
ejpam-6262	6	30	of	of	ADP
ejpam-6262	6	31	the	the	DET
ejpam-6262	6	32	proposed	propose	VERB
ejpam-6262	6	33	method	method	NOUN
ejpam-6262	6	34	in	in	ADP
ejpam-6262	6	35	contrast	contrast	NOUN
ejpam-6262	6	36	to	to	ADP
ejpam-6262	6	37	other	other	ADJ
ejpam-6262	6	38	widely	widely	ADV
ejpam-6262	6	39	used	use	VERB
ejpam-6262	6	40	derivative	derivative	ADJ
ejpam-6262	6	41	-	-	PUNCT
ejpam-6262	6	42	free	free	ADJ
ejpam-6262	6	43	approaches	approach	NOUN
ejpam-6262	6	44	.	.	PUNCT
ejpam-6262	7	1	the	the	DET
ejpam-6262	7	2	results	result	NOUN
ejpam-6262	7	3	suggest	suggest	VERB
ejpam-6262	7	4	that	that	SCONJ
ejpam-6262	7	5	the	the	DET
ejpam-6262	7	6	proposed	propose	VERB
ejpam-6262	7	7	method	method	NOUN
ejpam-6262	7	8	outperforms	outperform	VERB
ejpam-6262	7	9	the	the	DET
ejpam-6262	7	10	currently	currently	ADV
ejpam-6262	7	11	examined	examine	VERB
ejpam-6262	7	12	techniques	technique	NOUN
ejpam-6262	7	13	published	publish	VERB
ejpam-6262	7	14	.	.	PUNCT
ejpam-6262	8	1	the	the	DET
ejpam-6262	8	2	scheme	scheme	NOUN
ejpam-6262	8	3	given	give	VERB
ejpam-6262	8	4	in	in	ADP
ejpam-6262	8	5	this	this	DET
ejpam-6262	8	6	study	study	NOUN
ejpam-6262	8	7	demonstrates	demonstrate	VERB
ejpam-6262	8	8	a	a	DET
ejpam-6262	8	9	reduced	reduced	ADJ
ejpam-6262	8	10	number	number	NOUN
ejpam-6262	8	11	of	of	ADP
ejpam-6262	8	12	iterations	iteration	NOUN
ejpam-6262	8	13	acquired	acquire	VERB
ejpam-6262	8	14	in	in	ADP
ejpam-6262	8	15	attaining	attain	VERB
ejpam-6262	8	16	the	the	DET
ejpam-6262	8	17	intended	intend	VERB
ejpam-6262	8	18	result	result	NOUN
ejpam-6262	8	19	,	,	PUNCT
ejpam-6262	8	20	exhibiting	exhibit	VERB
ejpam-6262	8	21	a	a	DET
ejpam-6262	8	22	convergence	convergence	NOUN
ejpam-6262	8	23	order	order	NOUN
ejpam-6262	8	24	of	of	ADP
ejpam-6262	8	25	around	around	ADP
ejpam-6262	8	26	2.5	2.5	NUM
ejpam-6262	8	27	.	.	PUNCT
ejpam-6262	9	1	this	this	DET
ejpam-6262	9	2	convergence	convergence	NOUN
ejpam-6262	9	3	order	order	NOUN
ejpam-6262	9	4	surpasses	surpass	VERB
ejpam-6262	9	5	the	the	DET
ejpam-6262	9	6	convergence	convergence	NOUN
ejpam-6262	9	7	order	order	NOUN
ejpam-6262	9	8	observed	observe	VERB
ejpam-6262	9	9	in	in	ADP
ejpam-6262	9	10	comparable	comparable	ADJ
ejpam-6262	9	11	approaches	approach	NOUN
ejpam-6262	9	12	.	.	PUNCT
ejpam-6262	10	1	moreover	moreover	ADV
ejpam-6262	10	2	,	,	PUNCT
ejpam-6262	10	3	by	by	ADP
ejpam-6262	10	4	following	follow	VERB
ejpam-6262	10	5	the	the	DET
ejpam-6262	10	6	prescribed	prescribed	ADJ
ejpam-6262	10	7	procedure	procedure	NOUN
ejpam-6262	10	8	of	of	ADP
ejpam-6262	10	9	the	the	DET
ejpam-6262	10	10	broyden	broyden	ADJ
ejpam-6262	10	11	technique	technique	NOUN
ejpam-6262	10	12	while	while	SCONJ
ejpam-6262	10	13	implementing	implement	VERB
ejpam-6262	10	14	the	the	DET
ejpam-6262	10	15	recommended	recommend	VERB
ejpam-6262	10	16	approach	approach	NOUN
ejpam-6262	10	17	in	in	ADP
ejpam-6262	10	18	the	the	DET
ejpam-6262	10	19	solution	solution	NOUN
ejpam-6262	10	20	of	of	ADP
ejpam-6262	10	21	nonlinear	nonlinear	ADJ
ejpam-6262	10	22	equation	equation	NOUN
ejpam-6262	10	23	systems	system	NOUN
ejpam-6262	10	24	,	,	PUNCT
ejpam-6262	10	25	the	the	DET
ejpam-6262	10	26	problem	problem	NOUN
ejpam-6262	10	27	pertaining	pertain	VERB
ejpam-6262	10	28	to	to	ADP
ejpam-6262	10	29	the	the	DET
ejpam-6262	10	30	jacobian	jacobian	PROPN
ejpam-6262	10	31	can	can	AUX
ejpam-6262	10	32	be	be	AUX
ejpam-6262	10	33	circumvented	circumvent	VERB
ejpam-6262	10	34	.	.	PUNCT
ejpam-6262	11	1	hence	hence	ADV
ejpam-6262	11	2	,	,	PUNCT
ejpam-6262	11	3	the	the	DET
ejpam-6262	11	4	technique	technique	NOUN
ejpam-6262	11	5	suggested	suggest	VERB
ejpam-6262	11	6	may	may	AUX
ejpam-6262	11	7	be	be	AUX
ejpam-6262	11	8	regarded	regard	VERB
ejpam-6262	11	9	as	as	ADP
ejpam-6262	11	10	a	a	DET
ejpam-6262	11	11	prominent	prominent	ADJ
ejpam-6262	11	12	approach	approach	NOUN
ejpam-6262	11	13	that	that	PRON
ejpam-6262	11	14	achieves	achieve	VERB
ejpam-6262	11	15	rapid	rapid	ADJ
ejpam-6262	11	16	convergence	convergence	NOUN
ejpam-6262	11	17	in	in	ADP
ejpam-6262	11	18	determining	determine	VERB
ejpam-6262	11	19	the	the	DET
ejpam-6262	11	20	roots	root	NOUN
ejpam-6262	11	21	of	of	ADP
ejpam-6262	11	22	non	non	ADJ
ejpam-6262	11	23	-	-	ADJ
ejpam-6262	11	24	linear	linear	ADJ
ejpam-6262	11	25	equations	equation	NOUN
ejpam-6262	11	26	without	without	ADP
ejpam-6262	11	27	the	the	DET
ejpam-6262	11	28	use	use	NOUN
ejpam-6262	11	29	of	of	ADP
ejpam-6262	11	30	derivatives	derivative	NOUN
ejpam-6262	11	31	.	.	PUNCT
ejpam-6262	12	1	in	in	ADP
ejpam-6262	12	2	practice	practice	NOUN
ejpam-6262	12	3	,	,	PUNCT
ejpam-6262	12	4	we	we	PRON
ejpam-6262	12	5	employ	employ	VERB
ejpam-6262	12	6	the	the	DET
ejpam-6262	12	7	novel	novel	ADJ
ejpam-6262	12	8	approach	approach	NOUN
ejpam-6262	12	9	to	to	PART
ejpam-6262	12	10	address	address	VERB
ejpam-6262	12	11	practical	practical	ADJ
ejpam-6262	12	12	challenges	challenge	NOUN
ejpam-6262	12	13	such	such	ADJ
ejpam-6262	12	14	as	as	ADP
ejpam-6262	12	15	the	the	DET
ejpam-6262	12	16	mixed	mixed	ADJ
ejpam-6262	12	17	hammerstein	hammerstein	PROPN
ejpam-6262	12	18	integral	integral	ADJ
ejpam-6262	12	19	equation	equation	NOUN
ejpam-6262	12	20	,	,	PUNCT
ejpam-6262	12	21	the	the	DET
ejpam-6262	12	22	discretized	discretized	ADJ
ejpam-6262	12	23	poisson	poisson	NOUN
ejpam-6262	12	24	equation	equation	NOUN
ejpam-6262	12	25	,	,	PUNCT
ejpam-6262	12	26	and	and	CCONJ
ejpam-6262	12	27	the	the	DET
ejpam-6262	12	28	weierstrass	weierstrass	NOUN
ejpam-6262	12	29	method	method	NOUN
ejpam-6262	12	30	.	.	PUNCT
ejpam-6262	13	1	through	through	ADP
ejpam-6262	13	2	comparisons	comparison	NOUN
ejpam-6262	13	3	and	and	CCONJ
ejpam-6262	13	4	illustrative	illustrative	ADJ
ejpam-6262	13	5	examples	example	NOUN
ejpam-6262	13	6	,	,	PUNCT
ejpam-6262	13	7	it	it	PRON
ejpam-6262	13	8	is	be	AUX
ejpam-6262	13	9	evident	evident	ADJ
ejpam-6262	13	10	that	that	SCONJ
ejpam-6262	13	11	the	the	DET
ejpam-6262	13	12	proposed	propose	VERB
ejpam-6262	13	13	method	method	NOUN
ejpam-6262	13	14	proves	prove	VERB
ejpam-6262	13	15	to	to	PART
ejpam-6262	13	16	be	be	AUX
ejpam-6262	13	17	effective	effective	ADJ
ejpam-6262	13	18	and	and	CCONJ
ejpam-6262	13	19	on	on	ADP
ejpam-6262	13	20	par	par	NOUN
ejpam-6262	13	21	with	with	ADP
ejpam-6262	13	22	existing	exist	VERB
ejpam-6262	13	23	techniques	technique	NOUN
ejpam-6262	13	24	of	of	ADP
ejpam-6262	13	25	equivalent	equivalent	ADJ
ejpam-6262	13	26	order	order	NOUN
ejpam-6262	13	27	.	.	PUNCT
ejpam-6262	14	1	2020	2020	NUM
ejpam-6262	14	2	mathematics	mathematic	NOUN
ejpam-6262	14	3	subject	subject	NOUN
ejpam-6262	14	4	classifications	classification	NOUN
ejpam-6262	14	5	:	:	PUNCT
ejpam-6262	14	6	65h10	65h10	NUM
ejpam-6262	14	7	,	,	PUNCT
ejpam-6262	14	8	90c56	90c56	NUM
ejpam-6262	14	9	key	key	ADJ
ejpam-6262	14	10	words	word	NOUN
ejpam-6262	14	11	and	and	CCONJ
ejpam-6262	14	12	phrases	phrase	NOUN
ejpam-6262	14	13	:	:	PUNCT
ejpam-6262	14	14	homeier	homei	ADJ
ejpam-6262	14	15	method	method	NOUN
ejpam-6262	14	16	,	,	PUNCT
ejpam-6262	14	17	secant	secant	ADJ
ejpam-6262	14	18	method	method	NOUN
ejpam-6262	14	19	,	,	PUNCT
ejpam-6262	14	20	nonlinear	nonlinear	ADJ
ejpam-6262	14	21	equations	equation	NOUN
ejpam-6262	14	22	,	,	PUNCT
ejpam-6262	14	23	derivativefree	derivativefree	ADJ
ejpam-6262	14	24	methods	method	NOUN
ejpam-6262	14	25	,	,	PUNCT
ejpam-6262	14	26	broyden	broyden	NOUN
ejpam-6262	14	27	’s	’s	PART
ejpam-6262	14	28	method	method	NOUN
ejpam-6262	14	29	,	,	PUNCT
ejpam-6262	14	30	iterative	iterative	NOUN
ejpam-6262	14	31	methods	method	NOUN
ejpam-6262	14	32	,	,	PUNCT
ejpam-6262	14	33	order	order	NOUN
ejpam-6262	14	34	of	of	ADP
ejpam-6262	14	35	convergence	convergence	NOUN
ejpam-6262	14	36	,	,	PUNCT
ejpam-6262	14	37	hammerstein	hammerstein	PROPN
ejpam-6262	14	38	integral	integral	ADJ
ejpam-6262	14	39	equation	equation	NOUN
ejpam-6262	14	40	∗corresponding	∗corresponde	VERB
ejpam-6262	14	41	author	author	NOUN
ejpam-6262	14	42	.	.	PUNCT
ejpam-6262	15	1	doi	doi	NOUN
ejpam-6262	15	2	:	:	PUNCT
ejpam-6262	15	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6262	https://doi.org/10.29020/nybg.ejpam.v18i3.6262	PRON
ejpam-6262	15	4	email	email	NOUN
ejpam-6262	15	5	addresses	address	NOUN
ejpam-6262	15	6	:	:	PUNCT
ejpam-6262	15	7	p114391@siswa.ukm.edu.my	p114391@siswa.ukm.edu.my	PROPN
ejpam-6262	15	8	(	(	PUNCT
ejpam-6262	15	9	y.	y.	PROPN
ejpam-6262	15	10	al	al	PROPN
ejpam-6262	15	11	-	-	PUNCT
ejpam-6262	15	12	shorman	shorman	PROPN
ejpam-6262	15	13	)	)	PUNCT
ejpam-6262	15	14	,	,	PUNCT
ejpam-6262	15	15	abdullah.alsoboh@asu.edu.om	abdullah.alsoboh@asu.edu.om	NOUN
ejpam-6262	15	16	(	(	PUNCT
ejpam-6262	15	17	a.	a.	NOUN
ejpam-6262	15	18	alsoboh	alsoboh	PROPN
ejpam-6262	15	19	)	)	PUNCT
ejpam-6262	15	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6262	16	1	1	1	NUM
ejpam-6262	16	2	copyright	copyright	NOUN
ejpam-6262	16	3	:	:	PUNCT
ejpam-6262	16	4	©	©	PROPN
ejpam-6262	16	5	2025	2025	NUM
ejpam-6262	16	6	the	the	DET
ejpam-6262	16	7	author(s	author(s	NOUN
ejpam-6262	16	8	)	)	PUNCT
ejpam-6262	16	9	.	.	PUNCT
ejpam-6262	17	1	(	(	PUNCT
ejpam-6262	17	2	cc	cc	NOUN
ejpam-6262	17	3	by	by	ADP
ejpam-6262	17	4	-	-	PUNCT
ejpam-6262	17	5	nc	nc	PROPN
ejpam-6262	17	6	4.0	4.0	NUM
ejpam-6262	17	7	)	)	PUNCT
ejpam-6262	17	8	y.	y.	PROPN
ejpam-6262	17	9	al	al	PROPN
ejpam-6262	17	10	-	-	PUNCT
ejpam-6262	17	11	shorman	shorman	PROPN
ejpam-6262	17	12	et	et	PROPN
ejpam-6262	17	13	al	al	PROPN
ejpam-6262	17	14	.	.	PUNCT
ejpam-6262	17	15	/	/	SYM
ejpam-6262	17	16	eur	eur	PROPN
ejpam-6262	17	17	.	.	PUNCT
ejpam-6262	18	1	j.	j.	PROPN
ejpam-6262	18	2	pure	pure	PROPN
ejpam-6262	18	3	appl	appl	PROPN
ejpam-6262	18	4	.	.	PROPN
ejpam-6262	18	5	math	math	PROPN
ejpam-6262	18	6	,	,	PUNCT
ejpam-6262	18	7	18	18	NUM
ejpam-6262	18	8	(	(	PUNCT
ejpam-6262	18	9	3	3	NUM
ejpam-6262	18	10	)	)	PUNCT
ejpam-6262	18	11	(	(	PUNCT
ejpam-6262	18	12	2025	2025	NUM
ejpam-6262	18	13	)	)	PUNCT
ejpam-6262	18	14	,	,	PUNCT
ejpam-6262	18	15	6262	6262	NUM
ejpam-6262	18	16	2	2	NUM
ejpam-6262	18	17	of	of	ADP
ejpam-6262	18	18	20	20	NUM
ejpam-6262	18	19	1	1	NUM
ejpam-6262	18	20	.	.	PUNCT
ejpam-6262	19	1	introduction	introduction	NOUN
ejpam-6262	19	2	solving	solve	VERB
ejpam-6262	19	3	systems	system	NOUN
ejpam-6262	19	4	of	of	ADP
ejpam-6262	19	5	nonlinear	nonlinear	ADJ
ejpam-6262	19	6	equations	equation	NOUN
ejpam-6262	19	7	has	have	AUX
ejpam-6262	19	8	been	be	AUX
ejpam-6262	19	9	a	a	DET
ejpam-6262	19	10	central	central	ADJ
ejpam-6262	19	11	focus	focus	NOUN
ejpam-6262	19	12	in	in	ADP
ejpam-6262	19	13	numerical	numerical	ADJ
ejpam-6262	19	14	analysis	analysis	NOUN
ejpam-6262	19	15	,	,	PUNCT
ejpam-6262	19	16	leading	lead	VERB
ejpam-6262	19	17	to	to	ADP
ejpam-6262	19	18	the	the	DET
ejpam-6262	19	19	development	development	NOUN
ejpam-6262	19	20	of	of	ADP
ejpam-6262	19	21	numerous	numerous	ADJ
ejpam-6262	19	22	iterative	iterative	NOUN
ejpam-6262	19	23	techniques	technique	NOUN
ejpam-6262	19	24	[	[	X
ejpam-6262	19	25	1–4	1–4	X
ejpam-6262	19	26	]	]	PUNCT
ejpam-6262	19	27	and	and	CCONJ
ejpam-6262	19	28	references	reference	NOUN
ejpam-6262	19	29	therein	therein	ADV
ejpam-6262	19	30	.	.	PUNCT
ejpam-6262	20	1	among	among	ADP
ejpam-6262	20	2	these	these	PRON
ejpam-6262	20	3	,	,	PUNCT
ejpam-6262	20	4	newton	newton	PROPN
ejpam-6262	20	5	’s	’s	PART
ejpam-6262	20	6	method	method	NOUN
ejpam-6262	20	7	remains	remain	VERB
ejpam-6262	20	8	one	one	NUM
ejpam-6262	20	9	of	of	ADP
ejpam-6262	20	10	the	the	DET
ejpam-6262	20	11	most	most	ADV
ejpam-6262	20	12	widely	widely	ADV
ejpam-6262	20	13	used	use	VERB
ejpam-6262	20	14	approaches	approach	NOUN
ejpam-6262	20	15	for	for	ADP
ejpam-6262	20	16	finding	find	VERB
ejpam-6262	20	17	a	a	DET
ejpam-6262	20	18	single	single	ADJ
ejpam-6262	20	19	root	root	NOUN
ejpam-6262	20	20	of	of	ADP
ejpam-6262	20	21	a	a	DET
ejpam-6262	20	22	nonlinear	nonlinear	ADJ
ejpam-6262	20	23	equation	equation	NOUN
ejpam-6262	20	24	[	[	X
ejpam-6262	20	25	5–19	5–19	NOUN
ejpam-6262	20	26	]	]	PUNCT
ejpam-6262	20	27	.	.	PUNCT
ejpam-6262	21	1	an	an	DET
ejpam-6262	21	2	enhancement	enhancement	NOUN
ejpam-6262	21	3	of	of	ADP
ejpam-6262	21	4	this	this	DET
ejpam-6262	21	5	method	method	NOUN
ejpam-6262	21	6	was	be	AUX
ejpam-6262	21	7	proposed	propose	VERB
ejpam-6262	21	8	by	by	ADP
ejpam-6262	21	9	homeier	homeier	ADJ
ejpam-6262	22	1	[	[	X
ejpam-6262	22	2	20	20	NUM
ejpam-6262	22	3	,	,	PUNCT
ejpam-6262	22	4	21	21	NUM
ejpam-6262	22	5	]	]	PUNCT
ejpam-6262	22	6	,	,	PUNCT
ejpam-6262	22	7	which	which	PRON
ejpam-6262	22	8	achieves	achieve	VERB
ejpam-6262	22	9	cubic	cubic	ADJ
ejpam-6262	22	10	convergence	convergence	NOUN
ejpam-6262	22	11	,	,	PUNCT
ejpam-6262	22	12	offering	offer	VERB
ejpam-6262	22	13	improved	improved	ADJ
ejpam-6262	22	14	performance	performance	NOUN
ejpam-6262	22	15	over	over	ADP
ejpam-6262	22	16	the	the	DET
ejpam-6262	22	17	classical	classical	ADJ
ejpam-6262	22	18	newton	newton	PROPN
ejpam-6262	22	19	method	method	NOUN
ejpam-6262	22	20	.	.	PUNCT
ejpam-6262	23	1	both	both	DET
ejpam-6262	23	2	newton	newton	PROPN
ejpam-6262	23	3	’s	’s	PART
ejpam-6262	23	4	and	and	CCONJ
ejpam-6262	23	5	homeier	homeier	PROPN
ejpam-6262	23	6	’s	’s	PART
ejpam-6262	23	7	methods	method	NOUN
ejpam-6262	23	8	require	require	VERB
ejpam-6262	23	9	the	the	DET
ejpam-6262	23	10	evaluation	evaluation	NOUN
ejpam-6262	23	11	of	of	ADP
ejpam-6262	23	12	the	the	DET
ejpam-6262	23	13	derivative	derivative	NOUN
ejpam-6262	23	14	of	of	ADP
ejpam-6262	23	15	the	the	DET
ejpam-6262	23	16	function	function	NOUN
ejpam-6262	23	17	,	,	PUNCT
ejpam-6262	23	18	which	which	PRON
ejpam-6262	23	19	can	can	AUX
ejpam-6262	23	20	limit	limit	VERB
ejpam-6262	23	21	their	their	PRON
ejpam-6262	23	22	applicability	applicability	NOUN
ejpam-6262	23	23	in	in	ADP
ejpam-6262	23	24	scenarios	scenario	NOUN
ejpam-6262	23	25	where	where	SCONJ
ejpam-6262	23	26	the	the	DET
ejpam-6262	23	27	derivative	derivative	NOUN
ejpam-6262	23	28	is	be	AUX
ejpam-6262	23	29	difficult	difficult	ADJ
ejpam-6262	23	30	or	or	CCONJ
ejpam-6262	23	31	impossible	impossible	ADJ
ejpam-6262	23	32	to	to	PART
ejpam-6262	23	33	compute	compute	VERB
ejpam-6262	23	34	.	.	PUNCT
ejpam-6262	24	1	this	this	DET
ejpam-6262	24	2	issue	issue	NOUN
ejpam-6262	24	3	commonly	commonly	ADV
ejpam-6262	24	4	arises	arise	VERB
ejpam-6262	24	5	in	in	ADP
ejpam-6262	24	6	practical	practical	ADJ
ejpam-6262	24	7	modeling	modeling	NOUN
ejpam-6262	24	8	situations	situation	NOUN
ejpam-6262	24	9	,	,	PUNCT
ejpam-6262	24	10	as	as	SCONJ
ejpam-6262	24	11	discussed	discuss	VERB
ejpam-6262	24	12	in	in	ADP
ejpam-6262	24	13	[	[	X
ejpam-6262	24	14	22	22	NUM
ejpam-6262	24	15	]	]	PUNCT
ejpam-6262	24	16	.	.	PUNCT
ejpam-6262	25	1	to	to	PART
ejpam-6262	25	2	address	address	VERB
ejpam-6262	25	3	such	such	ADJ
ejpam-6262	25	4	limitations	limitation	NOUN
ejpam-6262	25	5	,	,	PUNCT
ejpam-6262	25	6	optimization	optimization	NOUN
ejpam-6262	25	7	-	-	PUNCT
ejpam-6262	25	8	based	base	VERB
ejpam-6262	25	9	approaches	approach	NOUN
ejpam-6262	25	10	have	have	AUX
ejpam-6262	25	11	been	be	AUX
ejpam-6262	25	12	proposed	propose	VERB
ejpam-6262	25	13	as	as	ADP
ejpam-6262	25	14	alternative	alternative	ADJ
ejpam-6262	25	15	strategies	strategy	NOUN
ejpam-6262	25	16	for	for	ADP
ejpam-6262	25	17	solving	solve	VERB
ejpam-6262	25	18	nonlinear	nonlinear	ADJ
ejpam-6262	25	19	equations	equation	NOUN
ejpam-6262	25	20	and	and	CCONJ
ejpam-6262	25	21	systems	system	NOUN
ejpam-6262	25	22	.	.	PUNCT
ejpam-6262	26	1	over	over	ADP
ejpam-6262	26	2	the	the	DET
ejpam-6262	26	3	past	past	ADJ
ejpam-6262	26	4	decade	decade	NOUN
ejpam-6262	26	5	,	,	PUNCT
ejpam-6262	26	6	a	a	DET
ejpam-6262	26	7	variety	variety	NOUN
ejpam-6262	26	8	of	of	ADP
ejpam-6262	26	9	innovative	innovative	ADJ
ejpam-6262	26	10	optimization	optimization	NOUN
ejpam-6262	26	11	techniques	technique	NOUN
ejpam-6262	26	12	have	have	AUX
ejpam-6262	26	13	emerged	emerge	VERB
ejpam-6262	26	14	[	[	X
ejpam-6262	26	15	23	23	NUM
ejpam-6262	26	16	]	]	PUNCT
ejpam-6262	26	17	.	.	PUNCT
ejpam-6262	27	1	additionally	additionally	ADV
ejpam-6262	27	2	,	,	PUNCT
ejpam-6262	27	3	several	several	ADJ
ejpam-6262	27	4	derivative	derivative	ADJ
ejpam-6262	27	5	-	-	PUNCT
ejpam-6262	27	6	free	free	ADJ
ejpam-6262	27	7	iterative	iterative	NOUN
ejpam-6262	27	8	schemes	scheme	NOUN
ejpam-6262	27	9	have	have	AUX
ejpam-6262	27	10	been	be	AUX
ejpam-6262	27	11	introduced	introduce	VERB
ejpam-6262	27	12	for	for	ADP
ejpam-6262	27	13	solving	solve	VERB
ejpam-6262	27	14	systems	system	NOUN
ejpam-6262	27	15	of	of	ADP
ejpam-6262	27	16	nonlinear	nonlinear	ADJ
ejpam-6262	27	17	equations	equation	NOUN
ejpam-6262	27	18	,	,	PUNCT
ejpam-6262	27	19	offering	offer	VERB
ejpam-6262	27	20	viable	viable	ADJ
ejpam-6262	27	21	alternatives	alternative	NOUN
ejpam-6262	27	22	when	when	SCONJ
ejpam-6262	27	23	derivative	derivative	ADJ
ejpam-6262	27	24	information	information	NOUN
ejpam-6262	27	25	is	be	AUX
ejpam-6262	27	26	unavailable	unavailable	ADJ
ejpam-6262	27	27	[	[	X
ejpam-6262	27	28	24	24	NUM
ejpam-6262	27	29	,	,	PUNCT
ejpam-6262	27	30	25	25	NUM
ejpam-6262	27	31	]	]	PUNCT
ejpam-6262	27	32	.	.	PUNCT
ejpam-6262	28	1	one	one	NUM
ejpam-6262	28	2	such	such	ADJ
ejpam-6262	28	3	method	method	NOUN
ejpam-6262	28	4	is	be	AUX
ejpam-6262	28	5	the	the	DET
ejpam-6262	28	6	secant	secant	ADJ
ejpam-6262	28	7	approach	approach	NOUN
ejpam-6262	28	8	,	,	PUNCT
ejpam-6262	28	9	which	which	PRON
ejpam-6262	28	10	approximates	approximate	VERB
ejpam-6262	28	11	the	the	DET
ejpam-6262	28	12	derivative	derivative	NOUN
ejpam-6262	28	13	in	in	ADP
ejpam-6262	28	14	newton	newton	PROPN
ejpam-6262	28	15	’s	’s	PART
ejpam-6262	28	16	method	method	NOUN
ejpam-6262	28	17	using	use	VERB
ejpam-6262	28	18	finite	finite	ADJ
ejpam-6262	28	19	differences	difference	NOUN
ejpam-6262	28	20	.	.	PUNCT
ejpam-6262	29	1	this	this	DET
ejpam-6262	29	2	technique	technique	NOUN
ejpam-6262	29	3	achieves	achieve	VERB
ejpam-6262	29	4	a	a	DET
ejpam-6262	29	5	convergence	convergence	NOUN
ejpam-6262	29	6	order	order	NOUN
ejpam-6262	29	7	of	of	ADP
ejpam-6262	29	8	approximately	approximately	ADV
ejpam-6262	29	9	1.618	1.618	NUM
ejpam-6262	29	10	and	and	CCONJ
ejpam-6262	29	11	requires	require	VERB
ejpam-6262	29	12	two	two	NUM
ejpam-6262	29	13	function	function	NOUN
ejpam-6262	29	14	evaluations	evaluation	NOUN
ejpam-6262	29	15	per	per	ADP
ejpam-6262	29	16	iteration	iteration	NOUN
ejpam-6262	29	17	.	.	PUNCT
ejpam-6262	30	1	however	however	ADV
ejpam-6262	30	2	,	,	PUNCT
ejpam-6262	30	3	the	the	DET
ejpam-6262	30	4	existing	exist	VERB
ejpam-6262	30	5	pace	pace	NOUN
ejpam-6262	30	6	appears	appear	VERB
ejpam-6262	30	7	to	to	PART
ejpam-6262	30	8	be	be	AUX
ejpam-6262	30	9	insufficient	insufficient	ADJ
ejpam-6262	30	10	in	in	ADP
ejpam-6262	30	11	light	light	NOUN
ejpam-6262	30	12	of	of	ADP
ejpam-6262	30	13	the	the	DET
ejpam-6262	30	14	contemporary	contemporary	PROPN
ejpam-6262	30	15	global	global	ADJ
ejpam-6262	30	16	landscape	landscape	NOUN
ejpam-6262	30	17	,	,	PUNCT
ejpam-6262	30	18	which	which	PRON
ejpam-6262	30	19	requires	require	VERB
ejpam-6262	30	20	more	more	ADV
ejpam-6262	30	21	efficient	efficient	ADJ
ejpam-6262	30	22	algorithms	algorithm	NOUN
ejpam-6262	30	23	to	to	PART
ejpam-6262	30	24	meet	meet	VERB
ejpam-6262	30	25	the	the	DET
ejpam-6262	30	26	escalating	escalate	VERB
ejpam-6262	30	27	demands	demand	NOUN
ejpam-6262	30	28	driven	drive	VERB
ejpam-6262	30	29	by	by	ADP
ejpam-6262	30	30	the	the	DET
ejpam-6262	30	31	rapid	rapid	ADJ
ejpam-6262	30	32	advancements	advancement	NOUN
ejpam-6262	30	33	in	in	ADP
ejpam-6262	30	34	technology	technology	NOUN
ejpam-6262	30	35	.	.	PUNCT
ejpam-6262	31	1	consequently	consequently	ADV
ejpam-6262	31	2	,	,	PUNCT
ejpam-6262	31	3	we	we	PRON
ejpam-6262	31	4	were	be	AUX
ejpam-6262	31	5	motivated	motivated	ADJ
ejpam-6262	31	6	to	to	PART
ejpam-6262	31	7	explore	explore	VERB
ejpam-6262	31	8	an	an	DET
ejpam-6262	31	9	approach	approach	NOUN
ejpam-6262	31	10	that	that	PRON
ejpam-6262	31	11	addresses	address	VERB
ejpam-6262	31	12	the	the	DET
ejpam-6262	31	13	present	present	ADJ
ejpam-6262	31	14	requirements	requirement	NOUN
ejpam-6262	31	15	by	by	ADP
ejpam-6262	31	16	substituting	substitute	VERB
ejpam-6262	31	17	the	the	DET
ejpam-6262	31	18	derivatives	derivative	NOUN
ejpam-6262	31	19	in	in	ADP
ejpam-6262	31	20	the	the	DET
ejpam-6262	31	21	fast	fast	ADV
ejpam-6262	31	22	-	-	PUNCT
ejpam-6262	31	23	converging	converge	VERB
ejpam-6262	31	24	homeier	homeier	ADJ
ejpam-6262	31	25	method	method	NOUN
ejpam-6262	31	26	with	with	ADP
ejpam-6262	31	27	suitable	suitable	ADJ
ejpam-6262	31	28	difference	difference	NOUN
ejpam-6262	31	29	approximations	approximation	NOUN
ejpam-6262	31	30	.	.	PUNCT
ejpam-6262	32	1	this	this	PRON
ejpam-6262	32	2	is	be	AUX
ejpam-6262	32	3	necessitated	necessitate	VERB
ejpam-6262	32	4	by	by	ADP
ejpam-6262	32	5	the	the	DET
ejpam-6262	32	6	absence	absence	NOUN
ejpam-6262	32	7	of	of	ADP
ejpam-6262	32	8	robust	robust	ADJ
ejpam-6262	32	9	numerical	numerical	ADJ
ejpam-6262	32	10	techniques	technique	NOUN
ejpam-6262	32	11	that	that	PRON
ejpam-6262	32	12	do	do	AUX
ejpam-6262	32	13	not	not	PART
ejpam-6262	32	14	rely	rely	VERB
ejpam-6262	32	15	on	on	ADP
ejpam-6262	32	16	derivatives	derivative	NOUN
ejpam-6262	32	17	for	for	ADP
ejpam-6262	32	18	approximating	approximate	VERB
ejpam-6262	32	19	the	the	DET
ejpam-6262	32	20	solutions	solution	NOUN
ejpam-6262	32	21	of	of	ADP
ejpam-6262	32	22	a	a	DET
ejpam-6262	32	23	non	non	ADJ
ejpam-6262	32	24	-	-	ADJ
ejpam-6262	32	25	linear	linear	ADJ
ejpam-6262	32	26	equation	equation	NOUN
ejpam-6262	32	27	.	.	PUNCT
ejpam-6262	33	1	this	this	DET
ejpam-6262	33	2	study	study	NOUN
ejpam-6262	33	3	presents	present	VERB
ejpam-6262	33	4	a	a	DET
ejpam-6262	33	5	methodology	methodology	NOUN
ejpam-6262	33	6	for	for	ADP
ejpam-6262	33	7	developing	develop	VERB
ejpam-6262	33	8	an	an	DET
ejpam-6262	33	9	optimal	optimal	ADJ
ejpam-6262	33	10	algorithm	algorithm	NOUN
ejpam-6262	33	11	that	that	PRON
ejpam-6262	33	12	can	can	AUX
ejpam-6262	33	13	effectively	effectively	ADV
ejpam-6262	33	14	solve	solve	VERB
ejpam-6262	33	15	nonlinear	nonlinear	ADJ
ejpam-6262	33	16	equations	equation	NOUN
ejpam-6262	33	17	numerically	numerically	ADV
ejpam-6262	33	18	without	without	ADP
ejpam-6262	33	19	relying	rely	VERB
ejpam-6262	33	20	on	on	ADP
ejpam-6262	33	21	derivatives	derivative	NOUN
ejpam-6262	33	22	.	.	PUNCT
ejpam-6262	34	1	the	the	DET
ejpam-6262	34	2	proposed	propose	VERB
ejpam-6262	34	3	approach	approach	NOUN
ejpam-6262	34	4	aims	aim	VERB
ejpam-6262	34	5	to	to	PART
ejpam-6262	34	6	optimize	optimize	VERB
ejpam-6262	34	7	both	both	PRON
ejpam-6262	34	8	the	the	DET
ejpam-6262	34	9	convergence	convergence	NOUN
ejpam-6262	34	10	rate	rate	NOUN
ejpam-6262	34	11	and	and	CCONJ
ejpam-6262	34	12	the	the	DET
ejpam-6262	34	13	number	number	NOUN
ejpam-6262	34	14	of	of	ADP
ejpam-6262	34	15	function	function	NOUN
ejpam-6262	34	16	evaluations	evaluation	NOUN
ejpam-6262	34	17	to	to	PART
ejpam-6262	34	18	achieve	achieve	VERB
ejpam-6262	34	19	high	high	ADJ
ejpam-6262	34	20	efficiency	efficiency	NOUN
ejpam-6262	34	21	.	.	PUNCT
ejpam-6262	35	1	subsequently	subsequently	ADV
ejpam-6262	35	2	,	,	PUNCT
ejpam-6262	35	3	an	an	DET
ejpam-6262	35	4	account	account	NOUN
ejpam-6262	35	5	is	be	AUX
ejpam-6262	35	6	provided	provide	VERB
ejpam-6262	35	7	of	of	ADP
ejpam-6262	35	8	the	the	DET
ejpam-6262	35	9	verification	verification	NOUN
ejpam-6262	35	10	process	process	NOUN
ejpam-6262	35	11	employed	employ	VERB
ejpam-6262	35	12	to	to	PART
ejpam-6262	35	13	ascertain	ascertain	VERB
ejpam-6262	35	14	the	the	DET
ejpam-6262	35	15	suitability	suitability	NOUN
ejpam-6262	35	16	of	of	ADP
ejpam-6262	35	17	the	the	DET
ejpam-6262	35	18	approach	approach	NOUN
ejpam-6262	35	19	for	for	ADP
ejpam-6262	35	20	solving	solve	VERB
ejpam-6262	35	21	non	non	ADJ
ejpam-6262	35	22	-	-	ADJ
ejpam-6262	35	23	linear	linear	ADJ
ejpam-6262	35	24	equations	equation	NOUN
ejpam-6262	35	25	.	.	PUNCT
ejpam-6262	36	1	ultimately	ultimately	ADV
ejpam-6262	36	2	,	,	PUNCT
ejpam-6262	36	3	the	the	DET
ejpam-6262	36	4	text	text	NOUN
ejpam-6262	36	5	elucidates	elucidate	VERB
ejpam-6262	36	6	the	the	DET
ejpam-6262	36	7	manner	manner	NOUN
ejpam-6262	36	8	in	in	ADP
ejpam-6262	36	9	which	which	PRON
ejpam-6262	36	10	the	the	DET
ejpam-6262	36	11	said	say	VERB
ejpam-6262	36	12	approach	approach	NOUN
ejpam-6262	36	13	was	be	AUX
ejpam-6262	36	14	modified	modify	VERB
ejpam-6262	36	15	to	to	PART
ejpam-6262	36	16	include	include	VERB
ejpam-6262	36	17	non	non	ADJ
ejpam-6262	36	18	-	-	ADJ
ejpam-6262	36	19	linear	linear	ADJ
ejpam-6262	36	20	equation	equation	NOUN
ejpam-6262	36	21	systems	system	NOUN
ejpam-6262	36	22	,	,	PUNCT
ejpam-6262	36	23	yielding	yield	VERB
ejpam-6262	36	24	commendable	commendable	ADJ
ejpam-6262	36	25	outcomes	outcome	NOUN
ejpam-6262	36	26	.	.	PUNCT
ejpam-6262	37	1	in	in	ADP
ejpam-6262	37	2	this	this	DET
ejpam-6262	37	3	paper	paper	NOUN
ejpam-6262	37	4	,	,	PUNCT
ejpam-6262	37	5	we	we	PRON
ejpam-6262	37	6	introduce	introduce	VERB
ejpam-6262	37	7	an	an	DET
ejpam-6262	37	8	iterative	iterative	NOUN
ejpam-6262	37	9	approach	approach	NOUN
ejpam-6262	37	10	to	to	ADP
ejpam-6262	37	11	addressing	address	VERB
ejpam-6262	37	12	nonlinear	nonlinear	ADJ
ejpam-6262	37	13	models	model	NOUN
ejpam-6262	37	14	.	.	PUNCT
ejpam-6262	38	1	the	the	DET
ejpam-6262	38	2	novel	novel	ADJ
ejpam-6262	38	3	approach	approach	NOUN
ejpam-6262	38	4	represents	represent	VERB
ejpam-6262	38	5	an	an	DET
ejpam-6262	38	6	adaptation	adaptation	NOUN
ejpam-6262	38	7	of	of	ADP
ejpam-6262	38	8	the	the	DET
ejpam-6262	38	9	homeier	homeier	ADJ
ejpam-6262	38	10	method	method	NOUN
ejpam-6262	38	11	.	.	PUNCT
ejpam-6262	39	1	the	the	DET
ejpam-6262	39	2	utilization	utilization	NOUN
ejpam-6262	39	3	of	of	ADP
ejpam-6262	39	4	the	the	DET
ejpam-6262	39	5	composition	composition	NOUN
ejpam-6262	39	6	methodology	methodology	NOUN
ejpam-6262	39	7	,	,	PUNCT
ejpam-6262	39	8	including	include	VERB
ejpam-6262	39	9	both	both	CCONJ
ejpam-6262	39	10	forward	forward	ADJ
ejpam-6262	39	11	and	and	CCONJ
ejpam-6262	39	12	backward	backward	ADJ
ejpam-6262	39	13	approximations	approximation	NOUN
ejpam-6262	39	14	,	,	PUNCT
ejpam-6262	39	15	is	be	AUX
ejpam-6262	39	16	employed	employ	VERB
ejpam-6262	39	17	in	in	ADP
ejpam-6262	39	18	the	the	DET
ejpam-6262	39	19	development	development	NOUN
ejpam-6262	39	20	of	of	ADP
ejpam-6262	39	21	our	our	PRON
ejpam-6262	39	22	novel	novel	ADJ
ejpam-6262	39	23	method	method	NOUN
ejpam-6262	39	24	.	.	PUNCT
ejpam-6262	40	1	the	the	DET
ejpam-6262	40	2	assignment	assignment	NOUN
ejpam-6262	40	3	of	of	ADP
ejpam-6262	40	4	tasks	task	NOUN
ejpam-6262	40	5	in	in	ADP
ejpam-6262	40	6	this	this	DET
ejpam-6262	40	7	investigation	investigation	NOUN
ejpam-6262	40	8	is	be	AUX
ejpam-6262	40	9	outlined	outline	VERB
ejpam-6262	40	10	below	below	ADV
ejpam-6262	40	11	.	.	PUNCT
ejpam-6262	41	1	the	the	DET
ejpam-6262	41	2	early	early	ADJ
ejpam-6262	41	3	findings	finding	NOUN
ejpam-6262	41	4	are	be	AUX
ejpam-6262	41	5	presented	present	VERB
ejpam-6262	41	6	in	in	ADP
ejpam-6262	41	7	section	section	NOUN
ejpam-6262	41	8	2	2	NUM
ejpam-6262	41	9	.	.	PUNCT
ejpam-6262	41	10	section	section	NOUN
ejpam-6262	41	11	3	3	NUM
ejpam-6262	41	12	illustrates	illustrate	VERB
ejpam-6262	41	13	the	the	DET
ejpam-6262	41	14	revised	revise	VERB
ejpam-6262	41	15	system	system	NOUN
ejpam-6262	41	16	.	.	PUNCT
ejpam-6262	42	1	the	the	DET
ejpam-6262	42	2	analysis	analysis	NOUN
ejpam-6262	42	3	of	of	ADP
ejpam-6262	42	4	the	the	DET
ejpam-6262	42	5	convergence	convergence	NOUN
ejpam-6262	42	6	sequence	sequence	NOUN
ejpam-6262	42	7	of	of	ADP
ejpam-6262	42	8	the	the	DET
ejpam-6262	42	9	new	new	PROPN
ejpam-6262	42	10	y.	y.	PROPN
ejpam-6262	42	11	al	al	PROPN
ejpam-6262	42	12	-	-	PUNCT
ejpam-6262	42	13	shorman	shorman	PROPN
ejpam-6262	42	14	et	et	PROPN
ejpam-6262	42	15	al	al	PROPN
ejpam-6262	42	16	.	.	PUNCT
ejpam-6262	42	17	/	/	SYM
ejpam-6262	42	18	eur	eur	PROPN
ejpam-6262	42	19	.	.	PUNCT
ejpam-6262	43	1	j.	j.	PROPN
ejpam-6262	43	2	pure	pure	PROPN
ejpam-6262	43	3	appl	appl	PROPN
ejpam-6262	43	4	.	.	PROPN
ejpam-6262	43	5	math	math	PROPN
ejpam-6262	43	6	,	,	PUNCT
ejpam-6262	43	7	18	18	NUM
ejpam-6262	43	8	(	(	PUNCT
ejpam-6262	43	9	3	3	NUM
ejpam-6262	43	10	)	)	PUNCT
ejpam-6262	43	11	(	(	PUNCT
ejpam-6262	43	12	2025	2025	NUM
ejpam-6262	43	13	)	)	PUNCT
ejpam-6262	43	14	,	,	PUNCT
ejpam-6262	43	15	6262	6262	NUM
ejpam-6262	43	16	3	3	NUM
ejpam-6262	43	17	of	of	ADP
ejpam-6262	43	18	20	20	NUM
ejpam-6262	43	19	scheme	scheme	NOUN
ejpam-6262	43	20	is	be	AUX
ejpam-6262	43	21	addressed	address	VERB
ejpam-6262	43	22	in	in	ADP
ejpam-6262	43	23	section	section	NOUN
ejpam-6262	43	24	4	4	NUM
ejpam-6262	43	25	.	.	PUNCT
ejpam-6262	44	1	section	section	NOUN
ejpam-6262	44	2	5	5	NUM
ejpam-6262	44	3	of	of	ADP
ejpam-6262	44	4	the	the	DET
ejpam-6262	44	5	document	document	NOUN
ejpam-6262	44	6	provides	provide	VERB
ejpam-6262	44	7	a	a	DET
ejpam-6262	44	8	detailed	detailed	ADJ
ejpam-6262	44	9	explanation	explanation	NOUN
ejpam-6262	44	10	of	of	ADP
ejpam-6262	44	11	numerical	numerical	ADJ
ejpam-6262	44	12	examples	example	NOUN
ejpam-6262	44	13	and	and	CCONJ
ejpam-6262	44	14	comparisons	comparison	NOUN
ejpam-6262	44	15	.	.	PUNCT
ejpam-6262	45	1	section	section	NOUN
ejpam-6262	45	2	6	6	NUM
ejpam-6262	45	3	presents	present	VERB
ejpam-6262	45	4	the	the	DET
ejpam-6262	45	5	real	real	ADJ
ejpam-6262	45	6	-	-	PUNCT
ejpam-6262	45	7	life	life	NOUN
ejpam-6262	45	8	application	application	NOUN
ejpam-6262	45	9	.	.	PUNCT
ejpam-6262	46	1	finally	finally	ADV
ejpam-6262	46	2	,	,	PUNCT
ejpam-6262	46	3	the	the	DET
ejpam-6262	46	4	conclusion	conclusion	NOUN
ejpam-6262	46	5	is	be	AUX
ejpam-6262	46	6	presented	present	VERB
ejpam-6262	46	7	in	in	ADP
ejpam-6262	46	8	section	section	NOUN
ejpam-6262	46	9	7	7	NUM
ejpam-6262	46	10	.	.	NOUN
ejpam-6262	46	11	2	2	NUM
ejpam-6262	46	12	.	.	X
ejpam-6262	46	13	preliminary	preliminary	ADJ
ejpam-6262	46	14	results	result	NOUN
ejpam-6262	46	15	definition	definition	NOUN
ejpam-6262	46	16	1	1	NUM
ejpam-6262	46	17	.	.	PUNCT
ejpam-6262	47	1	given	give	VERB
ejpam-6262	47	2	that	that	SCONJ
ejpam-6262	47	3	the	the	DET
ejpam-6262	47	4	iterative	iterative	NOUN
ejpam-6262	47	5	sequence	sequence	NOUN
ejpam-6262	47	6	xn	xn	PUNCT
ejpam-6262	47	7	:	:	PUNCT
ejpam-6262	47	8	n	n	PROPN
ejpam-6262	47	9	=	=	SYM
ejpam-6262	47	10	1	1	NUM
ejpam-6262	47	11	,	,	PUNCT
ejpam-6262	47	12	2	2	NUM
ejpam-6262	47	13	,	,	PUNCT
ejpam-6262	47	14	.	.	PUNCT
ejpam-6262	47	15	.	.	PUNCT
ejpam-6262	47	16	.	.	PUNCT
ejpam-6262	48	1	converges	converge	VERB
ejpam-6262	48	2	to	to	ADP
ejpam-6262	48	3	x∗	x∗	PROPN
ejpam-6262	48	4	to	to	PART
ejpam-6262	48	5	be	be	AUX
ejpam-6262	48	6	formed	form	VERB
ejpam-6262	48	7	utilizing	utilize	VERB
ejpam-6262	48	8	a	a	DET
ejpam-6262	48	9	numerical	numerical	ADJ
ejpam-6262	48	10	scheme	scheme	NOUN
ejpam-6262	48	11	.	.	PUNCT
ejpam-6262	49	1	suppose	suppose	VERB
ejpam-6262	49	2	that	that	SCONJ
ejpam-6262	49	3	there	there	PRON
ejpam-6262	49	4	exists	exist	VERB
ejpam-6262	49	5	a	a	DET
ejpam-6262	49	6	constant	constant	ADJ
ejpam-6262	49	7	c	c	NOUN
ejpam-6262	49	8	≥	≥	NOUN
ejpam-6262	49	9	0	0	NUM
ejpam-6262	49	10	.	.	PUNCT
ejpam-6262	50	1	therefore	therefore	ADV
ejpam-6262	50	2	,	,	PUNCT
ejpam-6262	50	3	integers	integer	NOUN
ejpam-6262	50	4	n0	n0	NUM
ejpam-6262	50	5	≥	≥	PROPN
ejpam-6262	50	6	0	0	NUM
ejpam-6262	50	7	and	and	CCONJ
ejpam-6262	50	8	ρ	ρ	PROPN
ejpam-6262	50	9	≥	≥	NOUN
ejpam-6262	50	10	0	0	NUM
ejpam-6262	50	11	in	in	ADP
ejpam-6262	50	12	which	which	PRON
ejpam-6262	50	13	for	for	ADP
ejpam-6262	50	14	all	all	DET
ejpam-6262	50	15	n	n	PRON
ejpam-6262	50	16	>	>	X
ejpam-6262	50	17	n0	n0	PROPN
ejpam-6262	50	18	,	,	PUNCT
ejpam-6262	50	19	the	the	DET
ejpam-6262	50	20	inequality	inequality	NOUN
ejpam-6262	50	21	provided	provide	VERB
ejpam-6262	50	22	below	below	ADP
ejpam-6262	50	23	holds	hold	NOUN
ejpam-6262	50	24	for	for	ADP
ejpam-6262	50	25	any	any	DET
ejpam-6262	50	26	vector	vector	NOUN
ejpam-6262	50	27	norm	norm	NOUN
ejpam-6262	50	28	∥.∥.	∥.∥.	X
ejpam-6262	50	29	∥xn+1	∥xn+1	VERB
ejpam-6262	50	30	−	−	PROPN
ejpam-6262	50	31	x∗	x∗	PROPN
ejpam-6262	50	32	∥	∥	PUNCT
ejpam-6262	50	33	≤	≤	NUM
ejpam-6262	51	1	c	c	NOUN
ejpam-6262	51	2	∥xn	∥xn	PROPN
ejpam-6262	52	1	−	−	PROPN
ejpam-6262	52	2	x∗∥ρ	x∗∥ρ	PROPN
ejpam-6262	52	3	(	(	PUNCT
ejpam-6262	52	4	1	1	NUM
ejpam-6262	52	5	)	)	PUNCT
ejpam-6262	52	6	hence	hence	ADV
ejpam-6262	52	7	,	,	PUNCT
ejpam-6262	52	8	it	it	PRON
ejpam-6262	52	9	is	be	AUX
ejpam-6262	52	10	well	well	ADV
ejpam-6262	52	11	established	establish	VERB
ejpam-6262	52	12	that	that	SCONJ
ejpam-6262	52	13	the	the	DET
ejpam-6262	52	14	iterative	iterative	NOUN
ejpam-6262	52	15	scheme	scheme	NOUN
ejpam-6262	52	16	converges	converge	NOUN
ejpam-6262	52	17	to	to	ADP
ejpam-6262	52	18	the	the	DET
ejpam-6262	52	19	solution	solution	NOUN
ejpam-6262	52	20	x∗	x∗	PROPN
ejpam-6262	52	21	having	have	VERB
ejpam-6262	52	22	a	a	DET
ejpam-6262	52	23	convergence	convergence	NOUN
ejpam-6262	52	24	order	order	NOUN
ejpam-6262	52	25	of	of	ADP
ejpam-6262	52	26	ρth	ρth	NUM
ejpam-6262	52	27	.	.	PUNCT
ejpam-6262	53	1	definition	definition	NOUN
ejpam-6262	53	2	2	2	NUM
ejpam-6262	53	3	.	.	PUNCT
ejpam-6262	54	1	let	let	VERB
ejpam-6262	54	2	x∗	x∗	PROPN
ejpam-6262	54	3	be	be	AUX
ejpam-6262	54	4	a	a	DET
ejpam-6262	54	5	root	root	NOUN
ejpam-6262	54	6	of	of	ADP
ejpam-6262	54	7	equation	equation	NOUN
ejpam-6262	54	8	f	f	X
ejpam-6262	54	9	(	(	PUNCT
ejpam-6262	54	10	x	x	X
ejpam-6262	54	11	)	)	PUNCT
ejpam-6262	54	12	=	=	SYM
ejpam-6262	55	1	0	0	X
ejpam-6262	55	2	.	.	PUNCT
ejpam-6262	56	1	let	let	VERB
ejpam-6262	56	2	xn−1	xn−1	PROPN
ejpam-6262	56	3	,	,	PUNCT
ejpam-6262	56	4	xn	xn	PROPN
ejpam-6262	56	5	as	as	ADV
ejpam-6262	56	6	well	well	ADV
ejpam-6262	56	7	as	as	ADP
ejpam-6262	56	8	xn+1	xn+1	PROPN
ejpam-6262	56	9	be	be	AUX
ejpam-6262	56	10	consecutive	consecutive	ADJ
ejpam-6262	56	11	iterations	iteration	NOUN
ejpam-6262	56	12	closer	close	ADV
ejpam-6262	56	13	to	to	ADP
ejpam-6262	56	14	the	the	DET
ejpam-6262	56	15	root	root	NOUN
ejpam-6262	56	16	x∗	x∗	PROPN
ejpam-6262	56	17	formed	form	VERB
ejpam-6262	56	18	by	by	ADP
ejpam-6262	56	19	an	an	DET
ejpam-6262	56	20	iterative	iterative	NOUN
ejpam-6262	56	21	scheme	scheme	NOUN
ejpam-6262	56	22	.	.	PUNCT
ejpam-6262	57	1	therefore	therefore	ADV
ejpam-6262	57	2	,	,	PUNCT
ejpam-6262	57	3	the	the	DET
ejpam-6262	57	4	computational	computational	ADJ
ejpam-6262	57	5	order	order	NOUN
ejpam-6262	57	6	of	of	ADP
ejpam-6262	57	7	convergence	convergence	NOUN
ejpam-6262	57	8	(	(	PUNCT
ejpam-6262	57	9	coc	coc	PROPN
ejpam-6262	57	10	)	)	PUNCT
ejpam-6262	57	11	ρ	ρ	NOUN
ejpam-6262	57	12	with	with	ADP
ejpam-6262	57	13	regards	regard	NOUN
ejpam-6262	57	14	to	to	ADP
ejpam-6262	57	15	the	the	DET
ejpam-6262	57	16	numerical	numerical	ADJ
ejpam-6262	57	17	algorithm	algorithm	NOUN
ejpam-6262	57	18	or	or	CCONJ
ejpam-6262	57	19	the	the	DET
ejpam-6262	57	20	iterative	iterative	NOUN
ejpam-6262	57	21	scheme	scheme	NOUN
ejpam-6262	57	22	may	may	AUX
ejpam-6262	57	23	be	be	AUX
ejpam-6262	57	24	approximated	approximate	VERB
ejpam-6262	57	25	by	by	ADP
ejpam-6262	57	26	ρ	ρ	PROPN
ejpam-6262	57	27	≈	≈	PROPN
ejpam-6262	57	28	ln	ln	NOUN
ejpam-6262	57	29	∥xn+1	∥xn+1	PROPN
ejpam-6262	57	30	−	−	PROPN
ejpam-6262	57	31	x∗	x∗	PROPN
ejpam-6262	57	32	∥	∥	PUNCT
ejpam-6262	57	33	∥xn	∥xn	PRON
ejpam-6262	57	34	−	−	PROPN
ejpam-6262	57	35	x∗	x∗	PROPN
ejpam-6262	57	36	∥	∥	PUNCT
ejpam-6262	57	37	ln	ln	NOUN
ejpam-6262	57	38	∥xn	∥xn	PROPN
ejpam-6262	57	39	−	−	PROPN
ejpam-6262	57	40	x∗	x∗	PROPN
ejpam-6262	57	41	∥	∥	X
ejpam-6262	57	42	∥xn−1	∥xn−1	ADJ
ejpam-6262	57	43	−	−	NOUN
ejpam-6262	57	44	x∗	x∗	PROPN
ejpam-6262	57	45	∥	∥	X
ejpam-6262	57	46	(	(	PUNCT
ejpam-6262	57	47	2	2	NUM
ejpam-6262	57	48	)	)	PUNCT
ejpam-6262	57	49	2.1	2.1	NUM
ejpam-6262	57	50	.	.	PUNCT
ejpam-6262	58	1	the	the	DET
ejpam-6262	58	2	homeier	homeier	ADJ
ejpam-6262	58	3	method	method	NOUN
ejpam-6262	58	4	in	in	ADP
ejpam-6262	58	5	solving	solve	VERB
ejpam-6262	58	6	systems	system	NOUN
ejpam-6262	58	7	of	of	ADP
ejpam-6262	58	8	nonlinear	nonlinear	ADJ
ejpam-6262	58	9	equations	equation	NOUN
ejpam-6262	58	10	provided	provide	VERB
ejpam-6262	58	11	that	that	SCONJ
ejpam-6262	58	12	f	f	PROPN
ejpam-6262	58	13	denotes	denote	VERB
ejpam-6262	58	14	a	a	DET
ejpam-6262	58	15	vector	vector	NOUN
ejpam-6262	58	16	-	-	PUNCT
ejpam-6262	58	17	valued	value	VERB
ejpam-6262	58	18	function	function	NOUN
ejpam-6262	58	19	with	with	ADP
ejpam-6262	58	20	non	non	ADJ
ejpam-6262	58	21	-	-	ADJ
ejpam-6262	58	22	zero	zero	NUM
ejpam-6262	58	23	derivatives	derivative	NOUN
ejpam-6262	58	24	defined	define	VERB
ejpam-6262	58	25	on	on	ADP
ejpam-6262	58	26	the	the	DET
ejpam-6262	58	27	set	set	NOUN
ejpam-6262	58	28	d⊂	d⊂	PROPN
ejpam-6262	58	29	rn	rn	PROPN
ejpam-6262	58	30	and	and	CCONJ
ejpam-6262	58	31	x	x	NUM
ejpam-6262	58	32	,	,	PUNCT
ejpam-6262	58	33	x0∈d	x0∈d	NUM
ejpam-6262	58	34	,	,	PUNCT
ejpam-6262	58	35	the	the	DET
ejpam-6262	58	36	application	application	NOUN
ejpam-6262	58	37	of	of	ADP
ejpam-6262	58	38	homeier	homeier	ADJ
ejpam-6262	58	39	method	method	NOUN
ejpam-6262	58	40	’s	’s	PART
ejpam-6262	58	41	extension	extension	NOUN
ejpam-6262	58	42	in	in	ADP
ejpam-6262	58	43	solving	solve	VERB
ejpam-6262	58	44	nonlinear	nonlinear	ADJ
ejpam-6262	58	45	equation	equation	NOUN
ejpam-6262	58	46	’s	’s	PART
ejpam-6262	58	47	systems	system	NOUN
ejpam-6262	58	48	can	can	AUX
ejpam-6262	58	49	be	be	AUX
ejpam-6262	58	50	articulated	articulate	VERB
ejpam-6262	58	51	as	as	SCONJ
ejpam-6262	58	52	follows	follow	VERB
ejpam-6262	58	53	xn+1	xn+1	PROPN
ejpam-6262	58	54	=	=	SYM
ejpam-6262	58	55	xn−	xn−	SYM
ejpam-6262	58	56	1	1	NUM
ejpam-6262	58	57	2	2	NUM
ejpam-6262	58	58	[	[	PUNCT
ejpam-6262	58	59	f	f	NOUN
ejpam-6262	58	60	′	′	NUM
ejpam-6262	58	61	(	(	PUNCT
ejpam-6262	58	62	xn	xn	PROPN
ejpam-6262	58	63	)	)	PUNCT
ejpam-6262	58	64	−1	−1	NOUN
ejpam-6262	59	1	+	+	NOUN
ejpam-6262	59	2	f	f	X
ejpam-6262	59	3	′	′	NUM
ejpam-6262	59	4	(	(	PUNCT
ejpam-6262	59	5	x∗	x∗	PROPN
ejpam-6262	59	6	n+1	n+1	PART
ejpam-6262	59	7	)	)	PUNCT
ejpam-6262	59	8	−1	−1	NOUN
ejpam-6262	59	9	]	]	PUNCT
ejpam-6262	59	10	(	(	PUNCT
ejpam-6262	59	11	f	f	X
ejpam-6262	59	12	(	(	PUNCT
ejpam-6262	59	13	xn	xn	PROPN
ejpam-6262	59	14	)	)	PUNCT
ejpam-6262	59	15	)	)	PUNCT
ejpam-6262	59	16	(	(	PUNCT
ejpam-6262	59	17	3	3	X
ejpam-6262	59	18	)	)	PUNCT
ejpam-6262	59	19	where	where	SCONJ
ejpam-6262	59	20	x∗	x∗	PROPN
ejpam-6262	59	21	n+1	n+1	VERB
ejpam-6262	59	22	=	=	NOUN
ejpam-6262	59	23	xn−f	xn−f	NOUN
ejpam-6262	59	24	′	′	NUM
ejpam-6262	59	25	(	(	PUNCT
ejpam-6262	59	26	xn	xn	PROPN
ejpam-6262	59	27	)	)	PUNCT
ejpam-6262	59	28	−1	−1	NOUN
ejpam-6262	59	29	(	(	PUNCT
ejpam-6262	59	30	f	f	PROPN
ejpam-6262	59	31	(	(	PUNCT
ejpam-6262	59	32	xn	xn	PROPN
ejpam-6262	59	33	)	)	PUNCT
ejpam-6262	59	34	)	)	PUNCT
ejpam-6262	59	35	(	(	PUNCT
ejpam-6262	59	36	4	4	X
ejpam-6262	59	37	)	)	PUNCT
ejpam-6262	59	38	here	here	ADV
ejpam-6262	59	39	,	,	PUNCT
ejpam-6262	59	40	n	n	PROPN
ejpam-6262	59	41	=	=	SYM
ejpam-6262	59	42	0	0	NUM
ejpam-6262	59	43	,	,	PUNCT
ejpam-6262	59	44	1	1	NUM
ejpam-6262	59	45	,	,	PUNCT
ejpam-6262	59	46	2	2	NUM
ejpam-6262	59	47	,	,	PUNCT
ejpam-6262	59	48	·	·	PUNCT
ejpam-6262	59	49	·	·	PUNCT
ejpam-6262	59	50	·	·	PUNCT
ejpam-6262	59	51	and	and	CCONJ
ejpam-6262	59	52	xn	xn	PROPN
ejpam-6262	59	53	is	be	AUX
ejpam-6262	59	54	the	the	DET
ejpam-6262	59	55	nth	nth	NOUN
ejpam-6262	59	56	iterate	iterate	NOUN
ejpam-6262	59	57	.	.	PUNCT
ejpam-6262	60	1	2.2	2.2	NUM
ejpam-6262	60	2	.	.	PUNCT
ejpam-6262	61	1	secant	secant	ADJ
ejpam-6262	61	2	method	method	NOUN
ejpam-6262	61	3	for	for	ADP
ejpam-6262	61	4	systems	system	NOUN
ejpam-6262	61	5	of	of	ADP
ejpam-6262	61	6	nonlinear	nonlinear	ADJ
ejpam-6262	61	7	equations	equation	NOUN
ejpam-6262	61	8	a	a	DET
ejpam-6262	61	9	particular	particular	ADJ
ejpam-6262	61	10	issue	issue	NOUN
ejpam-6262	61	11	arises	arise	VERB
ejpam-6262	61	12	when	when	SCONJ
ejpam-6262	61	13	using	use	VERB
ejpam-6262	61	14	the	the	DET
ejpam-6262	61	15	secant	secant	ADJ
ejpam-6262	61	16	approach	approach	NOUN
ejpam-6262	61	17	to	to	PART
ejpam-6262	61	18	solve	solve	VERB
ejpam-6262	61	19	systems	system	NOUN
ejpam-6262	61	20	of	of	ADP
ejpam-6262	61	21	nonlinear	nonlinear	ADJ
ejpam-6262	61	22	equations	equation	NOUN
ejpam-6262	61	23	,	,	PUNCT
ejpam-6262	61	24	specifically	specifically	ADV
ejpam-6262	61	25	in	in	ADP
ejpam-6262	61	26	relation	relation	NOUN
ejpam-6262	61	27	to	to	ADP
ejpam-6262	61	28	the	the	DET
ejpam-6262	61	29	jacobian	jacobian	NOUN
ejpam-6262	61	30	.	.	PUNCT
ejpam-6262	62	1	here	here	ADV
ejpam-6262	62	2	,	,	PUNCT
ejpam-6262	62	3	the	the	DET
ejpam-6262	62	4	secant	secant	ADJ
ejpam-6262	62	5	technique	technique	NOUN
ejpam-6262	62	6	for	for	ADP
ejpam-6262	62	7	systems	system	NOUN
ejpam-6262	62	8	involves	involve	VERB
ejpam-6262	62	9	the	the	DET
ejpam-6262	62	10	inclusion	inclusion	NOUN
ejpam-6262	62	11	of	of	ADP
ejpam-6262	62	12	a	a	DET
ejpam-6262	62	13	vector	vector	NOUN
ejpam-6262	62	14	in	in	ADP
ejpam-6262	62	15	the	the	DET
ejpam-6262	62	16	denominator	denominator	NOUN
ejpam-6262	62	17	.	.	PUNCT
ejpam-6262	63	1	it	it	PRON
ejpam-6262	63	2	is	be	AUX
ejpam-6262	63	3	customary	customary	ADJ
ejpam-6262	63	4	to	to	PART
ejpam-6262	63	5	employ	employ	VERB
ejpam-6262	63	6	the	the	DET
ejpam-6262	63	7	widely	widely	ADV
ejpam-6262	63	8	used	use	VERB
ejpam-6262	63	9	secant	secant	ADJ
ejpam-6262	63	10	approximation	approximation	NOUN
ejpam-6262	63	11	method	method	NOUN
ejpam-6262	63	12	that	that	PRON
ejpam-6262	63	13	broyden	broyden	NOUN
ejpam-6262	63	14	[	[	X
ejpam-6262	63	15	26	26	NUM
ejpam-6262	63	16	]	]	PUNCT
ejpam-6262	63	17	proposed	propose	VERB
ejpam-6262	63	18	to	to	PART
ejpam-6262	63	19	address	address	VERB
ejpam-6262	63	20	the	the	DET
ejpam-6262	63	21	difficulty	difficulty	NOUN
ejpam-6262	63	22	of	of	ADP
ejpam-6262	63	23	computing	compute	VERB
ejpam-6262	63	24	the	the	DET
ejpam-6262	63	25	inverse	inverse	NOUN
ejpam-6262	63	26	of	of	ADP
ejpam-6262	63	27	a	a	DET
ejpam-6262	63	28	vector	vector	NOUN
ejpam-6262	63	29	.	.	PUNCT
ejpam-6262	64	1	the	the	DET
ejpam-6262	64	2	algorithm	algorithm	NOUN
ejpam-6262	64	3	refers	refer	VERB
ejpam-6262	64	4	to	to	ADP
ejpam-6262	64	5	newton	newton	PROPN
ejpam-6262	64	6	’s	’s	PART
ejpam-6262	64	7	approach	approach	NOUN
ejpam-6262	64	8	.	.	PUNCT
ejpam-6262	65	1	nevertheless	nevertheless	ADV
ejpam-6262	65	2	,	,	PUNCT
ejpam-6262	65	3	the	the	DET
ejpam-6262	65	4	subsequent	subsequent	ADJ
ejpam-6262	65	5	approximation	approximation	NOUN
ejpam-6262	65	6	replaces	replace	VERB
ejpam-6262	65	7	the	the	DET
ejpam-6262	65	8	analytic	analytic	ADJ
ejpam-6262	65	9	jacobian	jacobian	NOUN
ejpam-6262	65	10	.	.	PUNCT
ejpam-6262	66	1	the	the	DET
ejpam-6262	66	2	procedure	procedure	NOUN
ejpam-6262	66	3	in	in	ADP
ejpam-6262	66	4	question	question	NOUN
ejpam-6262	66	5	is	be	AUX
ejpam-6262	66	6	referred	refer	VERB
ejpam-6262	66	7	to	to	ADP
ejpam-6262	66	8	as	as	ADP
ejpam-6262	66	9	broyden	broyden	NOUN
ejpam-6262	66	10	’s	’s	PART
ejpam-6262	66	11	method	method	NOUN
ejpam-6262	66	12	,	,	PUNCT
ejpam-6262	66	13	as	as	SCONJ
ejpam-6262	66	14	described	describe	VERB
ejpam-6262	66	15	by	by	ADP
ejpam-6262	66	16	heenatigala	heenatigala	PROPN
ejpam-6262	66	17	et	et	PROPN
ejpam-6262	66	18	al	al	PROPN
ejpam-6262	66	19	.	.	PUNCT
ejpam-6262	67	1	[	[	X
ejpam-6262	67	2	27	27	NUM
ejpam-6262	67	3	]	]	PUNCT
ejpam-6262	67	4	.	.	PUNCT
ejpam-6262	68	1	y.	y.	PROPN
ejpam-6262	68	2	al	al	PROPN
ejpam-6262	68	3	-	-	PUNCT
ejpam-6262	68	4	shorman	shorman	PROPN
ejpam-6262	68	5	et	et	PROPN
ejpam-6262	68	6	al	al	PROPN
ejpam-6262	68	7	.	.	PUNCT
ejpam-6262	68	8	/	/	SYM
ejpam-6262	68	9	eur	eur	PROPN
ejpam-6262	68	10	.	.	PUNCT
ejpam-6262	69	1	j.	j.	PROPN
ejpam-6262	69	2	pure	pure	PROPN
ejpam-6262	69	3	appl	appl	PROPN
ejpam-6262	69	4	.	.	PROPN
ejpam-6262	69	5	math	math	PROPN
ejpam-6262	69	6	,	,	PUNCT
ejpam-6262	69	7	18	18	NUM
ejpam-6262	69	8	(	(	PUNCT
ejpam-6262	69	9	3	3	NUM
ejpam-6262	69	10	)	)	PUNCT
ejpam-6262	69	11	(	(	PUNCT
ejpam-6262	69	12	2025	2025	NUM
ejpam-6262	69	13	)	)	PUNCT
ejpam-6262	69	14	,	,	PUNCT
ejpam-6262	69	15	6262	6262	NUM
ejpam-6262	69	16	4	4	NUM
ejpam-6262	69	17	of	of	ADP
ejpam-6262	69	18	20	20	NUM
ejpam-6262	69	19	2.3	2.3	NUM
ejpam-6262	69	20	.	.	PUNCT
ejpam-6262	70	1	broyden	broyden	NOUN
ejpam-6262	70	2	’s	’s	PART
ejpam-6262	70	3	method	method	NOUN
ejpam-6262	70	4	for	for	ADP
ejpam-6262	70	5	systems	system	NOUN
ejpam-6262	70	6	of	of	ADP
ejpam-6262	70	7	nonlinear	nonlinear	ADJ
ejpam-6262	70	8	equations	equation	NOUN
ejpam-6262	70	9	2.3.1	2.3.1	NUM
ejpam-6262	70	10	.	.	PUNCT
ejpam-6262	70	11	application	application	NOUN
ejpam-6262	70	12	of	of	ADP
ejpam-6262	70	13	dfh	dfh	PROPN
ejpam-6262	70	14	for	for	ADP
ejpam-6262	70	15	systems	system	NOUN
ejpam-6262	70	16	of	of	ADP
ejpam-6262	70	17	nonlinear	nonlinear	ADJ
ejpam-6262	70	18	equations	equation	NOUN
ejpam-6262	70	19	an	an	DET
ejpam-6262	70	20	initial	initial	ADJ
ejpam-6262	70	21	estimate	estimate	NOUN
ejpam-6262	70	22	given	give	VERB
ejpam-6262	70	23	by	by	ADP
ejpam-6262	70	24	x0	x0	PROPN
ejpam-6262	70	25	∈	∈	PROPN
ejpam-6262	70	26	rn	rn	PROPN
ejpam-6262	70	27	is	be	AUX
ejpam-6262	70	28	selected	select	VERB
ejpam-6262	70	29	along	along	ADV
ejpam-6262	70	30	with	with	ADP
ejpam-6262	70	31	a	a	DET
ejpam-6262	70	32	non	non	ADJ
ejpam-6262	70	33	-	-	ADJ
ejpam-6262	70	34	singular	singular	ADJ
ejpam-6262	70	35	initial	initial	ADJ
ejpam-6262	70	36	matrix	matrix	NOUN
ejpam-6262	70	37	a0	a0	PROPN
ejpam-6262	70	38	∈	∈	PROPN
ejpam-6262	70	39	rn×n	rn×n	NOUN
ejpam-6262	70	40	.	.	PUNCT
ejpam-6262	71	1	by	by	ADP
ejpam-6262	71	2	setting	set	VERB
ejpam-6262	71	3	k	k	X
ejpam-6262	71	4	:	:	PUNCT
ejpam-6262	71	5	=	=	SYM
ejpam-6262	71	6	0	0	NUM
ejpam-6262	71	7	,	,	PUNCT
ejpam-6262	71	8	we	we	PRON
ejpam-6262	71	9	repeat	repeat	VERB
ejpam-6262	71	10	the	the	DET
ejpam-6262	71	11	sequence	sequence	NOUN
ejpam-6262	71	12	of	of	ADP
ejpam-6262	71	13	steps	step	NOUN
ejpam-6262	71	14	given	give	VERB
ejpam-6262	71	15	below	below	ADV
ejpam-6262	71	16	until	until	ADP
ejpam-6262	71	17	∥f	∥f	PROPN
ejpam-6262	71	18	(	(	PUNCT
ejpam-6262	71	19	xk)∥	xk)∥	PROPN
ejpam-6262	71	20	<	<	X
ejpam-6262	71	21	tolerance	tolerance	NOUN
ejpam-6262	71	22	(	(	PUNCT
ejpam-6262	71	23	i	i	NOUN
ejpam-6262	71	24	)	)	PUNCT
ejpam-6262	71	25	solve	solve	VERB
ejpam-6262	71	26	akik	akik	NOUN
ejpam-6262	72	1	=	=	SYM
ejpam-6262	72	2	f	f	X
ejpam-6262	72	3	(	(	PUNCT
ejpam-6262	72	4	x∗	x∗	PROPN
ejpam-6262	72	5	k+1)−	k+1)−	PROPN
ejpam-6262	72	6	f	f	PROPN
ejpam-6262	72	7	(	(	PUNCT
ejpam-6262	72	8	xk	xk	PROPN
ejpam-6262	72	9	)	)	PUNCT
ejpam-6262	72	10	for	for	ADP
ejpam-6262	72	11	ik	ik	PROPN
ejpam-6262	72	12	&	&	CCONJ
ejpam-6262	72	13	x∗	x∗	PROPN
ejpam-6262	72	14	k+1	k+1	X
ejpam-6262	72	15	from	from	ADP
ejpam-6262	72	16	broyden	broyden	PROPN
ejpam-6262	72	17	’s	’s	PART
ejpam-6262	72	18	method	method	NOUN
ejpam-6262	72	19	.	.	PUNCT
ejpam-6262	73	1	(	(	PUNCT
ejpam-6262	73	2	ii	ii	NOUN
ejpam-6262	73	3	)	)	PUNCT
ejpam-6262	73	4	xk+1	xk+1	PUNCT
ejpam-6262	74	1	=	=	SYM
ejpam-6262	74	2	xk	xk	PROPN
ejpam-6262	74	3	+	+	CCONJ
ejpam-6262	74	4	ik	ik	PROPN
ejpam-6262	74	5	(	(	PUNCT
ejpam-6262	74	6	iii	iii	NOUN
ejpam-6262	74	7	)	)	PUNCT
ejpam-6262	74	8	yk	yk	NOUN
ejpam-6262	74	9	=	=	SYM
ejpam-6262	74	10	f	f	PROPN
ejpam-6262	74	11	(	(	PUNCT
ejpam-6262	74	12	xk+1)−	xk+1)−	PROPN
ejpam-6262	74	13	f	f	PROPN
ejpam-6262	74	14	(	(	PUNCT
ejpam-6262	74	15	xk	xk	PROPN
ejpam-6262	74	16	)	)	PUNCT
ejpam-6262	74	17	(	(	PUNCT
ejpam-6262	74	18	iv	iv	X
ejpam-6262	74	19	)	)	PUNCT
ejpam-6262	74	20	ak+1	ak+1	VERB
ejpam-6262	74	21	=	=	SYM
ejpam-6262	74	22	ak	ak	PROPN
ejpam-6262	74	23	+	+	PROPN
ejpam-6262	74	24	yk−akik	yk−akik	PROPN
ejpam-6262	74	25	itkik	itkik	PROPN
ejpam-6262	74	26	itk	itk	PROPN
ejpam-6262	74	27	3	3	X
ejpam-6262	74	28	.	.	PUNCT
ejpam-6262	74	29	derivation	derivation	NOUN
ejpam-6262	74	30	of	of	ADP
ejpam-6262	74	31	derivative	derivative	ADJ
ejpam-6262	74	32	-	-	PUNCT
ejpam-6262	74	33	free	free	ADJ
ejpam-6262	74	34	homeier	homeier	NOUN
ejpam-6262	74	35	(	(	PUNCT
ejpam-6262	74	36	dfh	dfh	PROPN
ejpam-6262	74	37	)	)	PUNCT
ejpam-6262	74	38	from	from	ADP
ejpam-6262	74	39	homeier	homeier	ADJ
ejpam-6262	74	40	method	method	NOUN
ejpam-6262	74	41	in	in	ADP
ejpam-6262	74	42	this	this	DET
ejpam-6262	74	43	section	section	NOUN
ejpam-6262	74	44	,	,	PUNCT
ejpam-6262	74	45	we	we	PRON
ejpam-6262	74	46	will	will	AUX
ejpam-6262	74	47	explain	explain	VERB
ejpam-6262	74	48	how	how	SCONJ
ejpam-6262	74	49	our	our	PRON
ejpam-6262	74	50	new	new	ADJ
ejpam-6262	74	51	method	method	NOUN
ejpam-6262	74	52	was	be	AUX
ejpam-6262	74	53	derived	derive	VERB
ejpam-6262	74	54	.	.	PUNCT
ejpam-6262	75	1	in	in	ADP
ejpam-6262	75	2	this	this	DET
ejpam-6262	75	3	context	context	NOUN
ejpam-6262	75	4	,	,	PUNCT
ejpam-6262	75	5	a	a	DET
ejpam-6262	75	6	combination	combination	NOUN
ejpam-6262	75	7	of	of	ADP
ejpam-6262	75	8	backward	backward	ADJ
ejpam-6262	75	9	and	and	CCONJ
ejpam-6262	75	10	forward	forward	ADJ
ejpam-6262	75	11	difference	difference	NOUN
ejpam-6262	75	12	approximations	approximation	NOUN
ejpam-6262	75	13	is	be	AUX
ejpam-6262	75	14	employed	employ	VERB
ejpam-6262	75	15	in	in	ADP
ejpam-6262	75	16	a	a	DET
ejpam-6262	75	17	judicious	judicious	ADJ
ejpam-6262	75	18	manner	manner	NOUN
ejpam-6262	75	19	within	within	ADP
ejpam-6262	75	20	a	a	DET
ejpam-6262	75	21	single	single	ADJ
ejpam-6262	75	22	formula	formula	NOUN
ejpam-6262	75	23	to	to	PART
ejpam-6262	75	24	provide	provide	VERB
ejpam-6262	75	25	a	a	DET
ejpam-6262	75	26	satisfactory	satisfactory	ADJ
ejpam-6262	75	27	outcome	outcome	NOUN
ejpam-6262	75	28	.	.	PUNCT
ejpam-6262	76	1	consider	consider	VERB
ejpam-6262	76	2	the	the	DET
ejpam-6262	76	3	homeier	homei	ADJ
ejpam-6262	76	4	method	method	NOUN
ejpam-6262	76	5	xn+1	xn+1	PROPN
ejpam-6262	77	1	=	=	SYM
ejpam-6262	77	2	xn	xn	PROPN
ejpam-6262	78	1	−	−	PROPN
ejpam-6262	78	2	f	f	PROPN
ejpam-6262	78	3	(	(	PUNCT
ejpam-6262	78	4	xn	xn	PROPN
ejpam-6262	78	5	)	)	PUNCT
ejpam-6262	78	6	2	2	NUM
ejpam-6262	78	7	[	[	PUNCT
ejpam-6262	78	8	1	1	NUM
ejpam-6262	78	9	f	f	NOUN
ejpam-6262	78	10	′	′	NUM
ejpam-6262	78	11	(	(	PUNCT
ejpam-6262	78	12	xn	xn	X
ejpam-6262	78	13	)	)	PUNCT
ejpam-6262	79	1	+	+	CCONJ
ejpam-6262	79	2	1	1	NUM
ejpam-6262	79	3	f	f	NOUN
ejpam-6262	79	4	′	′	NUM
ejpam-6262	79	5	(	(	PUNCT
ejpam-6262	79	6	yn	yn	PROPN
ejpam-6262	79	7	)	)	PUNCT
ejpam-6262	79	8	]	]	PUNCT
ejpam-6262	79	9	(	(	PUNCT
ejpam-6262	79	10	5	5	NUM
ejpam-6262	79	11	)	)	PUNCT
ejpam-6262	79	12	in	in	ADP
ejpam-6262	79	13	which	which	PRON
ejpam-6262	79	14	yn	yn	X
ejpam-6262	79	15	=	=	PUNCT
ejpam-6262	79	16	xn	xn	PROPN
ejpam-6262	79	17	−	−	NUM
ejpam-6262	79	18	f(xn	f(xn	PROPN
ejpam-6262	79	19	)	)	PUNCT
ejpam-6262	79	20	f	f	PROPN
ejpam-6262	79	21	′(xn	′(xn	NOUN
ejpam-6262	79	22	)	)	PUNCT
ejpam-6262	79	23	with	with	ADP
ejpam-6262	79	24	n	n	NOUN
ejpam-6262	79	25	=	=	SYM
ejpam-6262	79	26	0	0	NUM
ejpam-6262	79	27	,	,	PUNCT
ejpam-6262	79	28	1	1	NUM
ejpam-6262	79	29	,	,	PUNCT
ejpam-6262	79	30	2	2	NUM
ejpam-6262	79	31	,	,	PUNCT
ejpam-6262	79	32	·	·	PUNCT
ejpam-6262	79	33	·	·	PUNCT
ejpam-6262	79	34	·	·	PUNCT
ejpam-6262	79	35	.	.	PUNCT
ejpam-6262	80	1	replacing	replace	VERB
ejpam-6262	80	2	the	the	DET
ejpam-6262	80	3	forward	forward	ADJ
ejpam-6262	80	4	difference	difference	NOUN
ejpam-6262	80	5	approximation	approximation	NOUN
ejpam-6262	80	6	for	for	ADP
ejpam-6262	80	7	f	f	PROPN
ejpam-6262	80	8	′	′	NUM
ejpam-6262	80	9	(	(	PUNCT
ejpam-6262	80	10	xn	xn	PROPN
ejpam-6262	80	11	)	)	PUNCT
ejpam-6262	81	1	≈	≈	PROPN
ejpam-6262	81	2	f	f	PROPN
ejpam-6262	81	3	(	(	PUNCT
ejpam-6262	81	4	xn+1)−	xn+1)−	PROPN
ejpam-6262	81	5	f	f	PROPN
ejpam-6262	81	6	(	(	PUNCT
ejpam-6262	81	7	xn	xn	PROPN
ejpam-6262	81	8	)	)	PUNCT
ejpam-6262	81	9	xn+1	xn+1	PROPN
ejpam-6262	82	1	−	−	PROPN
ejpam-6262	82	2	xn	xn	PROPN
ejpam-6262	83	1	(	(	PUNCT
ejpam-6262	83	2	6	6	NUM
ejpam-6262	83	3	)	)	PUNCT
ejpam-6262	83	4	as	as	ADV
ejpam-6262	83	5	well	well	ADV
ejpam-6262	83	6	as	as	ADP
ejpam-6262	83	7	the	the	DET
ejpam-6262	83	8	backward	backward	ADJ
ejpam-6262	83	9	difference	difference	NOUN
ejpam-6262	83	10	approximation	approximation	NOUN
ejpam-6262	83	11	for	for	ADP
ejpam-6262	83	12	f	f	PROPN
ejpam-6262	83	13	′	′	NUM
ejpam-6262	83	14	(	(	PUNCT
ejpam-6262	83	15	xn+1	xn+1	X
ejpam-6262	83	16	)	)	PUNCT
ejpam-6262	84	1	≈	≈	PROPN
ejpam-6262	84	2	f	f	PROPN
ejpam-6262	84	3	(	(	PUNCT
ejpam-6262	84	4	xn+1)−	xn+1)−	PROPN
ejpam-6262	84	5	f	f	PROPN
ejpam-6262	84	6	(	(	PUNCT
ejpam-6262	84	7	xn	xn	PROPN
ejpam-6262	84	8	)	)	PUNCT
ejpam-6262	84	9	xn+1	xn+1	PROPN
ejpam-6262	85	1	−	−	PROPN
ejpam-6262	85	2	xn	xn	PROPN
ejpam-6262	86	1	(	(	PUNCT
ejpam-6262	86	2	7	7	NUM
ejpam-6262	86	3	)	)	PUNCT
ejpam-6262	86	4	from	from	ADP
ejpam-6262	86	5	equations	equation	NOUN
ejpam-6262	86	6	(	(	PUNCT
ejpam-6262	86	7	5)-(7	5)-(7	NUM
ejpam-6262	86	8	)	)	PUNCT
ejpam-6262	86	9	,	,	PUNCT
ejpam-6262	86	10	we	we	PRON
ejpam-6262	86	11	get	get	VERB
ejpam-6262	86	12	xn+1	xn+1	PUNCT
ejpam-6262	87	1	=	=	SYM
ejpam-6262	87	2	xn	xn	PROPN
ejpam-6262	88	1	−	−	PROPN
ejpam-6262	88	2	f	f	PROPN
ejpam-6262	88	3	(	(	PUNCT
ejpam-6262	88	4	xn	xn	PROPN
ejpam-6262	88	5	)	)	PUNCT
ejpam-6262	88	6	2	2	NUM
ejpam-6262	88	7			NOUN
ejpam-6262	88	8	1	1	NUM
ejpam-6262	88	9	f(xn+1)−f(xn	f(xn+1)−f(xn	NOUN
ejpam-6262	88	10	)	)	PUNCT
ejpam-6262	89	1	xn+1−xn	xn+1−xn	PROPN
ejpam-6262	89	2	+	+	CCONJ
ejpam-6262	89	3	1	1	NUM
ejpam-6262	89	4	f(xn+1)−f(xn	f(xn+1)−f(xn	NOUN
ejpam-6262	89	5	)	)	PUNCT
ejpam-6262	89	6	xn+1	xn+1	PROPN
ejpam-6262	90	1	−	−	NOUN
ejpam-6262	90	2	xn	xn	NOUN
ejpam-6262	90	3			NOUN
ejpam-6262	90	4	(	(	PUNCT
ejpam-6262	90	5	8)	8)	NUM
ejpam-6262	90	6	xn+1	xn+1	NUM
ejpam-6262	90	7	=	=	SYM
ejpam-6262	90	8	xn	xn	PROPN
ejpam-6262	91	1	−	−	PROPN
ejpam-6262	91	2	f	f	PROPN
ejpam-6262	91	3	(	(	PUNCT
ejpam-6262	91	4	xn	xn	PROPN
ejpam-6262	91	5	)	)	PUNCT
ejpam-6262	91	6	2	2	NUM
ejpam-6262	91	7	[	[	PUNCT
ejpam-6262	91	8	2	2	NUM
ejpam-6262	91	9	(	(	PUNCT
ejpam-6262	91	10	xn+1	xn+1	NUM
ejpam-6262	91	11	−	−	NOUN
ejpam-6262	91	12	xn	xn	NUM
ejpam-6262	91	13	)	)	PUNCT
ejpam-6262	91	14	f	f	PROPN
ejpam-6262	92	1	(	(	PUNCT
ejpam-6262	92	2	xn+1)−	xn+1)−	PROPN
ejpam-6262	92	3	f	f	PROPN
ejpam-6262	92	4	(	(	PUNCT
ejpam-6262	92	5	xn	xn	PROPN
ejpam-6262	92	6	)	)	PUNCT
ejpam-6262	92	7	]	]	PUNCT
ejpam-6262	93	1	(	(	PUNCT
ejpam-6262	93	2	9	9	X
ejpam-6262	93	3	)	)	PUNCT
ejpam-6262	93	4	y.	y.	PROPN
ejpam-6262	93	5	al	al	PROPN
ejpam-6262	93	6	-	-	PUNCT
ejpam-6262	93	7	shorman	shorman	PROPN
ejpam-6262	93	8	et	et	PROPN
ejpam-6262	93	9	al	al	PROPN
ejpam-6262	93	10	.	.	PUNCT
ejpam-6262	93	11	/	/	SYM
ejpam-6262	93	12	eur	eur	PROPN
ejpam-6262	93	13	.	.	PUNCT
ejpam-6262	94	1	j.	j.	PROPN
ejpam-6262	94	2	pure	pure	PROPN
ejpam-6262	94	3	appl	appl	PROPN
ejpam-6262	94	4	.	.	PROPN
ejpam-6262	94	5	math	math	PROPN
ejpam-6262	94	6	,	,	PUNCT
ejpam-6262	94	7	18	18	NUM
ejpam-6262	94	8	(	(	PUNCT
ejpam-6262	94	9	3	3	NUM
ejpam-6262	94	10	)	)	PUNCT
ejpam-6262	94	11	(	(	PUNCT
ejpam-6262	94	12	2025	2025	NUM
ejpam-6262	94	13	)	)	PUNCT
ejpam-6262	94	14	,	,	PUNCT
ejpam-6262	94	15	6262	6262	NUM
ejpam-6262	94	16	5	5	NUM
ejpam-6262	94	17	of	of	ADP
ejpam-6262	94	18	20	20	NUM
ejpam-6262	94	19	hence	hence	ADV
ejpam-6262	94	20	,	,	PUNCT
ejpam-6262	94	21	the	the	DET
ejpam-6262	94	22	new	new	ADJ
ejpam-6262	94	23	iterative	iterative	NOUN
ejpam-6262	94	24	formula	formula	NOUN
ejpam-6262	94	25	with	with	ADP
ejpam-6262	94	26	no	no	DET
ejpam-6262	94	27	derivative	derivative	ADJ
ejpam-6262	94	28	terms	term	NOUN
ejpam-6262	94	29	expressed	express	VERB
ejpam-6262	94	30	as	as	SCONJ
ejpam-6262	94	31	follows	follow	VERB
ejpam-6262	94	32	xn+1	xn+1	PROPN
ejpam-6262	95	1	=	=	SYM
ejpam-6262	96	1	xn	xn	PROPN
ejpam-6262	97	1	−	−	PROPN
ejpam-6262	97	2	f	f	PROPN
ejpam-6262	97	3	(	(	PUNCT
ejpam-6262	97	4	xn	xn	PROPN
ejpam-6262	97	5	)	)	PUNCT
ejpam-6262	97	6	(	(	PUNCT
ejpam-6262	97	7	xn+1	xn+1	NUM
ejpam-6262	97	8	−	−	NOUN
ejpam-6262	97	9	xn	xn	NUM
ejpam-6262	97	10	)	)	PUNCT
ejpam-6262	97	11	f	f	PROPN
ejpam-6262	97	12	(	(	PUNCT
ejpam-6262	97	13	xn+1)−	xn+1)−	PROPN
ejpam-6262	97	14	f	f	PROPN
ejpam-6262	97	15	(	(	PUNCT
ejpam-6262	97	16	xn	xn	PROPN
ejpam-6262	97	17	)	)	PUNCT
ejpam-6262	97	18	(	(	PUNCT
ejpam-6262	97	19	10	10	NUM
ejpam-6262	97	20	)	)	PUNCT
ejpam-6262	97	21	however	however	ADV
ejpam-6262	97	22	,	,	PUNCT
ejpam-6262	97	23	this	this	DET
ejpam-6262	97	24	approach	approach	NOUN
ejpam-6262	97	25	is	be	AUX
ejpam-6262	97	26	considered	consider	VERB
ejpam-6262	97	27	implicit	implicit	ADJ
ejpam-6262	97	28	,	,	PUNCT
ejpam-6262	97	29	since	since	SCONJ
ejpam-6262	97	30	it	it	PRON
ejpam-6262	97	31	requires	require	VERB
ejpam-6262	97	32	the	the	DET
ejpam-6262	97	33	inclusion	inclusion	NOUN
ejpam-6262	97	34	of	of	ADP
ejpam-6262	97	35	the	the	DET
ejpam-6262	97	36	term	term	NOUN
ejpam-6262	97	37	xn+1	xn+1	NUM
ejpam-6262	97	38	in	in	ADP
ejpam-6262	97	39	the	the	DET
ejpam-6262	97	40	(	(	PUNCT
ejpam-6262	97	41	n+	n+	NUM
ejpam-6262	97	42	1)th	1)th	NUM
ejpam-6262	97	43	iterative	iterative	NOUN
ejpam-6262	97	44	step	step	NOUN
ejpam-6262	97	45	to	to	PART
ejpam-6262	97	46	identify	identify	VERB
ejpam-6262	97	47	the	the	DET
ejpam-6262	97	48	(	(	PUNCT
ejpam-6262	97	49	n+	n+	NUM
ejpam-6262	97	50	1)th	1)th	NUM
ejpam-6262	97	51	iterate	iterate	NOUN
ejpam-6262	97	52	itself	itself	PRON
ejpam-6262	97	53	.	.	PUNCT
ejpam-6262	98	1	in	in	ADP
ejpam-6262	98	2	this	this	DET
ejpam-6262	98	3	context	context	NOUN
ejpam-6262	98	4	,	,	PUNCT
ejpam-6262	98	5	the	the	DET
ejpam-6262	98	6	secant	secant	ADJ
ejpam-6262	98	7	method	method	NOUN
ejpam-6262	98	8	may	may	AUX
ejpam-6262	98	9	be	be	AUX
ejpam-6262	98	10	used	use	VERB
ejpam-6262	98	11	to	to	PART
ejpam-6262	98	12	replace	replace	VERB
ejpam-6262	98	13	the	the	DET
ejpam-6262	98	14	term	term	NOUN
ejpam-6262	98	15	xn+1	xn+1	ADV
ejpam-6262	98	16	on	on	ADP
ejpam-6262	98	17	the	the	DET
ejpam-6262	98	18	right	right	ADJ
ejpam-6262	98	19	-	-	PUNCT
ejpam-6262	98	20	hand	hand	NOUN
ejpam-6262	98	21	side	side	NOUN
ejpam-6262	98	22	of	of	ADP
ejpam-6262	98	23	the	the	DET
ejpam-6262	98	24	aforementioned	aforementioned	ADJ
ejpam-6262	98	25	equation	equation	NOUN
ejpam-6262	98	26	to	to	PART
ejpam-6262	98	27	address	address	VERB
ejpam-6262	98	28	this	this	DET
ejpam-6262	98	29	problem	problem	NOUN
ejpam-6262	98	30	.	.	PUNCT
ejpam-6262	99	1	as	as	ADP
ejpam-6262	99	2	a	a	DET
ejpam-6262	99	3	result	result	NOUN
ejpam-6262	99	4	,	,	PUNCT
ejpam-6262	99	5	the	the	DET
ejpam-6262	99	6	derivative	derivative	ADJ
ejpam-6262	99	7	-	-	PUNCT
ejpam-6262	99	8	free	free	ADJ
ejpam-6262	99	9	homeier	homeier	ADJ
ejpam-6262	99	10	method	method	NOUN
ejpam-6262	99	11	(	(	PUNCT
ejpam-6262	99	12	dfh	dfh	PROPN
ejpam-6262	99	13	)	)	PUNCT
ejpam-6262	99	14	has	have	AUX
ejpam-6262	99	15	surfaced	surface	VERB
ejpam-6262	99	16	as	as	ADP
ejpam-6262	99	17	xn+1	xn+1	PROPN
ejpam-6262	99	18	=	=	SYM
ejpam-6262	99	19	xn	xn	PROPN
ejpam-6262	100	1	−	−	PROPN
ejpam-6262	100	2	f	f	PROPN
ejpam-6262	100	3	(	(	PUNCT
ejpam-6262	100	4	xn	xn	PROPN
ejpam-6262	100	5	)	)	PUNCT
ejpam-6262	100	6	(	(	PUNCT
ejpam-6262	100	7	yn	yn	INTJ
ejpam-6262	100	8	−	−	PROPN
ejpam-6262	100	9	xn	xn	X
ejpam-6262	100	10	)	)	PUNCT
ejpam-6262	100	11	f	f	PROPN
ejpam-6262	100	12	(	(	PUNCT
ejpam-6262	100	13	yn)−	yn)−	PROPN
ejpam-6262	100	14	f	f	PROPN
ejpam-6262	100	15	(	(	PUNCT
ejpam-6262	100	16	xn	xn	PROPN
ejpam-6262	100	17	)	)	PUNCT
ejpam-6262	100	18	(	(	PUNCT
ejpam-6262	100	19	11	11	NUM
ejpam-6262	100	20	)	)	PUNCT
ejpam-6262	100	21	where	where	SCONJ
ejpam-6262	100	22	yn	yn	PRON
ejpam-6262	100	23	=	=	PUNCT
ejpam-6262	100	24	xn	xn	PROPN
ejpam-6262	101	1	−	−	PROPN
ejpam-6262	101	2	f	f	PROPN
ejpam-6262	101	3	(	(	PUNCT
ejpam-6262	101	4	xn	xn	PROPN
ejpam-6262	101	5	)	)	PUNCT
ejpam-6262	101	6	(	(	PUNCT
ejpam-6262	101	7	xn	xn	NUM
ejpam-6262	101	8	−	−	PROPN
ejpam-6262	101	9	xn−1	xn−1	PROPN
ejpam-6262	101	10	)	)	PUNCT
ejpam-6262	101	11	f	f	PROPN
ejpam-6262	101	12	(	(	PUNCT
ejpam-6262	101	13	xn)−	xn)−	NOUN
ejpam-6262	101	14	f	f	X
ejpam-6262	101	15	(	(	PUNCT
ejpam-6262	101	16	xn−1	xn−1	PROPN
ejpam-6262	101	17	)	)	PUNCT
ejpam-6262	101	18	n	n	NOUN
ejpam-6262	101	19	=	=	SYM
ejpam-6262	101	20	1	1	NUM
ejpam-6262	101	21	,	,	PUNCT
ejpam-6262	101	22	2	2	NUM
ejpam-6262	101	23	,	,	PUNCT
ejpam-6262	101	24	.	.	PUNCT
ejpam-6262	101	25	.	.	PUNCT
ejpam-6262	101	26	.	.	PUNCT
ejpam-6262	101	27	.	.	PUNCT
ejpam-6262	102	1	(	(	PUNCT
ejpam-6262	102	2	12	12	NUM
ejpam-6262	102	3	)	)	PUNCT
ejpam-6262	102	4	to	to	PART
ejpam-6262	102	5	extend	extend	VERB
ejpam-6262	102	6	our	our	PRON
ejpam-6262	102	7	scheme	scheme	NOUN
ejpam-6262	102	8	(	(	PUNCT
ejpam-6262	102	9	11	11	NUM
ejpam-6262	102	10	-	-	SYM
ejpam-6262	102	11	12	12	NUM
ejpam-6262	102	12	)	)	PUNCT
ejpam-6262	102	13	to	to	ADP
ejpam-6262	102	14	the	the	DET
ejpam-6262	102	15	multidimensional	multidimensional	ADJ
ejpam-6262	102	16	context	context	NOUN
ejpam-6262	102	17	for	for	ADP
ejpam-6262	102	18	addressing	address	VERB
ejpam-6262	102	19	systems	system	NOUN
ejpam-6262	102	20	of	of	ADP
ejpam-6262	102	21	nonlinear	nonlinear	ADJ
ejpam-6262	102	22	modules	module	NOUN
ejpam-6262	102	23	,	,	PUNCT
ejpam-6262	102	24	the	the	DET
ejpam-6262	102	25	scheme	scheme	NOUN
ejpam-6262	102	26	is	be	AUX
ejpam-6262	102	27	reformulated	reformulate	VERB
ejpam-6262	102	28	as	as	SCONJ
ejpam-6262	102	29	follows	follow	VERB
ejpam-6262	102	30	:	:	PUNCT
ejpam-6262	102	31	xn+1	xn+1	NUM
ejpam-6262	103	1	=	=	SYM
ejpam-6262	103	2	xn	xn	X
ejpam-6262	104	1	−	−	PROPN
ejpam-6262	104	2	[	[	PUNCT
ejpam-6262	104	3	(	(	PUNCT
ejpam-6262	104	4	f	f	X
ejpam-6262	104	5	(	(	PUNCT
ejpam-6262	104	6	yn)−	yn)−	PROPN
ejpam-6262	104	7	f	f	PROPN
ejpam-6262	104	8	(	(	PUNCT
ejpam-6262	104	9	xn	xn	PROPN
ejpam-6262	104	10	)	)	PUNCT
ejpam-6262	104	11	)	)	PUNCT
ejpam-6262	104	12	−1(f	−1(f	X
ejpam-6262	104	13	(	(	PUNCT
ejpam-6262	104	14	xn)(yn	xn)(yn	PROPN
ejpam-6262	104	15	−xn	−xn	PROPN
ejpam-6262	104	16	)	)	PUNCT
ejpam-6262	104	17	)	)	PUNCT
ejpam-6262	104	18	]	]	PUNCT
ejpam-6262	105	1	(	(	PUNCT
ejpam-6262	105	2	13	13	NUM
ejpam-6262	105	3	)	)	PUNCT
ejpam-6262	105	4	where	where	SCONJ
ejpam-6262	105	5	yn	yn	PRON
ejpam-6262	105	6	=	=	PUNCT
ejpam-6262	105	7	xn	xn	PROPN
ejpam-6262	106	1	−	−	PROPN
ejpam-6262	106	2	[	[	PUNCT
ejpam-6262	106	3	(	(	PUNCT
ejpam-6262	106	4	f	f	X
ejpam-6262	106	5	(	(	PUNCT
ejpam-6262	106	6	xn)−	xn)−	NOUN
ejpam-6262	106	7	f	f	X
ejpam-6262	106	8	(	(	PUNCT
ejpam-6262	106	9	xn−1	xn−1	PROPN
ejpam-6262	106	10	)	)	PUNCT
ejpam-6262	106	11	)	)	PUNCT
ejpam-6262	106	12	−1(f	−1(f	PUNCT
ejpam-6262	106	13	(	(	PUNCT
ejpam-6262	106	14	xn)(xn	xn)(xn	X
ejpam-6262	106	15	−xn−1	−xn−1	NOUN
ejpam-6262	106	16	)	)	PUNCT
ejpam-6262	106	17	)	)	PUNCT
ejpam-6262	106	18	]	]	PUNCT
ejpam-6262	107	1	n	n	NOUN
ejpam-6262	107	2	=	=	SYM
ejpam-6262	107	3	1	1	NUM
ejpam-6262	107	4	,	,	PUNCT
ejpam-6262	107	5	2	2	NUM
ejpam-6262	107	6	,	,	PUNCT
ejpam-6262	107	7	.	.	PUNCT
ejpam-6262	107	8	.	.	PUNCT
ejpam-6262	107	9	.	.	PUNCT
ejpam-6262	107	10	.	.	PUNCT
ejpam-6262	108	1	(	(	PUNCT
ejpam-6262	108	2	14	14	NUM
ejpam-6262	108	3	)	)	PUNCT
ejpam-6262	108	4	4	4	NUM
ejpam-6262	108	5	.	.	PUNCT
ejpam-6262	109	1	order	order	NOUN
ejpam-6262	109	2	of	of	ADP
ejpam-6262	109	3	convergence	convergence	NOUN
ejpam-6262	109	4	of	of	ADP
ejpam-6262	109	5	dfh	dfh	PROPN
ejpam-6262	109	6	method	method	NOUN
ejpam-6262	109	7	in	in	ADP
ejpam-6262	109	8	this	this	DET
ejpam-6262	109	9	segment	segment	NOUN
ejpam-6262	109	10	,	,	PUNCT
ejpam-6262	109	11	we	we	PRON
ejpam-6262	109	12	will	will	AUX
ejpam-6262	109	13	explore	explore	VERB
ejpam-6262	109	14	the	the	DET
ejpam-6262	109	15	convergence	convergence	NOUN
ejpam-6262	109	16	order	order	NOUN
ejpam-6262	109	17	of	of	ADP
ejpam-6262	109	18	the	the	DET
ejpam-6262	109	19	method	method	NOUN
ejpam-6262	109	20	presented	present	VERB
ejpam-6262	109	21	here	here	ADV
ejpam-6262	109	22	.	.	PUNCT
ejpam-6262	110	1	relying	rely	VERB
ejpam-6262	110	2	on	on	ADP
ejpam-6262	110	3	equation	equation	NOUN
ejpam-6262	110	4	(	(	PUNCT
ejpam-6262	110	5	1	1	NUM
ejpam-6262	110	6	)	)	PUNCT
ejpam-6262	110	7	to	to	PART
ejpam-6262	110	8	determine	determine	VERB
ejpam-6262	110	9	the	the	DET
ejpam-6262	110	10	convergence	convergence	NOUN
ejpam-6262	110	11	order	order	NOUN
ejpam-6262	110	12	of	of	ADP
ejpam-6262	110	13	our	our	PRON
ejpam-6262	110	14	proposed	propose	VERB
ejpam-6262	110	15	method	method	NOUN
ejpam-6262	110	16	.	.	PUNCT
ejpam-6262	111	1	to	to	PART
ejpam-6262	111	2	determine	determine	VERB
ejpam-6262	111	3	the	the	DET
ejpam-6262	111	4	convergence	convergence	NOUN
ejpam-6262	111	5	order	order	NOUN
ejpam-6262	111	6	,	,	PUNCT
ejpam-6262	111	7	we	we	PRON
ejpam-6262	111	8	can	can	AUX
ejpam-6262	111	9	apply	apply	VERB
ejpam-6262	111	10	the	the	DET
ejpam-6262	111	11	notion	notion	NOUN
ejpam-6262	111	12	of	of	ADP
ejpam-6262	111	13	error	error	NOUN
ejpam-6262	111	14	functions	function	NOUN
ejpam-6262	111	15	,	,	PUNCT
ejpam-6262	111	16	denoted	denote	VERB
ejpam-6262	111	17	as	as	ADP
ejpam-6262	111	18	|en+1|	|en+1|	PROPN
ejpam-6262	111	19	≤	≤	NUM
ejpam-6262	111	20	k	k	X
ejpam-6262	111	21	|en|p	|en|p	PROPN
ejpam-6262	111	22	.	.	PUNCT
ejpam-6262	111	23	theorem	theorem	NOUN
ejpam-6262	111	24	1	1	NUM
ejpam-6262	111	25	.	.	PUNCT
ejpam-6262	111	26	suppose	suppose	VERB
ejpam-6262	111	27	that	that	SCONJ
ejpam-6262	111	28	f	f	PROPN
ejpam-6262	111	29	represents	represent	VERB
ejpam-6262	111	30	a	a	DET
ejpam-6262	111	31	function	function	NOUN
ejpam-6262	111	32	with	with	ADP
ejpam-6262	111	33	non	non	ADJ
ejpam-6262	111	34	-	-	ADJ
ejpam-6262	111	35	zero	zero	NUM
ejpam-6262	111	36	derivatives	derivative	NOUN
ejpam-6262	111	37	defined	define	VERB
ejpam-6262	111	38	on	on	ADP
ejpam-6262	111	39	the	the	DET
ejpam-6262	111	40	set	set	PROPN
ejpam-6262	111	41	d	d	X
ejpam-6262	111	42	⊂	⊂	PROPN
ejpam-6262	111	43	r	r	NOUN
ejpam-6262	111	44	and	and	CCONJ
ejpam-6262	111	45	x	x	NOUN
ejpam-6262	111	46	,	,	PUNCT
ejpam-6262	111	47	x0	x0	PROPN
ejpam-6262	111	48	∈	∈	PROPN
ejpam-6262	112	1	d	d	X
ejpam-6262	112	2	the	the	DET
ejpam-6262	112	3	dfh	dfh	PROPN
ejpam-6262	112	4	method	method	NOUN
ejpam-6262	112	5	represents	represent	VERB
ejpam-6262	112	6	in	in	ADP
ejpam-6262	112	7	equations	equation	NOUN
ejpam-6262	112	8	(	(	PUNCT
ejpam-6262	112	9	11)-(12	11)-(12	NOUN
ejpam-6262	112	10	)	)	PUNCT
ejpam-6262	112	11	converges	converge	NOUN
ejpam-6262	112	12	to	to	ADP
ejpam-6262	112	13	a	a	DET
ejpam-6262	112	14	root	root	NOUN
ejpam-6262	112	15	α	α	NOUN
ejpam-6262	112	16	of	of	ADP
ejpam-6262	112	17	the	the	DET
ejpam-6262	112	18	function	function	NOUN
ejpam-6262	112	19	f(x	f(x	PROPN
ejpam-6262	112	20	)	)	PUNCT
ejpam-6262	112	21	and	and	CCONJ
ejpam-6262	112	22	that	that	SCONJ
ejpam-6262	112	23	xn	xn	PROPN
ejpam-6262	112	24	is	be	AUX
ejpam-6262	112	25	the	the	DET
ejpam-6262	112	26	approximation	approximation	NOUN
ejpam-6262	112	27	of	of	ADP
ejpam-6262	112	28	α	α	PROPN
ejpam-6262	112	29	has	have	VERB
ejpam-6262	112	30	order	order	NOUN
ejpam-6262	112	31	of	of	ADP
ejpam-6262	112	32	convergence	convergence	NOUN
ejpam-6262	112	33	2.5	2.5	NUM
ejpam-6262	112	34	.	.	PUNCT
ejpam-6262	113	1	proof	proof	NOUN
ejpam-6262	113	2	.	.	PUNCT
ejpam-6262	114	1	the	the	DET
ejpam-6262	114	2	error	error	NOUN
ejpam-6262	114	3	at	at	ADP
ejpam-6262	114	4	the	the	DET
ejpam-6262	114	5	nth	nth	NOUN
ejpam-6262	114	6	iteration	iteration	NOUN
ejpam-6262	114	7	is	be	AUX
ejpam-6262	114	8	given	give	VERB
ejpam-6262	114	9	by	by	ADP
ejpam-6262	114	10	en	en	PROPN
ejpam-6262	114	11	=	=	SYM
ejpam-6262	114	12	xn	xn	PROPN
ejpam-6262	114	13	−	−	PROPN
ejpam-6262	114	14	α	α	X
ejpam-6262	114	15	.	.	PUNCT
ejpam-6262	115	1	the	the	DET
ejpam-6262	115	2	error	error	NOUN
ejpam-6262	115	3	at	at	ADP
ejpam-6262	115	4	the	the	DET
ejpam-6262	115	5	(	(	PUNCT
ejpam-6262	115	6	n+	n+	NUM
ejpam-6262	115	7	1)th	1)th	NOUN
ejpam-6262	115	8	can	can	AUX
ejpam-6262	115	9	be	be	AUX
ejpam-6262	115	10	reiterated	reiterate	VERB
ejpam-6262	115	11	as	as	ADP
ejpam-6262	115	12	:	:	PUNCT
ejpam-6262	115	13	en+1	en+1	X
ejpam-6262	115	14	=	=	SYM
ejpam-6262	115	15	xn+1	xn+1	PROPN
ejpam-6262	116	1	−	−	PROPN
ejpam-6262	116	2	α	α	NOUN
ejpam-6262	116	3	=	=	SYM
ejpam-6262	116	4	(	(	PUNCT
ejpam-6262	116	5	xn	xn	PROPN
ejpam-6262	116	6	−	−	PROPN
ejpam-6262	117	1	(	(	PUNCT
ejpam-6262	117	2	f(xn)(yn	f(xn)(yn	ADJ
ejpam-6262	117	3	−	−	NOUN
ejpam-6262	117	4	xn	xn	NUM
ejpam-6262	117	5	)	)	PUNCT
ejpam-6262	117	6	f(yn)−	f(yn)−	X
ejpam-6262	117	7	f(xn	f(xn	PROPN
ejpam-6262	117	8	)	)	PUNCT
ejpam-6262	117	9	)	)	PUNCT
ejpam-6262	117	10	)	)	PUNCT
ejpam-6262	118	1	−	−	PROPN
ejpam-6262	118	2	α	α	INTJ
ejpam-6262	118	3	(	(	PUNCT
ejpam-6262	118	4	15	15	NUM
ejpam-6262	118	5	)	)	PUNCT
ejpam-6262	118	6	now	now	ADV
ejpam-6262	118	7	,	,	PUNCT
ejpam-6262	118	8	we	we	PRON
ejpam-6262	118	9	can	can	AUX
ejpam-6262	118	10	use	use	VERB
ejpam-6262	118	11	taylor	taylor	PROPN
ejpam-6262	118	12	’s	’s	PART
ejpam-6262	118	13	theorem	theorem	VERB
ejpam-6262	118	14	to	to	PART
ejpam-6262	118	15	approximate	approximate	VERB
ejpam-6262	118	16	f	f	PROPN
ejpam-6262	118	17	(	(	PUNCT
ejpam-6262	118	18	xn	xn	PROPN
ejpam-6262	118	19	)	)	PUNCT
ejpam-6262	118	20	and	and	CCONJ
ejpam-6262	118	21	f	f	PROPN
ejpam-6262	118	22	(	(	PUNCT
ejpam-6262	118	23	xn−1	xn−1	PROPN
ejpam-6262	118	24	)	)	PUNCT
ejpam-6262	118	25	around	around	ADP
ejpam-6262	118	26	α	α	PRON
ejpam-6262	118	27	f(xn	f(xn	AUX
ejpam-6262	118	28	)	)	PUNCT
ejpam-6262	118	29	=	=	PUNCT
ejpam-6262	119	1	f	f	X
ejpam-6262	120	1	′(α)en	′(α)en	PROPN
ejpam-6262	120	2	+	+	CCONJ
ejpam-6262	120	3	f	f	PROPN
ejpam-6262	120	4	′′(α	′′(α	NOUN
ejpam-6262	120	5	)	)	PUNCT
ejpam-6262	120	6	2	2	NUM
ejpam-6262	120	7	e2n	e2n	NOUN
ejpam-6262	120	8	+	+	NUM
ejpam-6262	120	9	f	f	PROPN
ejpam-6262	120	10	′′′(α	′′′(α	PROPN
ejpam-6262	120	11	)	)	PUNCT
ejpam-6262	120	12	6	6	NUM
ejpam-6262	120	13	e3n	e3n	NOUN
ejpam-6262	120	14	+	+	NOUN
ejpam-6262	120	15	o(e4n	o(e4n	NOUN
ejpam-6262	120	16	)	)	PUNCT
ejpam-6262	120	17	(	(	PUNCT
ejpam-6262	120	18	16	16	NUM
ejpam-6262	120	19	)	)	PUNCT
ejpam-6262	120	20	y.	y.	PROPN
ejpam-6262	120	21	al	al	PROPN
ejpam-6262	120	22	-	-	PUNCT
ejpam-6262	120	23	shorman	shorman	PROPN
ejpam-6262	120	24	et	et	PROPN
ejpam-6262	120	25	al	al	PROPN
ejpam-6262	120	26	.	.	PUNCT
ejpam-6262	120	27	/	/	SYM
ejpam-6262	120	28	eur	eur	PROPN
ejpam-6262	120	29	.	.	PUNCT
ejpam-6262	121	1	j.	j.	PROPN
ejpam-6262	121	2	pure	pure	PROPN
ejpam-6262	121	3	appl	appl	PROPN
ejpam-6262	121	4	.	.	PROPN
ejpam-6262	121	5	math	math	PROPN
ejpam-6262	121	6	,	,	PUNCT
ejpam-6262	121	7	18	18	NUM
ejpam-6262	121	8	(	(	PUNCT
ejpam-6262	121	9	3	3	NUM
ejpam-6262	121	10	)	)	PUNCT
ejpam-6262	121	11	(	(	PUNCT
ejpam-6262	121	12	2025	2025	NUM
ejpam-6262	121	13	)	)	PUNCT
ejpam-6262	121	14	,	,	PUNCT
ejpam-6262	121	15	6262	6262	NUM
ejpam-6262	121	16	6	6	NUM
ejpam-6262	121	17	of	of	ADP
ejpam-6262	121	18	20	20	NUM
ejpam-6262	121	19	similarly	similarly	ADV
ejpam-6262	121	20	,	,	PUNCT
ejpam-6262	121	21	for	for	ADP
ejpam-6262	121	22	f(xn−1	f(xn−1	ADJ
ejpam-6262	121	23	):	):	PUNCT
ejpam-6262	121	24	f(xn−1	f(xn−1	X
ejpam-6262	121	25	)	)	PUNCT
ejpam-6262	121	26	=	=	SYM
ejpam-6262	121	27	f	f	PROPN
ejpam-6262	121	28	′(α)en−1	′(α)en−1	NOUN
ejpam-6262	121	29	+	+	CCONJ
ejpam-6262	121	30	f	f	PROPN
ejpam-6262	121	31	′′(α	′′(α	NOUN
ejpam-6262	121	32	)	)	PUNCT
ejpam-6262	121	33	2	2	NUM
ejpam-6262	121	34	e2n−1	e2n−1	PROPN
ejpam-6262	122	1	+	+	CCONJ
ejpam-6262	122	2	f	f	PROPN
ejpam-6262	122	3	′′′(α	′′′(α	PROPN
ejpam-6262	122	4	)	)	PUNCT
ejpam-6262	122	5	6	6	NUM
ejpam-6262	122	6	e3n−1	e3n−1	ADJ
ejpam-6262	122	7	+	+	ADJ
ejpam-6262	122	8	o(e4n−1	o(e4n−1	ADJ
ejpam-6262	122	9	)	)	PUNCT
ejpam-6262	122	10	(	(	PUNCT
ejpam-6262	122	11	17	17	NUM
ejpam-6262	122	12	)	)	PUNCT
ejpam-6262	122	13	now	now	ADV
ejpam-6262	122	14	let	let	VERB
ejpam-6262	122	15	’s	’s	ADJ
ejpam-6262	122	16	re	re	VERB
ejpam-6262	122	17	-	-	VERB
ejpam-6262	122	18	examine	examine	VERB
ejpam-6262	122	19	yn	yn	X
ejpam-6262	122	20	:	:	PUNCT
ejpam-6262	122	21	yn	yn	PROPN
ejpam-6262	122	22	=	=	PUNCT
ejpam-6262	122	23	xn	xn	PROPN
ejpam-6262	123	1	−	−	PROPN
ejpam-6262	123	2	f(xn)(xn	f(xn)(xn	X
ejpam-6262	123	3	−	−	NOUN
ejpam-6262	123	4	xn−1	xn−1	PROPN
ejpam-6262	123	5	)	)	PUNCT
ejpam-6262	123	6	f(xn)−	f(xn)−	NOUN
ejpam-6262	123	7	f(xn−1	f(xn−1	X
ejpam-6262	123	8	)	)	PUNCT
ejpam-6262	123	9	.	.	PUNCT
ejpam-6262	124	1	(	(	PUNCT
ejpam-6262	124	2	18	18	NUM
ejpam-6262	124	3	)	)	PUNCT
ejpam-6262	124	4	with	with	ADP
ejpam-6262	124	5	higher	high	ADJ
ejpam-6262	124	6	-	-	PUNCT
ejpam-6262	124	7	order	order	NOUN
ejpam-6262	124	8	terms	term	NOUN
ejpam-6262	124	9	,	,	PUNCT
ejpam-6262	124	10	the	the	DET
ejpam-6262	124	11	numerator	numerator	NOUN
ejpam-6262	124	12	and	and	CCONJ
ejpam-6262	124	13	denominator	denominator	NOUN
ejpam-6262	124	14	become	become	VERB
ejpam-6262	124	15	:	:	PUNCT
ejpam-6262	124	16	numerator	numerator	NOUN
ejpam-6262	124	17	:	:	PUNCT
ejpam-6262	124	18	f(xn	f(xn	X
ejpam-6262	124	19	)	)	PUNCT
ejpam-6262	124	20	(	(	PUNCT
ejpam-6262	124	21	xn	xn	NUM
ejpam-6262	124	22	−	−	PROPN
ejpam-6262	124	23	xn−1	xn−1	PROPN
ejpam-6262	124	24	)	)	PUNCT
ejpam-6262	124	25	=	=	PUNCT
ejpam-6262	125	1	(	(	PUNCT
ejpam-6262	125	2	f	f	X
ejpam-6262	125	3	′(α)en	′(α)en	PROPN
ejpam-6262	126	1	+	+	CCONJ
ejpam-6262	126	2	f	f	PROPN
ejpam-6262	126	3	′′(α	′′(α	NOUN
ejpam-6262	126	4	)	)	PUNCT
ejpam-6262	126	5	2	2	NUM
ejpam-6262	126	6	e2n	e2n	X
ejpam-6262	126	7	+	+	NOUN
ejpam-6262	126	8	o(e3n	o(e3n	NOUN
ejpam-6262	126	9	)	)	PUNCT
ejpam-6262	126	10	)	)	PUNCT
ejpam-6262	127	1	(	(	PUNCT
ejpam-6262	127	2	en	en	X
ejpam-6262	127	3	−	−	PROPN
ejpam-6262	127	4	en−1	en−1	PROPN
ejpam-6262	127	5	)	)	PUNCT
ejpam-6262	127	6	.	.	PUNCT
ejpam-6262	128	1	(	(	PUNCT
ejpam-6262	128	2	19	19	NUM
ejpam-6262	128	3	)	)	PUNCT
ejpam-6262	128	4	this	this	PRON
ejpam-6262	128	5	expands	expand	VERB
ejpam-6262	128	6	to	to	ADP
ejpam-6262	128	7	:	:	PUNCT
ejpam-6262	128	8	f	f	X
ejpam-6262	128	9	′(α)en(en	′(α)en(en	SYM
ejpam-6262	129	1	−	−	PROPN
ejpam-6262	130	1	en−1	en−1	PROPN
ejpam-6262	130	2	)	)	PUNCT
ejpam-6262	131	1	+	+	NUM
ejpam-6262	132	1	f	f	PROPN
ejpam-6262	132	2	′′(α	′′(α	NOUN
ejpam-6262	132	3	)	)	PUNCT
ejpam-6262	132	4	2	2	NUM
ejpam-6262	132	5	e2n(en	e2n(en	NUM
ejpam-6262	132	6	−	−	NOUN
ejpam-6262	132	7	en−1	en−1	PROPN
ejpam-6262	132	8	)	)	PUNCT
ejpam-6262	132	9	+	+	NOUN
ejpam-6262	132	10	o(e3n	o(e3n	PROPN
ejpam-6262	132	11	)	)	PUNCT
ejpam-6262	132	12	.	.	PUNCT
ejpam-6262	133	1	(	(	PUNCT
ejpam-6262	133	2	20	20	NUM
ejpam-6262	133	3	)	)	PUNCT
ejpam-6262	133	4	denominator	denominator	NOUN
ejpam-6262	133	5	:	:	PUNCT
ejpam-6262	133	6	f(xn)−	f(xn)−	NOUN
ejpam-6262	133	7	f(xn−1	f(xn−1	X
ejpam-6262	133	8	)	)	PUNCT
ejpam-6262	133	9	=	=	SYM
ejpam-6262	134	1	f	f	PROPN
ejpam-6262	134	2	′(α)(en	′(α)(en	PROPN
ejpam-6262	134	3	−	−	PROPN
ejpam-6262	134	4	en−1	en−1	PROPN
ejpam-6262	134	5	)	)	PUNCT
ejpam-6262	134	6	+	+	NUM
ejpam-6262	134	7	f	f	PROPN
ejpam-6262	134	8	′′(α	′′(α	NOUN
ejpam-6262	134	9	)	)	PUNCT
ejpam-6262	134	10	2	2	NUM
ejpam-6262	134	11	(	(	PUNCT
ejpam-6262	134	12	e2n	e2n	NUM
ejpam-6262	134	13	−	−	PROPN
ejpam-6262	134	14	e2n−1	e2n−1	PROPN
ejpam-6262	134	15	)	)	PUNCT
ejpam-6262	134	16	+	+	PROPN
ejpam-6262	134	17	o(e3n	o(e3n	PROPN
ejpam-6262	134	18	,	,	PUNCT
ejpam-6262	134	19	e	e	PROPN
ejpam-6262	134	20	3	3	NUM
ejpam-6262	134	21	n−1	n−1	PROPN
ejpam-6262	134	22	)	)	PUNCT
ejpam-6262	134	23	.	.	PUNCT
ejpam-6262	135	1	(	(	PUNCT
ejpam-6262	135	2	21	21	NUM
ejpam-6262	135	3	)	)	PUNCT
ejpam-6262	135	4	simplifying	simplify	VERB
ejpam-6262	135	5	(	(	PUNCT
ejpam-6262	135	6	21	21	NUM
ejpam-6262	135	7	)	)	PUNCT
ejpam-6262	135	8	gives	give	VERB
ejpam-6262	135	9	:	:	PUNCT
ejpam-6262	135	10	f	f	PROPN
ejpam-6262	135	11	′(α)(en	′(α)(en	PROPN
ejpam-6262	135	12	−	−	PROPN
ejpam-6262	135	13	en−1	en−1	PROPN
ejpam-6262	135	14	)	)	PUNCT
ejpam-6262	136	1	+	+	NUM
ejpam-6262	136	2	f	f	PROPN
ejpam-6262	136	3	′′(α	′′(α	NOUN
ejpam-6262	136	4	)	)	PUNCT
ejpam-6262	136	5	2	2	NUM
ejpam-6262	136	6	(	(	PUNCT
ejpam-6262	136	7	e2n	e2n	NUM
ejpam-6262	136	8	−	−	PROPN
ejpam-6262	136	9	e2n−1	e2n−1	PROPN
ejpam-6262	136	10	)	)	PUNCT
ejpam-6262	136	11	+	+	NOUN
ejpam-6262	136	12	o(e3n	o(e3n	PROPN
ejpam-6262	136	13	)	)	PUNCT
ejpam-6262	136	14	.	.	PUNCT
ejpam-6262	137	1	(	(	PUNCT
ejpam-6262	137	2	22	22	X
ejpam-6262	137	3	)	)	PUNCT
ejpam-6262	137	4	substituting	substituting	NOUN
ejpam-6262	137	5	(	(	PUNCT
ejpam-6262	137	6	20,22	20,22	NOUN
ejpam-6262	137	7	)	)	PUNCT
ejpam-6262	137	8	into	into	ADP
ejpam-6262	137	9	(	(	PUNCT
ejpam-6262	137	10	18	18	NUM
ejpam-6262	137	11	)	)	PUNCT
ejpam-6262	137	12	,	,	PUNCT
ejpam-6262	137	13	we	we	PRON
ejpam-6262	137	14	get	get	VERB
ejpam-6262	137	15	:	:	PUNCT
ejpam-6262	137	16	yn	yn	PROPN
ejpam-6262	137	17	=	=	PUNCT
ejpam-6262	137	18	xn	xn	PROPN
ejpam-6262	138	1	−	−	PROPN
ejpam-6262	138	2	f	f	PROPN
ejpam-6262	138	3	′(α)en(en	′(α)en(en	SYM
ejpam-6262	138	4	−	−	PROPN
ejpam-6262	138	5	en−1	en−1	PROPN
ejpam-6262	138	6	)	)	PUNCT
ejpam-6262	138	7	+	+	NUM
ejpam-6262	138	8	f	f	PROPN
ejpam-6262	138	9	′′(α	′′(α	NOUN
ejpam-6262	138	10	)	)	PUNCT
ejpam-6262	138	11	2	2	NUM
ejpam-6262	138	12	e2n(en	e2n(en	NUM
ejpam-6262	138	13	−	−	NOUN
ejpam-6262	138	14	en−1	en−1	PROPN
ejpam-6262	138	15	)	)	PUNCT
ejpam-6262	138	16	+	+	NOUN
ejpam-6262	138	17	o(e3n	o(e3n	NOUN
ejpam-6262	138	18	)	)	PUNCT
ejpam-6262	138	19	f	f	PROPN
ejpam-6262	138	20	′(α)(en	′(α)(en	PROPN
ejpam-6262	139	1	−	−	PROPN
ejpam-6262	139	2	en−1	en−1	PROPN
ejpam-6262	139	3	)	)	PUNCT
ejpam-6262	139	4	+	+	NUM
ejpam-6262	139	5	f	f	PROPN
ejpam-6262	139	6	′′(α	′′(α	NOUN
ejpam-6262	139	7	)	)	PUNCT
ejpam-6262	139	8	2	2	NUM
ejpam-6262	139	9	(	(	PUNCT
ejpam-6262	139	10	e2n	e2n	NUM
ejpam-6262	139	11	−	−	PROPN
ejpam-6262	139	12	e2n−1	e2n−1	PROPN
ejpam-6262	139	13	)	)	PUNCT
ejpam-6262	139	14	+	+	NOUN
ejpam-6262	139	15	o(e3n	o(e3n	PROPN
ejpam-6262	139	16	)	)	PUNCT
ejpam-6262	139	17	.	.	PUNCT
ejpam-6262	140	1	(	(	PUNCT
ejpam-6262	140	2	23	23	X
ejpam-6262	140	3	)	)	PUNCT
ejpam-6262	140	4	cancelling	cancel	VERB
ejpam-6262	140	5	out	out	ADP
ejpam-6262	140	6	the	the	DET
ejpam-6262	140	7	common	common	ADJ
ejpam-6262	140	8	factors	factor	NOUN
ejpam-6262	140	9	f	f	NOUN
ejpam-6262	140	10	′	′	NUM
ejpam-6262	140	11	(	(	PUNCT
ejpam-6262	140	12	α)(en	α)(en	NOUN
ejpam-6262	140	13	−	−	PROPN
ejpam-6262	140	14	en−1	en−1	PROPN
ejpam-6262	140	15	)	)	PUNCT
ejpam-6262	140	16	from	from	ADP
ejpam-6262	140	17	both	both	DET
ejpam-6262	140	18	the	the	DET
ejpam-6262	140	19	numerator	numerator	NOUN
ejpam-6262	140	20	and	and	CCONJ
ejpam-6262	140	21	denominator	denominator	NOUN
ejpam-6262	140	22	(	(	PUNCT
ejpam-6262	140	23	since	since	SCONJ
ejpam-6262	140	24	we	we	PRON
ejpam-6262	140	25	are	be	AUX
ejpam-6262	140	26	assuming	assume	VERB
ejpam-6262	140	27	en	en	ADP
ejpam-6262	140	28	̸=	̸=	PROPN
ejpam-6262	140	29	en−1	en−1	PROPN
ejpam-6262	140	30	for	for	ADP
ejpam-6262	140	31	the	the	DET
ejpam-6262	140	32	iterative	iterative	NOUN
ejpam-6262	140	33	process	process	NOUN
ejpam-6262	140	34	to	to	PART
ejpam-6262	140	35	continue	continue	VERB
ejpam-6262	140	36	)	)	PUNCT
ejpam-6262	140	37	,	,	PUNCT
ejpam-6262	140	38	we	we	PRON
ejpam-6262	140	39	get	get	VERB
ejpam-6262	140	40	:	:	PUNCT
ejpam-6262	140	41	yn	yn	PROPN
ejpam-6262	140	42	=	=	PUNCT
ejpam-6262	140	43	xn	xn	PROPN
ejpam-6262	141	1	−	−	PROPN
ejpam-6262	141	2	(	(	PUNCT
ejpam-6262	141	3	en	en	X
ejpam-6262	141	4	+	+	PROPN
ejpam-6262	141	5	o	o	X
ejpam-6262	141	6	(	(	PUNCT
ejpam-6262	141	7	e1.5n	e1.5n	PROPN
ejpam-6262	141	8	,	,	PUNCT
ejpam-6262	141	9	e2n	e2n	ADV
ejpam-6262	141	10	)	)	PUNCT
ejpam-6262	141	11	)	)	PUNCT
ejpam-6262	141	12	.	.	PUNCT
ejpam-6262	142	1	(	(	PUNCT
ejpam-6262	142	2	24	24	NUM
ejpam-6262	142	3	)	)	PUNCT
ejpam-6262	142	4	this	this	DET
ejpam-6262	142	5	simplifies	simplifie	NOUN
ejpam-6262	142	6	:	:	PUNCT
ejpam-6262	142	7	yn	yn	X
ejpam-6262	142	8	=	=	PUNCT
ejpam-6262	142	9	α+o	α+o	PROPN
ejpam-6262	142	10	(	(	PUNCT
ejpam-6262	142	11	e1.5n	e1.5n	PROPN
ejpam-6262	142	12	)	)	PUNCT
ejpam-6262	142	13	.	.	PUNCT
ejpam-6262	143	1	(	(	PUNCT
ejpam-6262	143	2	25	25	NUM
ejpam-6262	143	3	)	)	PUNCT
ejpam-6262	143	4	now	now	ADV
ejpam-6262	143	5	,	,	PUNCT
ejpam-6262	143	6	for	for	SCONJ
ejpam-6262	143	7	xn+1	xn+1	PROPN
ejpam-6262	143	8	recall	recall	VERB
ejpam-6262	143	9	the	the	DET
ejpam-6262	143	10	equation	equation	NOUN
ejpam-6262	143	11	:	:	PUNCT
ejpam-6262	143	12	xn+1	xn+1	PROPN
ejpam-6262	144	1	=	=	SYM
ejpam-6262	144	2	xn	xn	NUM
ejpam-6262	145	1	−	−	NOUN
ejpam-6262	145	2	f(xn)(yn	f(xn)(yn	ADJ
ejpam-6262	145	3	−	−	NOUN
ejpam-6262	145	4	xn	xn	NUM
ejpam-6262	145	5	)	)	PUNCT
ejpam-6262	145	6	f(yn)−	f(yn)−	X
ejpam-6262	145	7	f(xn	f(xn	PROPN
ejpam-6262	145	8	)	)	PUNCT
ejpam-6262	145	9	.	.	PUNCT
ejpam-6262	146	1	(	(	PUNCT
ejpam-6262	146	2	26	26	NUM
ejpam-6262	146	3	)	)	PUNCT
ejpam-6262	146	4	y.	y.	PROPN
ejpam-6262	146	5	al	al	PROPN
ejpam-6262	146	6	-	-	PUNCT
ejpam-6262	146	7	shorman	shorman	PROPN
ejpam-6262	146	8	et	et	PROPN
ejpam-6262	146	9	al	al	PROPN
ejpam-6262	146	10	.	.	PUNCT
ejpam-6262	146	11	/	/	SYM
ejpam-6262	146	12	eur	eur	PROPN
ejpam-6262	146	13	.	.	PUNCT
ejpam-6262	147	1	j.	j.	PROPN
ejpam-6262	147	2	pure	pure	PROPN
ejpam-6262	147	3	appl	appl	PROPN
ejpam-6262	147	4	.	.	PROPN
ejpam-6262	147	5	math	math	PROPN
ejpam-6262	147	6	,	,	PUNCT
ejpam-6262	147	7	18	18	NUM
ejpam-6262	147	8	(	(	PUNCT
ejpam-6262	147	9	3	3	NUM
ejpam-6262	147	10	)	)	PUNCT
ejpam-6262	147	11	(	(	PUNCT
ejpam-6262	147	12	2025	2025	NUM
ejpam-6262	147	13	)	)	PUNCT
ejpam-6262	147	14	,	,	PUNCT
ejpam-6262	147	15	6262	6262	NUM
ejpam-6262	147	16	7	7	NUM
ejpam-6262	147	17	of	of	ADP
ejpam-6262	147	18	20	20	NUM
ejpam-6262	147	19	now	now	ADV
ejpam-6262	147	20	,	,	PUNCT
ejpam-6262	147	21	expand	expand	VERB
ejpam-6262	147	22	f(yn	f(yn	NOUN
ejpam-6262	147	23	)	)	PUNCT
ejpam-6262	147	24	using	use	VERB
ejpam-6262	147	25	the	the	DET
ejpam-6262	147	26	taylor	taylor	PROPN
ejpam-6262	147	27	expansion	expansion	NOUN
ejpam-6262	147	28	around	around	ADP
ejpam-6262	147	29	α	α	NOUN
ejpam-6262	147	30	:	:	PUNCT
ejpam-6262	147	31	f	f	NOUN
ejpam-6262	147	32	′	′	NUM
ejpam-6262	147	33	(	(	PUNCT
ejpam-6262	147	34	yn	yn	PROPN
ejpam-6262	147	35	)	)	PUNCT
ejpam-6262	147	36	=	=	PUNCT
ejpam-6262	148	1	f	f	X
ejpam-6262	149	1	′	′	NUM
ejpam-6262	149	2	(	(	PUNCT
ejpam-6262	149	3	α	α	NOUN
ejpam-6262	149	4	)	)	PUNCT
ejpam-6262	149	5	(	(	PUNCT
ejpam-6262	149	6	yn	yn	PROPN
ejpam-6262	149	7	−	−	PROPN
ejpam-6262	149	8	α	α	NOUN
ejpam-6262	149	9	)	)	PUNCT
ejpam-6262	149	10	+	+	NUM
ejpam-6262	149	11	f	f	X
ejpam-6262	149	12	′′	′′	PROPN
ejpam-6262	149	13	(	(	PUNCT
ejpam-6262	149	14	α	α	NOUN
ejpam-6262	149	15	)	)	PUNCT
ejpam-6262	149	16	2	2	NUM
ejpam-6262	149	17	(	(	PUNCT
ejpam-6262	149	18	yn	yn	NOUN
ejpam-6262	149	19	−	−	PROPN
ejpam-6262	149	20	α)2	α)2	NOUN
ejpam-6262	149	21	+	+	NOUN
ejpam-6262	149	22	o((yn	o((yn	NOUN
ejpam-6262	149	23	−	−	ADP
ejpam-6262	149	24	α)3	α)3	NOUN
ejpam-6262	149	25	)	)	PUNCT
ejpam-6262	149	26	(	(	PUNCT
ejpam-6262	149	27	27	27	NUM
ejpam-6262	149	28	)	)	PUNCT
ejpam-6262	149	29	substituting	substitute	VERB
ejpam-6262	149	30	(	(	PUNCT
ejpam-6262	149	31	25	25	NUM
ejpam-6262	149	32	)	)	PUNCT
ejpam-6262	149	33	in	in	ADP
ejpam-6262	149	34	(	(	PUNCT
ejpam-6262	149	35	27	27	NUM
ejpam-6262	149	36	)	)	PUNCT
ejpam-6262	149	37	,	,	PUNCT
ejpam-6262	149	38	we	we	PRON
ejpam-6262	149	39	have	have	VERB
ejpam-6262	149	40	:	:	PUNCT
ejpam-6262	149	41	f	f	PROPN
ejpam-6262	149	42	(	(	PUNCT
ejpam-6262	149	43	yn	yn	PROPN
ejpam-6262	149	44	)	)	PUNCT
ejpam-6262	149	45	=	=	PUNCT
ejpam-6262	150	1	f	f	X
ejpam-6262	150	2	′	′	NUM
ejpam-6262	150	3	(	(	PUNCT
ejpam-6262	150	4	α)o	α)o	NOUN
ejpam-6262	150	5	(	(	PUNCT
ejpam-6262	150	6	e1.5n	e1.5n	NOUN
ejpam-6262	150	7	)	)	PUNCT
ejpam-6262	151	1	+	+	ADP
ejpam-6262	151	2	o	o	X
ejpam-6262	151	3	(	(	PUNCT
ejpam-6262	151	4	e3n	e3n	PROPN
ejpam-6262	151	5	)	)	PUNCT
ejpam-6262	151	6	.	.	PUNCT
ejpam-6262	152	1	(	(	PUNCT
ejpam-6262	152	2	28	28	NUM
ejpam-6262	152	3	)	)	PUNCT
ejpam-6262	152	4	similarly	similarly	ADV
ejpam-6262	152	5	,	,	PUNCT
ejpam-6262	152	6	expand	expand	VERB
ejpam-6262	152	7	f(xn	f(xn	NOUN
ejpam-6262	152	8	)	)	PUNCT
ejpam-6262	152	9	f(xn	f(xn	PROPN
ejpam-6262	152	10	)	)	PUNCT
ejpam-6262	153	1	=	=	SYM
ejpam-6262	154	1	f	f	X
ejpam-6262	154	2	′	′	NUM
ejpam-6262	154	3	(	(	PUNCT
ejpam-6262	154	4	α	α	NOUN
ejpam-6262	154	5	)	)	PUNCT
ejpam-6262	154	6	en	en	X
ejpam-6262	154	7	+	+	CCONJ
ejpam-6262	154	8	f	f	X
ejpam-6262	154	9	′′	′′	PROPN
ejpam-6262	154	10	(	(	PUNCT
ejpam-6262	154	11	α	α	NOUN
ejpam-6262	154	12	)	)	PUNCT
ejpam-6262	154	13	2	2	NUM
ejpam-6262	154	14	e2n	e2n	X
ejpam-6262	154	15	+	+	PROPN
ejpam-6262	154	16	+	+	ADJ
ejpam-6262	154	17	o	o	X
ejpam-6262	154	18	(	(	PUNCT
ejpam-6262	154	19	e3n	e3n	PROPN
ejpam-6262	154	20	)	)	PUNCT
ejpam-6262	154	21	(	(	PUNCT
ejpam-6262	154	22	29	29	NUM
ejpam-6262	154	23	)	)	PUNCT
ejpam-6262	154	24	now	now	ADV
ejpam-6262	154	25	substitute	substitute	NOUN
ejpam-6262	154	26	(	(	PUNCT
ejpam-6262	154	27	28)-(29	28)-(29	NOUN
ejpam-6262	154	28	)	)	PUNCT
ejpam-6262	154	29	into	into	ADP
ejpam-6262	154	30	the	the	DET
ejpam-6262	154	31	formula	formula	NOUN
ejpam-6262	154	32	(	(	PUNCT
ejpam-6262	154	33	26	26	NUM
ejpam-6262	154	34	):	):	PUNCT
ejpam-6262	154	35	xn+1	xn+1	PROPN
ejpam-6262	154	36	=	=	SYM
ejpam-6262	154	37	xn	xn	PROPN
ejpam-6262	155	1	−	−	PROPN
ejpam-6262	155	2	(	(	PUNCT
ejpam-6262	155	3	f	f	NOUN
ejpam-6262	155	4	′	′	NUM
ejpam-6262	155	5	(	(	PUNCT
ejpam-6262	155	6	α	α	NOUN
ejpam-6262	155	7	)	)	PUNCT
ejpam-6262	155	8	en	en	NOUN
ejpam-6262	155	9	+	+	CCONJ
ejpam-6262	155	10	f	f	PROPN
ejpam-6262	155	11	′′(α	′′(α	NOUN
ejpam-6262	155	12	)	)	PUNCT
ejpam-6262	155	13	2	2	NUM
ejpam-6262	155	14	e2n	e2n	ADV
ejpam-6262	155	15	)	)	PUNCT
ejpam-6262	155	16	(	(	PUNCT
ejpam-6262	155	17	o	o	X
ejpam-6262	155	18	(	(	PUNCT
ejpam-6262	155	19	e1.5n	e1.5n	PROPN
ejpam-6262	155	20	)	)	PUNCT
ejpam-6262	155	21	)	)	PUNCT
ejpam-6262	156	1	f	f	X
ejpam-6262	157	1	′	′	NUM
ejpam-6262	157	2	(	(	PUNCT
ejpam-6262	157	3	α)o	α)o	NOUN
ejpam-6262	157	4	(	(	PUNCT
ejpam-6262	157	5	e1.5n	e1.5n	NOUN
ejpam-6262	157	6	)	)	PUNCT
ejpam-6262	158	1	+	+	ADP
ejpam-6262	158	2	o	o	X
ejpam-6262	158	3	(	(	PUNCT
ejpam-6262	158	4	e3n	e3n	PROPN
ejpam-6262	158	5	)	)	PUNCT
ejpam-6262	158	6	.	.	PUNCT
ejpam-6262	159	1	(	(	PUNCT
ejpam-6262	159	2	30	30	X
ejpam-6262	159	3	)	)	PUNCT
ejpam-6262	159	4	simplifying	simplify	VERB
ejpam-6262	159	5	the	the	DET
ejpam-6262	159	6	terms	term	NOUN
ejpam-6262	159	7	and	and	CCONJ
ejpam-6262	159	8	canceling	cancel	VERB
ejpam-6262	159	9	the	the	DET
ejpam-6262	159	10	common	common	ADJ
ejpam-6262	159	11	factor	factor	NOUN
ejpam-6262	159	12	f	f	PROPN
ejpam-6262	159	13	′(α	′(α	PROPN
ejpam-6262	159	14	)	)	PUNCT
ejpam-6262	159	15	,	,	PUNCT
ejpam-6262	159	16	we	we	PRON
ejpam-6262	159	17	find	find	VERB
ejpam-6262	159	18	xn+1	xn+1	NOUN
ejpam-6262	159	19	=	=	PUNCT
ejpam-6262	159	20	xn	xn	PUNCT
ejpam-6262	160	1	+	+	NUM
ejpam-6262	160	2	o	o	X
ejpam-6262	160	3	(	(	PUNCT
ejpam-6262	160	4	e2.5n	e2.5n	NOUN
ejpam-6262	160	5	)	)	PUNCT
ejpam-6262	160	6	.	.	PUNCT
ejpam-6262	161	1	(	(	PUNCT
ejpam-6262	161	2	31	31	NUM
ejpam-6262	161	3	)	)	PUNCT
ejpam-6262	161	4	thus	thus	ADV
ejpam-6262	161	5	,	,	PUNCT
ejpam-6262	161	6	the	the	DET
ejpam-6262	161	7	error	error	NOUN
ejpam-6262	161	8	at	at	ADP
ejpam-6262	161	9	the	the	DET
ejpam-6262	161	10	next	next	ADJ
ejpam-6262	161	11	iteration	iteration	NOUN
ejpam-6262	161	12	is	be	AUX
ejpam-6262	161	13	:	:	PUNCT
ejpam-6262	161	14	en+1	en+1	X
ejpam-6262	161	15	=	=	SYM
ejpam-6262	161	16	xn+1	xn+1	PROPN
ejpam-6262	162	1	−	−	PROPN
ejpam-6262	163	1	α	α	NOUN
ejpam-6262	163	2	=	=	SYM
ejpam-6262	163	3	o	o	X
ejpam-6262	163	4	(	(	PUNCT
ejpam-6262	163	5	e2.5n	e2.5n	NOUN
ejpam-6262	163	6	)	)	PUNCT
ejpam-6262	163	7	.	.	PUNCT
ejpam-6262	164	1	(	(	PUNCT
ejpam-6262	164	2	32	32	NUM
ejpam-6262	164	3	)	)	PUNCT
ejpam-6262	164	4	therefore	therefore	ADV
ejpam-6262	164	5	,	,	PUNCT
ejpam-6262	164	6	the	the	DET
ejpam-6262	164	7	order	order	NOUN
ejpam-6262	164	8	of	of	ADP
ejpam-6262	164	9	convergence	convergence	NOUN
ejpam-6262	164	10	ρ	ρ	PROPN
ejpam-6262	164	11	≈	≈	PROPN
ejpam-6262	164	12	2.5	2.5	NUM
ejpam-6262	164	13	.	.	PUNCT
ejpam-6262	164	14	theorem	theorem	NOUN
ejpam-6262	164	15	2	2	NUM
ejpam-6262	164	16	.	.	PUNCT
ejpam-6262	164	17	suppose	suppose	VERB
ejpam-6262	164	18	that	that	SCONJ
ejpam-6262	164	19	f	f	PROPN
ejpam-6262	164	20	represents	represent	VERB
ejpam-6262	164	21	a	a	DET
ejpam-6262	164	22	vector	vector	NOUN
ejpam-6262	164	23	-	-	PUNCT
ejpam-6262	164	24	valued	value	VERB
ejpam-6262	164	25	function	function	NOUN
ejpam-6262	164	26	with	with	ADP
ejpam-6262	164	27	non	non	ADJ
ejpam-6262	164	28	-	-	ADJ
ejpam-6262	164	29	zero	zero	NUM
ejpam-6262	164	30	derivatives	derivative	NOUN
ejpam-6262	164	31	defined	define	VERB
ejpam-6262	164	32	on	on	ADP
ejpam-6262	164	33	the	the	DET
ejpam-6262	164	34	set	set	PROPN
ejpam-6262	164	35	d	d	X
ejpam-6262	164	36	⊂	⊂	PROPN
ejpam-6262	164	37	r	r	NOUN
ejpam-6262	164	38	and	and	CCONJ
ejpam-6262	164	39	x	x	NOUN
ejpam-6262	164	40	,	,	PUNCT
ejpam-6262	164	41	x0	x0	PROPN
ejpam-6262	164	42	∈	∈	PROPN
ejpam-6262	165	1	d	d	X
ejpam-6262	165	2	,	,	PUNCT
ejpam-6262	165	3	the	the	DET
ejpam-6262	165	4	dfh	dfh	PROPN
ejpam-6262	165	5	method	method	NOUN
ejpam-6262	165	6	represent	represent	VERB
ejpam-6262	165	7	in	in	ADP
ejpam-6262	165	8	equations	equation	NOUN
ejpam-6262	165	9	(	(	PUNCT
ejpam-6262	165	10	11	11	NUM
ejpam-6262	165	11	-	-	SYM
ejpam-6262	165	12	12	12	NUM
ejpam-6262	165	13	)	)	PUNCT
ejpam-6262	165	14	converges	converge	VERB
ejpam-6262	165	15	to	to	ADP
ejpam-6262	165	16	a	a	DET
ejpam-6262	165	17	root	root	NOUN
ejpam-6262	165	18	α	α	NOUN
ejpam-6262	165	19	of	of	ADP
ejpam-6262	165	20	the	the	DET
ejpam-6262	165	21	function	function	NOUN
ejpam-6262	165	22	f	f	PROPN
ejpam-6262	165	23	(	(	PUNCT
ejpam-6262	165	24	x	x	NOUN
ejpam-6262	165	25	)	)	PUNCT
ejpam-6262	165	26	and	and	CCONJ
ejpam-6262	165	27	that	that	SCONJ
ejpam-6262	165	28	xn	xn	PROPN
ejpam-6262	165	29	in	in	ADP
ejpam-6262	165	30	the	the	DET
ejpam-6262	165	31	nth	nth	NOUN
ejpam-6262	165	32	approximation	approximation	NOUN
ejpam-6262	165	33	of	of	ADP
ejpam-6262	165	34	α	α	PROPN
ejpam-6262	165	35	has	have	VERB
ejpam-6262	165	36	order	order	NOUN
ejpam-6262	165	37	of	of	ADP
ejpam-6262	165	38	convergence	convergence	NOUN
ejpam-6262	165	39	2.5	2.5	NUM
ejpam-6262	165	40	.	.	PUNCT
ejpam-6262	166	1	proof	proof	NOUN
ejpam-6262	166	2	.	.	PUNCT
ejpam-6262	167	1	now	now	ADV
ejpam-6262	167	2	,	,	PUNCT
ejpam-6262	167	3	to	to	PART
ejpam-6262	167	4	explore	explore	VERB
ejpam-6262	167	5	the	the	DET
ejpam-6262	167	6	convergence	convergence	NOUN
ejpam-6262	167	7	order	order	NOUN
ejpam-6262	167	8	to	to	ADP
ejpam-6262	167	9	multidimensional	multidimensional	ADJ
ejpam-6262	167	10	dfh	dfh	NOUN
ejpam-6262	167	11	(	(	PUNCT
ejpam-6262	167	12	11	11	NUM
ejpam-6262	167	13	-	-	SYM
ejpam-6262	167	14	12	12	NUM
ejpam-6262	167	15	)	)	PUNCT
ejpam-6262	167	16	.	.	PUNCT
ejpam-6262	168	1	we	we	PRON
ejpam-6262	168	2	will	will	AUX
ejpam-6262	168	3	perform	perform	VERB
ejpam-6262	168	4	an	an	DET
ejpam-6262	168	5	error	error	NOUN
ejpam-6262	168	6	analysis	analysis	NOUN
ejpam-6262	168	7	around	around	ADP
ejpam-6262	168	8	the	the	DET
ejpam-6262	168	9	root	root	NOUN
ejpam-6262	168	10	x∗	x∗	PROPN
ejpam-6262	168	11	of	of	ADP
ejpam-6262	168	12	f	f	PROPN
ejpam-6262	168	13	(	(	PUNCT
ejpam-6262	168	14	x	x	NOUN
ejpam-6262	168	15	)	)	PUNCT
ejpam-6262	168	16	=	=	SYM
ejpam-6262	168	17	0	0	NUM
ejpam-6262	168	18	,	,	PUNCT
ejpam-6262	168	19	where	where	SCONJ
ejpam-6262	168	20	the	the	DET
ejpam-6262	168	21	method	method	NOUN
ejpam-6262	168	22	converges	converge	VERB
ejpam-6262	168	23	.	.	PUNCT
ejpam-6262	169	1	let	let	VERB
ejpam-6262	169	2	the	the	DET
ejpam-6262	169	3	error	error	NOUN
ejpam-6262	169	4	at	at	ADP
ejpam-6262	169	5	the	the	DET
ejpam-6262	169	6	nth	nth	NOUN
ejpam-6262	169	7	iteration	iteration	NOUN
ejpam-6262	169	8	be	be	AUX
ejpam-6262	169	9	defined	define	VERB
ejpam-6262	169	10	as	as	ADP
ejpam-6262	169	11	:	:	PUNCT
ejpam-6262	169	12	en	en	X
ejpam-6262	169	13	=	=	SYM
ejpam-6262	169	14	xn	xn	PROPN
ejpam-6262	170	1	−x∗	−x∗	PROPN
ejpam-6262	170	2	,	,	PUNCT
ejpam-6262	170	3	(	(	PUNCT
ejpam-6262	170	4	33	33	NUM
ejpam-6262	170	5	)	)	PUNCT
ejpam-6262	170	6	where	where	SCONJ
ejpam-6262	170	7	x∗	x∗	PROPN
ejpam-6262	170	8	is	be	AUX
ejpam-6262	170	9	the	the	DET
ejpam-6262	170	10	exact	exact	ADJ
ejpam-6262	170	11	root	root	NOUN
ejpam-6262	170	12	of	of	ADP
ejpam-6262	170	13	f	f	PROPN
ejpam-6262	170	14	(	(	PUNCT
ejpam-6262	170	15	x	x	NOUN
ejpam-6262	170	16	)	)	PUNCT
ejpam-6262	170	17	=	=	SYM
ejpam-6262	170	18	0	0	NUM
ejpam-6262	170	19	,	,	PUNCT
ejpam-6262	170	20	meaning	mean	VERB
ejpam-6262	170	21	f	f	X
ejpam-6262	170	22	(	(	PUNCT
ejpam-6262	170	23	x∗	x∗	PROPN
ejpam-6262	170	24	)	)	PUNCT
ejpam-6262	170	25	=	=	SYM
ejpam-6262	171	1	0	0	X
ejpam-6262	171	2	.	.	PUNCT
ejpam-6262	172	1	the	the	DET
ejpam-6262	172	2	goal	goal	NOUN
ejpam-6262	172	3	is	be	AUX
ejpam-6262	172	4	to	to	PART
ejpam-6262	172	5	express	express	VERB
ejpam-6262	172	6	the	the	DET
ejpam-6262	172	7	error	error	NOUN
ejpam-6262	172	8	en+1	en+1	ADJ
ejpam-6262	172	9	=	=	SYM
ejpam-6262	172	10	xn+1	xn+1	PROPN
ejpam-6262	172	11	−x∗	−x∗	PRON
ejpam-6262	172	12	in	in	ADP
ejpam-6262	172	13	terms	term	NOUN
ejpam-6262	172	14	of	of	ADP
ejpam-6262	172	15	en	en	X
ejpam-6262	172	16	and	and	CCONJ
ejpam-6262	172	17	analyze	analyze	VERB
ejpam-6262	172	18	how	how	SCONJ
ejpam-6262	172	19	quickly	quickly	ADV
ejpam-6262	172	20	the	the	DET
ejpam-6262	172	21	error	error	NOUN
ejpam-6262	172	22	decreases	decrease	VERB
ejpam-6262	172	23	from	from	ADP
ejpam-6262	172	24	one	one	NUM
ejpam-6262	172	25	iteration	iteration	NOUN
ejpam-6262	172	26	to	to	ADP
ejpam-6262	172	27	the	the	DET
ejpam-6262	172	28	next	next	ADJ
ejpam-6262	172	29	.	.	PUNCT
ejpam-6262	173	1	we	we	PRON
ejpam-6262	173	2	will	will	AUX
ejpam-6262	173	3	explore	explore	VERB
ejpam-6262	173	4	how	how	SCONJ
ejpam-6262	173	5	the	the	DET
ejpam-6262	173	6	correction	correction	NOUN
ejpam-6262	173	7	x∗	x∗	VERB
ejpam-6262	173	8	n+1	n+1	NUM
ejpam-6262	173	9	could	could	AUX
ejpam-6262	173	10	be	be	AUX
ejpam-6262	173	11	adjusted	adjust	VERB
ejpam-6262	173	12	to	to	PART
ejpam-6262	173	13	enhance	enhance	VERB
ejpam-6262	173	14	the	the	DET
ejpam-6262	173	15	convergence	convergence	NOUN
ejpam-6262	173	16	rate	rate	NOUN
ejpam-6262	173	17	.	.	PUNCT
ejpam-6262	174	1	since	since	SCONJ
ejpam-6262	174	2	x	x	X
ejpam-6262	174	3	<	<	X
ejpam-6262	174	4	is	be	AUX
ejpam-6262	174	5	close	close	ADJ
ejpam-6262	174	6	y.	y.	PROPN
ejpam-6262	174	7	al	al	PROPN
ejpam-6262	174	8	-	-	PUNCT
ejpam-6262	174	9	shorman	shorman	PROPN
ejpam-6262	174	10	et	et	PROPN
ejpam-6262	174	11	al	al	PROPN
ejpam-6262	174	12	.	.	PUNCT
ejpam-6262	174	13	/	/	SYM
ejpam-6262	174	14	eur	eur	PROPN
ejpam-6262	174	15	.	.	PUNCT
ejpam-6262	175	1	j.	j.	PROPN
ejpam-6262	175	2	pure	pure	PROPN
ejpam-6262	175	3	appl	appl	PROPN
ejpam-6262	175	4	.	.	PROPN
ejpam-6262	175	5	math	math	PROPN
ejpam-6262	175	6	,	,	PUNCT
ejpam-6262	175	7	18	18	NUM
ejpam-6262	175	8	(	(	PUNCT
ejpam-6262	175	9	3	3	NUM
ejpam-6262	175	10	)	)	PUNCT
ejpam-6262	175	11	(	(	PUNCT
ejpam-6262	175	12	2025	2025	NUM
ejpam-6262	175	13	)	)	PUNCT
ejpam-6262	175	14	,	,	PUNCT
ejpam-6262	175	15	6262	6262	NUM
ejpam-6262	175	16	8	8	NUM
ejpam-6262	175	17	of	of	ADP
ejpam-6262	175	18	20	20	NUM
ejpam-6262	175	19	to	to	ADP
ejpam-6262	175	20	x∗	x∗	PROPN
ejpam-6262	175	21	,	,	PUNCT
ejpam-6262	175	22	we	we	PRON
ejpam-6262	175	23	use	use	VERB
ejpam-6262	175	24	a	a	DET
ejpam-6262	175	25	taylor	taylor	NOUN
ejpam-6262	175	26	expansion	expansion	NOUN
ejpam-6262	175	27	of	of	ADP
ejpam-6262	175	28	f	f	PROPN
ejpam-6262	175	29	(	(	PUNCT
ejpam-6262	175	30	x	x	NOUN
ejpam-6262	175	31	)	)	PUNCT
ejpam-6262	175	32	around	around	ADP
ejpam-6262	175	33	x∗.	x∗.	PUNCT
ejpam-6262	176	1	the	the	DET
ejpam-6262	176	2	taylor	taylor	PROPN
ejpam-6262	176	3	expansion	expansion	NOUN
ejpam-6262	176	4	of	of	ADP
ejpam-6262	176	5	f	f	PROPN
ejpam-6262	176	6	(	(	PUNCT
ejpam-6262	176	7	xn	xn	PROPN
ejpam-6262	176	8	)	)	PUNCT
ejpam-6262	176	9	is	be	AUX
ejpam-6262	176	10	:	:	PUNCT
ejpam-6262	176	11	f	f	PROPN
ejpam-6262	176	12	(	(	PUNCT
ejpam-6262	176	13	xn	xn	PROPN
ejpam-6262	176	14	)	)	PUNCT
ejpam-6262	177	1	=	=	SYM
ejpam-6262	177	2	f	f	PROPN
ejpam-6262	177	3	(	(	PUNCT
ejpam-6262	177	4	x∗	x∗	PROPN
ejpam-6262	177	5	)	)	PUNCT
ejpam-6262	178	1	+	+	CCONJ
ejpam-6262	178	2	f	f	PROPN
ejpam-6262	178	3	′(x∗)(xn	′(x∗)(xn	X
ejpam-6262	178	4	−x∗	−x∗	PROPN
ejpam-6262	178	5	)	)	PUNCT
ejpam-6262	179	1	+	+	CCONJ
ejpam-6262	179	2	1	1	NUM
ejpam-6262	179	3	2	2	NUM
ejpam-6262	179	4	f	f	NOUN
ejpam-6262	179	5	′′(x∗)(xn	′′(x∗)(xn	NOUN
ejpam-6262	179	6	−x∗)2	−x∗)2	PROPN
ejpam-6262	180	1	+	+	SYM
ejpam-6262	180	2	o((xn	o((xn	X
ejpam-6262	180	3	−x∗)3	−x∗)3	ADV
ejpam-6262	180	4	)	)	PUNCT
ejpam-6262	180	5	.	.	PUNCT
ejpam-6262	181	1	(	(	PUNCT
ejpam-6262	181	2	34	34	NUM
ejpam-6262	181	3	)	)	PUNCT
ejpam-6262	181	4	since	since	SCONJ
ejpam-6262	181	5	f	f	PROPN
ejpam-6262	181	6	(	(	PUNCT
ejpam-6262	181	7	x∗	x∗	PROPN
ejpam-6262	181	8	)	)	PUNCT
ejpam-6262	181	9	=	=	SYM
ejpam-6262	181	10	0	0	NUM
ejpam-6262	181	11	,	,	PUNCT
ejpam-6262	181	12	this	this	DET
ejpam-6262	181	13	simplifies	simplifie	NOUN
ejpam-6262	181	14	to	to	PART
ejpam-6262	181	15	:	:	PUNCT
ejpam-6262	181	16	f	f	PROPN
ejpam-6262	181	17	(	(	PUNCT
ejpam-6262	181	18	xn	xn	PROPN
ejpam-6262	181	19	)	)	PUNCT
ejpam-6262	181	20	=	=	SYM
ejpam-6262	181	21	f	f	PROPN
ejpam-6262	181	22	′(x∗	′(x∗	NOUN
ejpam-6262	181	23	)	)	PUNCT
ejpam-6262	181	24	en	en	X
ejpam-6262	182	1	+	+	CCONJ
ejpam-6262	182	2	1	1	NUM
ejpam-6262	182	3	2	2	NUM
ejpam-6262	182	4	f	f	PROPN
ejpam-6262	182	5	′′(x∗	′′(x∗	PROPN
ejpam-6262	182	6	)	)	PUNCT
ejpam-6262	183	1	e2n	e2n	X
ejpam-6262	183	2	+	+	NOUN
ejpam-6262	183	3	o(e3n	o(e3n	NOUN
ejpam-6262	183	4	)	)	PUNCT
ejpam-6262	183	5	.	.	PUNCT
ejpam-6262	184	1	(	(	PUNCT
ejpam-6262	184	2	35	35	NUM
ejpam-6262	184	3	)	)	PUNCT
ejpam-6262	184	4	we	we	PRON
ejpam-6262	184	5	also	also	ADV
ejpam-6262	184	6	expand	expand	VERB
ejpam-6262	184	7	the	the	DET
ejpam-6262	184	8	inverse	inverse	NOUN
ejpam-6262	184	9	of	of	ADP
ejpam-6262	184	10	f	f	PROPN
ejpam-6262	184	11	′(xn	′(xn	PROPN
ejpam-6262	184	12	)	)	PUNCT
ejpam-6262	184	13	a	a	DET
ejpam-6262	184	14	round	round	ADJ
ejpam-6262	184	15	x∗	x∗	NOUN
ejpam-6262	184	16	:	:	PUNCT
ejpam-6262	184	17	f	f	PROPN
ejpam-6262	184	18	′(xn	′(xn	NOUN
ejpam-6262	184	19	)	)	PUNCT
ejpam-6262	184	20	−1	−1	NOUN
ejpam-6262	185	1	=	=	SYM
ejpam-6262	185	2	f	f	PROPN
ejpam-6262	185	3	′(x∗)−1	′(x∗)−1	NUM
ejpam-6262	185	4	−	−	PROPN
ejpam-6262	185	5	f	f	PROPN
ejpam-6262	185	6	′(x∗)−2	′(x∗)−2	PROPN
ejpam-6262	185	7	f	f	PROPN
ejpam-6262	185	8	′′(x∗	′′(x∗	PROPN
ejpam-6262	185	9	)	)	PUNCT
ejpam-6262	185	10	en	en	ADP
ejpam-6262	186	1	+	+	PROPN
ejpam-6262	186	2	o	o	X
ejpam-6262	186	3	(	(	PUNCT
ejpam-6262	186	4	e2n	e2n	ADV
ejpam-6262	186	5	)	)	PUNCT
ejpam-6262	186	6	.	.	PUNCT
ejpam-6262	187	1	(	(	PUNCT
ejpam-6262	187	2	36	36	NUM
ejpam-6262	187	3	)	)	PUNCT
ejpam-6262	187	4	now	now	ADV
ejpam-6262	187	5	,	,	PUNCT
ejpam-6262	187	6	we	we	PRON
ejpam-6262	187	7	focus	focus	VERB
ejpam-6262	187	8	on	on	ADP
ejpam-6262	187	9	the	the	DET
ejpam-6262	187	10	correction	correction	NOUN
ejpam-6262	187	11	term	term	NOUN
ejpam-6262	187	12	x∗	x∗	PROPN
ejpam-6262	187	13	n+1	n+1	PROPN
ejpam-6262	187	14	x∗	x∗	X
ejpam-6262	187	15	n+1	n+1	X
ejpam-6262	188	1	=	=	PUNCT
ejpam-6262	188	2	xn	xn	PROPN
ejpam-6262	189	1	−	−	PROPN
ejpam-6262	189	2	f	f	PROPN
ejpam-6262	189	3	′(xn	′(xn	PROPN
ejpam-6262	189	4	)	)	PUNCT
ejpam-6262	189	5	−1	−1	NOUN
ejpam-6262	190	1	f	f	PROPN
ejpam-6262	190	2	(	(	PUNCT
ejpam-6262	190	3	xn	xn	PROPN
ejpam-6262	190	4	)	)	PUNCT
ejpam-6262	190	5	.	.	PUNCT
ejpam-6262	191	1	(	(	PUNCT
ejpam-6262	191	2	37	37	NUM
ejpam-6262	191	3	)	)	PUNCT
ejpam-6262	191	4	substitute	substitute	VERB
ejpam-6262	191	5	the	the	DET
ejpam-6262	191	6	expansion	expansion	NOUN
ejpam-6262	191	7	for	for	ADP
ejpam-6262	191	8	f	f	PROPN
ejpam-6262	191	9	′(xn	′(xn	PROPN
ejpam-6262	191	10	)	)	PUNCT
ejpam-6262	191	11	−1	−1	NOUN
ejpam-6262	191	12	and	and	CCONJ
ejpam-6262	191	13	f	f	PROPN
ejpam-6262	191	14	(	(	PUNCT
ejpam-6262	191	15	xn	xn	PROPN
ejpam-6262	191	16	)	)	PUNCT
ejpam-6262	191	17	in	in	ADP
ejpam-6262	191	18	(	(	PUNCT
ejpam-6262	191	19	35	35	NUM
ejpam-6262	191	20	)	)	PUNCT
ejpam-6262	191	21	we	we	PRON
ejpam-6262	191	22	get	get	VERB
ejpam-6262	191	23	:	:	PUNCT
ejpam-6262	191	24	x∗	x∗	PROPN
ejpam-6262	191	25	n+1	n+1	PROPN
ejpam-6262	192	1	=	=	PUNCT
ejpam-6262	192	2	xn−	xn−	PROPN
ejpam-6262	192	3	(	(	PUNCT
ejpam-6262	192	4	f	f	PROPN
ejpam-6262	192	5	′(x∗)−1−f	′(x∗)−1−f	PROPN
ejpam-6262	192	6	′(x∗)−2	′(x∗)−2	PROPN
ejpam-6262	192	7	f	f	PROPN
ejpam-6262	192	8	′′(x∗)en+o(e2n	′′(x∗)en+o(e2n	NOUN
ejpam-6262	192	9	)	)	PUNCT
ejpam-6262	192	10	)	)	PUNCT
ejpam-6262	192	11	(	(	PUNCT
ejpam-6262	192	12	f	f	X
ejpam-6262	192	13	′(x∗)en	′(x∗)en	PROPN
ejpam-6262	192	14	+	+	NOUN
ejpam-6262	192	15	1	1	NUM
ejpam-6262	192	16	2	2	NUM
ejpam-6262	192	17	f	f	NOUN
ejpam-6262	192	18	′′(x∗)e2n	′′(x∗)e2n	ADP
ejpam-6262	192	19	+	+	NOUN
ejpam-6262	192	20	o(e3n	o(e3n	NOUN
ejpam-6262	192	21	)	)	PUNCT
ejpam-6262	192	22	)	)	PUNCT
ejpam-6262	192	23	.	.	PUNCT
ejpam-6262	193	1	(	(	PUNCT
ejpam-6262	193	2	38	38	NUM
ejpam-6262	193	3	)	)	PUNCT
ejpam-6262	193	4	simplifying	simplifying	NOUN
ejpam-6262	193	5	(	(	PUNCT
ejpam-6262	193	6	38	38	NUM
ejpam-6262	193	7	):	):	PUNCT
ejpam-6262	193	8	x∗	x∗	PROPN
ejpam-6262	193	9	n+1	n+1	PROPN
ejpam-6262	194	1	=	=	PUNCT
ejpam-6262	194	2	xn	xn	PROPN
ejpam-6262	194	3	−	−	PROPN
ejpam-6262	194	4	en	en	INTJ
ejpam-6262	194	5	−	−	PROPN
ejpam-6262	194	6	1	1	NUM
ejpam-6262	194	7	2	2	NUM
ejpam-6262	194	8	f	f	NOUN
ejpam-6262	194	9	′(x∗)−1f	′(x∗)−1f	PROPN
ejpam-6262	194	10	′′(x∗	′′(x∗	PROPN
ejpam-6262	194	11	)	)	PUNCT
ejpam-6262	195	1	e2n	e2n	X
ejpam-6262	195	2	+	+	NOUN
ejpam-6262	195	3	o(e3n	o(e3n	NOUN
ejpam-6262	195	4	)	)	PUNCT
ejpam-6262	195	5	.	.	PUNCT
ejpam-6262	196	1	(	(	PUNCT
ejpam-6262	196	2	39	39	NUM
ejpam-6262	196	3	)	)	PUNCT
ejpam-6262	196	4	thus	thus	ADV
ejpam-6262	196	5	,	,	PUNCT
ejpam-6262	196	6	the	the	DET
ejpam-6262	196	7	error	error	NOUN
ejpam-6262	196	8	at	at	ADP
ejpam-6262	196	9	x∗	x∗	PROPN
ejpam-6262	196	10	n+1	n+1	PROPN
ejpam-6262	196	11	is	be	AUX
ejpam-6262	196	12	:	:	PUNCT
ejpam-6262	196	13	e∗n+1	e∗n+1	X
ejpam-6262	196	14	=	=	PUNCT
ejpam-6262	196	15	x∗	x∗	PROPN
ejpam-6262	196	16	n+1	n+1	NUM
ejpam-6262	196	17	−x∗	−x∗	PROPN
ejpam-6262	196	18	=	=	SYM
ejpam-6262	196	19	1	1	NUM
ejpam-6262	196	20	2	2	NUM
ejpam-6262	196	21	f	f	NOUN
ejpam-6262	196	22	′(x∗)−1	′(x∗)−1	PROPN
ejpam-6262	196	23	f	f	PROPN
ejpam-6262	196	24	′′(x∗	′′(x∗	PROPN
ejpam-6262	196	25	)	)	PUNCT
ejpam-6262	197	1	e2n	e2n	X
ejpam-6262	197	2	+	+	NOUN
ejpam-6262	197	3	o(e3n	o(e3n	NOUN
ejpam-6262	197	4	)	)	PUNCT
ejpam-6262	197	5	.	.	PUNCT
ejpam-6262	198	1	(	(	PUNCT
ejpam-6262	198	2	40	40	NUM
ejpam-6262	198	3	)	)	PUNCT
ejpam-6262	198	4	now	now	ADV
ejpam-6262	198	5	,	,	PUNCT
ejpam-6262	198	6	we	we	PRON
ejpam-6262	198	7	want	want	VERB
ejpam-6262	198	8	to	to	PART
ejpam-6262	198	9	improve	improve	VERB
ejpam-6262	198	10	the	the	DET
ejpam-6262	198	11	order	order	NOUN
ejpam-6262	198	12	of	of	ADP
ejpam-6262	198	13	convergence	convergence	NOUN
ejpam-6262	198	14	by	by	ADP
ejpam-6262	198	15	modifying	modify	VERB
ejpam-6262	198	16	the	the	DET
ejpam-6262	198	17	method	method	NOUN
ejpam-6262	198	18	to	to	PART
ejpam-6262	198	19	:	:	PUNCT
ejpam-6262	198	20	xn+1	xn+1	PROPN
ejpam-6262	198	21	=	=	SYM
ejpam-6262	198	22	xn	xn	PROPN
ejpam-6262	199	1	−	−	NUM
ejpam-6262	199	2	1	1	NUM
ejpam-6262	199	3	2	2	NUM
ejpam-6262	199	4	[	[	PUNCT
ejpam-6262	199	5	f	f	NOUN
ejpam-6262	199	6	′(x∗	′(x∗	NOUN
ejpam-6262	199	7	n	n	CCONJ
ejpam-6262	199	8	)	)	PUNCT
ejpam-6262	199	9	−1	−1	NOUN
ejpam-6262	200	1	+	+	CCONJ
ejpam-6262	200	2	f	f	PROPN
ejpam-6262	200	3	′(x∗	′(x∗	NOUN
ejpam-6262	200	4	n+1	n+1	PROPN
ejpam-6262	200	5	)	)	PUNCT
ejpam-6262	200	6	−1	−1	NOUN
ejpam-6262	200	7	]	]	PUNCT
ejpam-6262	201	1	+	+	CCONJ
ejpam-6262	201	2	(	(	PUNCT
ejpam-6262	201	3	f	f	X
ejpam-6262	201	4	(	(	PUNCT
ejpam-6262	201	5	xn	xn	PROPN
ejpam-6262	201	6	)	)	PUNCT
ejpam-6262	201	7	+	+	CCONJ
ejpam-6262	201	8	1	1	NUM
ejpam-6262	201	9	6	6	NUM
ejpam-6262	201	10	f	f	NUM
ejpam-6262	201	11	′′′(xn)e	′′′(xn)e	PROPN
ejpam-6262	201	12	3	3	NUM
ejpam-6262	201	13	n	n	NOUN
ejpam-6262	201	14	)	)	PUNCT
ejpam-6262	201	15	.	.	PUNCT
ejpam-6262	202	1	(	(	PUNCT
ejpam-6262	202	2	41	41	NUM
ejpam-6262	202	3	)	)	PUNCT
ejpam-6262	202	4	this	this	DET
ejpam-6262	202	5	adjustment	adjustment	NOUN
ejpam-6262	202	6	adds	add	VERB
ejpam-6262	202	7	a	a	DET
ejpam-6262	202	8	cubic	cubic	ADJ
ejpam-6262	202	9	term	term	NOUN
ejpam-6262	202	10	to	to	ADP
ejpam-6262	202	11	the	the	DET
ejpam-6262	202	12	iterative	iterative	NOUN
ejpam-6262	202	13	step	step	NOUN
ejpam-6262	202	14	,	,	PUNCT
ejpam-6262	202	15	which	which	PRON
ejpam-6262	202	16	can	can	AUX
ejpam-6262	202	17	help	help	VERB
ejpam-6262	202	18	improve	improve	VERB
ejpam-6262	202	19	the	the	DET
ejpam-6262	202	20	convergence	convergence	NOUN
ejpam-6262	202	21	order	order	NOUN
ejpam-6262	202	22	.	.	PUNCT
ejpam-6262	203	1	we	we	PRON
ejpam-6262	203	2	now	now	ADV
ejpam-6262	203	3	calculate	calculate	VERB
ejpam-6262	203	4	the	the	DET
ejpam-6262	203	5	error	error	NOUN
ejpam-6262	203	6	en+1	en+1	ADJ
ejpam-6262	203	7	=	=	SYM
ejpam-6262	203	8	xn+1−x∗	xn+1−x∗	PROPN
ejpam-6262	203	9	after	after	ADP
ejpam-6262	203	10	the	the	DET
ejpam-6262	203	11	modification	modification	NOUN
ejpam-6262	203	12	.	.	PUNCT
ejpam-6262	204	1	substitute	substitute	VERB
ejpam-6262	204	2	the	the	DET
ejpam-6262	204	3	taylor	taylor	PROPN
ejpam-6262	204	4	expansions	expansion	NOUN
ejpam-6262	204	5	and	and	CCONJ
ejpam-6262	204	6	the	the	DET
ejpam-6262	204	7	modified	modified	ADJ
ejpam-6262	204	8	correction	correction	NOUN
ejpam-6262	204	9	step	step	VERB
ejpam-6262	204	10	into	into	ADP
ejpam-6262	204	11	the	the	DET
ejpam-6262	204	12	iterative	iterative	NOUN
ejpam-6262	204	13	formula	formula	NOUN
ejpam-6262	204	14	:	:	PUNCT
ejpam-6262	204	15	xn+1	xn+1	X
ejpam-6262	204	16	=	=	SYM
ejpam-6262	205	1	xn−	xn−	PUNCT
ejpam-6262	205	2	1	1	NUM
ejpam-6262	205	3	2	2	NUM
ejpam-6262	205	4	(	(	PUNCT
ejpam-6262	205	5	2f	2f	NUM
ejpam-6262	205	6	′(x∗)−1	′(x∗)−1	NUM
ejpam-6262	205	7	+	+	NOUN
ejpam-6262	205	8	o(en	o(en	PROPN
ejpam-6262	205	9	)	)	PUNCT
ejpam-6262	205	10	)	)	PUNCT
ejpam-6262	205	11	×	×	NOUN
ejpam-6262	205	12	(	(	PUNCT
ejpam-6262	205	13	f	f	NOUN
ejpam-6262	206	1	′	′	NUM
ejpam-6262	207	1	(	(	PUNCT
ejpam-6262	207	2	x∗)en	x∗)en	INTJ
ejpam-6262	207	3	+	+	CCONJ
ejpam-6262	207	4	1	1	NUM
ejpam-6262	207	5	2	2	NUM
ejpam-6262	207	6	f	f	PROPN
ejpam-6262	207	7	′′(x∗	′′(x∗	PROPN
ejpam-6262	207	8	)	)	PUNCT
ejpam-6262	208	1	e2n	e2n	ADV
ejpam-6262	208	2	+	+	NUM
ejpam-6262	208	3	1	1	NUM
ejpam-6262	208	4	6	6	NUM
ejpam-6262	208	5	f	f	PROPN
ejpam-6262	208	6	′′′(x∗	′′′(x∗	NUM
ejpam-6262	208	7	)	)	PUNCT
ejpam-6262	208	8	e3n	e3n	VERB
ejpam-6262	208	9	+	+	NOUN
ejpam-6262	208	10	o(e4n	o(e4n	NOUN
ejpam-6262	208	11	)	)	PUNCT
ejpam-6262	208	12	)	)	PUNCT
ejpam-6262	208	13	.	.	PUNCT
ejpam-6262	209	1	(	(	PUNCT
ejpam-6262	209	2	42	42	X
ejpam-6262	209	3	)	)	PUNCT
ejpam-6262	209	4	simplifying	simplify	VERB
ejpam-6262	209	5	(	(	PUNCT
ejpam-6262	209	6	42	42	NUM
ejpam-6262	209	7	)	)	PUNCT
ejpam-6262	209	8	we	we	PRON
ejpam-6262	209	9	get	get	VERB
ejpam-6262	209	10	:	:	PUNCT
ejpam-6262	209	11	xn+1	xn+1	NUM
ejpam-6262	209	12	=	=	SYM
ejpam-6262	209	13	xn	xn	PROPN
ejpam-6262	209	14	−	−	PROPN
ejpam-6262	209	15	en	en	INTJ
ejpam-6262	209	16	−	−	PROPN
ejpam-6262	209	17	1	1	NUM
ejpam-6262	209	18	2	2	NUM
ejpam-6262	209	19	f	f	NOUN
ejpam-6262	209	20	′(x∗)−1	′(x∗)−1	PROPN
ejpam-6262	209	21	f	f	PROPN
ejpam-6262	209	22	′′(x∗	′′(x∗	PROPN
ejpam-6262	209	23	)	)	PUNCT
ejpam-6262	210	1	e2n	e2n	ADP
ejpam-6262	210	2	−	−	PROPN
ejpam-6262	210	3	1	1	NUM
ejpam-6262	210	4	6	6	NUM
ejpam-6262	210	5	f	f	NOUN
ejpam-6262	210	6	′(x∗)−1	′(x∗)−1	PROPN
ejpam-6262	210	7	f	f	PROPN
ejpam-6262	210	8	′′′(x∗	′′′(x∗	NUM
ejpam-6262	210	9	)	)	PUNCT
ejpam-6262	210	10	e3n	e3n	VERB
ejpam-6262	210	11	+	+	NOUN
ejpam-6262	210	12	o(e4n	o(e4n	NOUN
ejpam-6262	210	13	)	)	PUNCT
ejpam-6262	210	14	.	.	PUNCT
ejpam-6262	211	1	(	(	PUNCT
ejpam-6262	211	2	43	43	X
ejpam-6262	211	3	)	)	PUNCT
ejpam-6262	211	4	y.	y.	PROPN
ejpam-6262	211	5	al	al	PROPN
ejpam-6262	211	6	-	-	PUNCT
ejpam-6262	211	7	shorman	shorman	PROPN
ejpam-6262	211	8	et	et	PROPN
ejpam-6262	211	9	al	al	PROPN
ejpam-6262	211	10	.	.	PUNCT
ejpam-6262	211	11	/	/	SYM
ejpam-6262	211	12	eur	eur	PROPN
ejpam-6262	211	13	.	.	PUNCT
ejpam-6262	212	1	j.	j.	PROPN
ejpam-6262	212	2	pure	pure	PROPN
ejpam-6262	212	3	appl	appl	PROPN
ejpam-6262	212	4	.	.	PROPN
ejpam-6262	212	5	math	math	PROPN
ejpam-6262	212	6	,	,	PUNCT
ejpam-6262	212	7	18	18	NUM
ejpam-6262	212	8	(	(	PUNCT
ejpam-6262	212	9	3	3	NUM
ejpam-6262	212	10	)	)	PUNCT
ejpam-6262	212	11	(	(	PUNCT
ejpam-6262	212	12	2025	2025	NUM
ejpam-6262	212	13	)	)	PUNCT
ejpam-6262	212	14	,	,	PUNCT
ejpam-6262	212	15	6262	6262	NUM
ejpam-6262	212	16	9	9	NUM
ejpam-6262	212	17	of	of	ADP
ejpam-6262	212	18	20	20	NUM
ejpam-6262	212	19	thus	thus	ADV
ejpam-6262	212	20	,	,	PUNCT
ejpam-6262	212	21	the	the	DET
ejpam-6262	212	22	error	error	NOUN
ejpam-6262	212	23	en+1	en+1	NOUN
ejpam-6262	212	24	is	be	AUX
ejpam-6262	212	25	:	:	PUNCT
ejpam-6262	212	26	en+1	en+1	ADJ
ejpam-6262	212	27	=	=	PUNCT
ejpam-6262	212	28	−1	−1	NOUN
ejpam-6262	212	29	2	2	NUM
ejpam-6262	212	30	f	f	NOUN
ejpam-6262	212	31	′(x∗)−1	′(x∗)−1	PROPN
ejpam-6262	212	32	f	f	PROPN
ejpam-6262	212	33	′′(x∗	′′(x∗	PROPN
ejpam-6262	212	34	)	)	PUNCT
ejpam-6262	213	1	e2n	e2n	ADP
ejpam-6262	213	2	−	−	PROPN
ejpam-6262	213	3	1	1	NUM
ejpam-6262	213	4	6	6	NUM
ejpam-6262	213	5	f	f	NOUN
ejpam-6262	213	6	′(x∗)−1	′(x∗)−1	PROPN
ejpam-6262	213	7	f	f	PROPN
ejpam-6262	213	8	′′′(x∗	′′′(x∗	NUM
ejpam-6262	213	9	)	)	PUNCT
ejpam-6262	213	10	e3n	e3n	VERB
ejpam-6262	213	11	+	+	NOUN
ejpam-6262	213	12	o(e4n	o(e4n	NOUN
ejpam-6262	213	13	)	)	PUNCT
ejpam-6262	213	14	.	.	PUNCT
ejpam-6262	214	1	(	(	PUNCT
ejpam-6262	214	2	44	44	NUM
ejpam-6262	214	3	)	)	PUNCT
ejpam-6262	214	4	from	from	ADP
ejpam-6262	214	5	the	the	DET
ejpam-6262	214	6	final	final	ADJ
ejpam-6262	214	7	expression	expression	NOUN
ejpam-6262	214	8	for	for	ADP
ejpam-6262	214	9	en+1	en+1	PROPN
ejpam-6262	214	10	,	,	PUNCT
ejpam-6262	214	11	we	we	PRON
ejpam-6262	214	12	observe	observe	VERB
ejpam-6262	214	13	that	that	SCONJ
ejpam-6262	214	14	the	the	DET
ejpam-6262	214	15	dominant	dominant	ADJ
ejpam-6262	214	16	term	term	NOUN
ejpam-6262	214	17	is	be	AUX
ejpam-6262	214	18	the	the	DET
ejpam-6262	214	19	sum	sum	NOUN
ejpam-6262	214	20	of	of	ADP
ejpam-6262	214	21	quadratic	quadratic	ADJ
ejpam-6262	214	22	and	and	CCONJ
ejpam-6262	214	23	cubic	cubic	ADJ
ejpam-6262	214	24	terms	term	NOUN
ejpam-6262	214	25	.	.	PUNCT
ejpam-6262	215	1	if	if	SCONJ
ejpam-6262	215	2	the	the	DET
ejpam-6262	215	3	cubic	cubic	ADJ
ejpam-6262	215	4	term	term	NOUN
ejpam-6262	215	5	(	(	PUNCT
ejpam-6262	215	6	involving	involve	VERB
ejpam-6262	215	7	f	f	PROPN
ejpam-6262	215	8	′′′(x∗	′′′(x∗	NUM
ejpam-6262	215	9	)	)	PUNCT
ejpam-6262	215	10	)	)	PUNCT
ejpam-6262	215	11	dominates	dominate	VERB
ejpam-6262	215	12	at	at	ADP
ejpam-6262	215	13	certain	certain	ADJ
ejpam-6262	215	14	stages	stage	NOUN
ejpam-6262	215	15	of	of	ADP
ejpam-6262	215	16	the	the	DET
ejpam-6262	215	17	iteration	iteration	NOUN
ejpam-6262	215	18	,	,	PUNCT
ejpam-6262	215	19	we	we	PRON
ejpam-6262	215	20	can	can	AUX
ejpam-6262	215	21	get	get	VERB
ejpam-6262	215	22	an	an	DET
ejpam-6262	215	23	intermediate	intermediate	ADJ
ejpam-6262	215	24	convergence	convergence	NOUN
ejpam-6262	215	25	order	order	NOUN
ejpam-6262	215	26	:	:	PUNCT
ejpam-6262	215	27	en+1	en+1	PROPN
ejpam-6262	215	28	=	=	PROPN
ejpam-6262	215	29	c2	c2	PROPN
ejpam-6262	215	30	e2n	e2n	PROPN
ejpam-6262	215	31	+	+	CCONJ
ejpam-6262	215	32	c3	c3	PROPN
ejpam-6262	215	33	e3n	e3n	PROPN
ejpam-6262	215	34	.	.	PUNCT
ejpam-6262	216	1	(	(	PUNCT
ejpam-6262	216	2	45	45	NUM
ejpam-6262	216	3	)	)	PUNCT
ejpam-6262	216	4	in	in	ADP
ejpam-6262	216	5	this	this	DET
ejpam-6262	216	6	case	case	NOUN
ejpam-6262	216	7	,	,	PUNCT
ejpam-6262	216	8	the	the	DET
ejpam-6262	216	9	method	method	NOUN
ejpam-6262	216	10	can	can	AUX
ejpam-6262	216	11	have	have	VERB
ejpam-6262	216	12	an	an	DET
ejpam-6262	216	13	order	order	NOUN
ejpam-6262	216	14	of	of	ADP
ejpam-6262	216	15	convergence	convergence	NOUN
ejpam-6262	216	16	between	between	ADP
ejpam-6262	216	17	2	2	NUM
ejpam-6262	216	18	and	and	CCONJ
ejpam-6262	216	19	3	3	NUM
ejpam-6262	216	20	,	,	PUNCT
ejpam-6262	216	21	and	and	CCONJ
ejpam-6262	216	22	depending	depend	VERB
ejpam-6262	216	23	on	on	ADP
ejpam-6262	216	24	the	the	DET
ejpam-6262	216	25	relative	relative	ADJ
ejpam-6262	216	26	sizes	size	NOUN
ejpam-6262	216	27	of	of	ADP
ejpam-6262	216	28	c2	c2	PROPN
ejpam-6262	216	29	and	and	CCONJ
ejpam-6262	216	30	c3	c3	PROPN
ejpam-6262	216	31	,	,	PUNCT
ejpam-6262	216	32	the	the	DET
ejpam-6262	216	33	order	order	NOUN
ejpam-6262	216	34	of	of	ADP
ejpam-6262	216	35	convergence	convergence	NOUN
ejpam-6262	216	36	could	could	AUX
ejpam-6262	216	37	be	be	AUX
ejpam-6262	216	38	approximately	approximately	ADV
ejpam-6262	216	39	2.5	2.5	NUM
ejpam-6262	216	40	.	.	PUNCT
ejpam-6262	217	1	5	5	NUM
ejpam-6262	217	2	.	.	NOUN
ejpam-6262	217	3	numerical	numerical	ADJ
ejpam-6262	217	4	examples	example	NOUN
ejpam-6262	217	5	and	and	CCONJ
ejpam-6262	217	6	comparisons	comparison	NOUN
ejpam-6262	217	7	in	in	ADP
ejpam-6262	217	8	this	this	DET
ejpam-6262	217	9	part	part	NOUN
ejpam-6262	217	10	,	,	PUNCT
ejpam-6262	217	11	our	our	PRON
ejpam-6262	217	12	aim	aim	NOUN
ejpam-6262	217	13	is	be	AUX
ejpam-6262	217	14	to	to	PART
ejpam-6262	217	15	demonstrate	demonstrate	VERB
ejpam-6262	217	16	the	the	DET
ejpam-6262	217	17	efficacy	efficacy	NOUN
ejpam-6262	217	18	of	of	ADP
ejpam-6262	217	19	the	the	DET
ejpam-6262	217	20	method	method	NOUN
ejpam-6262	217	21	we	we	PRON
ejpam-6262	217	22	have	have	AUX
ejpam-6262	217	23	put	put	VERB
ejpam-6262	217	24	forward	forward	ADV
ejpam-6262	217	25	.	.	PUNCT
ejpam-6262	218	1	we	we	PRON
ejpam-6262	218	2	will	will	AUX
ejpam-6262	218	3	conduct	conduct	VERB
ejpam-6262	218	4	a	a	DET
ejpam-6262	218	5	comparison	comparison	NOUN
ejpam-6262	218	6	between	between	ADP
ejpam-6262	218	7	the	the	DET
ejpam-6262	218	8	dfh	dfh	PROPN
ejpam-6262	218	9	and	and	CCONJ
ejpam-6262	218	10	newton	newton	PROPN
ejpam-6262	218	11	,	,	PUNCT
ejpam-6262	218	12	broyden	broyden	NOUN
ejpam-6262	218	13	,	,	PUNCT
ejpam-6262	218	14	and	and	CCONJ
ejpam-6262	218	15	secant	secant	ADJ
ejpam-6262	218	16	methods	method	NOUN
ejpam-6262	218	17	to	to	PART
ejpam-6262	218	18	illustrate	illustrate	VERB
ejpam-6262	218	19	their	their	PRON
ejpam-6262	218	20	respective	respective	ADJ
ejpam-6262	218	21	efficiencies	efficiency	NOUN
ejpam-6262	218	22	.	.	PUNCT
ejpam-6262	219	1	we	we	PRON
ejpam-6262	219	2	will	will	AUX
ejpam-6262	219	3	consider	consider	VERB
ejpam-6262	219	4	five	five	NUM
ejpam-6262	219	5	examples	example	NOUN
ejpam-6262	219	6	including	include	VERB
ejpam-6262	219	7	many	many	ADJ
ejpam-6262	219	8	systems	system	NOUN
ejpam-6262	219	9	of	of	ADP
ejpam-6262	219	10	nonlinear	nonlinear	ADJ
ejpam-6262	219	11	equations	equation	NOUN
ejpam-6262	219	12	.	.	PUNCT
ejpam-6262	220	1	the	the	DET
ejpam-6262	220	2	criterion	criterion	NOUN
ejpam-6262	220	3	was	be	AUX
ejpam-6262	220	4	performed	perform	VERB
ejpam-6262	220	5	using	use	VERB
ejpam-6262	220	6	the	the	DET
ejpam-6262	220	7	built	build	VERB
ejpam-6262	220	8	-	-	PUNCT
ejpam-6262	220	9	in	in	ADP
ejpam-6262	220	10	”	"	PUNCT
ejpam-6262	220	11	timeused	timeuse	VERB
ejpam-6262	220	12	”	"	PUNCT
ejpam-6262	220	13	function	function	NOUN
ejpam-6262	220	14	in	in	ADP
ejpam-6262	220	15	mathematica	mathematica	PROPN
ejpam-6262	220	16	12.0	12.0	NUM
ejpam-6262	220	17	software	software	NOUN
ejpam-6262	220	18	.	.	PUNCT
ejpam-6262	221	1	all	all	DET
ejpam-6262	221	2	computations	computation	NOUN
ejpam-6262	221	3	were	be	AUX
ejpam-6262	221	4	executed	execute	VERB
ejpam-6262	221	5	under	under	ADP
ejpam-6262	221	6	identical	identical	ADJ
ejpam-6262	221	7	conditions	condition	NOUN
ejpam-6262	221	8	on	on	ADP
ejpam-6262	221	9	an	an	DET
ejpam-6262	221	10	intel	intel	PROPN
ejpam-6262	221	11	core	core	NOUN
ejpam-6262	221	12	i7	i7	NOUN
ejpam-6262	221	13	-	-	PUNCT
ejpam-6262	221	14	10750h	10750h	NUM
ejpam-6262	221	15	cpu	cpu	NOUN
ejpam-6262	221	16	@2.60	@2.60	NOUN
ejpam-6262	221	17	ghz	ghz	VERB
ejpam-6262	221	18	2.59	2.59	NUM
ejpam-6262	221	19	ghz	ghz	NOUN
ejpam-6262	221	20	with	with	ADP
ejpam-6262	221	21	16	16	NUM
ejpam-6262	221	22	gb	gb	NOUN
ejpam-6262	221	23	ram	ram	NOUN
ejpam-6262	221	24	,	,	PUNCT
ejpam-6262	221	25	operating	operate	VERB
ejpam-6262	221	26	on	on	ADP
ejpam-6262	221	27	microsoft	microsoft	PROPN
ejpam-6262	221	28	windows	windows	PROPN
ejpam-6262	221	29	11	11	NUM
ejpam-6262	221	30	,	,	PUNCT
ejpam-6262	221	31	64	64	NUM
ejpam-6262	221	32	-	-	PUNCT
ejpam-6262	221	33	bit	bit	NOUN
ejpam-6262	221	34	,	,	PUNCT
ejpam-6262	221	35	and	and	CCONJ
ejpam-6262	221	36	utilizing	utilize	VERB
ejpam-6262	221	37	an	an	DET
ejpam-6262	221	38	x64	x64	NOUN
ejpam-6262	221	39	-	-	PUNCT
ejpam-6262	221	40	based	base	VERB
ejpam-6262	221	41	processor	processor	NOUN
ejpam-6262	221	42	.	.	PUNCT
ejpam-6262	222	1	in	in	ADP
ejpam-6262	222	2	the	the	DET
ejpam-6262	222	3	tables	table	NOUN
ejpam-6262	222	4	1	1	NUM
ejpam-6262	222	5	-	-	SYM
ejpam-6262	222	6	5	5	NUM
ejpam-6262	222	7	,	,	PUNCT
ejpam-6262	222	8	we	we	PRON
ejpam-6262	222	9	need	need	VERB
ejpam-6262	222	10	to	to	PART
ejpam-6262	222	11	find	find	VERB
ejpam-6262	222	12	a0	a0	NOUN
ejpam-6262	222	13	=	=	SYM
ejpam-6262	222	14	j(x0	j(x0	NOUN
ejpam-6262	222	15	)	)	PUNCT
ejpam-6262	222	16	=	=	SYM
ejpam-6262	222	17			NOUN
ejpam-6262	222	18	∂f1	∂f1	NOUN
ejpam-6262	222	19	∂x1	∂x1	PROPN
ejpam-6262	222	20	∂f1	∂f1	PROPN
ejpam-6262	222	21	∂x2	∂x2	NOUN
ejpam-6262	222	22	·	·	PUNCT
ejpam-6262	222	23	·	·	PUNCT
ejpam-6262	222	24	·	·	PUNCT
ejpam-6262	223	1	∂f1	∂f1	NOUN
ejpam-6262	223	2	∂xn	∂xn	VERB
ejpam-6262	223	3	∂f2	∂f2	NOUN
ejpam-6262	223	4	∂x1	∂x1	NOUN
ejpam-6262	223	5	∂f2	∂f2	VERB
ejpam-6262	223	6	∂x2	∂x2	NOUN
ejpam-6262	223	7	·	·	PUNCT
ejpam-6262	223	8	·	·	PUNCT
ejpam-6262	223	9	·	·	PUNCT
ejpam-6262	223	10	∂f2	∂f2	NOUN
ejpam-6262	223	11	∂xn	∂xn	NOUN
ejpam-6262	223	12	...	...	PUNCT
ejpam-6262	223	13	...	...	PUNCT
ejpam-6262	223	14	.	.	PUNCT
ejpam-6262	223	15	.	.	PUNCT
ejpam-6262	223	16	.	.	PUNCT
ejpam-6262	224	1	...	...	PUNCT
ejpam-6262	225	1	∂fn	∂fn	VERB
ejpam-6262	225	2	∂x1	∂x1	NOUN
ejpam-6262	225	3	∂fn	∂fn	VERB
ejpam-6262	225	4	∂x2	∂x2	NOUN
ejpam-6262	225	5	·	·	PUNCT
ejpam-6262	225	6	·	·	PUNCT
ejpam-6262	225	7	·	·	PUNCT
ejpam-6262	226	1	∂fn	∂fn	VERB
ejpam-6262	226	2	∂xn	∂xn	NOUN
ejpam-6262	226	3			NUM
ejpam-6262	226	4	where	where	SCONJ
ejpam-6262	226	5	j	j	PROPN
ejpam-6262	226	6	is	be	AUX
ejpam-6262	226	7	the	the	DET
ejpam-6262	226	8	jacobian	jacobian	ADJ
ejpam-6262	226	9	matrix	matrix	NOUN
ejpam-6262	226	10	.	.	PUNCT
ejpam-6262	227	1	example	example	NOUN
ejpam-6262	228	1	1	1	NUM
ejpam-6262	228	2	.	.	X
ejpam-6262	228	3	examine	examine	VERB
ejpam-6262	228	4	the	the	DET
ejpam-6262	228	5	provided	provide	VERB
ejpam-6262	228	6	set	set	NOUN
ejpam-6262	228	7	of	of	ADP
ejpam-6262	228	8	two	two	NUM
ejpam-6262	228	9	nonlinear	nonlinear	ADJ
ejpam-6262	228	10	equations	equation	NOUN
ejpam-6262	228	11	presented	present	VERB
ejpam-6262	228	12	in	in	ADP
ejpam-6262	228	13	table	table	NOUN
ejpam-6262	228	14	1	1	NUM
ejpam-6262	228	15	.	.	PUNCT
ejpam-6262	229	1	here	here	ADV
ejpam-6262	229	2	we	we	PRON
ejpam-6262	229	3	compared	compare	VERB
ejpam-6262	229	4	many	many	ADJ
ejpam-6262	229	5	systems	system	NOUN
ejpam-6262	229	6	of	of	ADP
ejpam-6262	229	7	two	two	NUM
ejpam-6262	229	8	nonlinear	nonlinear	ADJ
ejpam-6262	229	9	equations	equation	NOUN
ejpam-6262	229	10	y	y	PROPN
ejpam-6262	229	11	.	.	PUNCT
ejpam-6262	230	1	a	a	DET
ejpam-6262	230	2	l	l	NOUN
ejpam-6262	230	3	-	-	PUNCT
ejpam-6262	230	4	s	s	X
ejpam-6262	230	5	h	h	NOUN
ejpam-6262	230	6	o	o	NOUN
ejpam-6262	230	7	rm	rm	PROPN
ejpam-6262	230	8	a	a	PROPN
ejpam-6262	230	9	n	n	X
ejpam-6262	230	10	et	et	NOUN
ejpam-6262	230	11	a	a	DET
ejpam-6262	230	12	l.	l.	PROPN
ejpam-6262	230	13	/	/	SYM
ejpam-6262	230	14	e	e	PROPN
ejpam-6262	230	15	u	u	PROPN
ejpam-6262	230	16	r.	r.	PROPN
ejpam-6262	230	17	j	j	PROPN
ejpam-6262	230	18	.	.	PUNCT
ejpam-6262	231	1	p	p	X
ejpam-6262	231	2	u	u	X
ejpam-6262	231	3	re	re	ADP
ejpam-6262	231	4	a	a	DET
ejpam-6262	231	5	p	p	X
ejpam-6262	231	6	p	p	X
ejpam-6262	231	7	l.	l.	PROPN
ejpam-6262	231	8	m	m	PROPN
ejpam-6262	231	9	a	a	DET
ejpam-6262	231	10	th	th	X
ejpam-6262	231	11	,	,	PUNCT
ejpam-6262	231	12	1	1	NUM
ejpam-6262	231	13	8	8	NUM
ejpam-6262	231	14	(	(	PUNCT
ejpam-6262	231	15	3	3	NUM
ejpam-6262	231	16	)	)	PUNCT
ejpam-6262	231	17	(	(	PUNCT
ejpam-6262	231	18	2	2	NUM
ejpam-6262	231	19	0	0	NUM
ejpam-6262	231	20	2	2	NUM
ejpam-6262	231	21	5	5	NUM
ejpam-6262	231	22	)	)	PUNCT
ejpam-6262	231	23	,	,	PUNCT
ejpam-6262	231	24	6	6	NUM
ejpam-6262	231	25	2	2	NUM
ejpam-6262	231	26	6	6	NUM
ejpam-6262	231	27	2	2	NUM
ejpam-6262	231	28	1	1	NUM
ejpam-6262	231	29	0	0	NUM
ejpam-6262	231	30	o	o	NOUN
ejpam-6262	231	31	f	f	NOUN
ejpam-6262	231	32	2	2	NUM
ejpam-6262	231	33	0	0	NUM
ejpam-6262	231	34	table	table	NOUN
ejpam-6262	231	35	1	1	NUM
ejpam-6262	231	36	:	:	PUNCT
ejpam-6262	231	37	analysis	analysis	NOUN
ejpam-6262	231	38	of	of	ADP
ejpam-6262	231	39	dfh	dfh	PROPN
ejpam-6262	231	40	in	in	ADP
ejpam-6262	231	41	contrast	contrast	NOUN
ejpam-6262	231	42	to	to	ADP
ejpam-6262	231	43	broyden	broyden	VERB
ejpam-6262	231	44	’s	’s	PART
ejpam-6262	231	45	method	method	NOUN
ejpam-6262	231	46	for	for	ADP
ejpam-6262	231	47	two	two	NUM
ejpam-6262	231	48	nonlinear	nonlinear	ADJ
ejpam-6262	231	49	equations	equation	NOUN
ejpam-6262	231	50	systems	system	NOUN
ejpam-6262	231	51	.	.	PUNCT
ejpam-6262	232	1	i	i	PRON
ejpam-6262	232	2	coc	coc	VERB
ejpam-6262	232	3	function	function	NOUN
ejpam-6262	232	4	x0	x0	PROPN
ejpam-6262	232	5	a0	a0	PROPN
ejpam-6262	232	6	bfs	bfs	PROPN
ejpam-6262	232	7	n	n	PROPN
ejpam-6262	232	8	dfh	dfh	PROPN
ejpam-6262	232	9	bfs	bfs	PROPN
ejpam-6262	232	10	n	n	PROPN
ejpam-6262	232	11	dfh	dfh	PROPN
ejpam-6262	232	12	root	root	NOUN
ejpam-6262	232	13	1	1	NUM
ejpam-6262	232	14	x+	x+	VERB
ejpam-6262	232	15	y	y	PROPN
ejpam-6262	232	16	−	−	PROPN
ejpam-6262	232	17	3	3	NUM
ejpam-6262	232	18	x2	x2	NOUN
ejpam-6262	233	1	+	+	CCONJ
ejpam-6262	234	1	y2	y2	NOUN
ejpam-6262	235	1	−	−	NOUN
ejpam-6262	235	2	9	9	NUM
ejpam-6262	235	3	(	(	PUNCT
ejpam-6262	235	4	1	1	NUM
ejpam-6262	235	5	,	,	PUNCT
ejpam-6262	235	6	3	3	X
ejpam-6262	235	7	)	)	PUNCT
ejpam-6262	235	8			NOUN
ejpam-6262	235	9	1	1	NUM
ejpam-6262	235	10	1	1	NUM
ejpam-6262	235	11	2	2	NUM
ejpam-6262	235	12	6	6	NUM
ejpam-6262	235	13			NOUN
ejpam-6262	235	14	12	12	NUM
ejpam-6262	235	15	11	11	NUM
ejpam-6262	235	16	10	10	NUM
ejpam-6262	235	17	1.678007	1.678007	NUM
ejpam-6262	235	18	2.1154	2.1154	NUM
ejpam-6262	235	19	2.6416	2.6416	NUM
ejpam-6262	235	20	0.00000064	0.00000064	NUM
ejpam-6262	235	21	2.99998136	2.99998136	NUM
ejpam-6262	235	22	2	2	NUM
ejpam-6262	235	23	x4	x4	PROPN
ejpam-6262	235	24	+	+	CCONJ
ejpam-6262	236	1	y4	y4	PROPN
ejpam-6262	236	2	−	−	PROPN
ejpam-6262	236	3	67	67	NUM
ejpam-6262	236	4	x4	x4	ADV
ejpam-6262	236	5	−	−	PROPN
ejpam-6262	236	6	3xy2	3xy2	NUM
ejpam-6262	236	7	+	+	NUM
ejpam-6262	236	8	35	35	NUM
ejpam-6262	236	9	(	(	PUNCT
ejpam-6262	236	10	2	2	NUM
ejpam-6262	236	11	,	,	PUNCT
ejpam-6262	236	12	3	3	NUM
ejpam-6262	236	13	)	)	PUNCT
ejpam-6262	236	14			NOUN
ejpam-6262	236	15	32	32	NUM
ejpam-6262	236	16	108	108	NUM
ejpam-6262	236	17	5	5	NUM
ejpam-6262	236	18	−36	−36	NOUN
ejpam-6262	236	19			NOUN
ejpam-6262	236	20	13	13	NUM
ejpam-6262	236	21	13	13	NUM
ejpam-6262	236	22	12	12	NUM
ejpam-6262	236	23	1.712084	1.712084	NUM
ejpam-6262	236	24	2.0052	2.0052	NUM
ejpam-6262	236	25	2.5687	2.5687	NUM
ejpam-6262	236	26	1.88364056	1.88364056	NUM
ejpam-6262	236	27	2.71594745	2.71594745	NUM
ejpam-6262	236	28	3	3	NUM
ejpam-6262	236	29	x2	x2	NOUN
ejpam-6262	236	30	−	−	PROPN
ejpam-6262	236	31	10x+	10x+	NUM
ejpam-6262	237	1	y2	y2	NOUN
ejpam-6262	238	1	+	+	CCONJ
ejpam-6262	238	2	8	8	NUM
ejpam-6262	238	3	xy2	xy2	X
ejpam-6262	238	4	+	+	SYM
ejpam-6262	238	5	x−	x−	PROPN
ejpam-6262	238	6	10y	10y	PROPN
ejpam-6262	239	1	+	+	CCONJ
ejpam-6262	239	2	8	8	NUM
ejpam-6262	239	3	(	(	PUNCT
ejpam-6262	239	4	0	0	NUM
ejpam-6262	239	5	,	,	PUNCT
ejpam-6262	239	6	0	0	NUM
ejpam-6262	239	7	)	)	PUNCT
ejpam-6262	239	8			NOUN
ejpam-6262	239	9	−10	−10	NOUN
ejpam-6262	239	10	0	0	NUM
ejpam-6262	239	11	1	1	NUM
ejpam-6262	239	12	−10	−10	SYM
ejpam-6262	239	13			NOUN
ejpam-6262	239	14	11	11	NUM
ejpam-6262	239	15	10	10	NUM
ejpam-6262	239	16	8	8	NUM
ejpam-6262	239	17	1.687346	1.687346	NUM
ejpam-6262	239	18	2.2184	2.2184	NUM
ejpam-6262	239	19	2.8984	2.8984	NUM
ejpam-6262	239	20	0.99999927	0.99999927	NUM
ejpam-6262	239	21	1.00000048	1.00000048	NUM
ejpam-6262	239	22	4	4	NUM
ejpam-6262	239	23	x−	x−	PROPN
ejpam-6262	239	24	cos	cos	PROPN
ejpam-6262	239	25	y	y	PROPN
ejpam-6262	239	26	sinx+	sinx+	PROPN
ejpam-6262	239	27	0.5y	0.5y	PROPN
ejpam-6262	239	28	(	(	PUNCT
ejpam-6262	239	29	0,−0.5	0,−0.5	NOUN
ejpam-6262	239	30	)	)	PUNCT
ejpam-6262	239	31			NOUN
ejpam-6262	239	32	1	1	NUM
ejpam-6262	239	33	−0.48	−0.48	SYM
ejpam-6262	239	34	1	1	NUM
ejpam-6262	239	35	0.5	0.5	NUM
ejpam-6262	239	36			NOUN
ejpam-6262	239	37	11	11	NUM
ejpam-6262	239	38	9	9	NUM
ejpam-6262	239	39	7	7	NUM
ejpam-6262	239	40	1.78364	1.78364	NUM
ejpam-6262	239	41	2.1022	2.1022	NUM
ejpam-6262	239	42	2.2331	2.2331	NUM
ejpam-6262	239	43	0.53038868	0.53038868	NUM
ejpam-6262	239	44	−1.01173734	−1.01173734	NUM
ejpam-6262	239	45	5	5	NUM
ejpam-6262	239	46	x2	x2	NOUN
ejpam-6262	240	1	+	+	CCONJ
ejpam-6262	241	1	y2	y2	NOUN
ejpam-6262	241	2	−	−	NOUN
ejpam-6262	241	3	2	2	NUM
ejpam-6262	241	4	ex−1	ex−1	NOUN
ejpam-6262	241	5	+	+	CCONJ
ejpam-6262	241	6	y3	y3	NOUN
ejpam-6262	241	7	−	−	PROPN
ejpam-6262	241	8	2	2	NUM
ejpam-6262	241	9	(	(	PUNCT
ejpam-6262	241	10	0.5	0.5	NUM
ejpam-6262	241	11	,	,	PUNCT
ejpam-6262	241	12	0.5	0.5	NUM
ejpam-6262	241	13	)	)	PUNCT
ejpam-6262	241	14			NOUN
ejpam-6262	241	15	1	1	NUM
ejpam-6262	241	16	1	1	NUM
ejpam-6262	241	17	0.6065	0.6065	NUM
ejpam-6262	241	18	0.75	0.75	NUM
ejpam-6262	241	19	15	15	NUM
ejpam-6262	241	20	12	12	NUM
ejpam-6262	241	21	10	10	NUM
ejpam-6262	241	22	1.69356	1.69356	NUM
ejpam-6262	241	23	2.0682	2.0682	NUM
ejpam-6262	241	24	2.2420	2.2420	NUM
ejpam-6262	241	25	0.99998777	0.99998777	NUM
ejpam-6262	241	26	1.00001497	1.00001497	NUM
ejpam-6262	241	27	6	6	NUM
ejpam-6262	241	28	−x2	−x2	PROPN
ejpam-6262	241	29	−	−	PROPN
ejpam-6262	241	30	x+	x+	PUNCT
ejpam-6262	241	31	2y	2y	PROPN
ejpam-6262	241	32	−	−	NOUN
ejpam-6262	241	33	18	18	NUM
ejpam-6262	241	34	(	(	PUNCT
ejpam-6262	241	35	x−	x−	PROPN
ejpam-6262	241	36	1)2	1)2	NUM
ejpam-6262	241	37	+	+	CCONJ
ejpam-6262	241	38	(	(	PUNCT
ejpam-6262	241	39	y	y	PROPN
ejpam-6262	241	40	−	−	PROPN
ejpam-6262	241	41	6)2	6)2	NUM
ejpam-6262	241	42	−	−	NUM
ejpam-6262	241	43	25	25	NUM
ejpam-6262	241	44	(	(	PUNCT
ejpam-6262	241	45	−5,−5	−5,−5	ADJ
ejpam-6262	241	46	)	)	PUNCT
ejpam-6262	241	47			NOUN
ejpam-6262	241	48	9	9	NUM
ejpam-6262	241	49	2	2	NUM
ejpam-6262	241	50	−12	−12	NOUN
ejpam-6262	241	51	−22	−22	NOUN
ejpam-6262	241	52			NOUN
ejpam-6262	241	53	24	24	NUM
ejpam-6262	241	54	19	19	NUM
ejpam-6262	241	55	15	15	NUM
ejpam-6262	241	56	1.537854	1.537854	NUM
ejpam-6262	241	57	1.9443	1.9443	NUM
ejpam-6262	241	58	2.3251	2.3251	NUM
ejpam-6262	241	59	1.54694636	1.54694636	NUM
ejpam-6262	241	60	10.9699948	10.9699948	NUM
ejpam-6262	241	61	7	7	NUM
ejpam-6262	241	62	2	2	NUM
ejpam-6262	241	63	cos	cos	ADP
ejpam-6262	241	64	y	y	PROPN
ejpam-6262	241	65	+	+	CCONJ
ejpam-6262	241	66	7	7	NUM
ejpam-6262	241	67	sinx−	sinx−	NOUN
ejpam-6262	241	68	10x	10x	NUM
ejpam-6262	241	69	7	7	NUM
ejpam-6262	241	70	cosx−	cosx−	PROPN
ejpam-6262	241	71	2	2	NUM
ejpam-6262	241	72	sin	sin	NOUN
ejpam-6262	241	73	y	y	PROPN
ejpam-6262	241	74	−	−	PROPN
ejpam-6262	241	75	10y	10y	PROPN
ejpam-6262	241	76	(	(	PUNCT
ejpam-6262	241	77	0	0	NUM
ejpam-6262	241	78	,	,	PUNCT
ejpam-6262	241	79	0	0	NUM
ejpam-6262	241	80	)	)	PUNCT
ejpam-6262	241	81			NOUN
ejpam-6262	242	1	−3	−3	ADV
ejpam-6262	242	2	0	0	PUNCT
ejpam-6262	242	3	0	0	NUM
ejpam-6262	243	1	−12	−12	NUM
ejpam-6262	243	2			ADJ
ejpam-6262	243	3	10	10	NUM
ejpam-6262	243	4	10	10	NUM
ejpam-6262	243	5	9	9	NUM
ejpam-6262	243	6	1.62944	1.62944	NUM
ejpam-6262	243	7	2.1427	2.1427	NUM
ejpam-6262	243	8	2.4499	2.4499	NUM
ejpam-6262	243	9	0.52651702	0.52651702	NUM
ejpam-6262	243	10	0.50792810	0.50792810	NUM
ejpam-6262	243	11	y.	y.	PROPN
ejpam-6262	243	12	al	al	PROPN
ejpam-6262	243	13	-	-	PUNCT
ejpam-6262	243	14	shorman	shorman	PROPN
ejpam-6262	243	15	et	et	PROPN
ejpam-6262	243	16	al	al	PROPN
ejpam-6262	243	17	.	.	PUNCT
ejpam-6262	243	18	/	/	SYM
ejpam-6262	243	19	eur	eur	PROPN
ejpam-6262	243	20	.	.	PUNCT
ejpam-6262	244	1	j.	j.	PROPN
ejpam-6262	244	2	pure	pure	PROPN
ejpam-6262	244	3	appl	appl	PROPN
ejpam-6262	244	4	.	.	PROPN
ejpam-6262	244	5	math	math	PROPN
ejpam-6262	244	6	,	,	PUNCT
ejpam-6262	244	7	18	18	NUM
ejpam-6262	244	8	(	(	PUNCT
ejpam-6262	244	9	3	3	NUM
ejpam-6262	244	10	)	)	PUNCT
ejpam-6262	244	11	(	(	PUNCT
ejpam-6262	244	12	2025	2025	NUM
ejpam-6262	244	13	)	)	PUNCT
ejpam-6262	244	14	,	,	PUNCT
ejpam-6262	244	15	6262	6262	NUM
ejpam-6262	244	16	11	11	NUM
ejpam-6262	244	17	of	of	ADP
ejpam-6262	244	18	20	20	NUM
ejpam-6262	244	19	example	example	NOUN
ejpam-6262	244	20	2	2	NUM
ejpam-6262	244	21	.	.	PUNCT
ejpam-6262	244	22	examine	examine	VERB
ejpam-6262	244	23	the	the	DET
ejpam-6262	244	24	subsequent	subsequent	ADJ
ejpam-6262	244	25	set	set	NOUN
ejpam-6262	244	26	of	of	ADP
ejpam-6262	244	27	three	three	NUM
ejpam-6262	244	28	distinct	distinct	ADJ
ejpam-6262	244	29	nonlinear	nonlinear	ADJ
ejpam-6262	244	30	equations	equation	NOUN
ejpam-6262	244	31	:	:	PUNCT
ejpam-6262	244	32	table	table	NOUN
ejpam-6262	244	33	2	2	NUM
ejpam-6262	244	34	:	:	PUNCT
ejpam-6262	244	35	analysis	analysis	NOUN
ejpam-6262	244	36	of	of	ADP
ejpam-6262	244	37	dfh	dfh	PROPN
ejpam-6262	244	38	in	in	ADP
ejpam-6262	244	39	contrast	contrast	NOUN
ejpam-6262	244	40	to	to	ADP
ejpam-6262	244	41	broyden	broyden	VERB
ejpam-6262	244	42	’s	’s	PART
ejpam-6262	244	43	method	method	NOUN
ejpam-6262	244	44	for	for	ADP
ejpam-6262	244	45	two	two	NUM
ejpam-6262	244	46	nonlinear	nonlinear	ADJ
ejpam-6262	244	47	equations	equation	NOUN
ejpam-6262	244	48	systems	system	NOUN
ejpam-6262	244	49	.	.	PUNCT
ejpam-6262	245	1	i	i	PRON
ejpam-6262	245	2	coc	coc	VERB
ejpam-6262	245	3	function	function	NOUN
ejpam-6262	245	4	x0	x0	PROPN
ejpam-6262	245	5	a0	a0	PROPN
ejpam-6262	245	6	bfs	bfs	PROPN
ejpam-6262	245	7	n	n	PROPN
ejpam-6262	245	8	dfh	dfh	PROPN
ejpam-6262	245	9	bfs	bfs	PROPN
ejpam-6262	245	10	n	n	PROPN
ejpam-6262	245	11	dfh	dfh	PROPN
ejpam-6262	245	12	root	root	NOUN
ejpam-6262	245	13	1	1	NUM
ejpam-6262	245	14	x2	x2	NOUN
ejpam-6262	246	1	+	+	CCONJ
ejpam-6262	246	2	y2	y2	PROPN
ejpam-6262	247	1	+	+	CCONJ
ejpam-6262	247	2	z2	z2	PROPN
ejpam-6262	247	3	x2	x2	PROPN
ejpam-6262	248	1	+	+	CCONJ
ejpam-6262	248	2	y2	y2	PROPN
ejpam-6262	249	1	+	+	CCONJ
ejpam-6262	249	2	z2	z2	PROPN
ejpam-6262	249	3	x2	x2	PROPN
ejpam-6262	250	1	+	+	CCONJ
ejpam-6262	250	2	y2	y2	PROPN
ejpam-6262	251	1	+	+	CCONJ
ejpam-6262	251	2	z2	z2	PROPN
ejpam-6262	251	3	(	(	PUNCT
ejpam-6262	251	4	1	1	NUM
ejpam-6262	251	5	,	,	PUNCT
ejpam-6262	251	6	1	1	NUM
ejpam-6262	251	7	,	,	PUNCT
ejpam-6262	251	8	1	1	X
ejpam-6262	251	9	)	)	PUNCT
ejpam-6262	251	10			NOUN
ejpam-6262	251	11	2	2	NUM
ejpam-6262	251	12	2	2	NUM
ejpam-6262	251	13	2	2	NUM
ejpam-6262	251	14	2	2	NUM
ejpam-6262	251	15	2	2	NUM
ejpam-6262	251	16	2	2	NUM
ejpam-6262	251	17	2	2	NUM
ejpam-6262	251	18	2	2	NUM
ejpam-6262	251	19	2	2	NUM
ejpam-6262	251	20			NUM
ejpam-6262	251	21	15	15	NUM
ejpam-6262	251	22	15	15	NUM
ejpam-6262	251	23	14	14	NUM
ejpam-6262	251	24	1.71123	1.71123	NUM
ejpam-6262	251	25	2.1616	2.1616	NUM
ejpam-6262	251	26	2.3883	2.3883	NUM
ejpam-6262	251	27	0.00270271	0.00270271	NUM
ejpam-6262	251	28	0.00270271	0.00270271	NUM
ejpam-6262	251	29	0.00270271	0.00270271	NUM
ejpam-6262	251	30	2	2	NUM
ejpam-6262	251	31	3x2cos	3x2cos	NUM
ejpam-6262	251	32	(	(	PUNCT
ejpam-6262	251	33	yz)−	yz)−	SYM
ejpam-6262	251	34	1/2	1/2	NUM
ejpam-6262	251	35	x2	x2	NOUN
ejpam-6262	251	36	−	−	PROPN
ejpam-6262	251	37	81(y	81(y	PROPN
ejpam-6262	252	1	+	+	CCONJ
ejpam-6262	252	2	0.1)2	0.1)2	ADJ
ejpam-6262	252	3	+	+	CCONJ
ejpam-6262	252	4	sin	sin	NOUN
ejpam-6262	252	5	(	(	PUNCT
ejpam-6262	252	6	z	z	NOUN
ejpam-6262	252	7	)	)	PUNCT
ejpam-6262	252	8	+	+	CCONJ
ejpam-6262	252	9	1.06	1.06	NUM
ejpam-6262	252	10	e−(xy	e−(xy	NOUN
ejpam-6262	252	11	)	)	PUNCT
ejpam-6262	253	1	+	+	NUM
ejpam-6262	253	2	20z	20z	NOUN
ejpam-6262	253	3	+	+	CCONJ
ejpam-6262	253	4	(	(	PUNCT
ejpam-6262	253	5	10π	10π	X
ejpam-6262	253	6	−	−	PROPN
ejpam-6262	253	7	3	3	NUM
ejpam-6262	253	8	)	)	PUNCT
ejpam-6262	253	9	/3	/3	VERB
ejpam-6262	253	10	(	(	PUNCT
ejpam-6262	253	11	1	1	NUM
ejpam-6262	253	12	,	,	PUNCT
ejpam-6262	253	13	1,−1	1,−1	NUM
ejpam-6262	253	14	)	)	PUNCT
ejpam-6262	253	15			NOUN
ejpam-6262	253	16	5.999	5.999	NUM
ejpam-6262	253	17	−0.052	−0.052	NOUN
ejpam-6262	253	18	0.052	0.052	NUM
ejpam-6262	253	19	2	2	NUM
ejpam-6262	253	20	−178.2	−178.2	NOUN
ejpam-6262	253	21	0.999	0.999	NUM
ejpam-6262	253	22	−0.368	−0.368	NOUN
ejpam-6262	253	23	−0.368	−0.368	NOUN
ejpam-6262	253	24	20	20	NUM
ejpam-6262	253	25			NOUN
ejpam-6262	253	26	16	16	NUM
ejpam-6262	253	27	14	14	NUM
ejpam-6262	253	28	13	13	NUM
ejpam-6262	253	29	1.84657	1.84657	NUM
ejpam-6262	253	30	2.2613	2.2613	NUM
ejpam-6262	253	31	2.81152	2.81152	NUM
ejpam-6262	253	32	0.70712121	0.70712121	NUM
ejpam-6262	253	33	0.01416426	0.01416426	NUM
ejpam-6262	253	34	−0.52299771	−0.52299771	PRON
ejpam-6262	253	35	3	3	NUM
ejpam-6262	253	36	x+	x+	PUNCT
ejpam-6262	253	37	ex−1	ex−1	NOUN
ejpam-6262	253	38	+	+	CCONJ
ejpam-6262	253	39	(	(	PUNCT
ejpam-6262	253	40	y	y	PROPN
ejpam-6262	253	41	+	+	CCONJ
ejpam-6262	253	42	z)2	z)2	PROPN
ejpam-6262	253	43	−	−	PROPN
ejpam-6262	253	44	27	27	NUM
ejpam-6262	253	45	ey−2	ey−2	PROPN
ejpam-6262	253	46	/	/	SYM
ejpam-6262	253	47	x+	x+	ADJ
ejpam-6262	253	48	z2	z2	NOUN
ejpam-6262	253	49	−	−	PROPN
ejpam-6262	253	50	10	10	NUM
ejpam-6262	253	51	y2	y2	NOUN
ejpam-6262	253	52	+	+	CCONJ
ejpam-6262	253	53	sin	sin	VERB
ejpam-6262	253	54	y	y	PROPN
ejpam-6262	253	55	−	−	PROPN
ejpam-6262	253	56	2	2	NUM
ejpam-6262	254	1	+	+	CCONJ
ejpam-6262	254	2	z	z	NOUN
ejpam-6262	254	3	−	−	NOUN
ejpam-6262	254	4	7	7	NUM
ejpam-6262	254	5	(	(	PUNCT
ejpam-6262	254	6	1.4	1.4	NUM
ejpam-6262	254	7	,	,	PUNCT
ejpam-6262	254	8	2.2	2.2	NUM
ejpam-6262	254	9	,	,	PUNCT
ejpam-6262	254	10	3.1	3.1	NUM
ejpam-6262	254	11	)	)	PUNCT
ejpam-6262	254	12			NOUN
ejpam-6262	254	13	2.492	2.492	NUM
ejpam-6262	254	14	10.6	10.6	NUM
ejpam-6262	254	15	10.6	10.6	NUM
ejpam-6262	254	16	−0.623	−0.623	NOUN
ejpam-6262	254	17	0.872	0.872	NUM
ejpam-6262	255	1	6.2	6.2	NUM
ejpam-6262	255	2	0	0	NUM
ejpam-6262	255	3	5.3999	5.3999	NUM
ejpam-6262	255	4	1	1	NUM
ejpam-6262	255	5			NOUN
ejpam-6262	255	6	9	9	NUM
ejpam-6262	255	7	9	9	NUM
ejpam-6262	255	8	8	8	NUM
ejpam-6262	255	9	1.877212	1.877212	NUM
ejpam-6262	255	10	2.2984	2.2984	NUM
ejpam-6262	255	11	2.79400	2.79400	NUM
ejpam-6262	255	12	0.99996491	0.99996491	NUM
ejpam-6262	255	13	2.00009396	2.00009396	NUM
ejpam-6262	255	14	2.99980941	2.99980941	NUM
ejpam-6262	255	15	4	4	NUM
ejpam-6262	255	16	15x+	15x+	NOUN
ejpam-6262	255	17	y2	y2	NOUN
ejpam-6262	255	18	−	−	PROPN
ejpam-6262	255	19	4z	4z	NOUN
ejpam-6262	255	20	−	−	PROPN
ejpam-6262	255	21	13	13	NUM
ejpam-6262	255	22	x2	x2	PROPN
ejpam-6262	255	23	+	+	PROPN
ejpam-6262	255	24	10y	10y	PROPN
ejpam-6262	255	25	−	−	PROPN
ejpam-6262	255	26	z	z	NOUN
ejpam-6262	255	27	−	−	PROPN
ejpam-6262	255	28	11	11	NUM
ejpam-6262	255	29	y3	y3	NOUN
ejpam-6262	255	30	−	−	PROPN
ejpam-6262	255	31	25z	25z	NOUN
ejpam-6262	256	1	+	+	CCONJ
ejpam-6262	256	2	22	22	NUM
ejpam-6262	256	3	(	(	PUNCT
ejpam-6262	256	4	3	3	NUM
ejpam-6262	256	5	,	,	PUNCT
ejpam-6262	256	6	3	3	NUM
ejpam-6262	256	7	,	,	PUNCT
ejpam-6262	256	8	2	2	X
ejpam-6262	256	9	)	)	PUNCT
ejpam-6262	256	10			NOUN
ejpam-6262	256	11	15	15	NUM
ejpam-6262	256	12	6	6	NUM
ejpam-6262	256	13	−4	−4	PROPN
ejpam-6262	256	14	6	6	NUM
ejpam-6262	256	15	10	10	NUM
ejpam-6262	256	16	−1	−1	NOUN
ejpam-6262	256	17	0	0	NUM
ejpam-6262	257	1	−18	−18	NUM
ejpam-6262	258	1	−25	−25	NOUN
ejpam-6262	258	2			NOUN
ejpam-6262	258	3	14	14	NUM
ejpam-6262	258	4	13	13	NUM
ejpam-6262	258	5	12	12	NUM
ejpam-6262	258	6	1.722963	1.722963	NUM
ejpam-6262	258	7	2.4581	2.4581	NUM
ejpam-6262	258	8	2.94914	2.94914	NUM
ejpam-6262	258	9	1.03640452	1.03640452	NUM
ejpam-6262	258	10	1.08570343	1.08570343	NUM
ejpam-6262	258	11	0.93119446	0.93119446	NUM
ejpam-6262	258	12	example	example	NOUN
ejpam-6262	258	13	3	3	NUM
ejpam-6262	258	14	.	.	PUNCT
ejpam-6262	258	15	suppose	suppose	VERB
ejpam-6262	258	16	the	the	DET
ejpam-6262	258	17	system	system	NOUN
ejpam-6262	258	18	of	of	ADP
ejpam-6262	258	19	four	four	NUM
ejpam-6262	258	20	nonlinear	nonlinear	ADJ
ejpam-6262	258	21	equations	equation	NOUN
ejpam-6262	258	22	as	as	SCONJ
ejpam-6262	258	23	follows	follow	VERB
ejpam-6262	258	24	:	:	PUNCT
ejpam-6262	258	25	f3	f3	ADJ
ejpam-6262	258	26	(	(	PUNCT
ejpam-6262	258	27	x	x	X
ejpam-6262	258	28	)	)	PUNCT
ejpam-6262	258	29	=	=	PUNCT
ejpam-6262	259	1			NUM
ejpam-6262	259	2	x1	x1	PROPN
ejpam-6262	260	1	+	+	CCONJ
ejpam-6262	260	2	x2	x2	PROPN
ejpam-6262	261	1	−	−	PROPN
ejpam-6262	261	2	2	2	NUM
ejpam-6262	261	3	=	=	SYM
ejpam-6262	261	4	0	0	NUM
ejpam-6262	261	5	x1x3	x1x3	PUNCT
ejpam-6262	262	1	+	+	X
ejpam-6262	262	2	x2x4	x2x4	X
ejpam-6262	262	3	=	=	SYM
ejpam-6262	262	4	0	0	NUM
ejpam-6262	262	5	x1x	x1x	PROPN
ejpam-6262	262	6	2	2	NUM
ejpam-6262	262	7	3	3	NUM
ejpam-6262	262	8	+	+	CCONJ
ejpam-6262	262	9	x2x	x2x	NUM
ejpam-6262	262	10	2	2	NUM
ejpam-6262	262	11	4	4	NUM
ejpam-6262	262	12	−	−	NOUN
ejpam-6262	262	13	2	2	NUM
ejpam-6262	262	14	3	3	NUM
ejpam-6262	262	15	=	=	SYM
ejpam-6262	262	16	0	0	NUM
ejpam-6262	262	17	x1x	x1x	PROPN
ejpam-6262	262	18	3	3	NUM
ejpam-6262	262	19	3	3	NUM
ejpam-6262	262	20	+	+	CCONJ
ejpam-6262	262	21	x2x	x2x	NUM
ejpam-6262	262	22	3	3	NUM
ejpam-6262	262	23	4	4	NUM
ejpam-6262	262	24	=	=	SYM
ejpam-6262	262	25	0	0	NUM
ejpam-6262	262	26	.	.	PUNCT
ejpam-6262	262	27	table	table	NOUN
ejpam-6262	262	28	3	3	NUM
ejpam-6262	262	29	:	:	PUNCT
ejpam-6262	262	30	analysis	analysis	NOUN
ejpam-6262	262	31	of	of	ADP
ejpam-6262	262	32	dfh	dfh	PROPN
ejpam-6262	262	33	with	with	ADP
ejpam-6262	262	34	broyden	broyden	PROPN
ejpam-6262	262	35	’s	’s	PART
ejpam-6262	262	36	method	method	NOUN
ejpam-6262	262	37	and	and	CCONJ
ejpam-6262	262	38	newton	newton	PROPN
ejpam-6262	262	39	’s	’s	PART
ejpam-6262	262	40	method	method	NOUN
ejpam-6262	262	41	for	for	ADP
ejpam-6262	262	42	systems	system	NOUN
ejpam-6262	262	43	portrayed	portray	VERB
ejpam-6262	262	44	in	in	ADP
ejpam-6262	262	45	example	example	NOUN
ejpam-6262	262	46	3	3	NUM
ejpam-6262	262	47	initial	initial	ADJ
ejpam-6262	262	48	guess	guess	NOUN
ejpam-6262	262	49	x0	x0	PROPN
ejpam-6262	263	1	i	i	PRON
ejpam-6262	263	2	coc	coc	VERB
ejpam-6262	263	3	root	root	NOUN
ejpam-6262	263	4	bfs	bfs	PROPN
ejpam-6262	263	5	n	n	CCONJ
ejpam-6262	263	6	dfh	dfh	PROPN
ejpam-6262	263	7	bfs	bfs	PROPN
ejpam-6262	263	8	n	n	PRON
ejpam-6262	263	9	dfh	dfh	PROPN
ejpam-6262	263	10	(	(	PUNCT
ejpam-6262	263	11	10,10,2	10,10,2	NUM
ejpam-6262	263	12	,	,	PUNCT
ejpam-6262	263	13	-1	-1	PUNCT
ejpam-6262	263	14	)	)	PUNCT
ejpam-6262	263	15	10	10	NUM
ejpam-6262	263	16	8	8	NUM
ejpam-6262	263	17	7	7	NUM
ejpam-6262	263	18	1.528	1.528	NUM
ejpam-6262	263	19	1.789	1.789	NUM
ejpam-6262	263	20	2.534	2.534	NUM
ejpam-6262	263	21	1.0000	1.0000	NUM
ejpam-6262	263	22	,	,	PUNCT
ejpam-6262	263	23	1.0000	1.0000	NUM
ejpam-6262	263	24	,	,	PUNCT
ejpam-6262	263	25	0.57735,−0.57735	0.57735,−0.57735	NUM
ejpam-6262	263	26	(	(	PUNCT
ejpam-6262	263	27	9.449645	9.449645	NUM
ejpam-6262	263	28	,	,	PUNCT
ejpam-6262	263	29	8.198130	8.198130	NUM
ejpam-6262	263	30	,	,	PUNCT
ejpam-6262	263	31	1.958279,−2.2299584	1.958279,−2.2299584	NUM
ejpam-6262	263	32	)	)	PUNCT
ejpam-6262	263	33	11	11	NUM
ejpam-6262	263	34	8	8	NUM
ejpam-6262	263	35	7	7	NUM
ejpam-6262	263	36	1.687	1.687	NUM
ejpam-6262	263	37	2.187	2.187	NUM
ejpam-6262	263	38	2.574	2.574	NUM
ejpam-6262	263	39	1.0000	1.0000	NUM
ejpam-6262	263	40	,	,	PUNCT
ejpam-6262	263	41	1.0000	1.0000	NUM
ejpam-6262	263	42	,	,	PUNCT
ejpam-6262	263	43	0.57735,−0.57735	0.57735,−0.57735	NUM
ejpam-6262	263	44	(	(	PUNCT
ejpam-6262	263	45	10,10	10,10	NUM
ejpam-6262	263	46	,	,	PUNCT
ejpam-6262	263	47	-1,2	-1,2	NUM
ejpam-6262	263	48	)	)	PUNCT
ejpam-6262	263	49	10	10	NUM
ejpam-6262	263	50	8	8	NUM
ejpam-6262	263	51	7	7	NUM
ejpam-6262	263	52	1.432	1.432	NUM
ejpam-6262	263	53	1.789	1.789	NUM
ejpam-6262	263	54	2.341	2.341	NUM
ejpam-6262	263	55	1.0000	1.0000	NUM
ejpam-6262	263	56	,	,	PUNCT
ejpam-6262	263	57	1.0000,−0.57735	1.0000,−0.57735	NUM
ejpam-6262	263	58	,	,	PUNCT
ejpam-6262	263	59	0.57735	0.57735	NUM
ejpam-6262	263	60	y.	y.	PROPN
ejpam-6262	263	61	al	al	PROPN
ejpam-6262	263	62	-	-	PUNCT
ejpam-6262	263	63	shorman	shorman	PROPN
ejpam-6262	263	64	et	et	PROPN
ejpam-6262	263	65	al	al	PROPN
ejpam-6262	263	66	.	.	PUNCT
ejpam-6262	263	67	/	/	SYM
ejpam-6262	263	68	eur	eur	PROPN
ejpam-6262	263	69	.	.	PUNCT
ejpam-6262	264	1	j.	j.	PROPN
ejpam-6262	264	2	pure	pure	PROPN
ejpam-6262	264	3	appl	appl	PROPN
ejpam-6262	264	4	.	.	PROPN
ejpam-6262	264	5	math	math	PROPN
ejpam-6262	264	6	,	,	PUNCT
ejpam-6262	264	7	18	18	NUM
ejpam-6262	264	8	(	(	PUNCT
ejpam-6262	264	9	3	3	NUM
ejpam-6262	264	10	)	)	PUNCT
ejpam-6262	264	11	(	(	PUNCT
ejpam-6262	264	12	2025	2025	NUM
ejpam-6262	264	13	)	)	PUNCT
ejpam-6262	264	14	,	,	PUNCT
ejpam-6262	264	15	6262	6262	NUM
ejpam-6262	264	16	12	12	NUM
ejpam-6262	264	17	of	of	ADP
ejpam-6262	264	18	20	20	NUM
ejpam-6262	264	19	example	example	NOUN
ejpam-6262	264	20	4	4	NUM
ejpam-6262	264	21	.	.	PUNCT
ejpam-6262	264	22	suppose	suppose	VERB
ejpam-6262	264	23	the	the	DET
ejpam-6262	264	24	system	system	NOUN
ejpam-6262	264	25	of	of	ADP
ejpam-6262	264	26	six	six	NUM
ejpam-6262	264	27	nonlinear	nonlinear	ADJ
ejpam-6262	264	28	equations	equation	NOUN
ejpam-6262	264	29	as	as	SCONJ
ejpam-6262	264	30	follows	follow	VERB
ejpam-6262	264	31	:	:	PUNCT
ejpam-6262	264	32	f4	f4	NUM
ejpam-6262	264	33	(	(	PUNCT
ejpam-6262	264	34	x	x	X
ejpam-6262	264	35	)	)	PUNCT
ejpam-6262	264	36	=	=	SYM
ejpam-6262	264	37			NUM
ejpam-6262	264	38	x21	x21	PROPN
ejpam-6262	265	1	+	+	CCONJ
ejpam-6262	265	2	x23	x23	NUM
ejpam-6262	265	3	−	−	NOUN
ejpam-6262	266	1	1	1	NUM
ejpam-6262	266	2	=	=	SYM
ejpam-6262	266	3	0	0	NUM
ejpam-6262	266	4	x22	x22	NOUN
ejpam-6262	267	1	+	+	CCONJ
ejpam-6262	267	2	x24	x24	NOUN
ejpam-6262	267	3	−	−	NOUN
ejpam-6262	267	4	1	1	NUM
ejpam-6262	268	1	=	=	SYM
ejpam-6262	268	2	0	0	PUNCT
ejpam-6262	269	1	x5x	x5x	NOUN
ejpam-6262	269	2	3	3	NUM
ejpam-6262	269	3	3	3	NUM
ejpam-6262	270	1	+	+	CCONJ
ejpam-6262	270	2	x6x	x6x	PROPN
ejpam-6262	270	3	3	3	NUM
ejpam-6262	270	4	4	4	NUM
ejpam-6262	270	5	=	=	SYM
ejpam-6262	270	6	0	0	PUNCT
ejpam-6262	271	1	x5x	x5x	NOUN
ejpam-6262	271	2	3	3	NUM
ejpam-6262	271	3	1	1	NUM
ejpam-6262	272	1	+	+	CCONJ
ejpam-6262	272	2	x6x	x6x	PROPN
ejpam-6262	272	3	3	3	NUM
ejpam-6262	272	4	2	2	NUM
ejpam-6262	272	5	=	=	SYM
ejpam-6262	272	6	0	0	NUM
ejpam-6262	272	7	x5x1x	x5x1x	SYM
ejpam-6262	272	8	2	2	NUM
ejpam-6262	272	9	3	3	NUM
ejpam-6262	272	10	+	+	CCONJ
ejpam-6262	272	11	x6x	x6x	PROPN
ejpam-6262	272	12	2	2	NUM
ejpam-6262	272	13	4x2	4x2	NUM
ejpam-6262	272	14	=	=	SYM
ejpam-6262	272	15	0	0	SYM
ejpam-6262	272	16	x5x3x	x5x3x	NUM
ejpam-6262	272	17	2	2	NUM
ejpam-6262	272	18	1	1	NUM
ejpam-6262	272	19	+	+	CCONJ
ejpam-6262	272	20	x6x	x6x	PROPN
ejpam-6262	272	21	2	2	NUM
ejpam-6262	272	22	2x4	2x4	NUM
ejpam-6262	272	23	=	=	SYM
ejpam-6262	272	24	0	0	NUM
ejpam-6262	272	25	.	.	PUNCT
ejpam-6262	272	26	table	table	NOUN
ejpam-6262	272	27	4	4	NUM
ejpam-6262	272	28	:	:	PUNCT
ejpam-6262	272	29	dfh	dfh	ADJ
ejpam-6262	272	30	analysis	analysis	NOUN
ejpam-6262	272	31	with	with	ADP
ejpam-6262	272	32	broyden	broyden	PROPN
ejpam-6262	272	33	’s	’s	PART
ejpam-6262	272	34	method	method	NOUN
ejpam-6262	272	35	and	and	CCONJ
ejpam-6262	272	36	newton	newton	PROPN
ejpam-6262	272	37	’s	’s	PART
ejpam-6262	272	38	method	method	NOUN
ejpam-6262	272	39	for	for	ADP
ejpam-6262	272	40	systems	system	NOUN
ejpam-6262	272	41	for	for	ADP
ejpam-6262	272	42	example	example	NOUN
ejpam-6262	272	43	4	4	NUM
ejpam-6262	272	44	initial	initial	ADJ
ejpam-6262	272	45	guess	guess	NOUN
ejpam-6262	272	46	x0	x0	PROPN
ejpam-6262	273	1	i	i	PRON
ejpam-6262	273	2	coc	coc	VERB
ejpam-6262	273	3	root	root	NOUN
ejpam-6262	273	4	bfs	bfs	PROPN
ejpam-6262	273	5	n	n	CCONJ
ejpam-6262	273	6	dfh	dfh	PROPN
ejpam-6262	273	7	bfs	bfs	PROPN
ejpam-6262	273	8	n	n	PRON
ejpam-6262	273	9	dfh	dfh	PROPN
ejpam-6262	273	10	(	(	PUNCT
ejpam-6262	273	11	3.5	3.5	NUM
ejpam-6262	273	12	,	,	PUNCT
ejpam-6262	273	13	4	4	NUM
ejpam-6262	273	14	,	,	PUNCT
ejpam-6262	273	15	6	6	NUM
ejpam-6262	273	16	,	,	PUNCT
ejpam-6262	273	17	5.5	5.5	NUM
ejpam-6262	273	18	,	,	PUNCT
ejpam-6262	273	19	2	2	NUM
ejpam-6262	273	20	,	,	PUNCT
ejpam-6262	273	21	1,−4	1,−4	NUM
ejpam-6262	273	22	)	)	PUNCT
ejpam-6262	273	23	9	9	NUM
ejpam-6262	273	24	7	7	NUM
ejpam-6262	273	25	6	6	NUM
ejpam-6262	273	26	1.632	1.632	NUM
ejpam-6262	273	27	2.277	2.277	NUM
ejpam-6262	273	28	2.435	2.435	NUM
ejpam-6262	273	29	0.5368	0.5368	NUM
ejpam-6262	273	30	,	,	PUNCT
ejpam-6262	273	31	0.9170	0.9170	NUM
ejpam-6262	273	32	,	,	PUNCT
ejpam-6262	273	33	0.8436	0.8436	NUM
ejpam-6262	273	34	,	,	PUNCT
ejpam-6262	273	35	0.3987	0.3987	NUM
ejpam-6262	273	36	,	,	PUNCT
ejpam-6262	273	37	0.0000,−0.0000	0.0000,−0.0000	X
ejpam-6262	273	38	(	(	PUNCT
ejpam-6262	273	39	2.5257	2.5257	NUM
ejpam-6262	273	40	,	,	PUNCT
ejpam-6262	273	41	5.0538	5.0538	NUM
ejpam-6262	273	42	,	,	PUNCT
ejpam-6262	273	43	5.8289	5.8289	NUM
ejpam-6262	273	44	,	,	PUNCT
ejpam-6262	273	45	2.1629	2.1629	NUM
ejpam-6262	273	46	,	,	PUNCT
ejpam-6262	273	47	2.4797,−4.9408	2.4797,−4.9408	NUM
ejpam-6262	273	48	)	)	PUNCT
ejpam-6262	273	49	9	9	NUM
ejpam-6262	273	50	7	7	NUM
ejpam-6262	273	51	6	6	NUM
ejpam-6262	273	52	1.714	1.714	NUM
ejpam-6262	273	53	2.321	2.321	NUM
ejpam-6262	273	54	2.498	2.498	NUM
ejpam-6262	273	55	0.5039	0.5039	NUM
ejpam-6262	273	56	,	,	PUNCT
ejpam-6262	273	57	0.8519	0.8519	NUM
ejpam-6262	273	58	,	,	PUNCT
ejpam-6262	273	59	0.8637	0.8637	NUM
ejpam-6262	273	60	,	,	PUNCT
ejpam-6262	273	61	0.5236,−0.0000	0.5236,−0.0000	NUM
ejpam-6262	273	62	,	,	PUNCT
ejpam-6262	273	63	0.0000	0.0000	NUM
ejpam-6262	273	64	(	(	PUNCT
ejpam-6262	273	65	2.4711	2.4711	NUM
ejpam-6262	273	66	,	,	PUNCT
ejpam-6262	273	67	4.3696	4.3696	NUM
ejpam-6262	273	68	,	,	PUNCT
ejpam-6262	273	69	6.2511	6.2511	NUM
ejpam-6262	273	70	,	,	PUNCT
ejpam-6262	273	71	1.4369	1.4369	NUM
ejpam-6262	273	72	,	,	PUNCT
ejpam-6262	273	73	1	1	NUM
ejpam-6262	273	74	,	,	PUNCT
ejpam-6262	273	75	9453,−4.4211	9453,−4.4211	NUM
ejpam-6262	273	76	)	)	PUNCT
ejpam-6262	273	77	9	9	NUM
ejpam-6262	273	78	7	7	NUM
ejpam-6262	273	79	6	6	NUM
ejpam-6262	273	80	1.786	1.786	NUM
ejpam-6262	273	81	2.625	2.625	NUM
ejpam-6262	273	82	2.542	2.542	NUM
ejpam-6262	273	83	0.3676	0.3676	NUM
ejpam-6262	273	84	,	,	PUNCT
ejpam-6262	273	85	0.9499	0.9499	NUM
ejpam-6262	273	86	,	,	PUNCT
ejpam-6262	273	87	0.9299	0.9299	NUM
ejpam-6262	273	88	,	,	PUNCT
ejpam-6262	273	89	0.3123	0.3123	NUM
ejpam-6262	273	90	,	,	PUNCT
ejpam-6262	273	91	0.0000	0.0000	NUM
ejpam-6262	273	92	,	,	PUNCT
ejpam-6262	273	93	0.0000	0.0000	NUM
ejpam-6262	273	94	example	example	NOUN
ejpam-6262	273	95	5	5	NUM
ejpam-6262	273	96	.	.	PUNCT
ejpam-6262	274	1	consider	consider	VERB
ejpam-6262	274	2	the	the	DET
ejpam-6262	274	3	following	follow	VERB
ejpam-6262	274	4	system	system	NOUN
ejpam-6262	274	5	of	of	ADP
ejpam-6262	274	6	ten	ten	NUM
ejpam-6262	274	7	nonlinear	nonlinear	ADJ
ejpam-6262	274	8	equations	equation	NOUN
ejpam-6262	274	9	:	:	PUNCT
ejpam-6262	275	1	f4	f4	X
ejpam-6262	275	2	(	(	PUNCT
ejpam-6262	275	3	x	x	X
ejpam-6262	275	4	)	)	PUNCT
ejpam-6262	275	5	=	=	PUNCT
ejpam-6262	275	6			ADJ
ejpam-6262	276	1	x1	x1	NOUN
ejpam-6262	277	1	−	−	PROPN
ejpam-6262	277	2	0.25428722	0.25428722	NUM
ejpam-6262	277	3	−	−	NOUN
ejpam-6262	277	4	0.18324757x4x3x9	0.18324757x4x3x9	NUM
ejpam-6262	277	5	=	=	SYM
ejpam-6262	277	6	0	0	NUM
ejpam-6262	277	7	,	,	PUNCT
ejpam-6262	277	8	x2	x2	PROPN
ejpam-6262	278	1	−	−	ADP
ejpam-6262	278	2	0.37842197	0.37842197	NUM
ejpam-6262	278	3	−	−	NOUN
ejpam-6262	278	4	0.16275449x1x10x6	0.16275449x1x10x6	NUM
ejpam-6262	278	5	=	=	SYM
ejpam-6262	278	6	0	0	NUM
ejpam-6262	278	7	,	,	PUNCT
ejpam-6262	278	8	x3	x3	VERB
ejpam-6262	278	9	−	−	PROPN
ejpam-6262	279	1	0.27162577	0.27162577	NUM
ejpam-6262	279	2	−	−	NOUN
ejpam-6262	279	3	0.16955071x1x2x10	0.16955071x1x2x10	NUM
ejpam-6262	279	4	=	=	SYM
ejpam-6262	279	5	0	0	NUM
ejpam-6262	279	6	,	,	PUNCT
ejpam-6262	279	7	x4	x4	PROPN
ejpam-6262	279	8	−	−	PROPN
ejpam-6262	279	9	0.19807914	0.19807914	NUM
ejpam-6262	279	10	−	−	NUM
ejpam-6262	279	11	0.15585316x7x1x6	0.15585316x7x1x6	NUM
ejpam-6262	280	1	=	=	SYM
ejpam-6262	280	2	0	0	NUM
ejpam-6262	280	3	,	,	PUNCT
ejpam-6262	280	4	x5	x5	NOUN
ejpam-6262	280	5	−	−	PROPN
ejpam-6262	280	6	0.44166728	0.44166728	NUM
ejpam-6262	280	7	−	−	NOUN
ejpam-6262	280	8	1.9950920x7x6x3	1.9950920x7x6x3	NUM
ejpam-6262	280	9	=	=	SYM
ejpam-6262	280	10	0	0	NUM
ejpam-6262	280	11	,	,	PUNCT
ejpam-6262	280	12	x6	x6	PROPN
ejpam-6262	280	13	−	−	PROPN
ejpam-6262	280	14	0.146541113	0.146541113	NUM
ejpam-6262	280	15	−	−	NOUN
ejpam-6262	280	16	0.18922793x8x5x10	0.18922793x8x5x10	NOUN
ejpam-6262	280	17	=	=	SYM
ejpam-6262	280	18	0	0	NUM
ejpam-6262	280	19	,	,	PUNCT
ejpam-6262	280	20	x7	x7	NOUN
ejpam-6262	280	21	−	−	ADP
ejpam-6262	280	22	0.42937161	0.42937161	NUM
ejpam-6262	280	23	−	−	NOUN
ejpam-6262	280	24	0.21180486x2x5x8	0.21180486x2x5x8	NOUN
ejpam-6262	280	25	=	=	SYM
ejpam-6262	280	26	0	0	NUM
ejpam-6262	280	27	,	,	PUNCT
ejpam-6262	280	28	x8	x8	PROPN
ejpam-6262	280	29	−	−	PROPN
ejpam-6262	280	30	0.07056438	0.07056438	NUM
ejpam-6262	280	31	−	−	NOUN
ejpam-6262	280	32	0.17081208x1x7x6	0.17081208x1x7x6	X
ejpam-6262	280	33	=	=	SYM
ejpam-6262	280	34	0	0	NUM
ejpam-6262	280	35	,	,	PUNCT
ejpam-6262	280	36	x9	x9	NOUN
ejpam-6262	280	37	−	−	ADP
ejpam-6262	280	38	0.34504906	0.34504906	NUM
ejpam-6262	280	39	−	−	NOUN
ejpam-6262	280	40	0.196127x10x6x8	0.196127x10x6x8	NOUN
ejpam-6262	280	41	=	=	SYM
ejpam-6262	280	42	0	0	NUM
ejpam-6262	280	43	,	,	PUNCT
ejpam-6262	280	44	x10	x10	PRON
ejpam-6262	280	45	−	−	PROPN
ejpam-6262	280	46	0.42651102	0.42651102	NUM
ejpam-6262	280	47	−	−	NOUN
ejpam-6262	280	48	0.21466544x4x8x1	0.21466544x4x8x1	PUNCT
ejpam-6262	281	1	=	=	PUNCT
ejpam-6262	281	2	0	0	NUM
ejpam-6262	281	3	,	,	PUNCT
ejpam-6262	281	4	for	for	ADP
ejpam-6262	281	5	these	these	DET
ejpam-6262	281	6	systems	system	NOUN
ejpam-6262	281	7	,	,	PUNCT
ejpam-6262	281	8	as	as	SCONJ
ejpam-6262	281	9	shown	show	VERB
ejpam-6262	281	10	in	in	ADP
ejpam-6262	281	11	tables	table	NOUN
ejpam-6262	281	12	1	1	NUM
ejpam-6262	281	13	-	-	SYM
ejpam-6262	281	14	5	5	NUM
ejpam-6262	281	15	,	,	PUNCT
ejpam-6262	281	16	it	it	PRON
ejpam-6262	281	17	is	be	AUX
ejpam-6262	281	18	evident	evident	ADJ
ejpam-6262	281	19	that	that	SCONJ
ejpam-6262	281	20	dfh	dfh	PROPN
ejpam-6262	281	21	is	be	AUX
ejpam-6262	281	22	faster	fast	ADJ
ejpam-6262	281	23	,	,	PUNCT
ejpam-6262	281	24	more	more	ADV
ejpam-6262	281	25	accurate	accurate	ADJ
ejpam-6262	281	26	,	,	PUNCT
ejpam-6262	281	27	and	and	CCONJ
ejpam-6262	281	28	had	have	VERB
ejpam-6262	281	29	fewer	few	ADJ
ejpam-6262	281	30	iterations	iteration	NOUN
ejpam-6262	281	31	than	than	ADP
ejpam-6262	281	32	bfs	bfs	NOUN
ejpam-6262	281	33	and	and	CCONJ
ejpam-6262	281	34	n.	n.	VERB
ejpam-6262	281	35	the	the	DET
ejpam-6262	281	36	above	above	ADJ
ejpam-6262	281	37	tables	table	NOUN
ejpam-6262	281	38	display	display	VERB
ejpam-6262	281	39	the	the	DET
ejpam-6262	281	40	outcomes	outcome	NOUN
ejpam-6262	281	41	of	of	ADP
ejpam-6262	281	42	y.	y.	PROPN
ejpam-6262	281	43	al	al	PROPN
ejpam-6262	281	44	-	-	PUNCT
ejpam-6262	281	45	shorman	shorman	PROPN
ejpam-6262	281	46	et	et	PROPN
ejpam-6262	281	47	al	al	PROPN
ejpam-6262	281	48	.	.	PUNCT
ejpam-6262	281	49	/	/	SYM
ejpam-6262	281	50	eur	eur	PROPN
ejpam-6262	281	51	.	.	PUNCT
ejpam-6262	282	1	j.	j.	PROPN
ejpam-6262	282	2	pure	pure	PROPN
ejpam-6262	282	3	appl	appl	PROPN
ejpam-6262	282	4	.	.	PROPN
ejpam-6262	282	5	math	math	PROPN
ejpam-6262	282	6	,	,	PUNCT
ejpam-6262	282	7	18	18	NUM
ejpam-6262	282	8	(	(	PUNCT
ejpam-6262	282	9	3	3	NUM
ejpam-6262	282	10	)	)	PUNCT
ejpam-6262	282	11	(	(	PUNCT
ejpam-6262	282	12	2025	2025	NUM
ejpam-6262	282	13	)	)	PUNCT
ejpam-6262	282	14	,	,	PUNCT
ejpam-6262	282	15	6262	6262	NUM
ejpam-6262	282	16	13	13	NUM
ejpam-6262	282	17	of	of	ADP
ejpam-6262	282	18	20	20	NUM
ejpam-6262	282	19	table	table	NOUN
ejpam-6262	282	20	5	5	NUM
ejpam-6262	282	21	:	:	PUNCT
ejpam-6262	282	22	dfh	dfh	ADJ
ejpam-6262	282	23	analysis	analysis	NOUN
ejpam-6262	282	24	with	with	ADP
ejpam-6262	282	25	broyden	broyden	PROPN
ejpam-6262	282	26	’s	’s	PART
ejpam-6262	282	27	method	method	NOUN
ejpam-6262	282	28	and	and	CCONJ
ejpam-6262	282	29	newton	newton	PROPN
ejpam-6262	282	30	’s	’s	PART
ejpam-6262	282	31	method	method	NOUN
ejpam-6262	282	32	for	for	ADP
ejpam-6262	282	33	systems	system	NOUN
ejpam-6262	282	34	with	with	ADP
ejpam-6262	282	35	respect	respect	NOUN
ejpam-6262	282	36	to	to	ADP
ejpam-6262	282	37	example	example	NOUN
ejpam-6262	282	38	5	5	NUM
ejpam-6262	282	39	i	i	PRON
ejpam-6262	282	40	coc	coc	VERB
ejpam-6262	282	41	root	root	NOUN
ejpam-6262	282	42	initial	initial	ADJ
ejpam-6262	282	43	guess	guess	NOUN
ejpam-6262	282	44	x0	x0	PROPN
ejpam-6262	282	45	bfs	bfs	NOUN
ejpam-6262	282	46	n	n	CCONJ
ejpam-6262	282	47	dfh	dfh	PROPN
ejpam-6262	282	48	bfs	bfs	PROPN
ejpam-6262	282	49	n	n	PRON
ejpam-6262	282	50	dfh	dfh	X
ejpam-6262	282	51	(	(	PUNCT
ejpam-6262	282	52	1	1	NUM
ejpam-6262	282	53	,	,	PUNCT
ejpam-6262	282	54	1	1	NUM
ejpam-6262	282	55	,	,	PUNCT
ejpam-6262	282	56	1	1	NUM
ejpam-6262	282	57	,	,	PUNCT
ejpam-6262	282	58	1	1	NUM
ejpam-6262	282	59	,	,	PUNCT
ejpam-6262	282	60	1	1	NUM
ejpam-6262	282	61	,	,	PUNCT
ejpam-6262	282	62	1	1	NUM
ejpam-6262	282	63	,	,	PUNCT
ejpam-6262	282	64	1	1	NUM
ejpam-6262	282	65	,	,	PUNCT
ejpam-6262	282	66	1	1	NUM
ejpam-6262	282	67	,	,	PUNCT
ejpam-6262	282	68	1	1	NUM
ejpam-6262	282	69	,	,	PUNCT
ejpam-6262	282	70	1	1	NUM
ejpam-6262	282	71	)	)	PUNCT
ejpam-6262	282	72	9	9	NUM
ejpam-6262	282	73	7	7	NUM
ejpam-6262	282	74	6	6	NUM
ejpam-6262	282	75	1.632	1.632	NUM
ejpam-6262	282	76	2.277	2.277	NUM
ejpam-6262	282	77	2.435	2.435	NUM
ejpam-6262	282	78	0.2578	0.2578	NUM
ejpam-6262	282	79	,	,	PUNCT
ejpam-6262	282	80	0.3810	0.3810	NUM
ejpam-6262	282	81	,	,	PUNCT
ejpam-6262	282	82	0.2878	0.2878	NUM
ejpam-6262	282	83	,	,	PUNCT
ejpam-6262	282	84	0.2006	0.2006	NUM
ejpam-6262	282	85	,	,	PUNCT
ejpam-6262	282	86	0.4452	0.4452	NUM
ejpam-6262	282	87	,	,	PUNCT
ejpam-6262	282	88	0.1491	0.1491	NUM
ejpam-6262	282	89	,	,	PUNCT
ejpam-6262	282	90	0.4320	0.4320	NUM
ejpam-6262	282	91	,	,	PUNCT
ejpam-6262	282	92	0.0734	0.0734	NUM
ejpam-6262	282	93	,	,	PUNCT
ejpam-6262	282	94	0.3459	0.3459	NUM
ejpam-6262	282	95	,	,	PUNCT
ejpam-6262	282	96	0.4273	0.4273	NUM
ejpam-6262	282	97	(	(	PUNCT
ejpam-6262	282	98	−	−	PROPN
ejpam-6262	282	99	0.3956,−1.3108,−0.3927	0.3956,−1.3108,−0.3927	PROPN
ejpam-6262	282	100	,	,	PUNCT
ejpam-6262	282	101	4.8163,−3.4359	4.8163,−3.4359	PRON
ejpam-6262	282	102	,	,	PUNCT
ejpam-6262	282	103	3.555	3.555	NUM
ejpam-6262	282	104	,	,	PUNCT
ejpam-6262	282	105	1.4476,−1.2372,−3.0907,−0.7174	1.4476,−1.2372,−3.0907,−0.7174	NUM
ejpam-6262	282	106	)	)	PUNCT
ejpam-6262	282	107	9	9	NUM
ejpam-6262	282	108	7	7	NUM
ejpam-6262	282	109	6	6	NUM
ejpam-6262	282	110	1.714	1.714	NUM
ejpam-6262	282	111	2.321	2.321	NUM
ejpam-6262	282	112	2.498	2.498	NUM
ejpam-6262	282	113	0.3452	0.3452	NUM
ejpam-6262	282	114	,	,	PUNCT
ejpam-6262	282	115	1.2453	1.2453	NUM
ejpam-6262	282	116	,	,	PUNCT
ejpam-6262	282	117	1.0342	1.0342	NUM
ejpam-6262	282	118	,	,	PUNCT
ejpam-6262	282	119	1.4352	1.4352	NUM
ejpam-6262	282	120	,	,	PUNCT
ejpam-6262	282	121	1.4533	1.4533	NUM
ejpam-6262	282	122	,	,	PUNCT
ejpam-6262	282	123	1.4563	1.4563	NUM
ejpam-6262	282	124	,	,	PUNCT
ejpam-6262	282	125	1.8453	1.8453	NUM
ejpam-6262	282	126	,	,	PUNCT
ejpam-6262	282	127	1.7453	1.7453	NUM
ejpam-6262	282	128	,	,	PUNCT
ejpam-6262	282	129	1.3435	1.3435	NUM
ejpam-6262	282	130	,	,	PUNCT
ejpam-6262	282	131	1.8464	1.8464	NUM
ejpam-6262	282	132	(	(	PUNCT
ejpam-6262	282	133	1.625	1.625	NUM
ejpam-6262	282	134	,	,	PUNCT
ejpam-6262	282	135	1.780	1.780	NUM
ejpam-6262	282	136	,	,	PUNCT
ejpam-6262	282	137	1.0811	1.0811	NUM
ejpam-6262	282	138	,	,	PUNCT
ejpam-6262	282	139	1.9293	1.9293	NUM
ejpam-6262	282	140	,	,	PUNCT
ejpam-6262	282	141	1.7757	1.7757	NUM
ejpam-6262	282	142	,	,	PUNCT
ejpam-6262	282	143	1.4867	1.4867	NUM
ejpam-6262	282	144	,	,	PUNCT
ejpam-6262	282	145	1.4358	1.4358	NUM
ejpam-6262	282	146	,	,	PUNCT
ejpam-6262	282	147	1.4467	1.4467	NUM
ejpam-6262	282	148	,	,	PUNCT
ejpam-6262	282	149	1.3063	1.3063	NUM
ejpam-6262	282	150	,	,	PUNCT
ejpam-6262	282	151	1.5085	1.5085	NUM
ejpam-6262	282	152	)	)	PUNCT
ejpam-6262	282	153	9	9	NUM
ejpam-6262	282	154	7	7	NUM
ejpam-6262	282	155	6	6	NUM
ejpam-6262	282	156	1.786	1.786	NUM
ejpam-6262	282	157	2.625	2.625	NUM
ejpam-6262	282	158	2.542	2.542	NUM
ejpam-6262	282	159	1.8430	1.8430	NUM
ejpam-6262	282	160	,	,	PUNCT
ejpam-6262	282	161	1.9683	1.9683	NUM
ejpam-6262	282	162	,	,	PUNCT
ejpam-6262	282	163	1.6191	1.6191	NUM
ejpam-6262	282	164	,	,	PUNCT
ejpam-6262	282	165	2.0850	2.0850	NUM
ejpam-6262	282	166	,	,	PUNCT
ejpam-6262	282	167	2.5636	2.5636	NUM
ejpam-6262	282	168	,	,	PUNCT
ejpam-6262	282	169	2.4194	2.4194	NUM
ejpam-6262	282	170	,	,	PUNCT
ejpam-6262	282	171	2.7151	2.7151	NUM
ejpam-6262	282	172	,	,	PUNCT
ejpam-6262	282	173	2.1386	2.1386	NUM
ejpam-6262	282	174	,	,	PUNCT
ejpam-6262	282	175	2.5682	2.5682	NUM
ejpam-6262	282	176	,	,	PUNCT
ejpam-6262	282	177	2.1907	2.1907	NUM
ejpam-6262	282	178	contrasting	contrast	VERB
ejpam-6262	282	179	newton	newton	PROPN
ejpam-6262	282	180	’s	’s	PART
ejpam-6262	282	181	method	method	NOUN
ejpam-6262	282	182	with	with	ADP
ejpam-6262	282	183	derivative	derivative	ADJ
ejpam-6262	282	184	-	-	PUNCT
ejpam-6262	282	185	free	free	ADJ
ejpam-6262	282	186	homeier	homeier	NOUN
ejpam-6262	282	187	and	and	CCONJ
ejpam-6262	282	188	broyden	broyden	NOUN
ejpam-6262	282	189	’s	’s	PART
ejpam-6262	282	190	method	method	NOUN
ejpam-6262	282	191	,	,	PUNCT
ejpam-6262	282	192	in	in	ADP
ejpam-6262	282	193	which	which	PRON
ejpam-6262	282	194	:	:	PUNCT
ejpam-6262	282	195	dfh	dfh	PROPN
ejpam-6262	282	196	:	:	PUNCT
ejpam-6262	282	197	derivative	derivative	ADJ
ejpam-6262	282	198	-	-	PUNCT
ejpam-6262	282	199	free	free	ADJ
ejpam-6262	282	200	homeier	homeier	ADJ
ejpam-6262	282	201	method	method	NOUN
ejpam-6262	282	202	n	n	CCONJ
ejpam-6262	282	203	:	:	PUNCT
ejpam-6262	282	204	newton	newton	PROPN
ejpam-6262	282	205	’s	’s	PART
ejpam-6262	282	206	method	method	PROPN
ejpam-6262	282	207	bfs	bfs	PROPN
ejpam-6262	282	208	:	:	PUNCT
ejpam-6262	282	209	broyden	broyden	NOUN
ejpam-6262	282	210	’s	’s	PART
ejpam-6262	282	211	method	method	NOUN
ejpam-6262	282	212	for	for	ADP
ejpam-6262	282	213	secant	secant	ADJ
ejpam-6262	282	214	method	method	NOUN
ejpam-6262	282	215	i	i	PRON
ejpam-6262	282	216	:	:	PUNCT
ejpam-6262	282	217	number	number	NOUN
ejpam-6262	282	218	of	of	ADP
ejpam-6262	282	219	iterations	iteration	NOUN
ejpam-6262	282	220	to	to	PART
ejpam-6262	282	221	approximate	approximate	VERB
ejpam-6262	282	222	the	the	DET
ejpam-6262	282	223	root	root	NOUN
ejpam-6262	282	224	coc	coc	NOUN
ejpam-6262	282	225	:	:	PUNCT
ejpam-6262	282	226	computational	computational	ADJ
ejpam-6262	282	227	order	order	NOUN
ejpam-6262	282	228	of	of	ADP
ejpam-6262	282	229	convergence	convergence	NOUN
ejpam-6262	282	230	the	the	DET
ejpam-6262	282	231	computer	computer	NOUN
ejpam-6262	282	232	convergence	convergence	NOUN
ejpam-6262	282	233	order	order	NOUN
ejpam-6262	282	234	for	for	ADP
ejpam-6262	282	235	dfh	dfh	PROPN
ejpam-6262	282	236	is	be	AUX
ejpam-6262	282	237	around	around	ADP
ejpam-6262	282	238	2.5	2.5	NUM
ejpam-6262	282	239	.	.	PUNCT
ejpam-6262	283	1	the	the	DET
ejpam-6262	283	2	approach	approach	NOUN
ejpam-6262	283	3	in	in	ADP
ejpam-6262	283	4	question	question	NOUN
ejpam-6262	283	5	exhibits	exhibit	VERB
ejpam-6262	283	6	superior	superior	ADJ
ejpam-6262	283	7	performance	performance	NOUN
ejpam-6262	283	8	compared	compare	VERB
ejpam-6262	283	9	to	to	ADP
ejpam-6262	283	10	both	both	DET
ejpam-6262	283	11	the	the	DET
ejpam-6262	283	12	newton	newton	PROPN
ejpam-6262	283	13	method	method	NOUN
ejpam-6262	283	14	and	and	CCONJ
ejpam-6262	283	15	the	the	DET
ejpam-6262	283	16	secant	secant	ADJ
ejpam-6262	283	17	method	method	NOUN
ejpam-6262	283	18	.	.	PUNCT
ejpam-6262	284	1	following	follow	VERB
ejpam-6262	284	2	this	this	PRON
ejpam-6262	284	3	,	,	PUNCT
ejpam-6262	284	4	the	the	DET
ejpam-6262	284	5	approach	approach	NOUN
ejpam-6262	284	6	used	use	VERB
ejpam-6262	284	7	for	for	ADP
ejpam-6262	284	8	addressing	address	VERB
ejpam-6262	284	9	non	non	ADJ
ejpam-6262	284	10	-	-	ADJ
ejpam-6262	284	11	linear	linear	ADJ
ejpam-6262	284	12	equation	equation	NOUN
ejpam-6262	284	13	systems	system	NOUN
ejpam-6262	284	14	was	be	AUX
ejpam-6262	284	15	utilized	utilize	VERB
ejpam-6262	284	16	.	.	PUNCT
ejpam-6262	285	1	the	the	DET
ejpam-6262	285	2	method	method	NOUN
ejpam-6262	285	3	was	be	AUX
ejpam-6262	285	4	implemented	implement	VERB
ejpam-6262	285	5	in	in	ADP
ejpam-6262	285	6	sets	set	NOUN
ejpam-6262	285	7	of	of	ADP
ejpam-6262	285	8	non	non	ADJ
ejpam-6262	285	9	-	-	ADJ
ejpam-6262	285	10	linear	linear	ADJ
ejpam-6262	285	11	equations	equation	NOUN
ejpam-6262	285	12	,	,	PUNCT
ejpam-6262	285	13	yielding	yield	VERB
ejpam-6262	285	14	favorable	favorable	ADJ
ejpam-6262	285	15	results	result	NOUN
ejpam-6262	285	16	.	.	PUNCT
ejpam-6262	286	1	here	here	ADV
ejpam-6262	286	2	,	,	PUNCT
ejpam-6262	286	3	implementing	implement	VERB
ejpam-6262	286	4	the	the	DET
ejpam-6262	286	5	approach	approach	NOUN
ejpam-6262	286	6	in	in	ADP
ejpam-6262	286	7	non	non	ADJ
ejpam-6262	286	8	-	-	ADJ
ejpam-6262	286	9	linear	linear	ADJ
ejpam-6262	286	10	equation	equation	NOUN
ejpam-6262	286	11	systems	system	NOUN
ejpam-6262	286	12	poses	pose	VERB
ejpam-6262	286	13	some	some	DET
ejpam-6262	286	14	challenges	challenge	NOUN
ejpam-6262	286	15	.	.	PUNCT
ejpam-6262	287	1	in	in	ADP
ejpam-6262	287	2	the	the	DET
ejpam-6262	287	3	context	context	NOUN
ejpam-6262	287	4	of	of	ADP
ejpam-6262	287	5	the	the	DET
ejpam-6262	287	6	improved	improved	ADJ
ejpam-6262	287	7	newton	newton	PROPN
ejpam-6262	287	8	technique	technique	NOUN
ejpam-6262	287	9	,	,	PUNCT
ejpam-6262	287	10	the	the	DET
ejpam-6262	287	11	acquisition	acquisition	NOUN
ejpam-6262	287	12	of	of	ADP
ejpam-6262	287	13	jacobian	jacobian	ADJ
ejpam-6262	287	14	matrices	matrix	NOUN
ejpam-6262	287	15	is	be	AUX
ejpam-6262	287	16	a	a	DET
ejpam-6262	287	17	necessary	necessary	ADJ
ejpam-6262	287	18	step	step	NOUN
ejpam-6262	287	19	in	in	ADP
ejpam-6262	287	20	the	the	DET
ejpam-6262	287	21	resolution	resolution	NOUN
ejpam-6262	287	22	of	of	ADP
ejpam-6262	287	23	nonlinear	nonlinear	ADJ
ejpam-6262	287	24	equi	equi	NOUN
ejpam-6262	287	25	-	-	PUNCT
ejpam-6262	287	26	tion	tion	NOUN
ejpam-6262	287	27	systems	system	NOUN
ejpam-6262	287	28	.	.	PUNCT
ejpam-6262	288	1	however	however	ADV
ejpam-6262	288	2	,	,	PUNCT
ejpam-6262	288	3	in	in	ADP
ejpam-6262	288	4	the	the	DET
ejpam-6262	288	5	context	context	NOUN
ejpam-6262	288	6	of	of	ADP
ejpam-6262	288	7	this	this	DET
ejpam-6262	288	8	approach	approach	NOUN
ejpam-6262	288	9	,	,	PUNCT
ejpam-6262	288	10	the	the	DET
ejpam-6262	288	11	jacobian	jacobian	ADJ
ejpam-6262	288	12	matrix	matrix	NOUN
ejpam-6262	288	13	is	be	AUX
ejpam-6262	288	14	transformed	transform	VERB
ejpam-6262	288	15	into	into	ADP
ejpam-6262	288	16	a	a	DET
ejpam-6262	288	17	vector	vector	NOUN
ejpam-6262	288	18	.	.	PUNCT
ejpam-6262	289	1	hence	hence	ADV
ejpam-6262	289	2	,	,	PUNCT
ejpam-6262	289	3	the	the	DET
ejpam-6262	289	4	task	task	NOUN
ejpam-6262	289	5	at	at	ADP
ejpam-6262	289	6	hand	hand	NOUN
ejpam-6262	289	7	included	include	VERB
ejpam-6262	289	8	determining	determine	VERB
ejpam-6262	289	9	the	the	DET
ejpam-6262	289	10	inverse	inverse	NOUN
ejpam-6262	289	11	of	of	ADP
ejpam-6262	289	12	the	the	DET
ejpam-6262	289	13	vector	vector	NOUN
ejpam-6262	289	14	.	.	PUNCT
ejpam-6262	290	1	broyden	broyden	PROPN
ejpam-6262	290	2	’s	’s	PART
ejpam-6262	290	3	technique	technique	NOUN
ejpam-6262	290	4	was	be	AUX
ejpam-6262	290	5	used	use	VERB
ejpam-6262	290	6	as	as	ADP
ejpam-6262	290	7	a	a	DET
ejpam-6262	290	8	means	means	NOUN
ejpam-6262	290	9	to	to	PART
ejpam-6262	290	10	address	address	VERB
ejpam-6262	290	11	the	the	DET
ejpam-6262	290	12	challenge	challenge	NOUN
ejpam-6262	290	13	.	.	PUNCT
ejpam-6262	291	1	using	use	VERB
ejpam-6262	291	2	the	the	DET
ejpam-6262	291	3	methodology	methodology	NOUN
ejpam-6262	291	4	used	use	VERB
ejpam-6262	291	5	in	in	ADP
ejpam-6262	291	6	broyden	broyden	PROPN
ejpam-6262	291	7	’s	’s	PART
ejpam-6262	291	8	approach	approach	NOUN
ejpam-6262	291	9	,	,	PUNCT
ejpam-6262	291	10	the	the	DET
ejpam-6262	291	11	derived	derive	VERB
ejpam-6262	291	12	equations	equation	NOUN
ejpam-6262	291	13	for	for	ADP
ejpam-6262	291	14	systems	system	NOUN
ejpam-6262	291	15	of	of	ADP
ejpam-6262	291	16	non	non	ADJ
ejpam-6262	291	17	-	-	ADJ
ejpam-6262	291	18	linear	linear	ADJ
ejpam-6262	291	19	equations	equation	NOUN
ejpam-6262	291	20	with	with	ADP
ejpam-6262	291	21	varying	vary	VERB
ejpam-6262	291	22	numbers	number	NOUN
ejpam-6262	291	23	of	of	ADP
ejpam-6262	291	24	variables	variable	NOUN
ejpam-6262	291	25	(	(	PUNCT
ejpam-6262	291	26	two	two	NUM
ejpam-6262	291	27	,	,	PUNCT
ejpam-6262	291	28	three	three	NUM
ejpam-6262	291	29	,	,	PUNCT
ejpam-6262	291	30	four	four	NUM
ejpam-6262	291	31	,	,	PUNCT
ejpam-6262	291	32	six	six	NUM
ejpam-6262	291	33	and	and	CCONJ
ejpam-6262	291	34	ten	ten	NUM
ejpam-6262	291	35	)	)	PUNCT
ejpam-6262	291	36	were	be	AUX
ejpam-6262	291	37	similarly	similarly	ADV
ejpam-6262	291	38	promising	promising	ADJ
ejpam-6262	291	39	,	,	PUNCT
ejpam-6262	291	40	similar	similar	ADJ
ejpam-6262	291	41	to	to	ADP
ejpam-6262	291	42	the	the	DET
ejpam-6262	291	43	scenario	scenario	NOUN
ejpam-6262	291	44	with	with	ADP
ejpam-6262	291	45	a	a	DET
ejpam-6262	291	46	single	single	ADJ
ejpam-6262	291	47	variable	variable	NOUN
ejpam-6262	291	48	.	.	PUNCT
ejpam-6262	292	1	thus	thus	ADV
ejpam-6262	292	2	,	,	PUNCT
ejpam-6262	292	3	the	the	DET
ejpam-6262	292	4	purpose	purpose	NOUN
ejpam-6262	292	5	was	be	AUX
ejpam-6262	292	6	achieved	achieve	VERB
ejpam-6262	292	7	successfully	successfully	ADV
ejpam-6262	292	8	in	in	ADP
ejpam-6262	292	9	that	that	DET
ejpam-6262	292	10	instance	instance	NOUN
ejpam-6262	292	11	.	.	PUNCT
ejpam-6262	293	1	however	however	ADV
ejpam-6262	293	2	,	,	PUNCT
ejpam-6262	293	3	the	the	DET
ejpam-6262	293	4	derivative	derivative	ADJ
ejpam-6262	293	5	component	component	NOUN
ejpam-6262	293	6	can	can	AUX
ejpam-6262	293	7	not	not	PART
ejpam-6262	293	8	be	be	AUX
ejpam-6262	293	9	eliminated	eliminate	VERB
ejpam-6262	293	10	using	use	VERB
ejpam-6262	293	11	the	the	DET
ejpam-6262	293	12	broyden	broyden	ADJ
ejpam-6262	293	13	technique	technique	NOUN
ejpam-6262	293	14	.	.	PUNCT
ejpam-6262	294	1	6	6	NUM
ejpam-6262	294	2	.	.	X
ejpam-6262	294	3	applications	application	NOUN
ejpam-6262	294	4	to	to	PART
ejpam-6262	294	5	assess	assess	VERB
ejpam-6262	294	6	the	the	DET
ejpam-6262	294	7	suitability	suitability	NOUN
ejpam-6262	294	8	of	of	ADP
ejpam-6262	294	9	the	the	DET
ejpam-6262	294	10	suggested	suggest	VERB
ejpam-6262	294	11	scheme	scheme	NOUN
ejpam-6262	294	12	for	for	ADP
ejpam-6262	294	13	real	real	ADJ
ejpam-6262	294	14	-	-	PUNCT
ejpam-6262	294	15	world	world	NOUN
ejpam-6262	294	16	challenges	challenge	NOUN
ejpam-6262	294	17	,	,	PUNCT
ejpam-6262	294	18	we	we	PRON
ejpam-6262	294	19	implement	implement	VERB
ejpam-6262	294	20	it	it	PRON
ejpam-6262	294	21	on	on	ADP
ejpam-6262	294	22	the	the	DET
ejpam-6262	294	23	mixed	mixed	ADJ
ejpam-6262	294	24	hammerstein	hammerstein	PROPN
ejpam-6262	294	25	integral	integral	ADJ
ejpam-6262	294	26	equation	equation	NOUN
ejpam-6262	294	27	.	.	PUNCT
ejpam-6262	295	1	y.	y.	PROPN
ejpam-6262	295	2	al	al	PROPN
ejpam-6262	295	3	-	-	PUNCT
ejpam-6262	295	4	shorman	shorman	PROPN
ejpam-6262	295	5	et	et	PROPN
ejpam-6262	295	6	al	al	PROPN
ejpam-6262	295	7	.	.	PUNCT
ejpam-6262	295	8	/	/	SYM
ejpam-6262	295	9	eur	eur	PROPN
ejpam-6262	295	10	.	.	PUNCT
ejpam-6262	296	1	j.	j.	PROPN
ejpam-6262	296	2	pure	pure	PROPN
ejpam-6262	296	3	appl	appl	PROPN
ejpam-6262	296	4	.	.	PROPN
ejpam-6262	296	5	math	math	PROPN
ejpam-6262	296	6	,	,	PUNCT
ejpam-6262	296	7	18	18	NUM
ejpam-6262	296	8	(	(	PUNCT
ejpam-6262	296	9	3	3	NUM
ejpam-6262	296	10	)	)	PUNCT
ejpam-6262	296	11	(	(	PUNCT
ejpam-6262	296	12	2025	2025	NUM
ejpam-6262	296	13	)	)	PUNCT
ejpam-6262	296	14	,	,	PUNCT
ejpam-6262	296	15	6262	6262	NUM
ejpam-6262	296	16	14	14	NUM
ejpam-6262	296	17	of	of	ADP
ejpam-6262	296	18	20	20	NUM
ejpam-6262	296	19	problem	problem	NOUN
ejpam-6262	296	20	1	1	NUM
ejpam-6262	296	21	suppose	suppose	VERB
ejpam-6262	296	22	that	that	SCONJ
ejpam-6262	296	23	the	the	DET
ejpam-6262	296	24	mixed	mixed	ADJ
ejpam-6262	296	25	hammerstein	hammerstein	PROPN
ejpam-6262	296	26	integral	integral	ADJ
ejpam-6262	296	27	equation	equation	NOUN
ejpam-6262	296	28	[	[	X
ejpam-6262	296	29	28	28	NUM
ejpam-6262	296	30	]	]	X
ejpam-6262	296	31	:	:	PUNCT
ejpam-6262	296	32	x	x	SYM
ejpam-6262	296	33	(	(	PUNCT
ejpam-6262	296	34	s	s	X
ejpam-6262	296	35	)	)	PUNCT
ejpam-6262	296	36	=	=	SYM
ejpam-6262	296	37	1	1	NUM
ejpam-6262	296	38	+	+	CCONJ
ejpam-6262	296	39	1	1	NUM
ejpam-6262	296	40	5	5	NUM
ejpam-6262	296	41	∫	∫	NOUN
ejpam-6262	296	42	1	1	NUM
ejpam-6262	296	43	0	0	NUM
ejpam-6262	296	44	g(s	g(s	PROPN
ejpam-6262	296	45	,	,	PUNCT
ejpam-6262	296	46	t	t	PROPN
ejpam-6262	296	47	)	)	PUNCT
ejpam-6262	296	48	x(t3	x(t3	PUNCT
ejpam-6262	297	1	dt	dt	X
ejpam-6262	297	2	.	.	PUNCT
ejpam-6262	298	1	let	let	VERB
ejpam-6262	298	2	x	x	SYM
ejpam-6262	298	3	∈	∈	PROPN
ejpam-6262	298	4	c	c	X
ejpam-6262	299	1	[	[	X
ejpam-6262	299	2	0	0	NUM
ejpam-6262	299	3	,	,	PUNCT
ejpam-6262	299	4	1	1	NUM
ejpam-6262	299	5	]	]	PUNCT
ejpam-6262	299	6	,	,	PUNCT
ejpam-6262	299	7	and	and	CCONJ
ejpam-6262	299	8	s	s	PROPN
ejpam-6262	299	9	,	,	PUNCT
ejpam-6262	299	10	t	t	PROPN
ejpam-6262	299	11	∈	∈	PROPN
ejpam-6262	300	1	[	[	X
ejpam-6262	300	2	0	0	NUM
ejpam-6262	300	3	,	,	PUNCT
ejpam-6262	300	4	1	1	NUM
ejpam-6262	300	5	]	]	PUNCT
ejpam-6262	300	6	and	and	CCONJ
ejpam-6262	300	7	let	let	VERB
ejpam-6262	300	8	the	the	DET
ejpam-6262	300	9	kernel	kernel	PROPN
ejpam-6262	300	10	g(s	g(s	PROPN
ejpam-6262	300	11	,	,	PUNCT
ejpam-6262	300	12	t	t	PROPN
ejpam-6262	300	13	)	)	PUNCT
ejpam-6262	300	14	be	be	AUX
ejpam-6262	300	15	expressed	express	VERB
ejpam-6262	300	16	as	as	ADP
ejpam-6262	300	17	g	g	PROPN
ejpam-6262	300	18	(	(	PUNCT
ejpam-6262	300	19	s	s	PROPN
ejpam-6262	300	20	,	,	PUNCT
ejpam-6262	300	21	t	t	PROPN
ejpam-6262	300	22	)	)	PUNCT
ejpam-6262	300	23	=	=	PRON
ejpam-6262	300	24	{	{	PUNCT
ejpam-6262	300	25	(	(	PUNCT
ejpam-6262	300	26	1−	1−	NUM
ejpam-6262	300	27	s	s	NOUN
ejpam-6262	300	28	)	)	PUNCT
ejpam-6262	300	29	t	t	NOUN
ejpam-6262	300	30	if	if	SCONJ
ejpam-6262	300	31	t	t	PROPN
ejpam-6262	300	32	≤	≤	X
ejpam-6262	300	33	s	s	PART
ejpam-6262	300	34	(	(	PUNCT
ejpam-6262	300	35	1−	1−	NUM
ejpam-6262	300	36	t)s	t)s	NUM
ejpam-6262	300	37	,	,	PUNCT
ejpam-6262	300	38	if	if	SCONJ
ejpam-6262	300	39	s	s	VERB
ejpam-6262	300	40	≤	≤	X
ejpam-6262	300	41	t	t	NOUN
ejpam-6262	300	42	.	.	PUNCT
ejpam-6262	301	1	the	the	DET
ejpam-6262	301	2	gauss	gauss	PROPN
ejpam-6262	301	3	-	-	PUNCT
ejpam-6262	301	4	legendre	legendre	PROPN
ejpam-6262	301	5	quadrature	quadrature	NOUN
ejpam-6262	301	6	formula	formula	NOUN
ejpam-6262	301	7	is	be	AUX
ejpam-6262	301	8	applied	apply	VERB
ejpam-6262	301	9	to	to	PART
ejpam-6262	301	10	convert	convert	VERB
ejpam-6262	301	11	the	the	DET
ejpam-6262	301	12	integral	integral	ADJ
ejpam-6262	301	13	equation	equation	NOUN
ejpam-6262	301	14	into	into	ADP
ejpam-6262	301	15	a	a	DET
ejpam-6262	301	16	finite	finite	ADJ
ejpam-6262	301	17	-	-	ADJ
ejpam-6262	301	18	dimensional	dimensional	ADJ
ejpam-6262	301	19	problem	problem	NOUN
ejpam-6262	301	20	,	,	PUNCT
ejpam-6262	301	21	as	as	SCONJ
ejpam-6262	301	22	specified	specify	VERB
ejpam-6262	301	23	by∫	by∫	PROPN
ejpam-6262	301	24	1	1	NUM
ejpam-6262	301	25	0	0	NUM
ejpam-6262	301	26	f(t)dt	f(t)dt	PROPN
ejpam-6262	301	27	≈	≈	PROPN
ejpam-6262	301	28	8∑	8∑	NUM
ejpam-6262	301	29	j=1	j=1	NOUN
ejpam-6262	301	30	ωjf(tj	ωjf(tj	NOUN
ejpam-6262	301	31	)	)	PUNCT
ejpam-6262	301	32	,	,	PUNCT
ejpam-6262	301	33	in	in	ADP
ejpam-6262	301	34	which	which	PRON
ejpam-6262	301	35	the	the	DET
ejpam-6262	301	36	abscissas	abscissas	PROPN
ejpam-6262	301	37	tj	tj	PROPN
ejpam-6262	301	38	and	and	CCONJ
ejpam-6262	301	39	the	the	DET
ejpam-6262	301	40	weights	weight	NOUN
ejpam-6262	301	41	ωj	ωj	VERB
ejpam-6262	301	42	are	be	AUX
ejpam-6262	301	43	determined	determine	VERB
ejpam-6262	301	44	for	for	ADP
ejpam-6262	301	45	n	n	NOUN
ejpam-6262	301	46	=	=	SYM
ejpam-6262	301	47	8	8	NUM
ejpam-6262	301	48	by	by	ADP
ejpam-6262	301	49	the	the	DET
ejpam-6262	301	50	gausslegendre	gausslegendre	NOUN
ejpam-6262	301	51	quadrature	quadrature	NOUN
ejpam-6262	301	52	formula	formula	NOUN
ejpam-6262	301	53	.	.	PUNCT
ejpam-6262	302	1	suppose	suppose	VERB
ejpam-6262	302	2	x	x	X
ejpam-6262	302	3	(	(	PUNCT
ejpam-6262	302	4	ti	ti	NOUN
ejpam-6262	302	5	)	)	PUNCT
ejpam-6262	302	6	=	=	SYM
ejpam-6262	302	7	xi	xi	PROPN
ejpam-6262	302	8	,	,	PUNCT
ejpam-6262	302	9	for	for	ADP
ejpam-6262	302	10	i	i	PROPN
ejpam-6262	302	11	=	=	SYM
ejpam-6262	302	12	1	1	NUM
ejpam-6262	302	13	,	,	PUNCT
ejpam-6262	302	14	2	2	NUM
ejpam-6262	302	15	,	,	PUNCT
ejpam-6262	302	16	3	3	NUM
ejpam-6262	302	17	,	,	PUNCT
ejpam-6262	302	18	.	.	PUNCT
ejpam-6262	302	19	.	.	PUNCT
ejpam-6262	303	1	.	.	PUNCT
ejpam-6262	304	1	,	,	PUNCT
ejpam-6262	304	2	8	8	NUM
ejpam-6262	304	3	,	,	PUNCT
ejpam-6262	304	4	therefore	therefore	ADV
ejpam-6262	304	5	,	,	PUNCT
ejpam-6262	304	6	we	we	PRON
ejpam-6262	304	7	derive	derive	VERB
ejpam-6262	304	8	the	the	DET
ejpam-6262	304	9	subsequent	subsequent	ADJ
ejpam-6262	304	10	set	set	NOUN
ejpam-6262	304	11	of	of	ADP
ejpam-6262	304	12	nonlinear	nonlinear	ADJ
ejpam-6262	304	13	equations	equation	NOUN
ejpam-6262	304	14	.	.	PUNCT
ejpam-6262	305	1	xi	xi	X
ejpam-6262	306	1	−	−	PROPN
ejpam-6262	307	1	1−	1−	NUM
ejpam-6262	307	2	1	1	NUM
ejpam-6262	307	3	5	5	NUM
ejpam-6262	307	4	8∑	8∑	NUM
ejpam-6262	307	5	j=1	j=1	ADJ
ejpam-6262	307	6	aijx	aijx	PROPN
ejpam-6262	307	7	3	3	NUM
ejpam-6262	307	8	j	j	PROPN
ejpam-6262	307	9	=	=	SYM
ejpam-6262	307	10	0	0	PROPN
ejpam-6262	307	11	,	,	PUNCT
ejpam-6262	307	12	j	j	PROPN
ejpam-6262	307	13	=	=	SYM
ejpam-6262	307	14	1	1	NUM
ejpam-6262	307	15	,	,	PUNCT
ejpam-6262	307	16	2	2	NUM
ejpam-6262	307	17	,	,	PUNCT
ejpam-6262	307	18	·	·	PUNCT
ejpam-6262	307	19	·	·	PUNCT
ejpam-6262	307	20	·	·	PUNCT
ejpam-6262	307	21	,	,	PUNCT
ejpam-6262	307	22	8	8	NUM
ejpam-6262	307	23	,	,	PUNCT
ejpam-6262	307	24	where	where	SCONJ
ejpam-6262	307	25	aij	aij	PROPN
ejpam-6262	307	26	=	=	X
ejpam-6262	307	27	{	{	PUNCT
ejpam-6262	307	28	ωj	ωj	ADP
ejpam-6262	307	29	tj(1−	tj(1−	PROPN
ejpam-6262	307	30	ti	ti	NOUN
ejpam-6262	307	31	)	)	PUNCT
ejpam-6262	307	32	if	if	SCONJ
ejpam-6262	307	33	j	j	PROPN
ejpam-6262	307	34	≤	≤	X
ejpam-6262	307	35	i	i	PRON
ejpam-6262	307	36	ωj	ωj	ADP
ejpam-6262	307	37	tj(1−	tj(1−	PROPN
ejpam-6262	307	38	tj	tj	NOUN
ejpam-6262	307	39	)	)	PUNCT
ejpam-6262	307	40	if	if	SCONJ
ejpam-6262	307	41	i	i	PRON
ejpam-6262	307	42	≤	≤	X
ejpam-6262	307	43	j	j	PROPN
ejpam-6262	307	44	.	.	PUNCT
ejpam-6262	308	1	in	in	ADP
ejpam-6262	308	2	which	which	PRON
ejpam-6262	308	3	the	the	DET
ejpam-6262	308	4	abscissas	abscissas	PROPN
ejpam-6262	308	5	tj	tj	PROPN
ejpam-6262	308	6	and	and	CCONJ
ejpam-6262	308	7	the	the	DET
ejpam-6262	308	8	weights	weight	NOUN
ejpam-6262	308	9	ωj	ωj	VERB
ejpam-6262	308	10	are	be	AUX
ejpam-6262	308	11	known	know	VERB
ejpam-6262	308	12	and	and	CCONJ
ejpam-6262	308	13	presented	present	VERB
ejpam-6262	308	14	in	in	ADP
ejpam-6262	308	15	tab.6	tab.6	PROPN
ejpam-6262	308	16	for	for	ADP
ejpam-6262	308	17	m	m	NOUN
ejpam-6262	308	18	=	=	NOUN
ejpam-6262	308	19	8	8	X
ejpam-6262	308	20	.	.	PUNCT
ejpam-6262	308	21	note	note	VERB
ejpam-6262	308	22	that	that	SCONJ
ejpam-6262	308	23	the	the	DET
ejpam-6262	308	24	initial	initial	ADJ
ejpam-6262	308	25	solutions	solution	NOUN
ejpam-6262	308	26	taken	take	VERB
ejpam-6262	308	27	into	into	ADP
ejpam-6262	308	28	consideration	consideration	NOUN
ejpam-6262	308	29	are	be	AUX
ejpam-6262	308	30	x0	x0	PROPN
ejpam-6262	308	31	=	=	PUNCT
ejpam-6262	308	32	{	{	PUNCT
ejpam-6262	308	33	0	0	NUM
ejpam-6262	308	34	,	,	PUNCT
ejpam-6262	308	35	0	0	NUM
ejpam-6262	308	36	,	,	PUNCT
ejpam-6262	308	37	0	0	NUM
ejpam-6262	308	38	,	,	PUNCT
ejpam-6262	308	39	0	0	NUM
ejpam-6262	308	40	,	,	PUNCT
ejpam-6262	308	41	0	0	NUM
ejpam-6262	308	42	,	,	PUNCT
ejpam-6262	308	43	0	0	NUM
ejpam-6262	308	44	,	,	PUNCT
ejpam-6262	308	45	0	0	NUM
ejpam-6262	308	46	,	,	PUNCT
ejpam-6262	308	47	0}t	0}t	NOUN
ejpam-6262	308	48	and	and	CCONJ
ejpam-6262	308	49	x0	x0	NUM
ejpam-6262	308	50	=	=	PUNCT
ejpam-6262	308	51	{	{	PUNCT
ejpam-6262	308	52	2	2	NUM
ejpam-6262	308	53	,	,	PUNCT
ejpam-6262	308	54	2	2	NUM
ejpam-6262	308	55	,	,	PUNCT
ejpam-6262	308	56	2	2	NUM
ejpam-6262	308	57	,	,	PUNCT
ejpam-6262	308	58	2	2	NUM
ejpam-6262	308	59	,	,	PUNCT
ejpam-6262	308	60	2	2	NUM
ejpam-6262	308	61	,	,	PUNCT
ejpam-6262	308	62	2	2	NUM
ejpam-6262	308	63	,	,	PUNCT
ejpam-6262	308	64	2	2	NUM
ejpam-6262	308	65	,	,	PUNCT
ejpam-6262	308	66	2}t	2}t	NUM
ejpam-6262	308	67	.	.	PUNCT
ejpam-6262	309	1	here	here	ADV
ejpam-6262	309	2	,	,	PUNCT
ejpam-6262	309	3	the	the	DET
ejpam-6262	309	4	exact	exact	ADJ
ejpam-6262	309	5	solution	solution	NOUN
ejpam-6262	309	6	to	to	ADP
ejpam-6262	309	7	this	this	DET
ejpam-6262	309	8	problem	problem	NOUN
ejpam-6262	309	9	is	be	AUX
ejpam-6262	309	10	the	the	DET
ejpam-6262	309	11	following	following	NOUN
ejpam-6262	309	12	.	.	PUNCT
ejpam-6262	310	1	α	α	X
ejpam-6262	310	2	=	=	PUNCT
ejpam-6262	310	3	{	{	PUNCT
ejpam-6262	310	4	1.002096245031	1.002096245031	NUM
ejpam-6262	310	5	.	.	PUNCT
ejpam-6262	310	6	.	.	PUNCT
ejpam-6262	310	7	.	.	PUNCT
ejpam-6262	311	1	,	,	PUNCT
ejpam-6262	311	2	1.009900316187	1.009900316187	NUM
ejpam-6262	311	3	.	.	PUNCT
ejpam-6262	311	4	.	.	PUNCT
ejpam-6262	312	1	.	.	PUNCT
ejpam-6262	313	1	,	,	PUNCT
ejpam-6262	313	2	1.019726960993	1.019726960993	NUM
ejpam-6262	313	3	.	.	PUNCT
ejpam-6262	313	4	.	.	PUNCT
ejpam-6262	314	1	.	.	PUNCT
ejpam-6262	315	1	,	,	PUNCT
ejpam-6262	315	2	1.026435743030	1.026435743030	NUM
ejpam-6262	315	3	.	.	PUNCT
ejpam-6262	315	4	.	.	PUNCT
ejpam-6262	316	1	.	.	PUNCT
ejpam-6262	317	1	,	,	PUNCT
ejpam-6262	317	2	1.026435743030	1.026435743030	NUM
ejpam-6262	317	3	.	.	PUNCT
ejpam-6262	317	4	.	.	PUNCT
ejpam-6262	318	1	.	.	PUNCT
ejpam-6262	319	1	,	,	PUNCT
ejpam-6262	319	2	1.019726960993	1.019726960993	NUM
ejpam-6262	319	3	.	.	PUNCT
ejpam-6262	319	4	.	.	PUNCT
ejpam-6262	320	1	.	.	PUNCT
ejpam-6262	321	1	,	,	PUNCT
ejpam-6262	321	2	1.009900316187	1.009900316187	NUM
ejpam-6262	321	3	.	.	PUNCT
ejpam-6262	321	4	.	.	PUNCT
ejpam-6262	322	1	.	.	PUNCT
ejpam-6262	323	1	,	,	PUNCT
ejpam-6262	323	2	1.002096245031	1.002096245031	NUM
ejpam-6262	323	3	.	.	PUNCT
ejpam-6262	323	4	.	.	PUNCT
ejpam-6262	323	5	.	.	PUNCT
ejpam-6262	324	1	}	}	PUNCT
ejpam-6262	324	2	t	t	NOUN
ejpam-6262	324	3	table	table	NOUN
ejpam-6262	324	4	6	6	NUM
ejpam-6262	324	5	:	:	PUNCT
ejpam-6262	324	6	abscissas	abscissa	NOUN
ejpam-6262	324	7	and	and	CCONJ
ejpam-6262	324	8	weights	weight	NOUN
ejpam-6262	324	9	of	of	ADP
ejpam-6262	324	10	gauss	gauss	ADJ
ejpam-6262	324	11	-	-	PUNCT
ejpam-6262	324	12	legendre	legendre	PROPN
ejpam-6262	324	13	quadrature	quadrature	NOUN
ejpam-6262	324	14	formula	formula	NOUN
ejpam-6262	324	15	for	for	ADP
ejpam-6262	324	16	m	m	PROPN
ejpam-6262	324	17	=	=	NOUN
ejpam-6262	324	18	8	8	NUM
ejpam-6262	324	19	.	.	PUNCT
ejpam-6262	325	1	j	j	PROPN
ejpam-6262	325	2	tj	tj	INTJ
ejpam-6262	325	3	ωj	ωj	ADP
ejpam-6262	325	4	1	1	NUM
ejpam-6262	325	5	0.0198550717512318841582195	0.0198550717512318841582195	NUM
ejpam-6262	325	6	.	.	PUNCT
ejpam-6262	325	7	.	.	PUNCT
ejpam-6262	325	8	.	.	PUNCT
ejpam-6262	326	1	0.0506142681451881295762656	0.0506142681451881295762656	NUM
ejpam-6262	326	2	.	.	PUNCT
ejpam-6262	326	3	.	.	PUNCT
ejpam-6262	326	4	.	.	PUNCT
ejpam-6262	327	1	2	2	NUM
ejpam-6262	327	2	0.1016667612931866302042230	0.1016667612931866302042230	NUM
ejpam-6262	327	3	.	.	PUNCT
ejpam-6262	327	4	.	.	PUNCT
ejpam-6262	327	5	.	.	PUNCT
ejpam-6262	328	1	0.1111905172266872352721779	0.1111905172266872352721779	NUM
ejpam-6262	328	2	.	.	PUNCT
ejpam-6262	328	3	.	.	PUNCT
ejpam-6262	328	4	.	.	PUNCT
ejpam-6262	329	1	3	3	NUM
ejpam-6262	329	2	0.2372337950418355070911304	0.2372337950418355070911304	NUM
ejpam-6262	329	3	.	.	PUNCT
ejpam-6262	329	4	.	.	PUNCT
ejpam-6262	329	5	.	.	PUNCT
ejpam-6262	330	1	0.1568533229389436436689811	0.1568533229389436436689811	NUM
ejpam-6262	330	2	.	.	PUNCT
ejpam-6262	330	3	.	.	PUNCT
ejpam-6262	330	4	.	.	PUNCT
ejpam-6262	331	1	4	4	NUM
ejpam-6262	331	2	0.4082826787521750975302619	0.4082826787521750975302619	NUM
ejpam-6262	331	3	.	.	PUNCT
ejpam-6262	331	4	.	.	PUNCT
ejpam-6262	331	5	.	.	PUNCT
ejpam-6262	332	1	0.1813418916891809914825752	0.1813418916891809914825752	NUM
ejpam-6262	332	2	.	.	PUNCT
ejpam-6262	332	3	.	.	PUNCT
ejpam-6262	332	4	.	.	PUNCT
ejpam-6262	333	1	5	5	NUM
ejpam-6262	333	2	0.5917173212478249024697380	0.5917173212478249024697380	NUM
ejpam-6262	333	3	.	.	PUNCT
ejpam-6262	333	4	.	.	PUNCT
ejpam-6262	333	5	.	.	PUNCT
ejpam-6262	334	1	0.1813418916891809914825752	0.1813418916891809914825752	NUM
ejpam-6262	334	2	.	.	PUNCT
ejpam-6262	334	3	.	.	PUNCT
ejpam-6262	334	4	.	.	PUNCT
ejpam-6262	335	1	6	6	NUM
ejpam-6262	335	2	0.7627662049581644929088695	0.7627662049581644929088695	NUM
ejpam-6262	335	3	.	.	PUNCT
ejpam-6262	335	4	.	.	PUNCT
ejpam-6262	335	5	.	.	PUNCT
ejpam-6262	336	1	0.1568533229389436436689811	0.1568533229389436436689811	NUM
ejpam-6262	336	2	.	.	PUNCT
ejpam-6262	336	3	.	.	PUNCT
ejpam-6262	336	4	.	.	PUNCT
ejpam-6262	337	1	7	7	NUM
ejpam-6262	337	2	0.8983332387068133697957769	0.8983332387068133697957769	NUM
ejpam-6262	337	3	.	.	PUNCT
ejpam-6262	337	4	.	.	PUNCT
ejpam-6262	337	5	.	.	PUNCT
ejpam-6262	338	1	0.1111905172266872352721779	0.1111905172266872352721779	NUM
ejpam-6262	338	2	.	.	PUNCT
ejpam-6262	338	3	.	.	PUNCT
ejpam-6262	338	4	.	.	PUNCT
ejpam-6262	339	1	8	8	NUM
ejpam-6262	339	2	0.9801449282487681158417804	0.9801449282487681158417804	NUM
ejpam-6262	339	3	.	.	PUNCT
ejpam-6262	339	4	.	.	PUNCT
ejpam-6262	339	5	.	.	PUNCT
ejpam-6262	340	1	0.0506142681451881295762656	0.0506142681451881295762656	NUM
ejpam-6262	340	2	.	.	PUNCT
ejpam-6262	340	3	.	.	PUNCT
ejpam-6262	340	4	.	.	PUNCT
ejpam-6262	341	1	y.	y.	PROPN
ejpam-6262	341	2	al	al	PROPN
ejpam-6262	341	3	-	-	PUNCT
ejpam-6262	341	4	shorman	shorman	PROPN
ejpam-6262	341	5	et	et	PROPN
ejpam-6262	341	6	al	al	PROPN
ejpam-6262	341	7	.	.	PUNCT
ejpam-6262	341	8	/	/	SYM
ejpam-6262	341	9	eur	eur	PROPN
ejpam-6262	341	10	.	.	PUNCT
ejpam-6262	342	1	j.	j.	PROPN
ejpam-6262	342	2	pure	pure	PROPN
ejpam-6262	342	3	appl	appl	PROPN
ejpam-6262	342	4	.	.	PROPN
ejpam-6262	342	5	math	math	PROPN
ejpam-6262	342	6	,	,	PUNCT
ejpam-6262	342	7	18	18	NUM
ejpam-6262	342	8	(	(	PUNCT
ejpam-6262	342	9	3	3	NUM
ejpam-6262	342	10	)	)	PUNCT
ejpam-6262	342	11	(	(	PUNCT
ejpam-6262	342	12	2025	2025	NUM
ejpam-6262	342	13	)	)	PUNCT
ejpam-6262	342	14	,	,	PUNCT
ejpam-6262	342	15	6262	6262	NUM
ejpam-6262	342	16	15	15	NUM
ejpam-6262	342	17	of	of	ADP
ejpam-6262	342	18	20	20	NUM
ejpam-6262	342	19	table	table	NOUN
ejpam-6262	342	20	7	7	NUM
ejpam-6262	342	21	reveals	reveal	VERB
ejpam-6262	342	22	that	that	SCONJ
ejpam-6262	342	23	the	the	DET
ejpam-6262	342	24	suggested	suggest	VERB
ejpam-6262	342	25	schemes	scheme	NOUN
ejpam-6262	342	26	show	show	VERB
ejpam-6262	342	27	effective	effective	ADJ
ejpam-6262	342	28	performance	performance	NOUN
ejpam-6262	342	29	and	and	CCONJ
ejpam-6262	342	30	are	be	AUX
ejpam-6262	342	31	on	on	ADP
ejpam-6262	342	32	par	par	NOUN
ejpam-6262	342	33	with	with	ADP
ejpam-6262	342	34	alternative	alternative	ADJ
ejpam-6262	342	35	iterative	iterative	NOUN
ejpam-6262	342	36	methodologies	methodology	NOUN
ejpam-6262	342	37	in	in	ADP
ejpam-6262	342	38	terms	term	NOUN
ejpam-6262	342	39	of	of	ADP
ejpam-6262	342	40	functionality	functionality	NOUN
ejpam-6262	342	41	.	.	PUNCT
ejpam-6262	343	1	table	table	NOUN
ejpam-6262	343	2	7	7	NUM
ejpam-6262	343	3	:	:	PUNCT
ejpam-6262	343	4	comparisons	comparison	NOUN
ejpam-6262	343	5	between	between	ADP
ejpam-6262	343	6	distinct	distinct	ADJ
ejpam-6262	343	7	methods	method	NOUN
ejpam-6262	343	8	for	for	ADP
ejpam-6262	343	9	problem	problem	NOUN
ejpam-6262	343	10	1	1	NUM
ejpam-6262	343	11	.	.	PUNCT
ejpam-6262	343	12	method	method	NOUN
ejpam-6262	343	13	x0	x0	PROPN
ejpam-6262	343	14	n	n	CCONJ
ejpam-6262	343	15	∥x1−x0∥	∥x1−x0∥	X
ejpam-6262	343	16	∥x2−x1∥	∥x2−x1∥	NUM
ejpam-6262	343	17	∥x3−x2∥	∥x3−x2∥	NUM
ejpam-6262	343	18	∥f	∥f	PROPN
ejpam-6262	343	19	(	(	PUNCT
ejpam-6262	343	20	x1)∥	x1)∥	PROPN
ejpam-6262	343	21	∥f	∥f	PROPN
ejpam-6262	343	22	(	(	PUNCT
ejpam-6262	343	23	x2)∥	x2)∥	PROPN
ejpam-6262	343	24	∥f	∥f	INTJ
ejpam-6262	343	25	(	(	PUNCT
ejpam-6262	343	26	x3)∥	x3)∥	PROPN
ejpam-6262	343	27	acoc	acoc	PROPN
ejpam-6262	343	28	bfs	bfs	PROPN
ejpam-6262	343	29	{	{	PUNCT
ejpam-6262	343	30	0	0	NUM
ejpam-6262	343	31	,	,	PUNCT
ejpam-6262	343	32	0	0	NUM
ejpam-6262	343	33	,	,	PUNCT
ejpam-6262	343	34	.	.	PUNCT
ejpam-6262	343	35	.	.	PUNCT
ejpam-6262	343	36	.	.	PUNCT
ejpam-6262	344	1	,	,	PUNCT
ejpam-6262	344	2	0}t	0}t	NOUN
ejpam-6262	344	3	12	12	NUM
ejpam-6262	344	4	2.890685	2.890685	NUM
ejpam-6262	344	5	div	div	NOUN
ejpam-6262	344	6	div	div	X
ejpam-6262	344	7	7.732e06	7.732e06	NUM
ejpam-6262	344	8	div	div	X
ejpam-6262	344	9	div	div	X
ejpam-6262	344	10	1.7	1.7	NUM
ejpam-6262	344	11	{	{	PUNCT
ejpam-6262	344	12	2	2	NUM
ejpam-6262	344	13	,	,	PUNCT
ejpam-6262	344	14	2	2	NUM
ejpam-6262	344	15	,	,	PUNCT
ejpam-6262	344	16	.	.	PUNCT
ejpam-6262	344	17	.	.	PUNCT
ejpam-6262	344	18	.	.	PUNCT
ejpam-6262	345	1	,	,	PUNCT
ejpam-6262	345	2	2}t	2}t	NUM
ejpam-6262	345	3	18	18	NUM
ejpam-6262	345	4	2.76676161	2.76676161	NUM
ejpam-6262	345	5	div	div	X
ejpam-6262	345	6	div	div	X
ejpam-6262	345	7	5.594e06	5.594e06	NUM
ejpam-6262	345	8	div	div	X
ejpam-6262	345	9	div	div	X
ejpam-6262	345	10	1.5	1.5	NUM
ejpam-6262	345	11	n	n	CCONJ
ejpam-6262	345	12	{	{	PUNCT
ejpam-6262	345	13	0	0	NUM
ejpam-6262	345	14	,	,	PUNCT
ejpam-6262	345	15	0	0	NUM
ejpam-6262	345	16	,	,	PUNCT
ejpam-6262	345	17	.	.	PUNCT
ejpam-6262	345	18	.	.	PUNCT
ejpam-6262	345	19	.	.	PUNCT
ejpam-6262	346	1	,	,	PUNCT
ejpam-6262	346	2	0}t	0}t	NOUN
ejpam-6262	346	3	50	50	NUM
ejpam-6262	346	4	2.890681	2.890681	NUM
ejpam-6262	346	5	div	div	NOUN
ejpam-6262	346	6	div	div	NOUN
ejpam-6262	346	7	7.215e13	7.215e13	NUM
ejpam-6262	346	8	div	div	X
ejpam-6262	346	9	div	div	X
ejpam-6262	346	10	2	2	NUM
ejpam-6262	346	11	{	{	PUNCT
ejpam-6262	346	12	2	2	NUM
ejpam-6262	346	13	,	,	PUNCT
ejpam-6262	346	14	2	2	NUM
ejpam-6262	346	15	,	,	PUNCT
ejpam-6262	346	16	.	.	PUNCT
ejpam-6262	346	17	.	.	PUNCT
ejpam-6262	347	1	.	.	PUNCT
ejpam-6262	348	1	,	,	PUNCT
ejpam-6262	348	2	2}t	2}t	NUM
ejpam-6262	348	3	50	50	NUM
ejpam-6262	348	4	2.76676164	2.76676164	NUM
ejpam-6262	348	5	div	div	X
ejpam-6262	348	6	div	div	NOUN
ejpam-6262	348	7	8.524e12	8.524e12	NOUN
ejpam-6262	348	8	div	div	NOUN
ejpam-6262	348	9	div	div	PROPN
ejpam-6262	348	10	2	2	NUM
ejpam-6262	348	11	dfh	dfh	NOUN
ejpam-6262	348	12	{	{	PUNCT
ejpam-6262	348	13	0	0	NUM
ejpam-6262	348	14	,	,	PUNCT
ejpam-6262	348	15	0	0	NUM
ejpam-6262	348	16	,	,	PUNCT
ejpam-6262	348	17	.	.	PUNCT
ejpam-6262	348	18	.	.	PUNCT
ejpam-6262	348	19	.	.	PUNCT
ejpam-6262	349	1	,	,	PUNCT
ejpam-6262	349	2	0}t	0}t	NOUN
ejpam-6262	349	3	4	4	NUM
ejpam-6262	349	4	2.86786	2.86786	NUM
ejpam-6262	349	5	0.00210	0.00210	NUM
ejpam-6262	349	6	4.710e-8	4.710e-8	NUM
ejpam-6262	349	7	0.00196	0.00196	NUM
ejpam-6262	349	8	4.669e-8	4.669e-8	NUM
ejpam-6262	349	9	1.809e-11	1.809e-11	NUM
ejpam-6262	349	10	2.5	2.5	NUM
ejpam-6262	349	11	{	{	PUNCT
ejpam-6262	349	12	2	2	NUM
ejpam-6262	349	13	,	,	PUNCT
ejpam-6262	349	14	2	2	NUM
ejpam-6262	349	15	,	,	PUNCT
ejpam-6262	349	16	.	.	PUNCT
ejpam-6262	349	17	.	.	PUNCT
ejpam-6262	349	18	.	.	PUNCT
ejpam-6262	350	1	,	,	PUNCT
ejpam-6262	350	2	2}t	2}t	NUM
ejpam-6262	350	3	6	6	NUM
ejpam-6262	350	4	2.76729	2.76729	NUM
ejpam-6262	350	5	0.03124	0.03124	NUM
ejpam-6262	351	1	0.000575	0.000575	NUM
ejpam-6262	351	2	0.02929	0.02929	NUM
ejpam-6262	351	3	0.000582	0.000582	NUM
ejpam-6262	351	4	1.206e-5	1.206e-5	NUM
ejpam-6262	351	5	2.5	2.5	NUM
ejpam-6262	351	6	problem	problem	NOUN
ejpam-6262	351	7	2	2	NUM
ejpam-6262	351	8	consider	consider	VERB
ejpam-6262	351	9	the	the	DET
ejpam-6262	351	10	discretized	discretized	ADJ
ejpam-6262	351	11	poisson	poisson	NOUN
ejpam-6262	351	12	equation	equation	NOUN
ejpam-6262	351	13	[	[	X
ejpam-6262	351	14	29	29	NUM
ejpam-6262	351	15	,	,	PUNCT
ejpam-6262	351	16	30	30	NUM
ejpam-6262	351	17	]	]	NUM
ejpam-6262	351	18	:	:	PUNCT
ejpam-6262	351	19	(	(	PUNCT
ejpam-6262	351	20	a	a	DET
ejpam-6262	351	21	common	common	ADJ
ejpam-6262	351	22	problem	problem	NOUN
ejpam-6262	351	23	in	in	ADP
ejpam-6262	351	24	computational	computational	ADJ
ejpam-6262	351	25	physics	physics	NOUN
ejpam-6262	351	26	and	and	CCONJ
ejpam-6262	351	27	engineering	engineering	NOUN
ejpam-6262	351	28	)	)	PUNCT
ejpam-6262	351	29	on	on	ADP
ejpam-6262	351	30	a	a	DET
ejpam-6262	351	31	grid	grid	NOUN
ejpam-6262	351	32	.	.	PUNCT
ejpam-6262	352	1	the	the	DET
ejpam-6262	352	2	equation	equation	NOUN
ejpam-6262	352	3	involves	involve	VERB
ejpam-6262	352	4	second	second	ADJ
ejpam-6262	352	5	-	-	PUNCT
ejpam-6262	352	6	order	order	NOUN
ejpam-6262	352	7	partial	partial	ADJ
ejpam-6262	352	8	derivatives	derivative	NOUN
ejpam-6262	352	9	and	and	CCONJ
ejpam-6262	352	10	can	can	AUX
ejpam-6262	352	11	be	be	AUX
ejpam-6262	352	12	expressed	express	VERB
ejpam-6262	352	13	as	as	ADP
ejpam-6262	352	14	:	:	PUNCT
ejpam-6262	352	15	∆u	∆u	PROPN
ejpam-6262	352	16	=	=	SYM
ejpam-6262	352	17	f	f	X
ejpam-6262	352	18	where	where	SCONJ
ejpam-6262	352	19	u	u	NOUN
ejpam-6262	352	20	is	be	AUX
ejpam-6262	352	21	the	the	DET
ejpam-6262	352	22	solution	solution	NOUN
ejpam-6262	352	23	function	function	NOUN
ejpam-6262	352	24	and	and	CCONJ
ejpam-6262	352	25	f	f	PROPN
ejpam-6262	352	26	is	be	AUX
ejpam-6262	352	27	the	the	DET
ejpam-6262	352	28	source	source	NOUN
ejpam-6262	352	29	term	term	NOUN
ejpam-6262	352	30	.	.	PUNCT
ejpam-6262	353	1	after	after	ADP
ejpam-6262	353	2	discretization	discretization	NOUN
ejpam-6262	353	3	using	use	VERB
ejpam-6262	353	4	finite	finite	ADJ
ejpam-6262	353	5	differences	difference	NOUN
ejpam-6262	353	6	on	on	ADP
ejpam-6262	353	7	a	a	DET
ejpam-6262	353	8	2d	2d	NUM
ejpam-6262	353	9	grid	grid	NOUN
ejpam-6262	353	10	,	,	PUNCT
ejpam-6262	353	11	we	we	PRON
ejpam-6262	353	12	end	end	VERB
ejpam-6262	353	13	up	up	ADP
ejpam-6262	353	14	with	with	ADP
ejpam-6262	353	15	a	a	DET
ejpam-6262	353	16	system	system	NOUN
ejpam-6262	353	17	of	of	ADP
ejpam-6262	353	18	nonlinear	nonlinear	ADJ
ejpam-6262	353	19	equations	equation	NOUN
ejpam-6262	353	20	,	,	PUNCT
ejpam-6262	353	21	where	where	SCONJ
ejpam-6262	353	22	the	the	DET
ejpam-6262	353	23	jacobian	jacobian	ADJ
ejpam-6262	353	24	matrix	matrix	NOUN
ejpam-6262	353	25	is	be	AUX
ejpam-6262	353	26	very	very	ADV
ejpam-6262	353	27	sparse	sparse	ADJ
ejpam-6262	353	28	(	(	PUNCT
ejpam-6262	353	29	each	each	DET
ejpam-6262	353	30	variable	variable	NOUN
ejpam-6262	353	31	interacts	interact	VERB
ejpam-6262	353	32	only	only	ADV
ejpam-6262	353	33	with	with	ADP
ejpam-6262	353	34	a	a	DET
ejpam-6262	353	35	few	few	ADJ
ejpam-6262	353	36	neighboring	neighboring	NOUN
ejpam-6262	353	37	variables	variable	NOUN
ejpam-6262	353	38	due	due	ADP
ejpam-6262	353	39	to	to	ADP
ejpam-6262	353	40	the	the	DET
ejpam-6262	353	41	grid	grid	NOUN
ejpam-6262	353	42	structure	structure	NOUN
ejpam-6262	353	43	)	)	PUNCT
ejpam-6262	353	44	.	.	PUNCT
ejpam-6262	354	1	in	in	ADP
ejpam-6262	354	2	the	the	DET
ejpam-6262	354	3	context	context	NOUN
ejpam-6262	354	4	of	of	ADP
ejpam-6262	354	5	solving	solve	VERB
ejpam-6262	354	6	nonlinear	nonlinear	ADJ
ejpam-6262	354	7	systems	system	NOUN
ejpam-6262	354	8	of	of	ADP
ejpam-6262	354	9	equations	equation	NOUN
ejpam-6262	354	10	,	,	PUNCT
ejpam-6262	354	11	methods	method	NOUN
ejpam-6262	354	12	that	that	PRON
ejpam-6262	354	13	take	take	VERB
ejpam-6262	354	14	advantage	advantage	NOUN
ejpam-6262	354	15	of	of	ADP
ejpam-6262	354	16	a	a	DET
ejpam-6262	354	17	sparse	sparse	ADJ
ejpam-6262	354	18	jacobian	jacobian	ADJ
ejpam-6262	354	19	structure	structure	NOUN
ejpam-6262	354	20	can	can	AUX
ejpam-6262	354	21	significantly	significantly	ADV
ejpam-6262	354	22	reduce	reduce	VERB
ejpam-6262	354	23	the	the	DET
ejpam-6262	354	24	computational	computational	ADJ
ejpam-6262	354	25	cost	cost	NOUN
ejpam-6262	354	26	,	,	PUNCT
ejpam-6262	354	27	especially	especially	ADV
ejpam-6262	354	28	for	for	ADP
ejpam-6262	354	29	large	large	ADJ
ejpam-6262	354	30	systems	system	NOUN
ejpam-6262	354	31	.	.	PUNCT
ejpam-6262	355	1	a	a	DET
ejpam-6262	355	2	sparse	sparse	ADJ
ejpam-6262	355	3	jacobian	jacobian	NOUN
ejpam-6262	355	4	implies	imply	VERB
ejpam-6262	355	5	that	that	SCONJ
ejpam-6262	355	6	many	many	ADJ
ejpam-6262	355	7	of	of	ADP
ejpam-6262	355	8	its	its	PRON
ejpam-6262	355	9	elements	element	NOUN
ejpam-6262	355	10	are	be	AUX
ejpam-6262	355	11	zero	zero	NUM
ejpam-6262	355	12	,	,	PUNCT
ejpam-6262	355	13	and	and	CCONJ
ejpam-6262	355	14	by	by	ADP
ejpam-6262	355	15	exploiting	exploit	VERB
ejpam-6262	355	16	this	this	DET
ejpam-6262	355	17	structure	structure	NOUN
ejpam-6262	355	18	,	,	PUNCT
ejpam-6262	355	19	one	one	PRON
ejpam-6262	355	20	can	can	AUX
ejpam-6262	355	21	avoid	avoid	VERB
ejpam-6262	355	22	unnecessary	unnecessary	ADJ
ejpam-6262	355	23	computations	computation	NOUN
ejpam-6262	355	24	involving	involve	VERB
ejpam-6262	355	25	these	these	DET
ejpam-6262	355	26	zeros	zero	NOUN
ejpam-6262	355	27	.	.	PUNCT
ejpam-6262	356	1	let	let	VERB
ejpam-6262	356	2	’s	’s	PRON
ejpam-6262	356	3	define	define	VERB
ejpam-6262	356	4	a	a	DET
ejpam-6262	356	5	simpler	simple	ADJ
ejpam-6262	356	6	system	system	NOUN
ejpam-6262	356	7	that	that	PRON
ejpam-6262	356	8	mimics	mimic	VERB
ejpam-6262	356	9	this	this	DET
ejpam-6262	356	10	structure	structure	NOUN
ejpam-6262	356	11	:	:	PUNCT
ejpam-6262	357	1	f	f	PROPN
ejpam-6262	357	2	(	(	PUNCT
ejpam-6262	357	3	x	x	X
ejpam-6262	357	4	)	)	PUNCT
ejpam-6262	357	5	=	=	SYM
ejpam-6262	357	6			NOUN
ejpam-6262	358	1	2x1	2x1	NUM
ejpam-6262	358	2	−	−	NOUN
ejpam-6262	358	3	x22	x22	NOUN
ejpam-6262	359	1	+	+	CCONJ
ejpam-6262	359	2	x24	x24	NUM
ejpam-6262	359	3	−	−	PROPN
ejpam-6262	360	1	1	1	NUM
ejpam-6262	360	2	x21	x21	NUM
ejpam-6262	360	3	+	+	CCONJ
ejpam-6262	360	4	2x2	2x2	NUM
ejpam-6262	360	5	−	−	NOUN
ejpam-6262	360	6	x23	x23	NOUN
ejpam-6262	360	7	−	−	PROPN
ejpam-6262	360	8	2	2	NUM
ejpam-6262	360	9	x22	x22	NOUN
ejpam-6262	360	10	+	+	CCONJ
ejpam-6262	360	11	2x3	2x3	NUM
ejpam-6262	360	12	−	−	NUM
ejpam-6262	360	13	x24	x24	NOUN
ejpam-6262	360	14	−	−	PROPN
ejpam-6262	360	15	1	1	NUM
ejpam-6262	360	16	x21	x21	NUM
ejpam-6262	360	17	−	−	NOUN
ejpam-6262	360	18	x23	x23	NOUN
ejpam-6262	361	1	+	+	CCONJ
ejpam-6262	361	2	2x4	2x4	NUM
ejpam-6262	361	3	−	−	SYM
ejpam-6262	361	4	2	2	NUM
ejpam-6262	361	5			NUM
ejpam-6262	361	6	=	=	SYM
ejpam-6262	361	7	0	0	NUM
ejpam-6262	361	8	this	this	DET
ejpam-6262	361	9	system	system	NOUN
ejpam-6262	361	10	exhibits	exhibit	VERB
ejpam-6262	361	11	nonlinear	nonlinear	ADJ
ejpam-6262	361	12	behavior	behavior	NOUN
ejpam-6262	361	13	and	and	CCONJ
ejpam-6262	361	14	has	have	VERB
ejpam-6262	361	15	a	a	DET
ejpam-6262	361	16	sparse	sparse	ADJ
ejpam-6262	361	17	jacobian	jacobian	NOUN
ejpam-6262	361	18	because	because	SCONJ
ejpam-6262	361	19	many	many	ADJ
ejpam-6262	361	20	partial	partial	ADJ
ejpam-6262	361	21	derivatives	derivative	NOUN
ejpam-6262	361	22	are	be	AUX
ejpam-6262	361	23	zero	zero	NUM
ejpam-6262	361	24	due	due	ADP
ejpam-6262	361	25	to	to	ADP
ejpam-6262	361	26	the	the	DET
ejpam-6262	361	27	structure	structure	NOUN
ejpam-6262	361	28	of	of	ADP
ejpam-6262	361	29	the	the	DET
ejpam-6262	361	30	equations	equation	NOUN
ejpam-6262	361	31	(	(	PUNCT
ejpam-6262	361	32	only	only	ADV
ejpam-6262	361	33	nearby	nearby	ADJ
ejpam-6262	361	34	variables	variable	NOUN
ejpam-6262	361	35	in	in	ADP
ejpam-6262	361	36	the	the	DET
ejpam-6262	361	37	y.	y.	PROPN
ejpam-6262	361	38	al	al	PROPN
ejpam-6262	361	39	-	-	PUNCT
ejpam-6262	361	40	shorman	shorman	PROPN
ejpam-6262	361	41	et	et	PROPN
ejpam-6262	361	42	al	al	PROPN
ejpam-6262	361	43	.	.	PUNCT
ejpam-6262	361	44	/	/	SYM
ejpam-6262	361	45	eur	eur	PROPN
ejpam-6262	361	46	.	.	PUNCT
ejpam-6262	362	1	j.	j.	PROPN
ejpam-6262	362	2	pure	pure	PROPN
ejpam-6262	362	3	appl	appl	PROPN
ejpam-6262	362	4	.	.	PROPN
ejpam-6262	362	5	math	math	PROPN
ejpam-6262	362	6	,	,	PUNCT
ejpam-6262	362	7	18	18	NUM
ejpam-6262	362	8	(	(	PUNCT
ejpam-6262	362	9	3	3	NUM
ejpam-6262	362	10	)	)	PUNCT
ejpam-6262	362	11	(	(	PUNCT
ejpam-6262	362	12	2025	2025	NUM
ejpam-6262	362	13	)	)	PUNCT
ejpam-6262	362	14	,	,	PUNCT
ejpam-6262	362	15	6262	6262	NUM
ejpam-6262	362	16	16	16	NUM
ejpam-6262	362	17	of	of	ADP
ejpam-6262	362	18	20	20	NUM
ejpam-6262	362	19	system	system	NOUN
ejpam-6262	362	20	affect	affect	VERB
ejpam-6262	362	21	each	each	DET
ejpam-6262	362	22	other	other	ADJ
ejpam-6262	362	23	)	)	PUNCT
ejpam-6262	362	24	.	.	PUNCT
ejpam-6262	363	1	the	the	DET
ejpam-6262	363	2	jacobian	jacobian	ADJ
ejpam-6262	363	3	matrix	matrix	NOUN
ejpam-6262	363	4	of	of	ADP
ejpam-6262	363	5	this	this	DET
ejpam-6262	363	6	system	system	NOUN
ejpam-6262	363	7	is	be	AUX
ejpam-6262	363	8	:	:	PUNCT
ejpam-6262	363	9	j(x	j(x	X
ejpam-6262	363	10	)	)	PUNCT
ejpam-6262	364	1	=	=	SYM
ejpam-6262	364	2			NOUN
ejpam-6262	364	3	2	2	NUM
ejpam-6262	364	4	−2x2	−2x2	NUM
ejpam-6262	364	5	0	0	NUM
ejpam-6262	364	6	2x4	2x4	NUM
ejpam-6262	364	7	2x1	2x1	NUM
ejpam-6262	364	8	2	2	NUM
ejpam-6262	364	9	−2x3	−2x3	NUM
ejpam-6262	364	10	0	0	NUM
ejpam-6262	364	11	0	0	NUM
ejpam-6262	364	12	2x2	2x2	NUM
ejpam-6262	364	13	2	2	NUM
ejpam-6262	364	14	−2x4	−2x4	NUM
ejpam-6262	364	15	2x1	2x1	NUM
ejpam-6262	364	16	0	0	NUM
ejpam-6262	364	17	−2x3	−2x3	NUM
ejpam-6262	364	18	2	2	NUM
ejpam-6262	364	19			NUM
ejpam-6262	364	20	=	=	SYM
ejpam-6262	364	21	0	0	NUM
ejpam-6262	365	1	this	this	DET
ejpam-6262	365	2	matrix	matrix	NOUN
ejpam-6262	365	3	is	be	AUX
ejpam-6262	365	4	sparse	sparse	ADJ
ejpam-6262	365	5	because	because	SCONJ
ejpam-6262	365	6	many	many	ADJ
ejpam-6262	365	7	elements	element	NOUN
ejpam-6262	365	8	are	be	AUX
ejpam-6262	365	9	zero	zero	NUM
ejpam-6262	365	10	,	,	PUNCT
ejpam-6262	365	11	which	which	PRON
ejpam-6262	365	12	allows	allow	VERB
ejpam-6262	365	13	us	we	PRON
ejpam-6262	365	14	to	to	PART
ejpam-6262	365	15	exploit	exploit	VERB
ejpam-6262	365	16	this	this	DET
ejpam-6262	365	17	structure	structure	NOUN
ejpam-6262	365	18	when	when	SCONJ
ejpam-6262	365	19	using	use	VERB
ejpam-6262	365	20	iterative	iterative	NOUN
ejpam-6262	365	21	methods	method	NOUN
ejpam-6262	365	22	like	like	ADP
ejpam-6262	365	23	the	the	DET
ejpam-6262	365	24	dfh	dfh	PROPN
ejpam-6262	365	25	method	method	NOUN
ejpam-6262	365	26	.	.	PUNCT
ejpam-6262	366	1	table	table	NOUN
ejpam-6262	366	2	8	8	NUM
ejpam-6262	366	3	:	:	PUNCT
ejpam-6262	366	4	comparisons	comparison	NOUN
ejpam-6262	366	5	between	between	ADP
ejpam-6262	366	6	distinct	distinct	ADJ
ejpam-6262	366	7	methods	method	NOUN
ejpam-6262	366	8	for	for	ADP
ejpam-6262	366	9	problem	problem	NOUN
ejpam-6262	366	10	2	2	NUM
ejpam-6262	366	11	.	.	PUNCT
ejpam-6262	366	12	method	method	PROPN
ejpam-6262	366	13	iterations	iteration	NOUN
ejpam-6262	366	14	time	time	NOUN
ejpam-6262	366	15	(	(	PUNCT
ejpam-6262	366	16	s	s	NOUN
ejpam-6262	366	17	)	)	PUNCT
ejpam-6262	366	18	final	final	ADJ
ejpam-6262	366	19	error	error	NOUN
ejpam-6262	366	20	newton	newton	PROPN
ejpam-6262	366	21	’s	’s	PART
ejpam-6262	366	22	method	method	NOUN
ejpam-6262	366	23	10	10	NUM
ejpam-6262	366	24	0.005	0.005	NUM
ejpam-6262	366	25	3.2×10e-7	3.2×10e-7	NUM
ejpam-6262	366	26	broyden	broyden	NOUN
ejpam-6262	366	27	’s	’s	PART
ejpam-6262	366	28	method	method	NOUN
ejpam-6262	366	29	35	35	NUM
ejpam-6262	366	30	0.007	0.007	NUM
ejpam-6262	366	31	1.1×10e-6	1.1×10e-6	NUM
ejpam-6262	366	32	dfh	dfh	NOUN
ejpam-6262	366	33	method	method	NOUN
ejpam-6262	366	34	20	20	NUM
ejpam-6262	366	35	0.004	0.004	NUM
ejpam-6262	366	36	9.0×10e-7	9.0×10e-7	NUM
ejpam-6262	366	37	in	in	ADP
ejpam-6262	366	38	this	this	DET
ejpam-6262	366	39	sparse	sparse	ADJ
ejpam-6262	366	40	system	system	NOUN
ejpam-6262	366	41	,	,	PUNCT
ejpam-6262	366	42	the	the	DET
ejpam-6262	366	43	dfh	dfh	PROPN
ejpam-6262	366	44	method	method	NOUN
ejpam-6262	366	45	proves	prove	VERB
ejpam-6262	366	46	to	to	PART
ejpam-6262	366	47	be	be	AUX
ejpam-6262	366	48	the	the	DET
ejpam-6262	366	49	best	good	ADJ
ejpam-6262	366	50	choice	choice	NOUN
ejpam-6262	366	51	.	.	PUNCT
ejpam-6262	367	1	it	it	PRON
ejpam-6262	367	2	avoids	avoid	VERB
ejpam-6262	367	3	the	the	DET
ejpam-6262	367	4	cost	cost	NOUN
ejpam-6262	367	5	of	of	ADP
ejpam-6262	367	6	an	an	DET
ejpam-6262	367	7	exact	exact	ADJ
ejpam-6262	367	8	jacobian	jacobian	ADJ
ejpam-6262	367	9	computation	computation	NOUN
ejpam-6262	367	10	while	while	SCONJ
ejpam-6262	367	11	maintaining	maintain	VERB
ejpam-6262	367	12	a	a	DET
ejpam-6262	367	13	lower	low	ADJ
ejpam-6262	367	14	total	total	ADJ
ejpam-6262	367	15	time	time	NOUN
ejpam-6262	367	16	and	and	CCONJ
ejpam-6262	367	17	a	a	DET
ejpam-6262	367	18	final	final	ADJ
ejpam-6262	367	19	error	error	NOUN
ejpam-6262	367	20	comparable	comparable	ADJ
ejpam-6262	367	21	to	to	ADP
ejpam-6262	367	22	that	that	PRON
ejpam-6262	367	23	of	of	ADP
ejpam-6262	367	24	newton	newton	PROPN
ejpam-6262	367	25	and	and	CCONJ
ejpam-6262	367	26	broyden	broyden	NOUN
ejpam-6262	367	27	’s	’s	PART
ejpam-6262	367	28	method	method	NOUN
ejpam-6262	367	29	.	.	PUNCT
ejpam-6262	368	1	this	this	DET
ejpam-6262	368	2	method	method	NOUN
ejpam-6262	368	3	is	be	AUX
ejpam-6262	368	4	particularly	particularly	ADV
ejpam-6262	368	5	efficient	efficient	ADJ
ejpam-6262	368	6	for	for	ADP
ejpam-6262	368	7	systems	system	NOUN
ejpam-6262	368	8	with	with	ADP
ejpam-6262	368	9	a	a	DET
ejpam-6262	368	10	sparse	sparse	ADJ
ejpam-6262	368	11	structure	structure	NOUN
ejpam-6262	368	12	where	where	SCONJ
ejpam-6262	368	13	the	the	DET
ejpam-6262	368	14	jacobian	jacobian	PROPN
ejpam-6262	368	15	is	be	AUX
ejpam-6262	368	16	costly	costly	ADJ
ejpam-6262	368	17	to	to	PART
ejpam-6262	368	18	compute	compute	VERB
ejpam-6262	368	19	directly	directly	ADV
ejpam-6262	368	20	.	.	PUNCT
ejpam-6262	369	1	problem	problem	NOUN
ejpam-6262	369	2	3	3	NUM
ejpam-6262	369	3	let	let	VERB
ejpam-6262	369	4	’s	’s	NOUN
ejpam-6262	369	5	first	first	ADV
ejpam-6262	369	6	recall	recall	VERB
ejpam-6262	369	7	the	the	DET
ejpam-6262	369	8	weierstrass	weierstrass	NOUN
ejpam-6262	369	9	method	method	NOUN
ejpam-6262	369	10	for	for	ADP
ejpam-6262	369	11	solving	solve	VERB
ejpam-6262	369	12	polynomial	polynomial	ADJ
ejpam-6262	369	13	systems	system	NOUN
ejpam-6262	369	14	[	[	X
ejpam-6262	369	15	31	31	NUM
ejpam-6262	369	16	,	,	PUNCT
ejpam-6262	369	17	32	32	NUM
ejpam-6262	369	18	]	]	PUNCT
ejpam-6262	369	19	given	give	VERB
ejpam-6262	369	20	a	a	DET
ejpam-6262	369	21	polynomial	polynomial	ADJ
ejpam-6262	369	22	p	p	NOUN
ejpam-6262	369	23	(	(	PUNCT
ejpam-6262	369	24	x	x	NOUN
ejpam-6262	369	25	)	)	PUNCT
ejpam-6262	369	26	=	=	SYM
ejpam-6262	370	1	anx	anx	ADJ
ejpam-6262	370	2	n	n	NOUN
ejpam-6262	370	3	+	+	CCONJ
ejpam-6262	370	4	an−1x	an−1x	PROPN
ejpam-6262	370	5	n−1	n−1	PROPN
ejpam-6262	370	6	+	+	CCONJ
ejpam-6262	370	7	·	·	PUNCT
ejpam-6262	370	8	·	·	PUNCT
ejpam-6262	370	9	·	·	PUNCT
ejpam-6262	370	10	+	+	NUM
ejpam-6262	370	11	a1x+	a1x+	NOUN
ejpam-6262	370	12	a0	a0	NOUN
ejpam-6262	370	13	,	,	PUNCT
ejpam-6262	370	14	the	the	DET
ejpam-6262	370	15	weierstrass	weierstrass	NOUN
ejpam-6262	370	16	method	method	NOUN
ejpam-6262	370	17	(	(	PUNCT
ejpam-6262	370	18	also	also	ADV
ejpam-6262	370	19	known	know	VERB
ejpam-6262	370	20	as	as	ADP
ejpam-6262	370	21	the	the	DET
ejpam-6262	370	22	durand	durand	PROPN
ejpam-6262	370	23	–	–	PUNCT
ejpam-6262	370	24	kerner	kerner	PROPN
ejpam-6262	370	25	method	method	PROPN
ejpam-6262	370	26	)	)	PUNCT
ejpam-6262	370	27	finds	find	VERB
ejpam-6262	370	28	all	all	DET
ejpam-6262	370	29	the	the	DET
ejpam-6262	370	30	roots	root	NOUN
ejpam-6262	370	31	of	of	ADP
ejpam-6262	370	32	the	the	DET
ejpam-6262	370	33	polynomial	polynomial	NOUN
ejpam-6262	370	34	by	by	ADP
ejpam-6262	370	35	iterating	iterate	VERB
ejpam-6262	370	36	through	through	ADP
ejpam-6262	370	37	the	the	DET
ejpam-6262	370	38	following	follow	VERB
ejpam-6262	370	39	formula	formula	NOUN
ejpam-6262	370	40	for	for	ADP
ejpam-6262	370	41	each	each	DET
ejpam-6262	370	42	root	root	NOUN
ejpam-6262	370	43	ri	ri	PROPN
ejpam-6262	370	44	:	:	PUNCT
ejpam-6262	371	1	r	r	NOUN
ejpam-6262	371	2	(	(	PUNCT
ejpam-6262	371	3	n+1	n+1	NOUN
ejpam-6262	371	4	)	)	PUNCT
ejpam-6262	371	5	i	i	NOUN
ejpam-6262	371	6	=	=	SYM
ejpam-6262	371	7	r	r	NOUN
ejpam-6262	371	8	(	(	PUNCT
ejpam-6262	371	9	n	n	CCONJ
ejpam-6262	371	10	)	)	PUNCT
ejpam-6262	371	11	i	i	PRON
ejpam-6262	371	12	−	−	VERB
ejpam-6262	372	1	p	p	X
ejpam-6262	372	2	(	(	PUNCT
ejpam-6262	372	3	r	r	NOUN
ejpam-6262	372	4	(	(	PUNCT
ejpam-6262	372	5	n	n	CCONJ
ejpam-6262	372	6	)	)	PUNCT
ejpam-6262	372	7	i	i	NOUN
ejpam-6262	372	8	)	)	PUNCT
ejpam-6262	373	1	n∏	n∏	PROPN
ejpam-6262	373	2	j	j	NOUN
ejpam-6262	373	3	̸=i	̸=i	NOUN
ejpam-6262	373	4	(	(	PUNCT
ejpam-6262	373	5	r	r	NOUN
ejpam-6262	373	6	(	(	PUNCT
ejpam-6262	373	7	n	n	CCONJ
ejpam-6262	373	8	)	)	PUNCT
ejpam-6262	373	9	i	i	PRON
ejpam-6262	373	10	−	−	VERB
ejpam-6262	373	11	r	r	NOUN
ejpam-6262	373	12	(	(	PUNCT
ejpam-6262	373	13	n	n	CCONJ
ejpam-6262	373	14	)	)	PUNCT
ejpam-6262	373	15	j	j	PROPN
ejpam-6262	373	16	)	)	PUNCT
ejpam-6262	373	17	,	,	PUNCT
ejpam-6262	373	18	for	for	ADP
ejpam-6262	373	19	i	i	PROPN
ejpam-6262	373	20	=	=	SYM
ejpam-6262	373	21	1	1	NUM
ejpam-6262	373	22	,	,	PUNCT
ejpam-6262	373	23	2	2	NUM
ejpam-6262	373	24	,	,	PUNCT
ejpam-6262	373	25	.	.	PUNCT
ejpam-6262	373	26	.	.	PUNCT
ejpam-6262	374	1	.	.	PUNCT
ejpam-6262	375	1	,	,	PUNCT
ejpam-6262	375	2	n	n	CCONJ
ejpam-6262	375	3	,	,	PUNCT
ejpam-6262	375	4	where	where	SCONJ
ejpam-6262	375	5	r	r	NOUN
ejpam-6262	375	6	(	(	PUNCT
ejpam-6262	375	7	k	k	X
ejpam-6262	375	8	)	)	PUNCT
ejpam-6262	375	9	i	i	PRON
ejpam-6262	375	10	denotes	denote	VERB
ejpam-6262	375	11	the	the	DET
ejpam-6262	375	12	approximation	approximation	NOUN
ejpam-6262	375	13	of	of	ADP
ejpam-6262	375	14	the	the	DET
ejpam-6262	375	15	i	i	PROPN
ejpam-6262	375	16	-	-	PUNCT
ejpam-6262	375	17	th	th	X
ejpam-6262	375	18	root	root	NOUN
ejpam-6262	375	19	at	at	ADP
ejpam-6262	375	20	the	the	DET
ejpam-6262	375	21	k	k	PROPN
ejpam-6262	375	22	-	-	PUNCT
ejpam-6262	375	23	th	th	VERB
ejpam-6262	375	24	iteration	iteration	NOUN
ejpam-6262	375	25	.	.	PUNCT
ejpam-6262	376	1	this	this	DET
ejpam-6262	376	2	formula	formula	NOUN
ejpam-6262	376	3	iteratively	iteratively	ADV
ejpam-6262	376	4	improves	improve	VERB
ejpam-6262	376	5	the	the	DET
ejpam-6262	376	6	estimates	estimate	NOUN
ejpam-6262	376	7	of	of	ADP
ejpam-6262	376	8	the	the	DET
ejpam-6262	376	9	roots	root	NOUN
ejpam-6262	376	10	by	by	ADP
ejpam-6262	376	11	simultaneously	simultaneously	ADV
ejpam-6262	376	12	updating	update	VERB
ejpam-6262	376	13	all	all	DET
ejpam-6262	376	14	the	the	DET
ejpam-6262	376	15	roots	root	NOUN
ejpam-6262	376	16	based	base	VERB
ejpam-6262	376	17	on	on	ADP
ejpam-6262	376	18	their	their	PRON
ejpam-6262	376	19	current	current	ADJ
ejpam-6262	376	20	estimates	estimate	NOUN
ejpam-6262	376	21	.	.	PUNCT
ejpam-6262	377	1	consider	consider	VERB
ejpam-6262	377	2	the	the	DET
ejpam-6262	377	3	following	follow	VERB
ejpam-6262	377	4	polynomial	polynomial	ADJ
ejpam-6262	377	5	system	system	NOUN
ejpam-6262	377	6	,	,	PUNCT
ejpam-6262	377	7	representing	represent	VERB
ejpam-6262	377	8	a	a	DET
ejpam-6262	377	9	cubic	cubic	ADJ
ejpam-6262	377	10	equation	equation	NOUN
ejpam-6262	377	11	in	in	ADP
ejpam-6262	377	12	two	two	NUM
ejpam-6262	377	13	variables	variable	NOUN
ejpam-6262	377	14	:	:	PUNCT
ejpam-6262	377	15	y.	y.	PROPN
ejpam-6262	377	16	al	al	PROPN
ejpam-6262	377	17	-	-	PUNCT
ejpam-6262	377	18	shorman	shorman	PROPN
ejpam-6262	377	19	et	et	PROPN
ejpam-6262	377	20	al	al	PROPN
ejpam-6262	377	21	.	.	PUNCT
ejpam-6262	377	22	/	/	SYM
ejpam-6262	377	23	eur	eur	PROPN
ejpam-6262	377	24	.	.	PUNCT
ejpam-6262	378	1	j.	j.	PROPN
ejpam-6262	378	2	pure	pure	PROPN
ejpam-6262	378	3	appl	appl	PROPN
ejpam-6262	378	4	.	.	PROPN
ejpam-6262	378	5	math	math	PROPN
ejpam-6262	378	6	,	,	PUNCT
ejpam-6262	378	7	18	18	NUM
ejpam-6262	378	8	(	(	PUNCT
ejpam-6262	378	9	3	3	NUM
ejpam-6262	378	10	)	)	PUNCT
ejpam-6262	378	11	(	(	PUNCT
ejpam-6262	378	12	2025	2025	NUM
ejpam-6262	378	13	)	)	PUNCT
ejpam-6262	378	14	,	,	PUNCT
ejpam-6262	378	15	6262	6262	NUM
ejpam-6262	378	16	17	17	NUM
ejpam-6262	378	17	of	of	ADP
ejpam-6262	378	18	20	20	NUM
ejpam-6262	378	19	f	f	NOUN
ejpam-6262	378	20	(	(	PUNCT
ejpam-6262	378	21	x	x	NOUN
ejpam-6262	378	22	)	)	PUNCT
ejpam-6262	378	23	=	=	SYM
ejpam-6262	378	24			NOUN
ejpam-6262	378	25	x31	x31	NUM
ejpam-6262	378	26	−	−	NUM
ejpam-6262	378	27	3	3	NUM
ejpam-6262	379	1	x1	x1	NUM
ejpam-6262	380	1	x22	x22	NOUN
ejpam-6262	381	1	−	−	PROPN
ejpam-6262	381	2	1	1	NUM
ejpam-6262	381	3	x32	x32	NOUN
ejpam-6262	381	4	−	−	PROPN
ejpam-6262	381	5	3	3	NUM
ejpam-6262	381	6	x21	x21	NUM
ejpam-6262	381	7	x2	x2	NOUN
ejpam-6262	381	8			NOUN
ejpam-6262	381	9	=	=	SYM
ejpam-6262	381	10	0	0	NUM
ejpam-6262	381	11	we	we	PRON
ejpam-6262	381	12	can	can	AUX
ejpam-6262	381	13	compare	compare	VERB
ejpam-6262	381	14	the	the	DET
ejpam-6262	381	15	three	three	NUM
ejpam-6262	381	16	methods	method	NOUN
ejpam-6262	381	17	(	(	PUNCT
ejpam-6262	381	18	newton	newton	PROPN
ejpam-6262	381	19	,	,	PUNCT
ejpam-6262	381	20	broyden	broyden	NOUN
ejpam-6262	381	21	,	,	PUNCT
ejpam-6262	381	22	and	and	CCONJ
ejpam-6262	381	23	dfh	dfh	PROPN
ejpam-6262	381	24	method	method	NOUN
ejpam-6262	381	25	)	)	PUNCT
ejpam-6262	381	26	as	as	ADV
ejpam-6262	381	27	well	well	ADV
ejpam-6262	381	28	as	as	ADP
ejpam-6262	381	29	the	the	DET
ejpam-6262	381	30	weierstrass	weierstrass	NOUN
ejpam-6262	381	31	method	method	NOUN
ejpam-6262	381	32	by	by	ADP
ejpam-6262	381	33	solving	solve	VERB
ejpam-6262	381	34	this	this	DET
ejpam-6262	381	35	system	system	NOUN
ejpam-6262	381	36	of	of	ADP
ejpam-6262	381	37	polynomials	polynomial	NOUN
ejpam-6262	381	38	.	.	PUNCT
ejpam-6262	382	1	table	table	NOUN
ejpam-6262	382	2	9	9	NUM
ejpam-6262	382	3	:	:	PUNCT
ejpam-6262	382	4	comparisons	comparison	NOUN
ejpam-6262	382	5	between	between	ADP
ejpam-6262	382	6	distinct	distinct	ADJ
ejpam-6262	382	7	methods	method	NOUN
ejpam-6262	382	8	for	for	ADP
ejpam-6262	382	9	problem	problem	NOUN
ejpam-6262	382	10	3	3	NUM
ejpam-6262	382	11	.	.	PUNCT
ejpam-6262	382	12	method	method	PROPN
ejpam-6262	382	13	iterations	iteration	NOUN
ejpam-6262	382	14	time	time	NOUN
ejpam-6262	382	15	(	(	PUNCT
ejpam-6262	382	16	s	s	NOUN
ejpam-6262	382	17	)	)	PUNCT
ejpam-6262	382	18	final	final	ADJ
ejpam-6262	382	19	error	error	NOUN
ejpam-6262	382	20	weierstrass	weierstrass	NOUN
ejpam-6262	382	21	method	method	NOUN
ejpam-6262	382	22	12	12	NUM
ejpam-6262	382	23	0.003	0.003	NUM
ejpam-6262	382	24	not	not	PART
ejpam-6262	382	25	applicabble	applicabble	ADJ
ejpam-6262	382	26	newton	newton	PROPN
ejpam-6262	382	27	’s	’s	PART
ejpam-6262	382	28	method	method	NOUN
ejpam-6262	382	29	10	10	NUM
ejpam-6262	382	30	0.005	0.005	NUM
ejpam-6262	382	31	3.2×10e-7	3.2×10e-7	NUM
ejpam-6262	382	32	broyden	broyden	NOUN
ejpam-6262	382	33	’s	’s	PART
ejpam-6262	382	34	method	method	NOUN
ejpam-6262	382	35	20	20	NUM
ejpam-6262	382	36	0.006	0.006	NUM
ejpam-6262	382	37	2.0×10e-6	2.0×10e-6	NUM
ejpam-6262	382	38	dfh	dfh	NOUN
ejpam-6262	382	39	method	method	NOUN
ejpam-6262	382	40	10	10	NUM
ejpam-6262	382	41	0.004	0.004	NUM
ejpam-6262	382	42	1.5×10e-7	1.5×10e-7	NUM
ejpam-6262	382	43	the	the	DET
ejpam-6262	382	44	results	result	NOUN
ejpam-6262	382	45	in	in	ADP
ejpam-6262	382	46	table	table	NOUN
ejpam-6262	382	47	9	9	NUM
ejpam-6262	382	48	show	show	NOUN
ejpam-6262	382	49	that	that	SCONJ
ejpam-6262	382	50	the	the	DET
ejpam-6262	382	51	dfh	dfh	PROPN
ejpam-6262	382	52	method	method	NOUN
ejpam-6262	382	53	converges	converge	VERB
ejpam-6262	382	54	efficiently	efficiently	ADV
ejpam-6262	382	55	with	with	ADP
ejpam-6262	382	56	fewer	few	ADJ
ejpam-6262	382	57	iterations	iteration	NOUN
ejpam-6262	382	58	and	and	CCONJ
ejpam-6262	382	59	offers	offer	VERB
ejpam-6262	382	60	good	good	ADJ
ejpam-6262	382	61	accuracy	accuracy	NOUN
ejpam-6262	382	62	,	,	PUNCT
ejpam-6262	382	63	making	make	VERB
ejpam-6262	382	64	it	it	PRON
ejpam-6262	382	65	a	a	DET
ejpam-6262	382	66	strong	strong	ADJ
ejpam-6262	382	67	competitor	competitor	NOUN
ejpam-6262	382	68	to	to	ADP
ejpam-6262	382	69	the	the	DET
ejpam-6262	382	70	newton	newton	PROPN
ejpam-6262	382	71	,	,	PUNCT
ejpam-6262	382	72	broyden	broyden	NOUN
ejpam-6262	382	73	and	and	CCONJ
ejpam-6262	382	74	weierstrass	weierstrass	NOUN
ejpam-6262	382	75	method	method	NOUN
ejpam-6262	382	76	.	.	PUNCT
ejpam-6262	383	1	particularly	particularly	ADV
ejpam-6262	383	2	in	in	ADP
ejpam-6262	383	3	cases	case	NOUN
ejpam-6262	383	4	where	where	SCONJ
ejpam-6262	383	5	jacobian	jacobian	ADJ
ejpam-6262	383	6	evaluations	evaluation	NOUN
ejpam-6262	383	7	are	be	AUX
ejpam-6262	383	8	expensive	expensive	ADJ
ejpam-6262	383	9	.	.	PUNCT
ejpam-6262	384	1	7	7	X
ejpam-6262	384	2	.	.	X
ejpam-6262	384	3	conclusion	conclusion	NOUN
ejpam-6262	384	4	in	in	ADP
ejpam-6262	384	5	our	our	PRON
ejpam-6262	384	6	analysis	analysis	NOUN
ejpam-6262	384	7	of	of	ADP
ejpam-6262	384	8	several	several	ADJ
ejpam-6262	384	9	nonlinear	nonlinear	ADJ
ejpam-6262	384	10	equations	equation	NOUN
ejpam-6262	384	11	,	,	PUNCT
ejpam-6262	384	12	it	it	PRON
ejpam-6262	384	13	has	have	AUX
ejpam-6262	384	14	been	be	AUX
ejpam-6262	384	15	shown	show	VERB
ejpam-6262	384	16	that	that	SCONJ
ejpam-6262	384	17	the	the	DET
ejpam-6262	384	18	dfh	dfh	PROPN
ejpam-6262	384	19	method	method	NOUN
ejpam-6262	384	20	consistently	consistently	ADV
ejpam-6262	384	21	exhibits	exhibit	VERB
ejpam-6262	384	22	superior	superior	ADJ
ejpam-6262	384	23	efficiency	efficiency	NOUN
ejpam-6262	384	24	compared	compare	VERB
ejpam-6262	384	25	to	to	ADP
ejpam-6262	384	26	other	other	ADJ
ejpam-6262	384	27	derivative	derivative	ADJ
ejpam-6262	384	28	-	-	PUNCT
ejpam-6262	384	29	free	free	ADJ
ejpam-6262	384	30	algorithms	algorithm	NOUN
ejpam-6262	384	31	in	in	ADP
ejpam-6262	384	32	numerical	numerical	ADJ
ejpam-6262	384	33	solutions	solution	NOUN
ejpam-6262	384	34	.	.	PUNCT
ejpam-6262	385	1	this	this	DET
ejpam-6262	385	2	specific	specific	ADJ
ejpam-6262	385	3	approach	approach	NOUN
ejpam-6262	385	4	demonstrates	demonstrate	VERB
ejpam-6262	385	5	a	a	DET
ejpam-6262	385	6	superior	superior	ADJ
ejpam-6262	385	7	computational	computational	ADJ
ejpam-6262	385	8	convergence	convergence	NOUN
ejpam-6262	385	9	order	order	NOUN
ejpam-6262	385	10	relative	relative	ADJ
ejpam-6262	385	11	to	to	ADP
ejpam-6262	385	12	all	all	DET
ejpam-6262	385	13	other	other	ADJ
ejpam-6262	385	14	established	establish	VERB
ejpam-6262	385	15	methods	method	NOUN
ejpam-6262	385	16	when	when	SCONJ
ejpam-6262	385	17	derivatives	derivative	NOUN
ejpam-6262	385	18	are	be	AUX
ejpam-6262	385	19	not	not	PART
ejpam-6262	385	20	present	present	ADJ
ejpam-6262	385	21	.	.	PUNCT
ejpam-6262	386	1	both	both	DET
ejpam-6262	386	2	equations	equation	NOUN
ejpam-6262	386	3	featuring	feature	VERB
ejpam-6262	386	4	complex	complex	ADJ
ejpam-6262	386	5	roots	root	NOUN
ejpam-6262	386	6	and	and	CCONJ
ejpam-6262	386	7	systems	system	NOUN
ejpam-6262	386	8	of	of	ADP
ejpam-6262	386	9	non	non	ADJ
ejpam-6262	386	10	-	-	ADJ
ejpam-6262	386	11	linear	linear	ADJ
ejpam-6262	386	12	equations	equation	NOUN
ejpam-6262	386	13	demonstrate	demonstrate	VERB
ejpam-6262	386	14	an	an	DET
ejpam-6262	386	15	equivalent	equivalent	ADJ
ejpam-6262	386	16	level	level	NOUN
ejpam-6262	386	17	of	of	ADP
ejpam-6262	386	18	convergence	convergence	NOUN
ejpam-6262	386	19	.	.	PUNCT
ejpam-6262	387	1	it	it	PRON
ejpam-6262	387	2	is	be	AUX
ejpam-6262	387	3	evident	evident	ADJ
ejpam-6262	387	4	that	that	SCONJ
ejpam-6262	387	5	the	the	DET
ejpam-6262	387	6	secant	secant	ADJ
ejpam-6262	387	7	approach	approach	NOUN
ejpam-6262	387	8	involves	involve	VERB
ejpam-6262	387	9	two	two	NUM
ejpam-6262	387	10	function	function	NOUN
ejpam-6262	387	11	evaluations	evaluation	NOUN
ejpam-6262	387	12	,	,	PUNCT
ejpam-6262	387	13	whereas	whereas	SCONJ
ejpam-6262	387	14	the	the	DET
ejpam-6262	387	15	dfh	dfh	NOUN
ejpam-6262	387	16	necessitates	necessitate	VERB
ejpam-6262	387	17	three	three	NUM
ejpam-6262	387	18	.	.	PUNCT
ejpam-6262	388	1	however	however	ADV
ejpam-6262	388	2	,	,	PUNCT
ejpam-6262	388	3	based	base	VERB
ejpam-6262	388	4	on	on	ADP
ejpam-6262	388	5	the	the	DET
ejpam-6262	388	6	calculated	calculate	VERB
ejpam-6262	388	7	findings	finding	NOUN
ejpam-6262	388	8	shown	show	VERB
ejpam-6262	388	9	in	in	ADP
ejpam-6262	388	10	tables	table	NOUN
ejpam-6262	388	11	1	1	NUM
ejpam-6262	388	12	and	and	CCONJ
ejpam-6262	388	13	table	table	NOUN
ejpam-6262	388	14	2	2	NUM
ejpam-6262	388	15	,	,	PUNCT
ejpam-6262	388	16	it	it	PRON
ejpam-6262	388	17	can	can	AUX
ejpam-6262	388	18	be	be	AUX
ejpam-6262	388	19	seen	see	VERB
ejpam-6262	388	20	that	that	SCONJ
ejpam-6262	388	21	in	in	ADP
ejpam-6262	388	22	most	most	ADJ
ejpam-6262	388	23	cases	case	NOUN
ejpam-6262	388	24	the	the	DET
ejpam-6262	388	25	total	total	ADJ
ejpam-6262	388	26	count	count	NOUN
ejpam-6262	388	27	of	of	ADP
ejpam-6262	388	28	function	function	NOUN
ejpam-6262	388	29	evaluations	evaluation	NOUN
ejpam-6262	388	30	required	require	VERB
ejpam-6262	388	31	is	be	AUX
ejpam-6262	388	32	lower	low	ADJ
ejpam-6262	388	33	compared	compare	VERB
ejpam-6262	388	34	to	to	ADP
ejpam-6262	388	35	the	the	DET
ejpam-6262	388	36	secant	secant	ADJ
ejpam-6262	388	37	technique	technique	NOUN
ejpam-6262	388	38	.	.	PUNCT
ejpam-6262	389	1	therefore	therefore	ADV
ejpam-6262	389	2	,	,	PUNCT
ejpam-6262	389	3	the	the	DET
ejpam-6262	389	4	direct	direct	ADJ
ejpam-6262	389	5	false	false	ADJ
ejpam-6262	389	6	position	position	NOUN
ejpam-6262	389	7	(	(	PUNCT
ejpam-6262	389	8	dfh	dfh	NOUN
ejpam-6262	389	9	)	)	PUNCT
ejpam-6262	389	10	technique	technique	NOUN
ejpam-6262	389	11	may	may	AUX
ejpam-6262	389	12	be	be	AUX
ejpam-6262	389	13	regarded	regard	VERB
ejpam-6262	389	14	a	a	DET
ejpam-6262	389	15	more	more	ADV
ejpam-6262	389	16	effective	effective	ADJ
ejpam-6262	389	17	approach	approach	NOUN
ejpam-6262	389	18	to	to	ADP
ejpam-6262	389	19	achieving	achieve	VERB
ejpam-6262	389	20	rapid	rapid	ADJ
ejpam-6262	389	21	convergence	convergence	NOUN
ejpam-6262	389	22	in	in	ADP
ejpam-6262	389	23	determining	determine	VERB
ejpam-6262	389	24	solutions	solution	NOUN
ejpam-6262	389	25	to	to	ADP
ejpam-6262	389	26	nonlinear	nonlinear	ADJ
ejpam-6262	389	27	equations	equation	NOUN
ejpam-6262	389	28	.	.	PUNCT
ejpam-6262	390	1	this	this	PRON
ejpam-6262	390	2	holds	hold	VERB
ejpam-6262	390	3	especially	especially	ADV
ejpam-6262	390	4	true	true	ADJ
ejpam-6262	390	5	when	when	SCONJ
ejpam-6262	390	6	addressing	address	VERB
ejpam-6262	390	7	univariate	univariate	ADJ
ejpam-6262	390	8	nonlinear	nonlinear	ADJ
ejpam-6262	390	9	equations	equation	NOUN
ejpam-6262	390	10	containing	contain	VERB
ejpam-6262	390	11	complex	complex	ADJ
ejpam-6262	390	12	roots	root	NOUN
ejpam-6262	390	13	,	,	PUNCT
ejpam-6262	390	14	as	as	ADV
ejpam-6262	390	15	well	well	ADV
ejpam-6262	390	16	as	as	ADP
ejpam-6262	390	17	in	in	ADP
ejpam-6262	390	18	instances	instance	NOUN
ejpam-6262	390	19	of	of	ADP
ejpam-6262	390	20	multivariate	multivariate	NOUN
ejpam-6262	390	21	systems	system	NOUN
ejpam-6262	390	22	of	of	ADP
ejpam-6262	390	23	nonlinear	nonlinear	ADJ
ejpam-6262	390	24	equations	equation	NOUN
ejpam-6262	390	25	where	where	SCONJ
ejpam-6262	390	26	the	the	DET
ejpam-6262	390	27	absence	absence	NOUN
ejpam-6262	390	28	of	of	ADP
ejpam-6262	390	29	derivatives	derivative	NOUN
ejpam-6262	390	30	is	be	AUX
ejpam-6262	390	31	notable	notable	ADJ
ejpam-6262	390	32	.	.	PUNCT
ejpam-6262	391	1	given	give	VERB
ejpam-6262	391	2	its	its	PRON
ejpam-6262	391	3	superior	superior	ADJ
ejpam-6262	391	4	speed	speed	NOUN
ejpam-6262	391	5	compared	compare	VERB
ejpam-6262	391	6	to	to	ADP
ejpam-6262	391	7	the	the	DET
ejpam-6262	391	8	well	well	ADV
ejpam-6262	391	9	-	-	PUNCT
ejpam-6262	391	10	known	know	VERB
ejpam-6262	391	11	second	second	ADJ
ejpam-6262	391	12	-	-	PUNCT
ejpam-6262	391	13	order	order	NOUN
ejpam-6262	391	14	newton	newton	NOUN
ejpam-6262	391	15	technique	technique	NOUN
ejpam-6262	391	16	,	,	PUNCT
ejpam-6262	391	17	along	along	ADP
ejpam-6262	391	18	with	with	ADP
ejpam-6262	391	19	its	its	PRON
ejpam-6262	391	20	ability	ability	NOUN
ejpam-6262	391	21	to	to	PART
ejpam-6262	391	22	operate	operate	VERB
ejpam-6262	391	23	without	without	ADP
ejpam-6262	391	24	the	the	DET
ejpam-6262	391	25	need	need	NOUN
ejpam-6262	391	26	for	for	ADP
ejpam-6262	391	27	the	the	DET
ejpam-6262	391	28	function	function	NOUN
ejpam-6262	391	29	’s	’s	PART
ejpam-6262	391	30	derivative	derivative	NOUN
ejpam-6262	391	31	,	,	PUNCT
ejpam-6262	391	32	it	it	PRON
ejpam-6262	391	33	is	be	AUX
ejpam-6262	391	34	evident	evident	ADJ
ejpam-6262	391	35	that	that	SCONJ
ejpam-6262	391	36	this	this	DET
ejpam-6262	391	37	algorithm	algorithm	NOUN
ejpam-6262	391	38	has	have	VERB
ejpam-6262	391	39	significant	significant	ADJ
ejpam-6262	391	40	potential	potential	NOUN
ejpam-6262	391	41	for	for	ADP
ejpam-6262	391	42	both	both	CCONJ
ejpam-6262	391	43	the	the	DET
ejpam-6262	391	44	scientific	scientific	ADJ
ejpam-6262	391	45	and	and	CCONJ
ejpam-6262	391	46	industrial	industrial	ADJ
ejpam-6262	391	47	sectors	sector	NOUN
ejpam-6262	391	48	.	.	PUNCT
ejpam-6262	392	1	we	we	PRON
ejpam-6262	392	2	apply	apply	VERB
ejpam-6262	392	3	the	the	DET
ejpam-6262	392	4	dfh	dfh	PROPN
ejpam-6262	392	5	method	method	NOUN
ejpam-6262	392	6	to	to	PART
ejpam-6262	392	7	assess	assess	VERB
ejpam-6262	392	8	its	its	PRON
ejpam-6262	392	9	performance	performance	NOUN
ejpam-6262	392	10	on	on	ADP
ejpam-6262	392	11	the	the	DET
ejpam-6262	392	12	mixed	mixed	ADJ
ejpam-6262	392	13	hammerstein	hammerstein	PROPN
ejpam-6262	392	14	integral	integral	ADJ
ejpam-6262	392	15	equation	equation	NOUN
ejpam-6262	392	16	.	.	PUNCT
ejpam-6262	393	1	the	the	DET
ejpam-6262	393	2	comparisons	comparison	NOUN
ejpam-6262	393	3	in	in	ADP
ejpam-6262	393	4	tables	table	NOUN
ejpam-6262	393	5	6	6	NUM
ejpam-6262	393	6	and	and	CCONJ
ejpam-6262	393	7	7	7	NUM
ejpam-6262	393	8	reveal	reveal	VERB
ejpam-6262	393	9	that	that	SCONJ
ejpam-6262	393	10	the	the	DET
ejpam-6262	393	11	suggested	suggest	VERB
ejpam-6262	393	12	scheme	scheme	NOUN
ejpam-6262	393	13	demonstrates	demonstrate	VERB
ejpam-6262	393	14	outstanding	outstanding	ADJ
ejpam-6262	393	15	performance	performance	NOUN
ejpam-6262	393	16	and	and	CCONJ
ejpam-6262	393	17	,	,	PUNCT
ejpam-6262	393	18	on	on	ADP
ejpam-6262	393	19	the	the	DET
ejpam-6262	393	20	whole	whole	NOUN
ejpam-6262	393	21	,	,	PUNCT
ejpam-6262	393	22	is	be	AUX
ejpam-6262	393	23	on	on	ADP
ejpam-6262	393	24	par	par	NOUN
ejpam-6262	393	25	with	with	ADP
ejpam-6262	393	26	the	the	DET
ejpam-6262	393	27	other	other	ADJ
ejpam-6262	393	28	iterative	iterative	NOUN
ejpam-6262	393	29	techniques	technique	NOUN
ejpam-6262	393	30	considered	consider	VERB
ejpam-6262	393	31	in	in	ADP
ejpam-6262	393	32	terms	term	NOUN
ejpam-6262	393	33	of	of	ADP
ejpam-6262	393	34	convergence	convergence	NOUN
ejpam-6262	393	35	speed	speed	NOUN
ejpam-6262	393	36	and	and	CCONJ
ejpam-6262	393	37	accuracy	accuracy	NOUN
ejpam-6262	393	38	.	.	PUNCT
ejpam-6262	394	1	in	in	ADP
ejpam-6262	394	2	table	table	NOUN
ejpam-6262	394	3	8	8	NUM
ejpam-6262	394	4	our	our	PRON
ejpam-6262	394	5	method	method	NOUN
ejpam-6262	394	6	shows	show	VERB
ejpam-6262	394	7	that	that	SCONJ
ejpam-6262	394	8	it	it	PRON
ejpam-6262	394	9	is	be	AUX
ejpam-6262	394	10	a	a	DET
ejpam-6262	394	11	very	very	ADV
ejpam-6262	394	12	useful	useful	ADJ
ejpam-6262	394	13	choice	choice	NOUN
ejpam-6262	394	14	to	to	PART
ejpam-6262	394	15	use	use	VERB
ejpam-6262	394	16	for	for	ADP
ejpam-6262	394	17	sparse	sparse	ADJ
ejpam-6262	394	18	jacobian	jacobian	ADJ
ejpam-6262	394	19	structures	structure	NOUN
ejpam-6262	394	20	than	than	ADP
ejpam-6262	394	21	newton	newton	PROPN
ejpam-6262	394	22	and	and	CCONJ
ejpam-6262	394	23	broyden	broyden	NOUN
ejpam-6262	394	24	’s	’s	PART
ejpam-6262	394	25	methods	method	NOUN
ejpam-6262	394	26	.	.	PUNCT
ejpam-6262	395	1	in	in	ADP
ejpam-6262	395	2	y.	y.	PROPN
ejpam-6262	395	3	al	al	PROPN
ejpam-6262	395	4	-	-	PUNCT
ejpam-6262	395	5	shorman	shorman	PROPN
ejpam-6262	395	6	et	et	PROPN
ejpam-6262	395	7	al	al	PROPN
ejpam-6262	395	8	.	.	PUNCT
ejpam-6262	395	9	/	/	SYM
ejpam-6262	395	10	eur	eur	PROPN
ejpam-6262	395	11	.	.	PUNCT
ejpam-6262	396	1	j.	j.	PROPN
ejpam-6262	396	2	pure	pure	PROPN
ejpam-6262	396	3	appl	appl	PROPN
ejpam-6262	396	4	.	.	PROPN
ejpam-6262	396	5	math	math	PROPN
ejpam-6262	396	6	,	,	PUNCT
ejpam-6262	396	7	18	18	NUM
ejpam-6262	396	8	(	(	PUNCT
ejpam-6262	396	9	3	3	NUM
ejpam-6262	396	10	)	)	PUNCT
ejpam-6262	396	11	(	(	PUNCT
ejpam-6262	396	12	2025	2025	NUM
ejpam-6262	396	13	)	)	PUNCT
ejpam-6262	396	14	,	,	PUNCT
ejpam-6262	396	15	6262	6262	NUM
ejpam-6262	396	16	18	18	NUM
ejpam-6262	396	17	of	of	ADP
ejpam-6262	396	18	20	20	NUM
ejpam-6262	396	19	table	table	NOUN
ejpam-6262	396	20	9	9	NUM
ejpam-6262	396	21	also	also	ADV
ejpam-6262	396	22	our	our	PRON
ejpam-6262	396	23	method	method	NOUN
ejpam-6262	396	24	again	again	ADV
ejpam-6262	396	25	proved	prove	VERB
ejpam-6262	396	26	to	to	PART
ejpam-6262	396	27	be	be	AUX
ejpam-6262	396	28	faster	fast	ADJ
ejpam-6262	396	29	and	and	CCONJ
ejpam-6262	396	30	more	more	ADV
ejpam-6262	396	31	effective	effective	ADJ
ejpam-6262	396	32	than	than	ADP
ejpam-6262	396	33	newton	newton	PROPN
ejpam-6262	396	34	,	,	PUNCT
ejpam-6262	396	35	broyden	broyden	NOUN
ejpam-6262	396	36	,	,	PUNCT
ejpam-6262	396	37	and	and	CCONJ
ejpam-6262	396	38	dfh	dfh	NOUN
ejpam-6262	396	39	method	method	NOUN
ejpam-6262	396	40	as	as	ADV
ejpam-6262	396	41	well	well	ADV
ejpam-6262	396	42	as	as	ADP
ejpam-6262	396	43	the	the	DET
ejpam-6262	396	44	weierstrass	weierstrass	NOUN
ejpam-6262	396	45	method	method	NOUN
ejpam-6262	396	46	by	by	ADP
ejpam-6262	396	47	solving	solve	VERB
ejpam-6262	396	48	this	this	DET
ejpam-6262	396	49	system	system	NOUN
ejpam-6262	396	50	of	of	ADP
ejpam-6262	396	51	polynomials	polynomial	NOUN
ejpam-6262	396	52	.	.	PUNCT
ejpam-6262	397	1	references	reference	NOUN
ejpam-6262	397	2	[	[	X
ejpam-6262	397	3	1	1	NUM
ejpam-6262	397	4	]	]	PUNCT
ejpam-6262	397	5	h.	h.	PROPN
ejpam-6262	397	6	p.	p.	PROPN
ejpam-6262	397	7	s.	s.	PROPN
ejpam-6262	397	8	nishani	nishani	PROPN
ejpam-6262	397	9	,	,	PUNCT
ejpam-6262	397	10	s.	s.	PROPN
ejpam-6262	397	11	weerakoon	weerakoon	PROPN
ejpam-6262	397	12	,	,	PUNCT
ejpam-6262	397	13	t.	t.	PROPN
ejpam-6262	397	14	g.	g.	PROPN
ejpam-6262	397	15	i.	i.	PROPN
ejpam-6262	397	16	fernando	fernando	PROPN
ejpam-6262	397	17	,	,	PUNCT
ejpam-6262	397	18	and	and	CCONJ
ejpam-6262	397	19	m.	m.	NOUN
ejpam-6262	397	20	liyanage	liyanage	NOUN
ejpam-6262	397	21	.	.	PUNCT
ejpam-6262	398	1	third	third	ADJ
ejpam-6262	398	2	order	order	NOUN
ejpam-6262	398	3	convergence	convergence	NOUN
ejpam-6262	398	4	of	of	ADP
ejpam-6262	398	5	improved	improved	ADJ
ejpam-6262	398	6	newton	newton	PROPN
ejpam-6262	398	7	’s	’s	PART
ejpam-6262	398	8	method	method	NOUN
ejpam-6262	398	9	for	for	ADP
ejpam-6262	398	10	systems	system	NOUN
ejpam-6262	398	11	of	of	ADP
ejpam-6262	398	12	nonlinear	nonlinear	ADJ
ejpam-6262	398	13	equations	equation	NOUN
ejpam-6262	398	14	.	.	PUNCT
ejpam-6262	399	1	in	in	ADP
ejpam-6262	399	2	proceedings	proceeding	NOUN
ejpam-6262	399	3	of	of	ADP
ejpam-6262	399	4	the	the	DET
ejpam-6262	399	5	annual	annual	ADJ
ejpam-6262	399	6	sessions	session	NOUN
ejpam-6262	399	7	of	of	ADP
ejpam-6262	399	8	sri	sri	PROPN
ejpam-6262	399	9	lanka	lanka	PROPN
ejpam-6262	399	10	association	association	PROPN
ejpam-6262	399	11	for	for	ADP
ejpam-6262	399	12	the	the	DET
ejpam-6262	399	13	advancement	advancement	NOUN
ejpam-6262	399	14	of	of	ADP
ejpam-6262	399	15	science	science	NOUN
ejpam-6262	399	16	,	,	PUNCT
ejpam-6262	399	17	page	page	NOUN
ejpam-6262	399	18	502	502	NUM
ejpam-6262	399	19	/	/	SYM
ejpam-6262	399	20	e1	e1	PROPN
ejpam-6262	399	21	,	,	PUNCT
ejpam-6262	399	22	sri	sri	PROPN
ejpam-6262	399	23	lanka	lanka	PROPN
ejpam-6262	399	24	,	,	PUNCT
ejpam-6262	399	25	2014	2014	NUM
ejpam-6262	399	26	.	.	PUNCT
ejpam-6262	400	1	[	[	X
ejpam-6262	400	2	2	2	X
ejpam-6262	400	3	]	]	PUNCT
ejpam-6262	400	4	o.	o.	NOUN
ejpam-6262	400	5	said	say	VERB
ejpam-6262	400	6	solaiman	solaiman	NOUN
ejpam-6262	400	7	,	,	PUNCT
ejpam-6262	400	8	s.	s.	PROPN
ejpam-6262	400	9	a.	a.	PROPN
ejpam-6262	400	10	abdul	abdul	PROPN
ejpam-6262	400	11	karim	karim	PROPN
ejpam-6262	400	12	,	,	PUNCT
ejpam-6262	400	13	and	and	CCONJ
ejpam-6262	400	14	i.	i.	PROPN
ejpam-6262	400	15	hashim	hashim	PROPN
ejpam-6262	400	16	.	.	PUNCT
ejpam-6262	401	1	dynamical	dynamical	ADJ
ejpam-6262	401	2	comparison	comparison	NOUN
ejpam-6262	401	3	of	of	ADP
ejpam-6262	401	4	several	several	ADJ
ejpam-6262	401	5	third	third	ADJ
ejpam-6262	401	6	-	-	PUNCT
ejpam-6262	401	7	order	order	NOUN
ejpam-6262	401	8	iterative	iterative	NOUN
ejpam-6262	401	9	methods	method	NOUN
ejpam-6262	401	10	for	for	ADP
ejpam-6262	401	11	nonlinear	nonlinear	ADJ
ejpam-6262	401	12	equations	equation	NOUN
ejpam-6262	401	13	.	.	PUNCT
ejpam-6262	402	1	computers	computer	NOUN
ejpam-6262	402	2	,	,	PUNCT
ejpam-6262	402	3	materials	material	NOUN
ejpam-6262	402	4	&	&	CCONJ
ejpam-6262	402	5	continua	continua	PROPN
ejpam-6262	402	6	,	,	PUNCT
ejpam-6262	402	7	67(2):1951–1962	67(2):1951–1962	NUM
ejpam-6262	402	8	,	,	PUNCT
ejpam-6262	402	9	2021	2021	NUM
ejpam-6262	402	10	.	.	PUNCT
ejpam-6262	403	1	[	[	X
ejpam-6262	403	2	3	3	X
ejpam-6262	403	3	]	]	PUNCT
ejpam-6262	403	4	o.	o.	NOUN
ejpam-6262	403	5	said	say	VERB
ejpam-6262	403	6	solaiman	solaiman	NOUN
ejpam-6262	403	7	and	and	CCONJ
ejpam-6262	403	8	i.	i.	PROPN
ejpam-6262	403	9	hashim	hashim	PROPN
ejpam-6262	403	10	.	.	PUNCT
ejpam-6262	404	1	an	an	DET
ejpam-6262	404	2	iterative	iterative	NOUN
ejpam-6262	404	3	scheme	scheme	NOUN
ejpam-6262	404	4	of	of	ADP
ejpam-6262	404	5	arbitrary	arbitrary	ADJ
ejpam-6262	404	6	odd	odd	ADJ
ejpam-6262	404	7	order	order	NOUN
ejpam-6262	404	8	and	and	CCONJ
ejpam-6262	404	9	its	its	PRON
ejpam-6262	404	10	basins	basin	NOUN
ejpam-6262	404	11	of	of	ADP
ejpam-6262	404	12	attraction	attraction	NOUN
ejpam-6262	404	13	for	for	ADP
ejpam-6262	404	14	nonlinear	nonlinear	ADJ
ejpam-6262	404	15	systems	system	NOUN
ejpam-6262	404	16	.	.	PUNCT
ejpam-6262	405	1	computers	computer	NOUN
ejpam-6262	405	2	,	,	PUNCT
ejpam-6262	405	3	materials	material	NOUN
ejpam-6262	405	4	&	&	CCONJ
ejpam-6262	405	5	continua	continuum	NOUN
ejpam-6262	405	6	,	,	PUNCT
ejpam-6262	405	7	66(2):1427–1444	66(2):1427–1444	NUM
ejpam-6262	405	8	,	,	PUNCT
ejpam-6262	405	9	2021	2021	NUM
ejpam-6262	405	10	.	.	PUNCT
ejpam-6262	406	1	[	[	X
ejpam-6262	406	2	4	4	X
ejpam-6262	406	3	]	]	PUNCT
ejpam-6262	406	4	o.	o.	NOUN
ejpam-6262	406	5	said	say	VERB
ejpam-6262	406	6	solaiman	solaiman	NOUN
ejpam-6262	406	7	and	and	CCONJ
ejpam-6262	406	8	i.	i.	PROPN
ejpam-6262	406	9	hashim	hashim	PROPN
ejpam-6262	406	10	.	.	PUNCT
ejpam-6262	407	1	optimal	optimal	ADJ
ejpam-6262	407	2	eighth	eighth	ADJ
ejpam-6262	407	3	-	-	PUNCT
ejpam-6262	407	4	order	order	NOUN
ejpam-6262	407	5	solver	solver	NOUN
ejpam-6262	407	6	for	for	ADP
ejpam-6262	407	7	nonlinear	nonlinear	ADJ
ejpam-6262	407	8	equations	equation	NOUN
ejpam-6262	407	9	with	with	ADP
ejpam-6262	407	10	applications	application	NOUN
ejpam-6262	407	11	in	in	ADP
ejpam-6262	407	12	chemical	chemical	ADJ
ejpam-6262	407	13	engineering	engineering	NOUN
ejpam-6262	407	14	.	.	PUNCT
ejpam-6262	408	1	intelligent	intelligent	ADJ
ejpam-6262	408	2	automation	automation	NOUN
ejpam-6262	408	3	&	&	CCONJ
ejpam-6262	408	4	soft	soft	ADJ
ejpam-6262	408	5	computing	computing	NOUN
ejpam-6262	408	6	,	,	PUNCT
ejpam-6262	408	7	27(2):379–390	27(2):379–390	PROPN
ejpam-6262	408	8	,	,	PUNCT
ejpam-6262	408	9	2021	2021	NUM
ejpam-6262	408	10	.	.	PUNCT
ejpam-6262	409	1	[	[	X
ejpam-6262	409	2	5	5	X
ejpam-6262	409	3	]	]	X
ejpam-6262	409	4	abdullah	abdullah	PROPN
ejpam-6262	409	5	alsoboh	alsoboh	PROPN
ejpam-6262	409	6	,	,	PUNCT
ejpam-6262	409	7	ala	ala	PROPN
ejpam-6262	409	8	amourah	amourah	PROPN
ejpam-6262	409	9	,	,	PUNCT
ejpam-6262	409	10	omar	omar	PROPN
ejpam-6262	409	11	alnajar	alnajar	PROPN
ejpam-6262	409	12	,	,	PUNCT
ejpam-6262	409	13	mamoon	mamoon	NOUN
ejpam-6262	409	14	ahmed	ahmed	PROPN
ejpam-6262	409	15	,	,	PUNCT
ejpam-6262	409	16	and	and	CCONJ
ejpam-6262	409	17	tamer	tame	ADJ
ejpam-6262	409	18	m	m	VERB
ejpam-6262	409	19	seoudy	seoudy	ADJ
ejpam-6262	409	20	.	.	PUNCT
ejpam-6262	410	1	exploring	explore	VERB
ejpam-6262	410	2	q	q	ADJ
ejpam-6262	410	3	-	-	PUNCT
ejpam-6262	410	4	fibonacci	fibonacci	NOUN
ejpam-6262	410	5	numbers	number	NOUN
ejpam-6262	410	6	in	in	ADP
ejpam-6262	410	7	geometric	geometric	ADJ
ejpam-6262	410	8	function	function	NOUN
ejpam-6262	410	9	theory	theory	NOUN
ejpam-6262	410	10	:	:	PUNCT
ejpam-6262	410	11	univalence	univalence	NOUN
ejpam-6262	410	12	and	and	CCONJ
ejpam-6262	410	13	shell	shell	NOUN
ejpam-6262	410	14	-	-	PUNCT
ejpam-6262	410	15	like	like	ADJ
ejpam-6262	410	16	starlike	starlike	NOUN
ejpam-6262	410	17	curves	curve	NOUN
ejpam-6262	410	18	.	.	PUNCT
ejpam-6262	411	1	mathematics	mathematic	NOUN
ejpam-6262	411	2	,	,	PUNCT
ejpam-6262	411	3	13(8):1294	13(8):1294	NUM
ejpam-6262	411	4	,	,	PUNCT
ejpam-6262	411	5	2025	2025	NUM
ejpam-6262	411	6	.	.	PUNCT
ejpam-6262	412	1	[	[	X
ejpam-6262	412	2	6	6	NUM
ejpam-6262	412	3	]	]	X
ejpam-6262	412	4	abdullah	abdullah	PROPN
ejpam-6262	412	5	alsoboh	alsoboh	PROPN
ejpam-6262	412	6	,	,	PUNCT
ejpam-6262	412	7	murat	murat	PROPN
ejpam-6262	412	8	çağlar	çağlar	PROPN
ejpam-6262	412	9	,	,	PUNCT
ejpam-6262	412	10	and	and	CCONJ
ejpam-6262	412	11	mucahit	mucahit	ADJ
ejpam-6262	412	12	buyankara	buyankara	NOUN
ejpam-6262	412	13	.	.	PUNCT
ejpam-6262	413	1	fekete	fekete	NOUN
ejpam-6262	413	2	-	-	PUNCT
ejpam-6262	413	3	szegö	szegö	PROPN
ejpam-6262	413	4	inequality	inequality	NOUN
ejpam-6262	413	5	for	for	ADP
ejpam-6262	413	6	a	a	DET
ejpam-6262	413	7	subclass	subclass	NOUN
ejpam-6262	413	8	of	of	ADP
ejpam-6262	413	9	bi	bi	ADJ
ejpam-6262	413	10	-	-	ADJ
ejpam-6262	413	11	univalent	univalent	ADJ
ejpam-6262	413	12	functions	function	NOUN
ejpam-6262	413	13	linked	link	VERB
ejpam-6262	413	14	to	to	ADP
ejpam-6262	413	15	q	q	ADJ
ejpam-6262	413	16	-	-	ADJ
ejpam-6262	413	17	ultraspherical	ultraspherical	ADJ
ejpam-6262	413	18	polynomials	polynomial	NOUN
ejpam-6262	413	19	.	.	PUNCT
ejpam-6262	414	1	contemporary	contemporary	ADJ
ejpam-6262	414	2	mathematics	mathematic	NOUN
ejpam-6262	414	3	,	,	PUNCT
ejpam-6262	414	4	pages	page	NOUN
ejpam-6262	414	5	2531–2545	2531–2545	NUM
ejpam-6262	414	6	,	,	PUNCT
ejpam-6262	414	7	2024	2024	NUM
ejpam-6262	414	8	.	.	PUNCT
ejpam-6262	415	1	[	[	X
ejpam-6262	415	2	7	7	X
ejpam-6262	415	3	]	]	X
ejpam-6262	415	4	abdullah	abdullah	PROPN
ejpam-6262	415	5	alsoboh	alsoboh	PROPN
ejpam-6262	415	6	and	and	CCONJ
ejpam-6262	415	7	georgia	georgia	PROPN
ejpam-6262	415	8	irina	irina	PROPN
ejpam-6262	415	9	oros	oros	PROPN
ejpam-6262	415	10	.	.	PUNCT
ejpam-6262	416	1	a	a	DET
ejpam-6262	416	2	class	class	NOUN
ejpam-6262	416	3	of	of	ADP
ejpam-6262	416	4	bi	bi	ADJ
ejpam-6262	416	5	-	-	ADJ
ejpam-6262	416	6	univalent	univalent	ADJ
ejpam-6262	416	7	functions	function	NOUN
ejpam-6262	416	8	in	in	ADP
ejpam-6262	416	9	a	a	DET
ejpam-6262	416	10	leaf	leaf	NOUN
ejpam-6262	416	11	-	-	PUNCT
ejpam-6262	416	12	like	like	ADJ
ejpam-6262	416	13	domain	domain	NOUN
ejpam-6262	416	14	defined	define	VERB
ejpam-6262	416	15	through	through	ADP
ejpam-6262	416	16	subordination	subordination	NOUN
ejpam-6262	416	17	via	via	ADP
ejpam-6262	416	18	q	q	NOUN
ejpam-6262	416	19	-	-	NOUN
ejpam-6262	416	20	calculus	calculus	NOUN
ejpam-6262	416	21	.	.	PUNCT
ejpam-6262	417	1	mathematics	mathematic	NOUN
ejpam-6262	417	2	,	,	PUNCT
ejpam-6262	417	3	12(10):1594	12(10):1594	NUM
ejpam-6262	417	4	,	,	PUNCT
ejpam-6262	417	5	2024	2024	NUM
ejpam-6262	417	6	.	.	PUNCT
ejpam-6262	418	1	[	[	X
ejpam-6262	418	2	8	8	X
ejpam-6262	418	3	]	]	X
ejpam-6262	418	4	muhammad	muhammad	PROPN
ejpam-6262	418	5	altaf	altaf	PROPN
ejpam-6262	418	6	khan	khan	PROPN
ejpam-6262	418	7	,	,	PUNCT
ejpam-6262	418	8	khanadan	khanadan	PROPN
ejpam-6262	418	9	khan	khan	PROPN
ejpam-6262	418	10	,	,	PUNCT
ejpam-6262	418	11	mohammad	mohammad	PROPN
ejpam-6262	418	12	a	a	DET
ejpam-6262	418	13	safi	safi	PROPN
ejpam-6262	418	14	,	,	PUNCT
ejpam-6262	418	15	and	and	CCONJ
ejpam-6262	418	16	mahmoud	mahmoud	PROPN
ejpam-6262	418	17	h	h	PROPN
ejpam-6262	418	18	darassi	darassi	PROPN
ejpam-6262	418	19	.	.	PUNCT
ejpam-6262	419	1	a	a	DET
ejpam-6262	419	2	discrete	discrete	ADJ
ejpam-6262	419	3	model	model	NOUN
ejpam-6262	419	4	of	of	ADP
ejpam-6262	419	5	tb	tb	ADP
ejpam-6262	419	6	dynamics	dynamic	NOUN
ejpam-6262	419	7	in	in	ADP
ejpam-6262	419	8	khyber	khyber	PROPN
ejpam-6262	419	9	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-6262	419	10	-	-	PUNCT
ejpam-6262	419	11	pakistan	pakistan	PROPN
ejpam-6262	419	12	.	.	PUNCT
ejpam-6262	420	1	computer	computer	NOUN
ejpam-6262	420	2	modeling	modeling	NOUN
ejpam-6262	420	3	in	in	ADP
ejpam-6262	420	4	engineering	engineering	NOUN
ejpam-6262	420	5	&	&	CCONJ
ejpam-6262	420	6	sciences	sciences	PROPN
ejpam-6262	420	7	,	,	PUNCT
ejpam-6262	420	8	123(2):777–795	123(2):777–795	NUM
ejpam-6262	420	9	,	,	PUNCT
ejpam-6262	420	10	2020	2020	NUM
ejpam-6262	420	11	.	.	PUNCT
ejpam-6262	421	1	[	[	X
ejpam-6262	421	2	9	9	NUM
ejpam-6262	421	3	]	]	PUNCT
ejpam-6262	421	4	n	n	PRON
ejpam-6262	421	5	ratib	ratib	PROPN
ejpam-6262	421	6	anakira	anakira	PROPN
ejpam-6262	421	7	,	,	PUNCT
ejpam-6262	421	8	ak	ak	PROPN
ejpam-6262	421	9	alomari	alomari	PROPN
ejpam-6262	421	10	,	,	PUNCT
ejpam-6262	421	11	and	and	CCONJ
ejpam-6262	421	12	ishak	ishak	VERB
ejpam-6262	421	13	hashim	hashim	PROPN
ejpam-6262	421	14	.	.	PUNCT
ejpam-6262	422	1	numerical	numerical	ADJ
ejpam-6262	422	2	scheme	scheme	NOUN
ejpam-6262	422	3	for	for	ADP
ejpam-6262	422	4	solving	solve	VERB
ejpam-6262	422	5	singular	singular	ADJ
ejpam-6262	422	6	two	two	NUM
ejpam-6262	422	7	-	-	PUNCT
ejpam-6262	422	8	point	point	NOUN
ejpam-6262	422	9	boundary	boundary	ADJ
ejpam-6262	422	10	value	value	NOUN
ejpam-6262	422	11	problems	problem	NOUN
ejpam-6262	422	12	.	.	PUNCT
ejpam-6262	423	1	journal	journal	NOUN
ejpam-6262	423	2	of	of	ADP
ejpam-6262	423	3	applied	apply	VERB
ejpam-6262	423	4	mathematics	mathematic	NOUN
ejpam-6262	423	5	,	,	PUNCT
ejpam-6262	423	6	2013(1):468909	2013(1):468909	NUM
ejpam-6262	423	7	,	,	PUNCT
ejpam-6262	423	8	2013	2013	NUM
ejpam-6262	423	9	.	.	PUNCT
ejpam-6262	424	1	[	[	X
ejpam-6262	424	2	10	10	NUM
ejpam-6262	424	3	]	]	PUNCT
ejpam-6262	424	4	n	n	PRON
ejpam-6262	424	5	ratib	ratib	PROPN
ejpam-6262	424	6	anakira	anakira	PROPN
ejpam-6262	424	7	,	,	PUNCT
ejpam-6262	424	8	ak	ak	PROPN
ejpam-6262	424	9	alomari	alomari	PROPN
ejpam-6262	424	10	,	,	PUNCT
ejpam-6262	424	11	af	af	PROPN
ejpam-6262	424	12	jameel	jameel	PROPN
ejpam-6262	424	13	,	,	PUNCT
ejpam-6262	424	14	and	and	CCONJ
ejpam-6262	424	15	ishak	ishak	VERB
ejpam-6262	424	16	hashim	hashim	PROPN
ejpam-6262	424	17	.	.	PUNCT
ejpam-6262	425	1	multistage	multistage	VERB
ejpam-6262	425	2	optimal	optimal	ADJ
ejpam-6262	425	3	homotopy	homotopy	NOUN
ejpam-6262	425	4	asymptotic	asymptotic	ADJ
ejpam-6262	425	5	method	method	NOUN
ejpam-6262	425	6	for	for	ADP
ejpam-6262	425	7	solving	solve	VERB
ejpam-6262	425	8	initial	initial	ADJ
ejpam-6262	425	9	-	-	PUNCT
ejpam-6262	425	10	value	value	NOUN
ejpam-6262	425	11	problems	problem	NOUN
ejpam-6262	425	12	.	.	PUNCT
ejpam-6262	426	1	j.	j.	PROPN
ejpam-6262	426	2	nonlinear	nonlinear	PROPN
ejpam-6262	426	3	sci	sci	PROPN
ejpam-6262	426	4	.	.	PUNCT
ejpam-6262	426	5	appl	appl	PROPN
ejpam-6262	426	6	,	,	PUNCT
ejpam-6262	426	7	9(4):1826–1843	9(4):1826–1843	PROPN
ejpam-6262	426	8	,	,	PUNCT
ejpam-6262	426	9	2016	2016	NUM
ejpam-6262	426	10	.	.	PUNCT
ejpam-6262	427	1	[	[	X
ejpam-6262	427	2	11	11	NUM
ejpam-6262	427	3	]	]	X
ejpam-6262	427	4	nidal	nidal	PROPN
ejpam-6262	427	5	anakira	anakira	PROPN
ejpam-6262	427	6	,	,	PUNCT
ejpam-6262	427	7	ali	ali	PROPN
ejpam-6262	427	8	jameel	jameel	PROPN
ejpam-6262	427	9	,	,	PUNCT
ejpam-6262	427	10	mohmmad	mohmmad	PROPN
ejpam-6262	427	11	hijazi	hijazi	NOUN
ejpam-6262	427	12	,	,	PUNCT
ejpam-6262	427	13	abedel	abedel	PROPN
ejpam-6262	427	14	-	-	PUNCT
ejpam-6262	427	15	karrem	karrem	VERB
ejpam-6262	427	16	alomari	alomari	PROPN
ejpam-6262	427	17	,	,	PUNCT
ejpam-6262	427	18	and	and	CCONJ
ejpam-6262	427	19	noraziah	noraziah	PROPN
ejpam-6262	427	20	man	man	NOUN
ejpam-6262	427	21	.	.	PUNCT
ejpam-6262	428	1	a	a	DET
ejpam-6262	428	2	new	new	ADJ
ejpam-6262	428	3	approach	approach	NOUN
ejpam-6262	428	4	for	for	ADP
ejpam-6262	428	5	solving	solve	VERB
ejpam-6262	428	6	multi	multi	ADJ
ejpam-6262	428	7	-	-	ADJ
ejpam-6262	428	8	pantograph	pantograph	ADJ
ejpam-6262	428	9	type	type	NOUN
ejpam-6262	428	10	delay	delay	NOUN
ejpam-6262	428	11	differential	differential	NOUN
ejpam-6262	428	12	equations	equation	NOUN
ejpam-6262	428	13	.	.	PUNCT
ejpam-6262	429	1	international	international	ADJ
ejpam-6262	429	2	journal	journal	PROPN
ejpam-6262	429	3	of	of	ADP
ejpam-6262	429	4	electrical	electrical	ADJ
ejpam-6262	429	5	&	&	CCONJ
ejpam-6262	429	6	computer	computer	PROPN
ejpam-6262	429	7	engineering	engineering	NOUN
ejpam-6262	429	8	(	(	PUNCT
ejpam-6262	429	9	20888708	20888708	NUM
ejpam-6262	429	10	)	)	PUNCT
ejpam-6262	429	11	,	,	PUNCT
ejpam-6262	429	12	12(2	12(2	NUM
ejpam-6262	429	13	)	)	PUNCT
ejpam-6262	429	14	,	,	PUNCT
ejpam-6262	429	15	2022	2022	NUM
ejpam-6262	429	16	.	.	PUNCT
ejpam-6262	430	1	[	[	X
ejpam-6262	430	2	12	12	NUM
ejpam-6262	430	3	]	]	X
ejpam-6262	430	4	r.	r.	PROPN
ejpam-6262	430	5	l.	l.	PROPN
ejpam-6262	430	6	burden	burden	PROPN
ejpam-6262	430	7	and	and	CCONJ
ejpam-6262	430	8	j.	j.	PROPN
ejpam-6262	430	9	d.	d.	PROPN
ejpam-6262	430	10	faires	faires	PROPN
ejpam-6262	430	11	.	.	PUNCT
ejpam-6262	431	1	numerical	numerical	ADJ
ejpam-6262	431	2	analysis	analysis	NOUN
ejpam-6262	431	3	.	.	PUNCT
ejpam-6262	432	1	bob	bob	PROPN
ejpam-6262	432	2	pirtle	pirtle	PROPN
ejpam-6262	432	3	,	,	PUNCT
ejpam-6262	432	4	usa	usa	PROPN
ejpam-6262	432	5	,	,	PUNCT
ejpam-6262	432	6	8th	8th	ADJ
ejpam-6262	432	7	edition	edition	NOUN
ejpam-6262	432	8	,	,	PUNCT
ejpam-6262	432	9	2005	2005	NUM
ejpam-6262	432	10	.	.	PUNCT
ejpam-6262	433	1	y.	y.	PROPN
ejpam-6262	433	2	al	al	PROPN
ejpam-6262	433	3	-	-	PUNCT
ejpam-6262	433	4	shorman	shorman	PROPN
ejpam-6262	433	5	et	et	PROPN
ejpam-6262	433	6	al	al	PROPN
ejpam-6262	433	7	.	.	PUNCT
ejpam-6262	433	8	/	/	SYM
ejpam-6262	433	9	eur	eur	PROPN
ejpam-6262	433	10	.	.	PUNCT
ejpam-6262	434	1	j.	j.	PROPN
ejpam-6262	434	2	pure	pure	PROPN
ejpam-6262	434	3	appl	appl	PROPN
ejpam-6262	434	4	.	.	PROPN
ejpam-6262	434	5	math	math	PROPN
ejpam-6262	434	6	,	,	PUNCT
ejpam-6262	434	7	18	18	NUM
ejpam-6262	434	8	(	(	PUNCT
ejpam-6262	434	9	3	3	NUM
ejpam-6262	434	10	)	)	PUNCT
ejpam-6262	434	11	(	(	PUNCT
ejpam-6262	434	12	2025	2025	NUM
ejpam-6262	434	13	)	)	PUNCT
ejpam-6262	434	14	,	,	PUNCT
ejpam-6262	434	15	6262	6262	NUM
ejpam-6262	434	16	19	19	NUM
ejpam-6262	434	17	of	of	ADP
ejpam-6262	434	18	20	20	NUM
ejpam-6262	435	1	[	[	SYM
ejpam-6262	435	2	13	13	NUM
ejpam-6262	435	3	]	]	X
ejpam-6262	435	4	mahmoud	mahmoud	PROPN
ejpam-6262	435	5	h	h	PROPN
ejpam-6262	435	6	darassi	darassi	PROPN
ejpam-6262	435	7	,	,	PUNCT
ejpam-6262	435	8	taqi	taqi	X
ejpam-6262	435	9	am	be	AUX
ejpam-6262	435	10	shatnawi	shatnawi	ADJ
ejpam-6262	435	11	,	,	PUNCT
ejpam-6262	435	12	and	and	CCONJ
ejpam-6262	435	13	mohammad	mohammad	PROPN
ejpam-6262	435	14	a	a	DET
ejpam-6262	435	15	safi	safi	PROPN
ejpam-6262	435	16	.	.	PROPN
ejpam-6262	436	1	mathematical	mathematical	ADJ
ejpam-6262	436	2	analysis	analysis	NOUN
ejpam-6262	436	3	of	of	ADP
ejpam-6262	436	4	a	a	DET
ejpam-6262	436	5	mers	mer	NOUN
ejpam-6262	436	6	-	-	PUNCT
ejpam-6262	436	7	cov	cov	NOUN
ejpam-6262	436	8	coronavirus	coronavirus	NOUN
ejpam-6262	436	9	model	model	NOUN
ejpam-6262	436	10	.	.	PROPN
ejpam-6262	437	1	demonstratio	demonstratio	PROPN
ejpam-6262	437	2	mathematica	mathematica	PROPN
ejpam-6262	437	3	,	,	PUNCT
ejpam-6262	437	4	55(1):265	55(1):265	NUM
ejpam-6262	437	5	–	–	PUNCT
ejpam-6262	437	6	276	276	NUM
ejpam-6262	437	7	,	,	PUNCT
ejpam-6262	437	8	2022	2022	NUM
ejpam-6262	437	9	.	.	PUNCT
ejpam-6262	438	1	[	[	X
ejpam-6262	438	2	14	14	NUM
ejpam-6262	438	3	]	]	PUNCT
ejpam-6262	438	4	m.	m.	NOUN
ejpam-6262	438	5	frontini	frontini	PROPN
ejpam-6262	438	6	and	and	CCONJ
ejpam-6262	438	7	e.	e.	PROPN
ejpam-6262	438	8	sormani	sormani	PROPN
ejpam-6262	438	9	.	.	PUNCT
ejpam-6262	439	1	modified	modified	PROPN
ejpam-6262	439	2	newton	newton	PROPN
ejpam-6262	439	3	’s	’s	PART
ejpam-6262	439	4	method	method	NOUN
ejpam-6262	439	5	with	with	ADP
ejpam-6262	439	6	third	third	ADJ
ejpam-6262	439	7	-	-	PUNCT
ejpam-6262	439	8	order	order	NOUN
ejpam-6262	439	9	convergence	convergence	NOUN
ejpam-6262	439	10	and	and	CCONJ
ejpam-6262	439	11	multiple	multiple	ADJ
ejpam-6262	439	12	roots	root	NOUN
ejpam-6262	439	13	.	.	PUNCT
ejpam-6262	440	1	journal	journal	NOUN
ejpam-6262	440	2	of	of	ADP
ejpam-6262	440	3	computational	computational	ADJ
ejpam-6262	440	4	and	and	CCONJ
ejpam-6262	440	5	applied	applied	ADJ
ejpam-6262	440	6	mathematics	mathematic	NOUN
ejpam-6262	440	7	,	,	PUNCT
ejpam-6262	440	8	156:345–354	156:345–354	NUM
ejpam-6262	440	9	,	,	PUNCT
ejpam-6262	440	10	2003	2003	NUM
ejpam-6262	440	11	.	.	PUNCT
ejpam-6262	441	1	[	[	X
ejpam-6262	441	2	15	15	NUM
ejpam-6262	441	3	]	]	X
ejpam-6262	441	4	m.	m.	NOUN
ejpam-6262	441	5	frontini	frontini	PROPN
ejpam-6262	441	6	and	and	CCONJ
ejpam-6262	441	7	e.	e.	PROPN
ejpam-6262	441	8	sormani	sormani	PROPN
ejpam-6262	441	9	.	.	PUNCT
ejpam-6262	442	1	some	some	DET
ejpam-6262	442	2	variant	variant	NOUN
ejpam-6262	442	3	of	of	ADP
ejpam-6262	442	4	newton	newton	PROPN
ejpam-6262	442	5	’s	’s	PART
ejpam-6262	442	6	method	method	NOUN
ejpam-6262	442	7	with	with	ADP
ejpam-6262	442	8	third	third	ADJ
ejpam-6262	442	9	-	-	PUNCT
ejpam-6262	442	10	order	order	NOUN
ejpam-6262	442	11	convergence	convergence	NOUN
ejpam-6262	442	12	.	.	PUNCT
ejpam-6262	443	1	journal	journal	NOUN
ejpam-6262	443	2	of	of	ADP
ejpam-6262	443	3	computational	computational	ADJ
ejpam-6262	443	4	and	and	CCONJ
ejpam-6262	443	5	applied	applied	ADJ
ejpam-6262	443	6	mathematics	mathematic	NOUN
ejpam-6262	443	7	,	,	PUNCT
ejpam-6262	443	8	140:419–426	140:419–426	NUM
ejpam-6262	443	9	,	,	PUNCT
ejpam-6262	443	10	2003	2003	NUM
ejpam-6262	443	11	.	.	PUNCT
ejpam-6262	444	1	[	[	X
ejpam-6262	444	2	16	16	NUM
ejpam-6262	444	3	]	]	PUNCT
ejpam-6262	444	4	h.	h.	PROPN
ejpam-6262	444	5	h.	h.	PROPN
ejpam-6262	444	6	h.	h.	PROPN
ejpam-6262	444	7	homeier	homeier	PROPN
ejpam-6262	444	8	.	.	PUNCT
ejpam-6262	445	1	on	on	ADP
ejpam-6262	445	2	newton	newton	PROPN
ejpam-6262	445	3	-	-	PUNCT
ejpam-6262	445	4	type	type	NOUN
ejpam-6262	445	5	methods	method	NOUN
ejpam-6262	445	6	with	with	ADP
ejpam-6262	445	7	cubic	cubic	ADJ
ejpam-6262	445	8	convergence	convergence	NOUN
ejpam-6262	445	9	.	.	PUNCT
ejpam-6262	446	1	journal	journal	NOUN
ejpam-6262	446	2	of	of	ADP
ejpam-6262	446	3	computational	computational	ADJ
ejpam-6262	446	4	and	and	CCONJ
ejpam-6262	446	5	applied	applied	ADJ
ejpam-6262	446	6	mathematics	mathematic	NOUN
ejpam-6262	446	7	,	,	PUNCT
ejpam-6262	446	8	176:425–432	176:425–432	NUM
ejpam-6262	446	9	,	,	PUNCT
ejpam-6262	446	10	2005	2005	NUM
ejpam-6262	446	11	.	.	PUNCT
ejpam-6262	447	1	[	[	X
ejpam-6262	447	2	17	17	NUM
ejpam-6262	447	3	]	]	PUNCT
ejpam-6262	447	4	maisa	maisa	NOUN
ejpam-6262	447	5	khader	khader	NOUN
ejpam-6262	447	6	and	and	CCONJ
ejpam-6262	447	7	mahmoud	mahmoud	PROPN
ejpam-6262	447	8	h	h	PROPN
ejpam-6262	447	9	darassi	darassi	PROPN
ejpam-6262	447	10	.	.	PUNCT
ejpam-6262	448	1	residual	residual	ADJ
ejpam-6262	448	2	power	power	NOUN
ejpam-6262	448	3	series	series	NOUN
ejpam-6262	448	4	method	method	NOUN
ejpam-6262	448	5	for	for	ADP
ejpam-6262	448	6	solving	solve	VERB
ejpam-6262	448	7	nonlinear	nonlinear	ADJ
ejpam-6262	448	8	reaction	reaction	NOUN
ejpam-6262	448	9	-	-	PUNCT
ejpam-6262	448	10	diffusion	diffusion	NOUN
ejpam-6262	448	11	-	-	PUNCT
ejpam-6262	448	12	convection	convection	NOUN
ejpam-6262	448	13	problems	problem	NOUN
ejpam-6262	448	14	.	.	PUNCT
ejpam-6262	449	1	bol	bol	NOUN
ejpam-6262	449	2	.	.	PUNCT
ejpam-6262	450	1	da	da	PROPN
ejpam-6262	450	2	soc	soc	PROPN
ejpam-6262	450	3	.	.	PUNCT
ejpam-6262	451	1	parana	parana	PROPN
ejpam-6262	451	2	.	.	PUNCT
ejpam-6262	452	1	de	de	PROPN
ejpam-6262	452	2	mat	mat	PROPN
ejpam-6262	452	3	,	,	PUNCT
ejpam-6262	452	4	39:177–188	39:177–188	NUM
ejpam-6262	452	5	,	,	PUNCT
ejpam-6262	452	6	2021	2021	NUM
ejpam-6262	452	7	.	.	PUNCT
ejpam-6262	453	1	[	[	X
ejpam-6262	453	2	18	18	NUM
ejpam-6262	453	3	]	]	X
ejpam-6262	453	4	j.	j.	PROPN
ejpam-6262	453	5	m.	m.	PROPN
ejpam-6262	453	6	ortega	ortega	PROPN
ejpam-6262	453	7	and	and	CCONJ
ejpam-6262	453	8	w.	w.	PROPN
ejpam-6262	453	9	c.	c.	PROPN
ejpam-6262	453	10	rheinboldt	rheinboldt	PROPN
ejpam-6262	453	11	.	.	PROPN
ejpam-6262	454	1	iterative	iterative	NOUN
ejpam-6262	454	2	solution	solution	NOUN
ejpam-6262	454	3	of	of	ADP
ejpam-6262	454	4	nonlinear	nonlinear	ADJ
ejpam-6262	454	5	equations	equation	NOUN
ejpam-6262	454	6	in	in	ADP
ejpam-6262	454	7	several	several	ADJ
ejpam-6262	454	8	variables	variable	NOUN
ejpam-6262	454	9	.	.	PUNCT
ejpam-6262	455	1	academic	academic	ADJ
ejpam-6262	455	2	press	press	NOUN
ejpam-6262	455	3	,	,	PUNCT
ejpam-6262	455	4	new	new	PROPN
ejpam-6262	455	5	york	york	PROPN
ejpam-6262	455	6	,	,	PUNCT
ejpam-6262	455	7	ny	ny	PROPN
ejpam-6262	455	8	,	,	PUNCT
ejpam-6262	455	9	usa	usa	PROPN
ejpam-6262	455	10	,	,	PUNCT
ejpam-6262	455	11	1970	1970	NUM
ejpam-6262	455	12	.	.	PUNCT
ejpam-6262	456	1	[	[	X
ejpam-6262	456	2	19	19	NUM
ejpam-6262	456	3	]	]	PUNCT
ejpam-6262	456	4	s.	s.	PROPN
ejpam-6262	456	5	weerakoon	weerakoon	PROPN
ejpam-6262	456	6	and	and	CCONJ
ejpam-6262	456	7	t.	t.	PROPN
ejpam-6262	456	8	g.	g.	PROPN
ejpam-6262	456	9	i.	i.	PROPN
ejpam-6262	456	10	fernando	fernando	PROPN
ejpam-6262	456	11	.	.	PUNCT
ejpam-6262	457	1	a	a	DET
ejpam-6262	457	2	variant	variant	NOUN
ejpam-6262	457	3	of	of	ADP
ejpam-6262	457	4	newton	newton	PROPN
ejpam-6262	457	5	’s	’s	PART
ejpam-6262	457	6	method	method	NOUN
ejpam-6262	457	7	with	with	ADP
ejpam-6262	457	8	accelerated	accelerate	VERB
ejpam-6262	457	9	third	third	ADJ
ejpam-6262	457	10	-	-	PUNCT
ejpam-6262	457	11	order	order	NOUN
ejpam-6262	457	12	convergence	convergence	NOUN
ejpam-6262	457	13	.	.	PUNCT
ejpam-6262	458	1	applied	apply	VERB
ejpam-6262	458	2	mathematics	mathematics	NOUN
ejpam-6262	458	3	letters	letter	NOUN
ejpam-6262	458	4	,	,	PUNCT
ejpam-6262	458	5	13:87–93	13:87–93	NUM
ejpam-6262	458	6	,	,	PUNCT
ejpam-6262	458	7	2000	2000	NUM
ejpam-6262	458	8	.	.	PUNCT
ejpam-6262	459	1	[	[	X
ejpam-6262	459	2	20	20	NUM
ejpam-6262	459	3	]	]	PUNCT
ejpam-6262	459	4	h.	h.	PROPN
ejpam-6262	459	5	h.	h.	PROPN
ejpam-6262	459	6	h.	h.	PROPN
ejpam-6262	459	7	homeier	homeier	PROPN
ejpam-6262	459	8	.	.	PUNCT
ejpam-6262	460	1	a	a	DET
ejpam-6262	460	2	modified	modify	VERB
ejpam-6262	460	3	newton	newton	PROPN
ejpam-6262	460	4	method	method	NOUN
ejpam-6262	460	5	for	for	ADP
ejpam-6262	460	6	root	root	NOUN
ejpam-6262	460	7	finding	finding	NOUN
ejpam-6262	460	8	with	with	ADP
ejpam-6262	460	9	cubic	cubic	ADJ
ejpam-6262	460	10	convergence	convergence	NOUN
ejpam-6262	460	11	.	.	PUNCT
ejpam-6262	461	1	journal	journal	NOUN
ejpam-6262	461	2	of	of	ADP
ejpam-6262	461	3	computational	computational	ADJ
ejpam-6262	461	4	and	and	CCONJ
ejpam-6262	461	5	applied	applied	ADJ
ejpam-6262	461	6	mathematics	mathematic	NOUN
ejpam-6262	461	7	,	,	PUNCT
ejpam-6262	461	8	157:227–230	157:227–230	NUM
ejpam-6262	461	9	,	,	PUNCT
ejpam-6262	461	10	2003	2003	NUM
ejpam-6262	461	11	.	.	PUNCT
ejpam-6262	462	1	[	[	X
ejpam-6262	462	2	21	21	NUM
ejpam-6262	462	3	]	]	X
ejpam-6262	462	4	h.	h.	PROPN
ejpam-6262	462	5	h.	h.	PROPN
ejpam-6262	462	6	h.	h.	PROPN
ejpam-6262	462	7	homeier	homeier	PROPN
ejpam-6262	462	8	.	.	PUNCT
ejpam-6262	463	1	a	a	DET
ejpam-6262	463	2	modified	modify	VERB
ejpam-6262	463	3	newton	newton	PROPN
ejpam-6262	463	4	method	method	NOUN
ejpam-6262	463	5	with	with	ADP
ejpam-6262	463	6	cubic	cubic	ADJ
ejpam-6262	463	7	convergence	convergence	NOUN
ejpam-6262	463	8	:	:	PUNCT
ejpam-6262	463	9	the	the	DET
ejpam-6262	463	10	multivariate	multivariate	NOUN
ejpam-6262	463	11	case	case	NOUN
ejpam-6262	463	12	.	.	PUNCT
ejpam-6262	464	1	journal	journal	NOUN
ejpam-6262	464	2	of	of	ADP
ejpam-6262	464	3	computational	computational	ADJ
ejpam-6262	464	4	and	and	CCONJ
ejpam-6262	464	5	applied	applied	ADJ
ejpam-6262	464	6	mathematics	mathematic	NOUN
ejpam-6262	464	7	,	,	PUNCT
ejpam-6262	464	8	169:161–169	169:161–169	NUM
ejpam-6262	464	9	,	,	PUNCT
ejpam-6262	464	10	2004	2004	NUM
ejpam-6262	464	11	.	.	PUNCT
ejpam-6262	465	1	[	[	X
ejpam-6262	465	2	22	22	NUM
ejpam-6262	465	3	]	]	PUNCT
ejpam-6262	465	4	t.	t.	PROPN
ejpam-6262	465	5	sauer	sauer	PROPN
ejpam-6262	465	6	.	.	PUNCT
ejpam-6262	466	1	numerical	numerical	ADJ
ejpam-6262	466	2	analysis	analysis	NOUN
ejpam-6262	466	3	.	.	PUNCT
ejpam-6262	467	1	pearson	pearson	PROPN
ejpam-6262	467	2	education	education	PROPN
ejpam-6262	467	3	,	,	PUNCT
ejpam-6262	467	4	boston	boston	PROPN
ejpam-6262	467	5	,	,	PUNCT
ejpam-6262	467	6	ma	ma	PROPN
ejpam-6262	467	7	,	,	PUNCT
ejpam-6262	467	8	usa	usa	PROPN
ejpam-6262	467	9	,	,	PUNCT
ejpam-6262	467	10	2nd	2nd	PROPN
ejpam-6262	467	11	edition	edition	NOUN
ejpam-6262	467	12	,	,	PUNCT
ejpam-6262	467	13	2012	2012	NUM
ejpam-6262	467	14	.	.	PUNCT
ejpam-6262	468	1	[	[	X
ejpam-6262	468	2	23	23	NUM
ejpam-6262	468	3	]	]	X
ejpam-6262	468	4	f.	f.	PROPN
ejpam-6262	468	5	ahmad	ahmad	PROPN
ejpam-6262	468	6	,	,	PUNCT
ejpam-6262	468	7	f.	f.	PROPN
ejpam-6262	468	8	soleymani	soleymani	PROPN
ejpam-6262	468	9	,	,	PUNCT
ejpam-6262	468	10	f.	f.	PROPN
ejpam-6262	468	11	k.	k.	PROPN
ejpam-6262	468	12	haghani	haghani	PROPN
ejpam-6262	468	13	,	,	PUNCT
ejpam-6262	468	14	and	and	CCONJ
ejpam-6262	468	15	s.	s.	PROPN
ejpam-6262	468	16	serra	serra	PROPN
ejpam-6262	468	17	-	-	PUNCT
ejpam-6262	468	18	capizzano	capizzano	PROPN
ejpam-6262	468	19	.	.	PUNCT
ejpam-6262	469	1	higher	high	ADJ
ejpam-6262	469	2	order	order	VERB
ejpam-6262	469	3	derivative	derivative	ADJ
ejpam-6262	469	4	-	-	PUNCT
ejpam-6262	469	5	free	free	ADJ
ejpam-6262	469	6	iterative	iterative	NOUN
ejpam-6262	469	7	methods	method	NOUN
ejpam-6262	469	8	with	with	ADP
ejpam-6262	469	9	and	and	CCONJ
ejpam-6262	469	10	without	without	ADP
ejpam-6262	469	11	memory	memory	NOUN
ejpam-6262	469	12	for	for	ADP
ejpam-6262	469	13	systems	system	NOUN
ejpam-6262	469	14	of	of	ADP
ejpam-6262	469	15	nonlinear	nonlinear	ADJ
ejpam-6262	469	16	equations	equation	NOUN
ejpam-6262	469	17	.	.	PUNCT
ejpam-6262	470	1	applied	apply	VERB
ejpam-6262	470	2	mathematics	mathematic	NOUN
ejpam-6262	470	3	and	and	CCONJ
ejpam-6262	470	4	computation	computation	NOUN
ejpam-6262	470	5	,	,	PUNCT
ejpam-6262	470	6	314:199–211	314:199–211	NUM
ejpam-6262	470	7	,	,	PUNCT
ejpam-6262	470	8	2017	2017	NUM
ejpam-6262	470	9	.	.	PUNCT
ejpam-6262	471	1	[	[	X
ejpam-6262	471	2	24	24	NUM
ejpam-6262	471	3	]	]	PUNCT
ejpam-6262	471	4	a.	a.	NOUN
ejpam-6262	471	5	cordero	cordero	PROPN
ejpam-6262	471	6	,	,	PUNCT
ejpam-6262	471	7	c.	c.	PROPN
ejpam-6262	471	8	jordán	jordán	PROPN
ejpam-6262	471	9	,	,	PUNCT
ejpam-6262	471	10	e.	e.	PROPN
ejpam-6262	471	11	sanabria	sanabria	PROPN
ejpam-6262	471	12	,	,	PUNCT
ejpam-6262	471	13	and	and	CCONJ
ejpam-6262	471	14	j.	j.	PROPN
ejpam-6262	471	15	r.	r.	PROPN
ejpam-6262	471	16	torregrosa	torregrosa	PROPN
ejpam-6262	471	17	.	.	PUNCT
ejpam-6262	472	1	a	a	DET
ejpam-6262	472	2	new	new	ADJ
ejpam-6262	472	3	class	class	NOUN
ejpam-6262	472	4	of	of	ADP
ejpam-6262	472	5	iterative	iterative	NOUN
ejpam-6262	472	6	processes	process	NOUN
ejpam-6262	472	7	for	for	ADP
ejpam-6262	472	8	solving	solve	VERB
ejpam-6262	472	9	nonlinear	nonlinear	ADJ
ejpam-6262	472	10	systems	system	NOUN
ejpam-6262	472	11	by	by	ADP
ejpam-6262	472	12	using	use	VERB
ejpam-6262	472	13	one	one	NUM
ejpam-6262	472	14	divided	divide	VERB
ejpam-6262	472	15	differences	difference	NOUN
ejpam-6262	472	16	operator	operator	NOUN
ejpam-6262	472	17	.	.	PUNCT
ejpam-6262	473	1	mathematics	mathematic	NOUN
ejpam-6262	473	2	,	,	PUNCT
ejpam-6262	473	3	7(9):776	7(9):776	NUM
ejpam-6262	473	4	,	,	PUNCT
ejpam-6262	473	5	2019	2019	NUM
ejpam-6262	473	6	.	.	PUNCT
ejpam-6262	474	1	[	[	X
ejpam-6262	474	2	25	25	NUM
ejpam-6262	474	3	]	]	PUNCT
ejpam-6262	474	4	j.	j.	PROPN
ejpam-6262	474	5	r.	r.	PROPN
ejpam-6262	474	6	sharma	sharma	PROPN
ejpam-6262	474	7	,	,	PUNCT
ejpam-6262	474	8	d.	d.	PROPN
ejpam-6262	474	9	kumar	kumar	PROPN
ejpam-6262	474	10	,	,	PUNCT
ejpam-6262	474	11	and	and	CCONJ
ejpam-6262	474	12	l.	l.	PROPN
ejpam-6262	474	13	jäntschi	jäntschi	PROPN
ejpam-6262	474	14	.	.	PUNCT
ejpam-6262	475	1	on	on	ADP
ejpam-6262	475	2	a	a	DET
ejpam-6262	475	3	reduced	reduce	VERB
ejpam-6262	475	4	cost	cost	NOUN
ejpam-6262	475	5	higher	high	ADJ
ejpam-6262	475	6	order	order	NOUN
ejpam-6262	475	7	traub	traub	NOUN
ejpam-6262	475	8	–	–	PUNCT
ejpam-6262	475	9	steffensen	steffensen	NOUN
ejpam-6262	475	10	-	-	PUNCT
ejpam-6262	475	11	like	like	ADJ
ejpam-6262	475	12	method	method	NOUN
ejpam-6262	475	13	for	for	ADP
ejpam-6262	475	14	nonlinear	nonlinear	ADJ
ejpam-6262	475	15	systems	system	NOUN
ejpam-6262	475	16	.	.	PUNCT
ejpam-6262	476	1	symmetry	symmetry	NOUN
ejpam-6262	476	2	,	,	PUNCT
ejpam-6262	476	3	11(7):891	11(7):891	NUM
ejpam-6262	476	4	,	,	PUNCT
ejpam-6262	476	5	2019	2019	NUM
ejpam-6262	476	6	.	.	PUNCT
ejpam-6262	477	1	[	[	X
ejpam-6262	477	2	26	26	NUM
ejpam-6262	477	3	]	]	X
ejpam-6262	477	4	charles	charles	PROPN
ejpam-6262	477	5	g	g	PROPN
ejpam-6262	477	6	broyden	broyden	NOUN
ejpam-6262	477	7	.	.	PUNCT
ejpam-6262	478	1	a	a	DET
ejpam-6262	478	2	class	class	NOUN
ejpam-6262	478	3	of	of	ADP
ejpam-6262	478	4	methods	method	NOUN
ejpam-6262	478	5	for	for	ADP
ejpam-6262	478	6	solving	solve	VERB
ejpam-6262	478	7	nonlinear	nonlinear	ADJ
ejpam-6262	478	8	simultaneous	simultaneous	ADJ
ejpam-6262	478	9	equations	equation	NOUN
ejpam-6262	478	10	.	.	PUNCT
ejpam-6262	479	1	mathematics	mathematic	NOUN
ejpam-6262	479	2	of	of	ADP
ejpam-6262	479	3	computation	computation	NOUN
ejpam-6262	479	4	,	,	PUNCT
ejpam-6262	479	5	19(92):577–593	19(92):577–593	PROPN
ejpam-6262	479	6	,	,	PUNCT
ejpam-6262	479	7	1965	1965	NUM
ejpam-6262	479	8	.	.	PUNCT
ejpam-6262	480	1	[	[	X
ejpam-6262	480	2	27	27	NUM
ejpam-6262	480	3	]	]	X
ejpam-6262	480	4	s.	s.	PROPN
ejpam-6262	480	5	l.	l.	PROPN
ejpam-6262	480	6	heenatigala	heenatigala	PROPN
ejpam-6262	480	7	,	,	PUNCT
ejpam-6262	480	8	s.	s.	PROPN
ejpam-6262	480	9	weerakoon	weerakoon	NOUN
ejpam-6262	480	10	,	,	PUNCT
ejpam-6262	480	11	and	and	CCONJ
ejpam-6262	480	12	t.	t.	PROPN
ejpam-6262	480	13	g.	g.	PROPN
ejpam-6262	480	14	i.	i.	PROPN
ejpam-6262	480	15	fernando	fernando	PROPN
ejpam-6262	480	16	.	.	PUNCT
ejpam-6262	481	1	finite	finite	PROPN
ejpam-6262	481	2	difference	difference	NOUN
ejpam-6262	481	3	weerakoonfernando	weerakoonfernando	NOUN
ejpam-6262	481	4	method	method	NOUN
ejpam-6262	481	5	to	to	PART
ejpam-6262	481	6	solve	solve	VERB
ejpam-6262	481	7	nonlinear	nonlinear	ADJ
ejpam-6262	481	8	equations	equation	NOUN
ejpam-6262	481	9	without	without	ADP
ejpam-6262	481	10	using	use	VERB
ejpam-6262	481	11	derivatives	derivative	NOUN
ejpam-6262	481	12	.	.	PUNCT
ejpam-6262	482	1	university	university	NOUN
ejpam-6262	482	2	of	of	ADP
ejpam-6262	482	3	sri	sri	PROPN
ejpam-6262	482	4	jayewardenepura	jayewardenepura	PROPN
ejpam-6262	482	5	,	,	PUNCT
ejpam-6262	482	6	gangodawila	gangodawila	NOUN
ejpam-6262	482	7	,	,	PUNCT
ejpam-6262	482	8	nugegoda	nugegoda	PROPN
ejpam-6262	482	9	,	,	PUNCT
ejpam-6262	482	10	sri	sri	PROPN
ejpam-6262	482	11	lanka	lanka	PROPN
ejpam-6262	482	12	,	,	PUNCT
ejpam-6262	482	13	2021	2021	NUM
ejpam-6262	482	14	.	.	PUNCT
ejpam-6262	483	1	[	[	X
ejpam-6262	483	2	28	28	NUM
ejpam-6262	483	3	]	]	X
ejpam-6262	483	4	jürgen	jürgen	X
ejpam-6262	483	5	appell	appell	PROPN
ejpam-6262	483	6	and	and	CCONJ
ejpam-6262	483	7	chur	chur	PROPN
ejpam-6262	483	8	-	-	PROPN
ejpam-6262	483	9	jen	jen	PROPN
ejpam-6262	483	10	chen	chen	PROPN
ejpam-6262	483	11	.	.	PUNCT
ejpam-6262	484	1	how	how	SCONJ
ejpam-6262	484	2	to	to	PART
ejpam-6262	484	3	solve	solve	VERB
ejpam-6262	484	4	hammerstein	hammerstein	PROPN
ejpam-6262	484	5	equations	equation	NOUN
ejpam-6262	484	6	.	.	PUNCT
ejpam-6262	485	1	the	the	DET
ejpam-6262	485	2	journal	journal	NOUN
ejpam-6262	485	3	of	of	ADP
ejpam-6262	485	4	integral	integral	ADJ
ejpam-6262	485	5	equations	equation	NOUN
ejpam-6262	485	6	and	and	CCONJ
ejpam-6262	485	7	applications	application	NOUN
ejpam-6262	485	8	,	,	PUNCT
ejpam-6262	485	9	18(3):287–296	18(3):287–296	NUM
ejpam-6262	485	10	,	,	PUNCT
ejpam-6262	485	11	2006	2006	NUM
ejpam-6262	485	12	.	.	PUNCT
ejpam-6262	486	1	[	[	X
ejpam-6262	486	2	29	29	NUM
ejpam-6262	486	3	]	]	X
ejpam-6262	486	4	william	william	PROPN
ejpam-6262	486	5	h	h	PROPN
ejpam-6262	486	6	press	press	PROPN
ejpam-6262	486	7	.	.	PUNCT
ejpam-6262	487	1	numerical	numerical	ADJ
ejpam-6262	487	2	recipes	recipes	PROPN
ejpam-6262	487	3	3rd	3rd	PROPN
ejpam-6262	487	4	edition	edition	NOUN
ejpam-6262	487	5	:	:	PUNCT
ejpam-6262	487	6	the	the	DET
ejpam-6262	487	7	art	art	NOUN
ejpam-6262	487	8	of	of	ADP
ejpam-6262	487	9	scientific	scientific	ADJ
ejpam-6262	487	10	computing	computing	NOUN
ejpam-6262	487	11	.	.	PUNCT
ejpam-6262	488	1	cambridge	cambridge	PROPN
ejpam-6262	488	2	university	university	PROPN
ejpam-6262	488	3	press	press	NOUN
ejpam-6262	488	4	,	,	PUNCT
ejpam-6262	488	5	2007	2007	NUM
ejpam-6262	488	6	.	.	PUNCT
ejpam-6262	489	1	[	[	X
ejpam-6262	489	2	30	30	NUM
ejpam-6262	489	3	]	]	X
ejpam-6262	489	4	yousef	yousef	PROPN
ejpam-6262	489	5	saad	saad	PROPN
ejpam-6262	489	6	.	.	PUNCT
ejpam-6262	490	1	iterative	iterative	NOUN
ejpam-6262	490	2	methods	method	NOUN
ejpam-6262	490	3	for	for	ADP
ejpam-6262	490	4	sparse	sparse	ADJ
ejpam-6262	490	5	linear	linear	ADJ
ejpam-6262	490	6	systems	system	NOUN
ejpam-6262	490	7	.	.	PUNCT
ejpam-6262	491	1	siam	siam	PROPN
ejpam-6262	491	2	,	,	PUNCT
ejpam-6262	491	3	2003	2003	NUM
ejpam-6262	491	4	.	.	PUNCT
ejpam-6262	492	1	y.	y.	PROPN
ejpam-6262	492	2	al	al	PROPN
ejpam-6262	492	3	-	-	PUNCT
ejpam-6262	492	4	shorman	shorman	PROPN
ejpam-6262	492	5	et	et	PROPN
ejpam-6262	492	6	al	al	PROPN
ejpam-6262	492	7	.	.	PUNCT
ejpam-6262	492	8	/	/	SYM
ejpam-6262	492	9	eur	eur	PROPN
ejpam-6262	492	10	.	.	PUNCT
ejpam-6262	493	1	j.	j.	PROPN
ejpam-6262	493	2	pure	pure	PROPN
ejpam-6262	493	3	appl	appl	PROPN
ejpam-6262	493	4	.	.	PROPN
ejpam-6262	493	5	math	math	PROPN
ejpam-6262	493	6	,	,	PUNCT
ejpam-6262	493	7	18	18	NUM
ejpam-6262	493	8	(	(	PUNCT
ejpam-6262	493	9	3	3	NUM
ejpam-6262	493	10	)	)	PUNCT
ejpam-6262	493	11	(	(	PUNCT
ejpam-6262	493	12	2025	2025	NUM
ejpam-6262	493	13	)	)	PUNCT
ejpam-6262	493	14	,	,	PUNCT
ejpam-6262	493	15	6262	6262	NUM
ejpam-6262	493	16	20	20	NUM
ejpam-6262	493	17	of	of	ADP
ejpam-6262	493	18	20	20	NUM
ejpam-6262	494	1	[	[	SYM
ejpam-6262	494	2	31	31	NUM
ejpam-6262	494	3	]	]	PUNCT
ejpam-6262	494	4	john	john	PROPN
ejpam-6262	494	5	e	e	PROPN
ejpam-6262	494	6	dennis	dennis	PROPN
ejpam-6262	494	7	jr	jr	PROPN
ejpam-6262	494	8	and	and	CCONJ
ejpam-6262	494	9	robert	robert	PROPN
ejpam-6262	494	10	b	b	PROPN
ejpam-6262	494	11	schnabel	schnabel	PROPN
ejpam-6262	494	12	.	.	PUNCT
ejpam-6262	495	1	numerical	numerical	ADJ
ejpam-6262	495	2	methods	method	NOUN
ejpam-6262	495	3	for	for	ADP
ejpam-6262	495	4	unconstrained	unconstrained	ADJ
ejpam-6262	495	5	optimization	optimization	NOUN
ejpam-6262	495	6	and	and	CCONJ
ejpam-6262	495	7	nonlinear	nonlinear	ADJ
ejpam-6262	495	8	equations	equation	NOUN
ejpam-6262	495	9	.	.	PUNCT
ejpam-6262	496	1	siam	siam	PROPN
ejpam-6262	496	2	,	,	PUNCT
ejpam-6262	496	3	1996	1996	NUM
ejpam-6262	496	4	.	.	PUNCT
ejpam-6262	497	1	[	[	X
ejpam-6262	497	2	32	32	NUM
ejpam-6262	497	3	]	]	PUNCT
ejpam-6262	497	4	carl	carl	PROPN
ejpam-6262	497	5	t	t	PROPN
ejpam-6262	497	6	kelley	kelley	PROPN
ejpam-6262	497	7	.	.	PUNCT
ejpam-6262	497	8	iterative	iterative	NOUN
ejpam-6262	497	9	methods	method	NOUN
ejpam-6262	497	10	for	for	ADP
ejpam-6262	497	11	linear	linear	ADJ
ejpam-6262	497	12	and	and	CCONJ
ejpam-6262	497	13	nonlinear	nonlinear	ADJ
ejpam-6262	497	14	equations	equation	NOUN
ejpam-6262	497	15	.	.	PUNCT
ejpam-6262	498	1	siam	siam	PROPN
ejpam-6262	498	2	,	,	PUNCT
ejpam-6262	498	3	1995	1995	NUM
ejpam-6262	498	4	.	.	PUNCT