id	sid	tid	token	lemma	pos
ejpam-4951	1	1	european	european	PROPN
ejpam-4951	1	2	journal	journal	PROPN
ejpam-4951	1	3	of	of	ADP
ejpam-4951	1	4	pure	pure	ADJ
ejpam-4951	1	5	and	and	CCONJ
ejpam-4951	1	6	applied	apply	VERB
ejpam-4951	1	7	mathematics	mathematic	NOUN
ejpam-4951	1	8	vol	vol	NOUN
ejpam-4951	1	9	.	.	PUNCT
ejpam-4951	2	1	16	16	NUM
ejpam-4951	2	2	,	,	PUNCT
ejpam-4951	2	3	no	no	INTJ
ejpam-4951	2	4	.	.	NOUN
ejpam-4951	2	5	4	4	NUM
ejpam-4951	2	6	,	,	PUNCT
ejpam-4951	2	7	2023	2023	NUM
ejpam-4951	2	8	,	,	PUNCT
ejpam-4951	2	9	2419	2419	NUM
ejpam-4951	2	10	-	-	SYM
ejpam-4951	2	11	2430	2430	NUM
ejpam-4951	2	12	issn	issn	PROPN
ejpam-4951	2	13	1307	1307	NUM
ejpam-4951	2	14	-	-	SYM
ejpam-4951	2	15	5543	5543	NUM
ejpam-4951	2	16	–	–	PUNCT
ejpam-4951	2	17	ejpam.com	ejpam.com	X
ejpam-4951	2	18	published	publish	VERB
ejpam-4951	2	19	by	by	ADP
ejpam-4951	2	20	new	new	PROPN
ejpam-4951	2	21	york	york	PROPN
ejpam-4951	2	22	business	business	PROPN
ejpam-4951	2	23	global	global	ADJ
ejpam-4951	2	24	new	new	ADJ
ejpam-4951	2	25	variants	variant	NOUN
ejpam-4951	2	26	of	of	ADP
ejpam-4951	2	27	newton	newton	PROPN
ejpam-4951	2	28	’s	’s	PART
ejpam-4951	2	29	method	method	NOUN
ejpam-4951	2	30	for	for	ADP
ejpam-4951	2	31	solving	solve	VERB
ejpam-4951	2	32	nonlinear	nonlinear	ADJ
ejpam-4951	2	33	equations	equation	NOUN
ejpam-4951	2	34	buddhi	buddhi	VERB
ejpam-4951	2	35	prasad	prasad	PROPN
ejpam-4951	2	36	sapkota1,∗	sapkota1,∗	PROPN
ejpam-4951	2	37	,	,	PUNCT
ejpam-4951	2	38	jivandhar	jivandhar	ADJ
ejpam-4951	2	39	jnawali1	jnawali1	NOUN
ejpam-4951	2	40	1	1	NUM
ejpam-4951	2	41	department	department	NOUN
ejpam-4951	2	42	of	of	ADP
ejpam-4951	2	43	mathematics	mathematic	NOUN
ejpam-4951	2	44	,	,	PUNCT
ejpam-4951	2	45	ratna	ratna	PROPN
ejpam-4951	2	46	rajyalaxmi	rajyalaxmi	PROPN
ejpam-4951	2	47	campus	campus	PROPN
ejpam-4951	2	48	,	,	PUNCT
ejpam-4951	2	49	tribhuvan	tribhuvan	PROPN
ejpam-4951	2	50	university	university	PROPN
ejpam-4951	2	51	,	,	PUNCT
ejpam-4951	2	52	kathmandu	kathmandu	NOUN
ejpam-4951	2	53	,	,	PUNCT
ejpam-4951	2	54	nepal	nepal	ADJ
ejpam-4951	2	55	abstract	abstract	NOUN
ejpam-4951	2	56	.	.	PUNCT
ejpam-4951	3	1	two	two	NUM
ejpam-4951	3	2	newton	newton	NOUN
ejpam-4951	3	3	-	-	PUNCT
ejpam-4951	3	4	type	type	NOUN
ejpam-4951	3	5	iterative	iterative	NOUN
ejpam-4951	3	6	techniques	technique	NOUN
ejpam-4951	3	7	have	have	AUX
ejpam-4951	3	8	been	be	AUX
ejpam-4951	3	9	created	create	VERB
ejpam-4951	3	10	in	in	ADP
ejpam-4951	3	11	this	this	DET
ejpam-4951	3	12	work	work	NOUN
ejpam-4951	3	13	to	to	PART
ejpam-4951	3	14	locate	locate	VERB
ejpam-4951	3	15	the	the	DET
ejpam-4951	3	16	true	true	ADJ
ejpam-4951	3	17	root	root	NOUN
ejpam-4951	3	18	of	of	ADP
ejpam-4951	3	19	univariate	univariate	ADJ
ejpam-4951	3	20	nonlinear	nonlinear	ADJ
ejpam-4951	3	21	equations	equation	NOUN
ejpam-4951	3	22	.	.	PUNCT
ejpam-4951	4	1	one	one	NUM
ejpam-4951	4	2	of	of	ADP
ejpam-4951	4	3	these	these	PRON
ejpam-4951	4	4	can	can	AUX
ejpam-4951	4	5	be	be	AUX
ejpam-4951	4	6	acquired	acquire	VERB
ejpam-4951	4	7	by	by	ADP
ejpam-4951	4	8	modifying	modify	VERB
ejpam-4951	4	9	the	the	DET
ejpam-4951	4	10	double	double	PROPN
ejpam-4951	4	11	newton	newton	PROPN
ejpam-4951	4	12	’s	’s	PART
ejpam-4951	4	13	method	method	NOUN
ejpam-4951	4	14	in	in	ADP
ejpam-4951	4	15	a	a	DET
ejpam-4951	4	16	straightforward	straightforward	ADJ
ejpam-4951	4	17	manner	manner	NOUN
ejpam-4951	4	18	,	,	PUNCT
ejpam-4951	4	19	while	while	SCONJ
ejpam-4951	4	20	the	the	DET
ejpam-4951	4	21	other	other	ADJ
ejpam-4951	4	22	can	can	AUX
ejpam-4951	4	23	be	be	AUX
ejpam-4951	4	24	gotten	get	VERB
ejpam-4951	4	25	by	by	ADP
ejpam-4951	4	26	modifying	modify	VERB
ejpam-4951	4	27	the	the	DET
ejpam-4951	4	28	midpoint	midpoint	NOUN
ejpam-4951	4	29	newton	newton	PROPN
ejpam-4951	4	30	’s	’s	PART
ejpam-4951	4	31	method	method	NOUN
ejpam-4951	4	32	.	.	PUNCT
ejpam-4951	5	1	the	the	DET
ejpam-4951	5	2	iterative	iterative	NOUN
ejpam-4951	5	3	approach	approach	NOUN
ejpam-4951	5	4	developed	develop	VERB
ejpam-4951	5	5	by	by	ADP
ejpam-4951	5	6	mcdougall	mcdougall	NOUN
ejpam-4951	5	7	and	and	CCONJ
ejpam-4951	5	8	wortherspoon	wortherspoon	NOUN
ejpam-4951	5	9	is	be	AUX
ejpam-4951	5	10	employed	employ	VERB
ejpam-4951	5	11	for	for	ADP
ejpam-4951	5	12	the	the	DET
ejpam-4951	5	13	change	change	NOUN
ejpam-4951	5	14	.	.	PUNCT
ejpam-4951	6	1	the	the	DET
ejpam-4951	6	2	study	study	NOUN
ejpam-4951	6	3	demonstrates	demonstrate	VERB
ejpam-4951	6	4	that	that	SCONJ
ejpam-4951	6	5	the	the	DET
ejpam-4951	6	6	modified	modify	VERB
ejpam-4951	6	7	double	double	PROPN
ejpam-4951	6	8	newton	newton	PROPN
ejpam-4951	6	9	’s	’s	PART
ejpam-4951	6	10	approach	approach	NOUN
ejpam-4951	6	11	outperforms	outperform	VERB
ejpam-4951	6	12	the	the	DET
ejpam-4951	6	13	current	current	ADJ
ejpam-4951	6	14	one	one	NUM
ejpam-4951	6	15	in	in	ADP
ejpam-4951	6	16	terms	term	NOUN
ejpam-4951	6	17	of	of	ADP
ejpam-4951	6	18	both	both	PRON
ejpam-4951	6	19	convergence	convergence	NOUN
ejpam-4951	6	20	order	order	NOUN
ejpam-4951	6	21	and	and	CCONJ
ejpam-4951	6	22	efficiency	efficiency	NOUN
ejpam-4951	6	23	index	index	NOUN
ejpam-4951	6	24	,	,	PUNCT
ejpam-4951	6	25	even	even	ADV
ejpam-4951	6	26	though	though	SCONJ
ejpam-4951	6	27	both	both	DET
ejpam-4951	6	28	methods	method	NOUN
ejpam-4951	6	29	assess	assess	VERB
ejpam-4951	6	30	the	the	DET
ejpam-4951	6	31	same	same	ADJ
ejpam-4951	6	32	amount	amount	NOUN
ejpam-4951	6	33	of	of	ADP
ejpam-4951	6	34	functions	function	NOUN
ejpam-4951	6	35	and	and	CCONJ
ejpam-4951	6	36	derivatives	derivative	NOUN
ejpam-4951	6	37	every	every	DET
ejpam-4951	6	38	iteration	iteration	NOUN
ejpam-4951	6	39	.	.	PUNCT
ejpam-4951	7	1	in	in	ADP
ejpam-4951	7	2	comparison	comparison	NOUN
ejpam-4951	7	3	to	to	ADP
ejpam-4951	7	4	the	the	DET
ejpam-4951	7	5	midpoint	midpoint	PROPN
ejpam-4951	7	6	newton	newton	PROPN
ejpam-4951	7	7	’s	’s	PART
ejpam-4951	7	8	technique	technique	NOUN
ejpam-4951	7	9	,	,	PUNCT
ejpam-4951	7	10	which	which	PRON
ejpam-4951	7	11	has	have	VERB
ejpam-4951	7	12	a	a	DET
ejpam-4951	7	13	convergence	convergence	NOUN
ejpam-4951	7	14	order	order	NOUN
ejpam-4951	7	15	of	of	ADP
ejpam-4951	7	16	3	3	NUM
ejpam-4951	7	17	,	,	PUNCT
ejpam-4951	7	18	the	the	DET
ejpam-4951	7	19	modified	modify	VERB
ejpam-4951	7	20	midpoint	midpoint	PROPN
ejpam-4951	7	21	newton	newton	PROPN
ejpam-4951	7	22	’s	’s	PART
ejpam-4951	7	23	method	method	NOUN
ejpam-4951	7	24	has	have	VERB
ejpam-4951	7	25	a	a	DET
ejpam-4951	7	26	convergence	convergence	NOUN
ejpam-4951	7	27	order	order	NOUN
ejpam-4951	7	28	of	of	ADP
ejpam-4951	7	29	5.25	5.25	NUM
ejpam-4951	7	30	and	and	CCONJ
ejpam-4951	7	31	requires	require	VERB
ejpam-4951	7	32	two	two	NUM
ejpam-4951	7	33	extra	extra	ADJ
ejpam-4951	7	34	functions	function	NOUN
ejpam-4951	7	35	to	to	PART
ejpam-4951	7	36	be	be	AUX
ejpam-4951	7	37	evaluated	evaluate	VERB
ejpam-4951	7	38	per	per	ADP
ejpam-4951	7	39	iteration	iteration	NOUN
ejpam-4951	7	40	.	.	PUNCT
ejpam-4951	8	1	in	in	ADP
ejpam-4951	8	2	order	order	NOUN
ejpam-4951	8	3	to	to	PART
ejpam-4951	8	4	evaluate	evaluate	VERB
ejpam-4951	8	5	the	the	DET
ejpam-4951	8	6	effectiveness	effectiveness	NOUN
ejpam-4951	8	7	of	of	ADP
ejpam-4951	8	8	recently	recently	ADV
ejpam-4951	8	9	introduced	introduce	VERB
ejpam-4951	8	10	approaches	approach	NOUN
ejpam-4951	8	11	with	with	ADP
ejpam-4951	8	12	current	current	ADJ
ejpam-4951	8	13	methods	method	NOUN
ejpam-4951	8	14	,	,	PUNCT
ejpam-4951	8	15	some	some	DET
ejpam-4951	8	16	numerical	numerical	ADJ
ejpam-4951	8	17	examples	example	NOUN
ejpam-4951	8	18	are	be	AUX
ejpam-4951	8	19	shown	show	VERB
ejpam-4951	8	20	in	in	ADP
ejpam-4951	8	21	the	the	DET
ejpam-4951	8	22	final	final	ADJ
ejpam-4951	8	23	section	section	NOUN
ejpam-4951	8	24	.	.	PUNCT
ejpam-4951	9	1	2020	2020	NUM
ejpam-4951	9	2	mathematics	mathematic	NOUN
ejpam-4951	9	3	subject	subject	NOUN
ejpam-4951	9	4	classifications	classification	NOUN
ejpam-4951	9	5	:	:	PUNCT
ejpam-4951	9	6	65h05	65h05	NUM
ejpam-4951	9	7	key	key	ADJ
ejpam-4951	9	8	words	word	NOUN
ejpam-4951	9	9	and	and	CCONJ
ejpam-4951	9	10	phrases	phrase	NOUN
ejpam-4951	9	11	:	:	PUNCT
ejpam-4951	9	12	newton	newton	PROPN
ejpam-4951	9	13	’s	’s	PART
ejpam-4951	9	14	method	method	PROPN
ejpam-4951	9	15	,	,	PUNCT
ejpam-4951	9	16	numerical	numerical	ADJ
ejpam-4951	9	17	method	method	NOUN
ejpam-4951	9	18	,	,	PUNCT
ejpam-4951	9	19	nonlinear	nonlinear	ADJ
ejpam-4951	9	20	equation	equation	NOUN
ejpam-4951	9	21	,	,	PUNCT
ejpam-4951	9	22	convergence	convergence	NOUN
ejpam-4951	9	23	,	,	PUNCT
ejpam-4951	9	24	efficiency	efficiency	NOUN
ejpam-4951	9	25	index	index	NOUN
ejpam-4951	9	26	1	1	NUM
ejpam-4951	9	27	.	.	PUNCT
ejpam-4951	9	28	introduction	introduction	NOUN
ejpam-4951	9	29	a	a	DET
ejpam-4951	9	30	collection	collection	NOUN
ejpam-4951	9	31	of	of	ADP
ejpam-4951	9	32	various	various	ADJ
ejpam-4951	9	33	nonlinear	nonlinear	ADJ
ejpam-4951	9	34	equations	equation	NOUN
ejpam-4951	9	35	with	with	ADP
ejpam-4951	9	36	objective	objective	ADJ
ejpam-4951	9	37	functions	function	NOUN
ejpam-4951	9	38	and/or	and/or	CCONJ
ejpam-4951	9	39	nonlinear	nonlinear	ADJ
ejpam-4951	9	40	constraint	constraint	NOUN
ejpam-4951	9	41	functions	function	NOUN
ejpam-4951	9	42	is	be	AUX
ejpam-4951	9	43	referred	refer	VERB
ejpam-4951	9	44	to	to	ADP
ejpam-4951	9	45	as	as	ADP
ejpam-4951	9	46	a	a	DET
ejpam-4951	9	47	nonlinear	nonlinear	ADJ
ejpam-4951	9	48	equation	equation	NOUN
ejpam-4951	9	49	system	system	NOUN
ejpam-4951	10	1	[	[	X
ejpam-4951	10	2	1	1	NUM
ejpam-4951	10	3	]	]	PUNCT
ejpam-4951	10	4	.	.	PUNCT
ejpam-4951	11	1	finding	find	VERB
ejpam-4951	11	2	the	the	DET
ejpam-4951	11	3	roots	root	NOUN
ejpam-4951	11	4	of	of	ADP
ejpam-4951	11	5	some	some	DET
ejpam-4951	11	6	nonlinear	nonlinear	ADJ
ejpam-4951	11	7	equation	equation	NOUN
ejpam-4951	11	8	systems	system	NOUN
ejpam-4951	11	9	requires	require	VERB
ejpam-4951	11	10	numerical	numerical	ADJ
ejpam-4951	11	11	approaches	approach	NOUN
ejpam-4951	11	12	.	.	PUNCT
ejpam-4951	12	1	the	the	DET
ejpam-4951	12	2	numerical	numerical	ADJ
ejpam-4951	12	3	approach	approach	NOUN
ejpam-4951	12	4	is	be	AUX
ejpam-4951	12	5	a	a	DET
ejpam-4951	12	6	strategy	strategy	NOUN
ejpam-4951	12	7	for	for	ADP
ejpam-4951	12	8	figuring	figure	VERB
ejpam-4951	12	9	out	out	ADP
ejpam-4951	12	10	mathematical	mathematical	ADJ
ejpam-4951	12	11	issues	issue	NOUN
ejpam-4951	12	12	so	so	SCONJ
ejpam-4951	12	13	that	that	SCONJ
ejpam-4951	12	14	they	they	PRON
ejpam-4951	12	15	may	may	AUX
ejpam-4951	12	16	be	be	AUX
ejpam-4951	12	17	resolved	resolve	VERB
ejpam-4951	12	18	using	use	VERB
ejpam-4951	12	19	standard	standard	ADJ
ejpam-4951	12	20	operations	operation	NOUN
ejpam-4951	12	21	like	like	ADP
ejpam-4951	12	22	add	add	VERB
ejpam-4951	12	23	,	,	PUNCT
ejpam-4951	12	24	subtract	subtract	ADJ
ejpam-4951	12	25	,	,	PUNCT
ejpam-4951	12	26	multiply	multiply	NOUN
ejpam-4951	12	27	,	,	PUNCT
ejpam-4951	12	28	and	and	CCONJ
ejpam-4951	12	29	divide	divide	VERB
ejpam-4951	12	30	.	.	PUNCT
ejpam-4951	13	1	one	one	NUM
ejpam-4951	13	2	of	of	ADP
ejpam-4951	13	3	the	the	DET
ejpam-4951	13	4	numerical	numerical	ADJ
ejpam-4951	13	5	techniques	technique	NOUN
ejpam-4951	13	6	for	for	ADP
ejpam-4951	13	7	resolving	resolve	VERB
ejpam-4951	13	8	a	a	DET
ejpam-4951	13	9	system	system	NOUN
ejpam-4951	13	10	of	of	ADP
ejpam-4951	13	11	nonlinear	nonlinear	ADJ
ejpam-4951	13	12	equations	equation	NOUN
ejpam-4951	13	13	is	be	AUX
ejpam-4951	13	14	the	the	DET
ejpam-4951	13	15	newton	newton	PROPN
ejpam-4951	13	16	method	method	NOUN
ejpam-4951	13	17	.	.	PUNCT
ejpam-4951	14	1	some	some	DET
ejpam-4951	14	2	mathematicians	mathematician	NOUN
ejpam-4951	14	3	are	be	AUX
ejpam-4951	14	4	modifying	modify	VERB
ejpam-4951	14	5	newton	newton	PROPN
ejpam-4951	14	6	methods	method	NOUN
ejpam-4951	14	7	to	to	PART
ejpam-4951	14	8	arrive	arrive	VERB
ejpam-4951	14	9	at	at	ADP
ejpam-4951	14	10	a	a	DET
ejpam-4951	14	11	novel	novel	ADJ
ejpam-4951	14	12	technique	technique	NOUN
ejpam-4951	14	13	.	.	PUNCT
ejpam-4951	15	1	the	the	DET
ejpam-4951	15	2	midpoint	midpoint	PROPN
ejpam-4951	15	3	newton	newton	PROPN
ejpam-4951	15	4	approach	approach	NOUN
ejpam-4951	15	5	,	,	PUNCT
ejpam-4951	15	6	which	which	PRON
ejpam-4951	15	7	can	can	AUX
ejpam-4951	15	8	find	find	VERB
ejpam-4951	15	9	the	the	DET
ejpam-4951	15	10	equation	equation	NOUN
ejpam-4951	15	11	’s	’s	PART
ejpam-4951	15	12	root	root	NOUN
ejpam-4951	15	13	more	more	ADV
ejpam-4951	15	14	quickly	quickly	ADV
ejpam-4951	15	15	[	[	X
ejpam-4951	15	16	13	13	NUM
ejpam-4951	15	17	]	]	PUNCT
ejpam-4951	15	18	is	be	AUX
ejpam-4951	15	19	the	the	DET
ejpam-4951	15	20	result	result	NOUN
ejpam-4951	15	21	∗corresponding	∗corresponde	VERB
ejpam-4951	15	22	author	author	NOUN
ejpam-4951	15	23	.	.	PUNCT
ejpam-4951	16	1	doi	doi	NOUN
ejpam-4951	16	2	:	:	PUNCT
ejpam-4951	16	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4951	https://doi.org/10.29020/nybg.ejpam.v16i4.4951	PROPN
ejpam-4951	16	4	email	email	NOUN
ejpam-4951	16	5	addresses	address	NOUN
ejpam-4951	16	6	:	:	PUNCT
ejpam-4951	16	7	buddi.sapkota@rrlc.tu.edu.np	buddi.sapkota@rrlc.tu.edu.np	PROPN
ejpam-4951	16	8	(	(	PUNCT
ejpam-4951	16	9	b.	b.	PROPN
ejpam-4951	16	10	sapkota	sapkota	PROPN
ejpam-4951	16	11	)	)	PUNCT
ejpam-4951	16	12	,	,	PUNCT
ejpam-4951	16	13	jivandhar.jnawali@rrlc.tu.edu.np	jivandhar.jnawali@rrlc.tu.edu.np	PROPN
ejpam-4951	16	14	(	(	PUNCT
ejpam-4951	16	15	j.	j.	PROPN
ejpam-4951	16	16	jnawali	jnawali	PROPN
ejpam-4951	16	17	)	)	PUNCT
ejpam-4951	16	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4951	16	19	2419	2419	NUM
ejpam-4951	16	20	©	©	PROPN
ejpam-4951	16	21	2023	2023	NUM
ejpam-4951	16	22	ejpam	ejpam	NOUN
ejpam-4951	16	23	all	all	DET
ejpam-4951	16	24	rights	right	NOUN
ejpam-4951	16	25	reserved	reserve	VERB
ejpam-4951	16	26	.	.	PUNCT
ejpam-4951	17	1	b.	b.	PROPN
ejpam-4951	17	2	sapkota	sapkota	PROPN
ejpam-4951	17	3	,	,	PUNCT
ejpam-4951	17	4	j.	j.	PROPN
ejpam-4951	17	5	jnawali	jnawali	PROPN
ejpam-4951	17	6	/	/	SYM
ejpam-4951	17	7	eur	eur	PROPN
ejpam-4951	17	8	.	.	PUNCT
ejpam-4951	18	1	j.	j.	PROPN
ejpam-4951	18	2	pure	pure	PROPN
ejpam-4951	18	3	appl	appl	PROPN
ejpam-4951	18	4	.	.	PROPN
ejpam-4951	18	5	math	math	PROPN
ejpam-4951	18	6	,	,	PUNCT
ejpam-4951	18	7	16	16	NUM
ejpam-4951	18	8	(	(	PUNCT
ejpam-4951	18	9	4	4	NUM
ejpam-4951	18	10	)	)	PUNCT
ejpam-4951	18	11	(	(	PUNCT
ejpam-4951	18	12	2023	2023	NUM
ejpam-4951	18	13	)	)	PUNCT
ejpam-4951	18	14	,	,	PUNCT
ejpam-4951	18	15	2419	2419	NUM
ejpam-4951	18	16	-	-	SYM
ejpam-4951	18	17	2430	2430	NUM
ejpam-4951	18	18	2420	2420	NUM
ejpam-4951	18	19	of	of	ADP
ejpam-4951	18	20	combining	combine	VERB
ejpam-4951	18	21	the	the	DET
ejpam-4951	18	22	newton	newton	PROPN
ejpam-4951	18	23	method	method	NOUN
ejpam-4951	18	24	and	and	CCONJ
ejpam-4951	18	25	the	the	DET
ejpam-4951	18	26	midpoint	midpoint	NOUN
ejpam-4951	18	27	rule	rule	NOUN
ejpam-4951	18	28	.	.	PUNCT
ejpam-4951	19	1	singh	singh	PROPN
ejpam-4951	19	2	mk	mk	PROPN
ejpam-4951	20	1	[	[	X
ejpam-4951	20	2	14	14	NUM
ejpam-4951	20	3	]	]	PUNCT
ejpam-4951	20	4	developed	developed	PROPN
ejpam-4951	20	5	newton	newton	PROPN
ejpam-4951	20	6	’s	’s	PART
ejpam-4951	20	7	method	method	NOUN
ejpam-4951	20	8	based	base	VERB
ejpam-4951	20	9	on	on	ADP
ejpam-4951	20	10	contra	contra	PROPN
ejpam-4951	20	11	harmonic	harmonic	PROPN
ejpam-4951	20	12	mean	mean	VERB
ejpam-4951	20	13	with	with	ADP
ejpam-4951	20	14	order	order	NOUN
ejpam-4951	20	15	of	of	ADP
ejpam-4951	20	16	convergence	convergence	NOUN
ejpam-4951	20	17	six	six	NUM
ejpam-4951	20	18	.	.	PUNCT
ejpam-4951	21	1	he	he	PRON
ejpam-4951	21	2	jh	jh	PROPN
ejpam-4951	21	3	extended	extend	VERB
ejpam-4951	21	4	the	the	DET
ejpam-4951	21	5	frequency	frequency	NOUN
ejpam-4951	21	6	-	-	PUNCT
ejpam-4951	21	7	amplitude	amplitude	NOUN
ejpam-4951	21	8	formulation	formulation	NOUN
ejpam-4951	21	9	to	to	PART
ejpam-4951	21	10	solve	solve	VERB
ejpam-4951	21	11	nonlinear	nonlinear	ADJ
ejpam-4951	21	12	conservative	conservative	ADJ
ejpam-4951	21	13	oscillators	oscillator	NOUN
ejpam-4951	21	14	with	with	ADP
ejpam-4951	21	15	general	general	ADJ
ejpam-4951	21	16	initial	initial	ADJ
ejpam-4951	21	17	conditions	condition	NOUN
ejpam-4951	21	18	which	which	PRON
ejpam-4951	21	19	is	be	AUX
ejpam-4951	21	20	similar	similar	ADJ
ejpam-4951	21	21	to	to	ADP
ejpam-4951	21	22	the	the	DET
ejpam-4951	21	23	hamiltonian	hamiltonian	ADJ
ejpam-4951	21	24	approach	approach	NOUN
ejpam-4951	21	25	.	.	PUNCT
ejpam-4951	22	1	finding	find	VERB
ejpam-4951	22	2	the	the	DET
ejpam-4951	22	3	solutions	solution	NOUN
ejpam-4951	22	4	to	to	ADP
ejpam-4951	22	5	nonlinear	nonlinear	ADJ
ejpam-4951	22	6	equations	equation	NOUN
ejpam-4951	22	7	is	be	AUX
ejpam-4951	22	8	one	one	NUM
ejpam-4951	22	9	of	of	ADP
ejpam-4951	22	10	the	the	DET
ejpam-4951	22	11	most	most	ADV
ejpam-4951	22	12	important	important	ADJ
ejpam-4951	22	13	and	and	CCONJ
ejpam-4951	22	14	challenging	challenging	ADJ
ejpam-4951	22	15	problems	problem	NOUN
ejpam-4951	22	16	in	in	ADP
ejpam-4951	22	17	almost	almost	ADV
ejpam-4951	22	18	all	all	PRON
ejpam-4951	22	19	areas	area	NOUN
ejpam-4951	22	20	of	of	ADP
ejpam-4951	22	21	science	science	NOUN
ejpam-4951	22	22	and	and	CCONJ
ejpam-4951	22	23	engineering	engineering	NOUN
ejpam-4951	22	24	,	,	PUNCT
ejpam-4951	22	25	but	but	CCONJ
ejpam-4951	22	26	solving	solve	VERB
ejpam-4951	22	27	such	such	ADJ
ejpam-4951	22	28	equations	equation	NOUN
ejpam-4951	22	29	analytically	analytically	ADV
ejpam-4951	22	30	is	be	AUX
ejpam-4951	22	31	almost	almost	ADV
ejpam-4951	22	32	impossible	impossible	ADJ
ejpam-4951	22	33	.	.	PUNCT
ejpam-4951	23	1	in	in	ADP
ejpam-4951	23	2	those	those	DET
ejpam-4951	23	3	situations	situation	NOUN
ejpam-4951	23	4	,	,	PUNCT
ejpam-4951	23	5	the	the	DET
ejpam-4951	23	6	construction	construction	NOUN
ejpam-4951	23	7	of	of	ADP
ejpam-4951	23	8	efficient	efficient	ADJ
ejpam-4951	23	9	numerical	numerical	ADJ
ejpam-4951	23	10	methods	method	NOUN
ejpam-4951	23	11	based	base	VERB
ejpam-4951	23	12	on	on	ADP
ejpam-4951	23	13	an	an	DET
ejpam-4951	23	14	iterative	iterative	NOUN
ejpam-4951	23	15	procedure	procedure	NOUN
ejpam-4951	23	16	for	for	ADP
ejpam-4951	23	17	finding	find	VERB
ejpam-4951	23	18	the	the	DET
ejpam-4951	23	19	roots	root	NOUN
ejpam-4951	23	20	of	of	ADP
ejpam-4951	23	21	such	such	ADJ
ejpam-4951	23	22	equations	equation	NOUN
ejpam-4951	23	23	becomes	become	VERB
ejpam-4951	23	24	a	a	DET
ejpam-4951	23	25	fascinating	fascinating	ADJ
ejpam-4951	23	26	and	and	CCONJ
ejpam-4951	23	27	attractive	attractive	ADJ
ejpam-4951	23	28	task	task	NOUN
ejpam-4951	23	29	.	.	PUNCT
ejpam-4951	24	1	in	in	ADP
ejpam-4951	24	2	literature	literature	NOUN
ejpam-4951	24	3	,	,	PUNCT
ejpam-4951	24	4	there	there	PRON
ejpam-4951	24	5	are	be	VERB
ejpam-4951	24	6	numerous	numerous	ADJ
ejpam-4951	24	7	methods	method	NOUN
ejpam-4951	24	8	available	available	ADJ
ejpam-4951	24	9	for	for	ADP
ejpam-4951	24	10	finding	find	VERB
ejpam-4951	24	11	the	the	DET
ejpam-4951	24	12	roots	root	NOUN
ejpam-4951	24	13	of	of	ADP
ejpam-4951	24	14	such	such	ADJ
ejpam-4951	24	15	equations	equation	NOUN
ejpam-4951	24	16	in	in	ADP
ejpam-4951	24	17	different	different	ADJ
ejpam-4951	24	18	situations	situation	NOUN
ejpam-4951	24	19	.	.	PUNCT
ejpam-4951	25	1	newton	newton	PROPN
ejpam-4951	25	2	’s	’s	PART
ejpam-4951	25	3	method	method	NOUN
ejpam-4951	25	4	is	be	AUX
ejpam-4951	25	5	one	one	NUM
ejpam-4951	25	6	of	of	ADP
ejpam-4951	25	7	the	the	DET
ejpam-4951	25	8	bestknown	bestknown	NOUN
ejpam-4951	25	9	and	and	CCONJ
ejpam-4951	25	10	most	most	ADV
ejpam-4951	25	11	frequently	frequently	ADV
ejpam-4951	25	12	used	use	VERB
ejpam-4951	25	13	basic	basic	ADJ
ejpam-4951	25	14	numerical	numerical	ADJ
ejpam-4951	25	15	methods	method	NOUN
ejpam-4951	25	16	to	to	PART
ejpam-4951	25	17	solve	solve	VERB
ejpam-4951	25	18	nonlinear	nonlinear	ADJ
ejpam-4951	25	19	equations	equation	NOUN
ejpam-4951	25	20	.	.	PUNCT
ejpam-4951	26	1	it	it	PRON
ejpam-4951	26	2	’s	’	VERB
ejpam-4951	26	3	an	an	DET
ejpam-4951	26	4	iterative	iterative	NOUN
ejpam-4951	26	5	formula	formula	NOUN
ejpam-4951	26	6	for	for	ADP
ejpam-4951	26	7	obtaining	obtain	VERB
ejpam-4951	26	8	the	the	DET
ejpam-4951	26	9	simple	simple	ADJ
ejpam-4951	26	10	root	root	NOUN
ejpam-4951	26	11	of	of	ADP
ejpam-4951	26	12	the	the	DET
ejpam-4951	26	13	nonlinear	nonlinear	ADJ
ejpam-4951	26	14	equation	equation	NOUN
ejpam-4951	26	15	in	in	ADP
ejpam-4951	26	16	similar	similar	ADJ
ejpam-4951	26	17	circumstances	circumstance	NOUN
ejpam-4951	26	18	,	,	PUNCT
ejpam-4951	26	19	developing	develop	VERB
ejpam-4951	26	20	effective	effective	ADJ
ejpam-4951	26	21	numerical	numerical	ADJ
ejpam-4951	26	22	algorithms	algorithm	NOUN
ejpam-4951	26	23	based	base	VERB
ejpam-4951	26	24	on	on	ADP
ejpam-4951	26	25	an	an	DET
ejpam-4951	26	26	iterative	iterative	NOUN
ejpam-4951	26	27	process	process	NOUN
ejpam-4951	26	28	to	to	PART
ejpam-4951	26	29	locate	locate	VERB
ejpam-4951	26	30	the	the	DET
ejpam-4951	26	31	roots	root	NOUN
ejpam-4951	26	32	of	of	ADP
ejpam-4951	26	33	such	such	ADJ
ejpam-4951	26	34	equations	equation	NOUN
ejpam-4951	26	35	turns	turn	VERB
ejpam-4951	26	36	out	out	ADP
ejpam-4951	26	37	to	to	PART
ejpam-4951	26	38	be	be	AUX
ejpam-4951	26	39	an	an	DET
ejpam-4951	26	40	intriguing	intriguing	ADJ
ejpam-4951	26	41	and	and	CCONJ
ejpam-4951	26	42	alluring	alluring	ADJ
ejpam-4951	26	43	task	task	NOUN
ejpam-4951	26	44	.	.	PUNCT
ejpam-4951	27	1	there	there	PRON
ejpam-4951	27	2	are	be	VERB
ejpam-4951	27	3	many	many	ADJ
ejpam-4951	27	4	techniques	technique	NOUN
ejpam-4951	27	5	described	describe	VERB
ejpam-4951	27	6	in	in	ADP
ejpam-4951	27	7	the	the	DET
ejpam-4951	27	8	literature	literature	NOUN
ejpam-4951	27	9	for	for	ADP
ejpam-4951	27	10	locating	locate	VERB
ejpam-4951	27	11	the	the	DET
ejpam-4951	27	12	roots	root	NOUN
ejpam-4951	27	13	of	of	ADP
ejpam-4951	27	14	these	these	DET
ejpam-4951	27	15	equations	equation	NOUN
ejpam-4951	27	16	in	in	ADP
ejpam-4951	27	17	various	various	ADJ
ejpam-4951	27	18	contexts	contexts	NOUN
ejpam-4951	27	19	.	.	PUNCT
ejpam-4951	28	1	one	one	NUM
ejpam-4951	28	2	of	of	ADP
ejpam-4951	28	3	the	the	DET
ejpam-4951	28	4	most	most	ADV
ejpam-4951	28	5	popular	popular	ADJ
ejpam-4951	28	6	and	and	CCONJ
ejpam-4951	28	7	widely	widely	ADV
ejpam-4951	28	8	used	use	VERB
ejpam-4951	28	9	fundamental	fundamental	ADJ
ejpam-4951	28	10	numerical	numerical	ADJ
ejpam-4951	28	11	techniques	technique	NOUN
ejpam-4951	28	12	for	for	ADP
ejpam-4951	28	13	solving	solve	VERB
ejpam-4951	28	14	nonlinear	nonlinear	ADJ
ejpam-4951	28	15	equations	equation	NOUN
ejpam-4951	28	16	is	be	AUX
ejpam-4951	28	17	newton	newton	PROPN
ejpam-4951	28	18	’s	’s	PART
ejpam-4951	28	19	method	method	NOUN
ejpam-4951	28	20	.	.	PUNCT
ejpam-4951	29	1	it	it	PRON
ejpam-4951	29	2	is	be	AUX
ejpam-4951	29	3	an	an	DET
ejpam-4951	29	4	iterative	iterative	NOUN
ejpam-4951	29	5	formula	formula	NOUN
ejpam-4951	29	6	for	for	ADP
ejpam-4951	29	7	finding	find	VERB
ejpam-4951	29	8	the	the	DET
ejpam-4951	29	9	nonlinear	nonlinear	ADJ
ejpam-4951	29	10	equation	equation	NOUN
ejpam-4951	29	11	’s	’s	PART
ejpam-4951	29	12	simple	simple	ADJ
ejpam-4951	29	13	root	root	NOUN
ejpam-4951	29	14	.	.	PUNCT
ejpam-4951	29	15	xn+1	xn+1	PUNCT
ejpam-4951	30	1	=	=	SYM
ejpam-4951	30	2	xn	xn	PROPN
ejpam-4951	31	1	−	−	NUM
ejpam-4951	31	2	f(xn	f(xn	PROPN
ejpam-4951	31	3	)	)	PUNCT
ejpam-4951	31	4	f	f	PROPN
ejpam-4951	31	5	′(xn	′(xn	NOUN
ejpam-4951	31	6	)	)	PUNCT
ejpam-4951	31	7	.	.	PUNCT
ejpam-4951	32	1	(	(	PUNCT
ejpam-4951	32	2	1	1	X
ejpam-4951	32	3	)	)	PUNCT
ejpam-4951	32	4	this	this	DET
ejpam-4951	32	5	method	method	NOUN
ejpam-4951	32	6	is	be	AUX
ejpam-4951	32	7	quadratically	quadratically	ADV
ejpam-4951	32	8	convergent	convergent	ADJ
ejpam-4951	32	9	[	[	X
ejpam-4951	32	10	2	2	NUM
ejpam-4951	32	11	]	]	PUNCT
ejpam-4951	32	12	and	and	CCONJ
ejpam-4951	32	13	its	its	PRON
ejpam-4951	32	14	efficiency	efficiency	NOUN
ejpam-4951	32	15	index	index	NOUN
ejpam-4951	32	16	is	be	AUX
ejpam-4951	32	17	1.414	1.414	NUM
ejpam-4951	32	18	[	[	X
ejpam-4951	32	19	9	9	NUM
ejpam-4951	32	20	]	]	PUNCT
ejpam-4951	32	21	.	.	PUNCT
ejpam-4951	33	1	during	during	ADP
ejpam-4951	33	2	the	the	DET
ejpam-4951	33	3	last	last	ADJ
ejpam-4951	33	4	two	two	NUM
ejpam-4951	33	5	decades	decade	NOUN
ejpam-4951	33	6	,	,	PUNCT
ejpam-4951	33	7	several	several	ADJ
ejpam-4951	33	8	higher	high	ADJ
ejpam-4951	33	9	-	-	PUNCT
ejpam-4951	33	10	order	order	NOUN
ejpam-4951	33	11	variants	variant	NOUN
ejpam-4951	33	12	of	of	ADP
ejpam-4951	33	13	newton	newton	PROPN
ejpam-4951	33	14	’s	’s	PART
ejpam-4951	33	15	methods	method	NOUN
ejpam-4951	33	16	have	have	AUX
ejpam-4951	33	17	appeared	appear	VERB
ejpam-4951	33	18	.	.	PUNCT
ejpam-4951	34	1	some	some	PRON
ejpam-4951	34	2	of	of	ADP
ejpam-4951	34	3	them	they	PRON
ejpam-4951	34	4	can	can	AUX
ejpam-4951	34	5	be	be	AUX
ejpam-4951	34	6	found	find	VERB
ejpam-4951	34	7	in	in	ADP
ejpam-4951	34	8	[	[	X
ejpam-4951	34	9	3]-[17	3]-[17	NUM
ejpam-4951	34	10	]	]	PUNCT
ejpam-4951	34	11	.	.	PUNCT
ejpam-4951	35	1	here	here	ADV
ejpam-4951	35	2	,	,	PUNCT
ejpam-4951	35	3	we	we	PRON
ejpam-4951	35	4	will	will	AUX
ejpam-4951	35	5	briefly	briefly	ADV
ejpam-4951	35	6	describe	describe	VERB
ejpam-4951	35	7	those	those	DET
ejpam-4951	35	8	methods	method	NOUN
ejpam-4951	35	9	that	that	PRON
ejpam-4951	35	10	encouraged	encourage	VERB
ejpam-4951	35	11	us	we	PRON
ejpam-4951	35	12	to	to	PART
ejpam-4951	35	13	carry	carry	VERB
ejpam-4951	35	14	out	out	ADP
ejpam-4951	35	15	our	our	PRON
ejpam-4951	35	16	own	own	ADJ
ejpam-4951	35	17	work	work	NOUN
ejpam-4951	35	18	.	.	PUNCT
ejpam-4951	36	1	now	now	ADV
ejpam-4951	36	2	,	,	PUNCT
ejpam-4951	36	3	consider	consider	VERB
ejpam-4951	36	4	double	double	PROPN
ejpam-4951	36	5	newton	newton	PROPN
ejpam-4951	36	6	’s	’s	PART
ejpam-4951	36	7	methods	method	NOUN
ejpam-4951	36	8	yn	yn	INTJ
ejpam-4951	36	9	=	=	PUNCT
ejpam-4951	37	1	xn	xn	PROPN
ejpam-4951	38	1	−	−	NUM
ejpam-4951	38	2	f(xn	f(xn	PROPN
ejpam-4951	38	3	)	)	PUNCT
ejpam-4951	38	4	f	f	PROPN
ejpam-4951	38	5	′(xn	′(xn	NOUN
ejpam-4951	38	6	)	)	PUNCT
ejpam-4951	38	7	,	,	PUNCT
ejpam-4951	38	8	xn+1	xn+1	PROPN
ejpam-4951	38	9	=	=	SYM
ejpam-4951	38	10	yn	yn	PROPN
ejpam-4951	38	11	−	−	PROPN
ejpam-4951	38	12	f(yn	f(yn	PROPN
ejpam-4951	38	13	)	)	PUNCT
ejpam-4951	38	14	f	f	NOUN
ejpam-4951	38	15	′(yn	′(yn	NOUN
ejpam-4951	38	16	)	)	PUNCT
ejpam-4951	38	17	.	.	PUNCT
ejpam-4951	39	1			NOUN
ejpam-4951	39	2	(	(	PUNCT
ejpam-4951	39	3	2	2	NUM
ejpam-4951	39	4	)	)	PUNCT
ejpam-4951	39	5	this	this	DET
ejpam-4951	39	6	method	method	NOUN
ejpam-4951	39	7	is	be	AUX
ejpam-4951	39	8	fourth	fourth	ADJ
ejpam-4951	39	9	-	-	PUNCT
ejpam-4951	39	10	order	order	NOUN
ejpam-4951	39	11	convergent	convergent	NOUN
ejpam-4951	39	12	[	[	X
ejpam-4951	39	13	11	11	NUM
ejpam-4951	39	14	,	,	PUNCT
ejpam-4951	39	15	15	15	NUM
ejpam-4951	39	16	]	]	PUNCT
ejpam-4951	39	17	and	and	CCONJ
ejpam-4951	39	18	its	its	PRON
ejpam-4951	39	19	efficiency	efficiency	NOUN
ejpam-4951	39	20	index	index	NOUN
ejpam-4951	39	21	is	be	AUX
ejpam-4951	39	22	the	the	DET
ejpam-4951	39	23	same	same	ADJ
ejpam-4951	39	24	as	as	ADP
ejpam-4951	39	25	newton	newton	PROPN
ejpam-4951	39	26	’s	’s	PART
ejpam-4951	39	27	method	method	NOUN
ejpam-4951	39	28	.	.	PUNCT
ejpam-4951	40	1	many	many	ADJ
ejpam-4951	40	2	researchers	researcher	NOUN
ejpam-4951	40	3	use	use	VERB
ejpam-4951	40	4	the	the	DET
ejpam-4951	40	5	numerical	numerical	ADJ
ejpam-4951	40	6	integration	integration	NOUN
ejpam-4951	40	7	technique	technique	NOUN
ejpam-4951	40	8	to	to	PART
ejpam-4951	40	9	improve	improve	VERB
ejpam-4951	40	10	the	the	DET
ejpam-4951	40	11	local	local	ADJ
ejpam-4951	40	12	order	order	NOUN
ejpam-4951	40	13	of	of	ADP
ejpam-4951	40	14	convergence	convergence	NOUN
ejpam-4951	40	15	of	of	ADP
ejpam-4951	40	16	newton	newton	PROPN
ejpam-4951	40	17	’s	’s	PART
ejpam-4951	40	18	method	method	NOUN
ejpam-4951	40	19	.	.	PUNCT
ejpam-4951	41	1	some	some	PRON
ejpam-4951	41	2	of	of	ADP
ejpam-4951	41	3	them	they	PRON
ejpam-4951	41	4	may	may	AUX
ejpam-4951	41	5	be	be	AUX
ejpam-4951	41	6	found	find	VERB
ejpam-4951	41	7	in	in	ADP
ejpam-4951	41	8	[	[	X
ejpam-4951	41	9	3–8	3–8	NUM
ejpam-4951	41	10	,	,	PUNCT
ejpam-4951	41	11	10	10	NUM
ejpam-4951	41	12	,	,	PUNCT
ejpam-4951	41	13	16	16	NUM
ejpam-4951	41	14	,	,	PUNCT
ejpam-4951	41	15	17	17	NUM
ejpam-4951	41	16	]	]	PUNCT
ejpam-4951	41	17	and	and	CCONJ
ejpam-4951	41	18	references	reference	NOUN
ejpam-4951	41	19	therein	therein	ADV
ejpam-4951	41	20	.	.	PUNCT
ejpam-4951	42	1	to	to	PART
ejpam-4951	42	2	get	get	VERB
ejpam-4951	42	3	the	the	DET
ejpam-4951	42	4	improved	improved	ADJ
ejpam-4951	42	5	convergence	convergence	NOUN
ejpam-4951	42	6	order	order	NOUN
ejpam-4951	42	7	of	of	ADP
ejpam-4951	42	8	newton	newton	PROPN
ejpam-4951	42	9	’s	’s	PART
ejpam-4951	42	10	method	method	NOUN
ejpam-4951	42	11	,	,	PUNCT
ejpam-4951	42	12	özban	özban	PROPN
ejpam-4951	42	13	in	in	ADP
ejpam-4951	42	14	[	[	PUNCT
ejpam-4951	42	15	13	13	NUM
ejpam-4951	42	16	]	]	PUNCT
ejpam-4951	42	17	considered	consider	VERB
ejpam-4951	42	18	newton	newton	PROPN
ejpam-4951	42	19	’s	’s	PART
ejpam-4951	42	20	theorem	theorem	VERB
ejpam-4951	42	21	f(x	f(x	PROPN
ejpam-4951	42	22	)	)	PUNCT
ejpam-4951	42	23	=	=	SYM
ejpam-4951	43	1	f(xn	f(xn	X
ejpam-4951	43	2	)	)	PUNCT
ejpam-4951	44	1	+	+	CCONJ
ejpam-4951	44	2	∫	∫	PUNCT
ejpam-4951	44	3	x	x	SYM
ejpam-4951	44	4	xn	xn	PROPN
ejpam-4951	44	5	f	f	PROPN
ejpam-4951	44	6	′(t	′(t	PROPN
ejpam-4951	44	7	)	)	PUNCT
ejpam-4951	44	8	dt	dt	PUNCT
ejpam-4951	44	9	(	(	PUNCT
ejpam-4951	44	10	3	3	NUM
ejpam-4951	44	11	)	)	PUNCT
ejpam-4951	44	12	and	and	CCONJ
ejpam-4951	44	13	used	use	VERB
ejpam-4951	44	14	the	the	DET
ejpam-4951	44	15	mid	mid	ADJ
ejpam-4951	44	16	-	-	ADJ
ejpam-4951	44	17	point	point	NOUN
ejpam-4951	44	18	rule	rule	NOUN
ejpam-4951	44	19	to	to	PART
ejpam-4951	44	20	approximate	approximate	VERB
ejpam-4951	44	21	the	the	DET
ejpam-4951	44	22	integral	integral	ADJ
ejpam-4951	44	23	,	,	PUNCT
ejpam-4951	44	24	that	that	PRON
ejpam-4951	44	25	is,∫	is,∫	VERB
ejpam-4951	44	26	x	x	SYM
ejpam-4951	44	27	xn	xn	PROPN
ejpam-4951	44	28	f	f	PROPN
ejpam-4951	44	29	′(t	′(t	PROPN
ejpam-4951	44	30	)	)	PUNCT
ejpam-4951	44	31	dt	dt	NOUN
ejpam-4951	45	1	=	=	PUNCT
ejpam-4951	45	2	(	(	PUNCT
ejpam-4951	45	3	x−	x−	PROPN
ejpam-4951	45	4	xn)f	xn)f	PROPN
ejpam-4951	45	5	′	′	NUM
ejpam-4951	46	1	(	(	PUNCT
ejpam-4951	46	2	x+	x+	X
ejpam-4951	46	3	xn	xn	X
ejpam-4951	46	4	)	)	PUNCT
ejpam-4951	46	5	2	2	NUM
ejpam-4951	46	6	.	.	PUNCT
ejpam-4951	47	1	(	(	PUNCT
ejpam-4951	47	2	4	4	X
ejpam-4951	47	3	)	)	PUNCT
ejpam-4951	47	4	b.	b.	PROPN
ejpam-4951	47	5	sapkota	sapkota	PROPN
ejpam-4951	47	6	,	,	PUNCT
ejpam-4951	47	7	j.	j.	PROPN
ejpam-4951	47	8	jnawali	jnawali	PROPN
ejpam-4951	47	9	/	/	SYM
ejpam-4951	47	10	eur	eur	PROPN
ejpam-4951	47	11	.	.	PUNCT
ejpam-4951	48	1	j.	j.	PROPN
ejpam-4951	48	2	pure	pure	PROPN
ejpam-4951	48	3	appl	appl	PROPN
ejpam-4951	48	4	.	.	PROPN
ejpam-4951	48	5	math	math	PROPN
ejpam-4951	48	6	,	,	PUNCT
ejpam-4951	48	7	16	16	NUM
ejpam-4951	48	8	(	(	PUNCT
ejpam-4951	48	9	4	4	NUM
ejpam-4951	48	10	)	)	PUNCT
ejpam-4951	48	11	(	(	PUNCT
ejpam-4951	48	12	2023	2023	NUM
ejpam-4951	48	13	)	)	PUNCT
ejpam-4951	48	14	,	,	PUNCT
ejpam-4951	48	15	2419	2419	NUM
ejpam-4951	48	16	-	-	SYM
ejpam-4951	48	17	2430	2430	NUM
ejpam-4951	48	18	2421	2421	NUM
ejpam-4951	48	19	then	then	ADV
ejpam-4951	48	20	,	,	PUNCT
ejpam-4951	48	21	they	they	PRON
ejpam-4951	48	22	explored	explore	VERB
ejpam-4951	48	23	the	the	DET
ejpam-4951	48	24	variant	variant	NOUN
ejpam-4951	48	25	of	of	ADP
ejpam-4951	48	26	newton	newton	PROPN
ejpam-4951	48	27	’s	’s	PART
ejpam-4951	48	28	method	method	NOUN
ejpam-4951	48	29	given	give	VERB
ejpam-4951	48	30	by	by	ADP
ejpam-4951	48	31	xn+1	xn+1	PROPN
ejpam-4951	48	32	=	=	SYM
ejpam-4951	48	33	xn	xn	PROPN
ejpam-4951	48	34	−	−	NUM
ejpam-4951	49	1	f(xn	f(xn	PROPN
ejpam-4951	49	2	)	)	PUNCT
ejpam-4951	49	3	f	f	PROPN
ejpam-4951	49	4	′(xn+x∗	′(xn+x∗	NUM
ejpam-4951	49	5	n	n	NUM
ejpam-4951	49	6	2	2	NUM
ejpam-4951	49	7	)	)	PUNCT
ejpam-4951	49	8	,	,	PUNCT
ejpam-4951	49	9	(	(	PUNCT
ejpam-4951	49	10	5	5	X
ejpam-4951	49	11	)	)	PUNCT
ejpam-4951	50	1	where	where	SCONJ
ejpam-4951	50	2	x∗n	x∗n	PUNCT
ejpam-4951	50	3	=	=	SYM
ejpam-4951	50	4	xn	xn	PROPN
ejpam-4951	50	5	−	−	NUM
ejpam-4951	50	6	f(xn	f(xn	PROPN
ejpam-4951	50	7	)	)	PUNCT
ejpam-4951	50	8	f	f	PROPN
ejpam-4951	50	9	′(xn	′(xn	NOUN
ejpam-4951	50	10	)	)	PUNCT
ejpam-4951	50	11	.	.	PUNCT
ejpam-4951	51	1	this	this	PRON
ejpam-4951	51	2	is	be	AUX
ejpam-4951	51	3	the	the	DET
ejpam-4951	51	4	midpoint	midpoint	PROPN
ejpam-4951	51	5	newton	newton	PROPN
ejpam-4951	51	6	’s	’s	PART
ejpam-4951	51	7	method	method	NOUN
ejpam-4951	51	8	and	and	CCONJ
ejpam-4951	51	9	it	it	PRON
ejpam-4951	51	10	has	have	AUX
ejpam-4951	51	11	been	be	AUX
ejpam-4951	51	12	proven	prove	VERB
ejpam-4951	51	13	that	that	SCONJ
ejpam-4951	51	14	its	its	PRON
ejpam-4951	51	15	convergence	convergence	NOUN
ejpam-4951	51	16	order	order	NOUN
ejpam-4951	51	17	is	be	AUX
ejpam-4951	51	18	3	3	NUM
ejpam-4951	51	19	.	.	PUNCT
ejpam-4951	52	1	recently	recently	ADV
ejpam-4951	52	2	,	,	PUNCT
ejpam-4951	52	3	mcdougall	mcdougall	PROPN
ejpam-4951	52	4	andwortherspoon	andwortherspoon	ADV
ejpam-4951	53	1	[	[	X
ejpam-4951	53	2	12	12	NUM
ejpam-4951	53	3	]	]	PUNCT
ejpam-4951	53	4	obtained	obtain	VERB
ejpam-4951	53	5	a	a	DET
ejpam-4951	53	6	variant	variant	NOUN
ejpam-4951	53	7	of	of	ADP
ejpam-4951	53	8	newton	newton	PROPN
ejpam-4951	53	9	’s	’s	PART
ejpam-4951	53	10	method	method	NOUN
ejpam-4951	53	11	having	have	VERB
ejpam-4951	53	12	the	the	DET
ejpam-4951	53	13	order	order	NOUN
ejpam-4951	53	14	of	of	ADP
ejpam-4951	53	15	convergence	convergence	NOUN
ejpam-4951	53	16	1	1	NUM
ejpam-4951	53	17	+	+	CCONJ
ejpam-4951	53	18	√	√	NUM
ejpam-4951	53	19	2	2	NUM
ejpam-4951	53	20	with	with	ADP
ejpam-4951	53	21	a	a	DET
ejpam-4951	53	22	minor	minor	ADJ
ejpam-4951	53	23	change	change	NOUN
ejpam-4951	53	24	in	in	ADP
ejpam-4951	53	25	newton	newton	PROPN
ejpam-4951	53	26	’s	’s	PART
ejpam-4951	53	27	method	method	NOUN
ejpam-4951	53	28	.	.	PUNCT
ejpam-4951	54	1	the	the	DET
ejpam-4951	54	2	method	method	NOUN
ejpam-4951	54	3	is	be	AUX
ejpam-4951	54	4	given	give	VERB
ejpam-4951	54	5	below	below	ADP
ejpam-4951	54	6	:	:	PUNCT
ejpam-4951	54	7	if	if	SCONJ
ejpam-4951	54	8	x0	x0	PROPN
ejpam-4951	54	9	is	be	AUX
ejpam-4951	54	10	the	the	DET
ejpam-4951	54	11	initial	initial	ADJ
ejpam-4951	54	12	approximate	approximate	ADJ
ejpam-4951	54	13	solution	solution	NOUN
ejpam-4951	54	14	,	,	PUNCT
ejpam-4951	54	15	we	we	PRON
ejpam-4951	54	16	can	can	AUX
ejpam-4951	54	17	write	write	VERB
ejpam-4951	54	18	x∗0	x∗0	NOUN
ejpam-4951	55	1	=	=	PUNCT
ejpam-4951	56	1	x0	x0	PROPN
ejpam-4951	57	1	−	−	PROPN
ejpam-4951	57	2	f(x0	f(x0	PROPN
ejpam-4951	57	3	)	)	PUNCT
ejpam-4951	57	4	f	f	PROPN
ejpam-4951	57	5	′(x0	′(x0	NOUN
ejpam-4951	57	6	)	)	PUNCT
ejpam-4951	57	7	,	,	PUNCT
ejpam-4951	57	8	x1	x1	PROPN
ejpam-4951	57	9	=	=	SYM
ejpam-4951	58	1	x0	x0	PROPN
ejpam-4951	58	2	−	−	PROPN
ejpam-4951	58	3	f(x0	f(x0	PROPN
ejpam-4951	58	4	)	)	PUNCT
ejpam-4951	59	1	f	f	PROPN
ejpam-4951	59	2	′[12(x0	′[12(x0	PROPN
ejpam-4951	59	3	+	+	CCONJ
ejpam-4951	59	4	x∗0	x∗0	PROPN
ejpam-4951	59	5	)	)	PUNCT
ejpam-4951	59	6	]	]	PUNCT
ejpam-4951	59	7	.	.	PUNCT
ejpam-4951	60	1			NOUN
ejpam-4951	60	2	(	(	PUNCT
ejpam-4951	60	3	6	6	NUM
ejpam-4951	60	4	)	)	PUNCT
ejpam-4951	60	5	for	for	ADP
ejpam-4951	60	6	n	n	PRON
ejpam-4951	60	7	≥	≥	NUM
ejpam-4951	60	8	1	1	NUM
ejpam-4951	60	9	,	,	PUNCT
ejpam-4951	60	10	we	we	PRON
ejpam-4951	60	11	have	have	VERB
ejpam-4951	60	12	x∗n	x∗n	NOUN
ejpam-4951	61	1	=	=	SYM
ejpam-4951	61	2	xn	xn	PROPN
ejpam-4951	62	1	−	−	NUM
ejpam-4951	62	2	f(xn	f(xn	PROPN
ejpam-4951	62	3	)	)	PUNCT
ejpam-4951	62	4	f	f	PROPN
ejpam-4951	62	5	′[12(xn−1	′[12(xn−1	ADJ
ejpam-4951	62	6	+	+	CCONJ
ejpam-4951	62	7	x∗n−1	x∗n−1	NUM
ejpam-4951	62	8	)	)	PUNCT
ejpam-4951	62	9	]	]	PUNCT
ejpam-4951	62	10	,	,	PUNCT
ejpam-4951	62	11	xn+1	xn+1	PROPN
ejpam-4951	62	12	=	=	SYM
ejpam-4951	62	13	xn	xn	PROPN
ejpam-4951	63	1	−	−	NUM
ejpam-4951	63	2	f(xn	f(xn	PROPN
ejpam-4951	63	3	)	)	PUNCT
ejpam-4951	63	4	f	f	PROPN
ejpam-4951	63	5	′[12(xn	′[12(xn	NOUN
ejpam-4951	64	1	+	+	CCONJ
ejpam-4951	64	2	x∗n	x∗n	NOUN
ejpam-4951	64	3	)	)	PUNCT
ejpam-4951	64	4	]	]	PUNCT
ejpam-4951	64	5	.	.	PUNCT
ejpam-4951	65	1			PRON
ejpam-4951	65	2	(	(	PUNCT
ejpam-4951	65	3	7	7	NUM
ejpam-4951	65	4	)	)	PUNCT
ejpam-4951	65	5	this	this	PRON
ejpam-4951	65	6	is	be	AUX
ejpam-4951	65	7	a	a	DET
ejpam-4951	65	8	kind	kind	NOUN
ejpam-4951	65	9	of	of	ADP
ejpam-4951	65	10	predictor	predictor	NOUN
ejpam-4951	65	11	-	-	PUNCT
ejpam-4951	65	12	corrector	corrector	NOUN
ejpam-4951	65	13	method	method	NOUN
ejpam-4951	65	14	.	.	PUNCT
ejpam-4951	66	1	in	in	ADP
ejpam-4951	66	2	newton	newton	PROPN
ejpam-4951	66	3	’s	’s	PART
ejpam-4951	66	4	method	method	NOUN
ejpam-4951	66	5	,	,	PUNCT
ejpam-4951	66	6	the	the	DET
ejpam-4951	66	7	derivatives	derivative	NOUN
ejpam-4951	66	8	are	be	AUX
ejpam-4951	66	9	calculated	calculate	VERB
ejpam-4951	66	10	at	at	ADP
ejpam-4951	66	11	the	the	DET
ejpam-4951	66	12	previously	previously	ADV
ejpam-4951	66	13	iterated	iterate	VERB
ejpam-4951	66	14	point	point	NOUN
ejpam-4951	66	15	,	,	PUNCT
ejpam-4951	66	16	but	but	CCONJ
ejpam-4951	66	17	in	in	ADP
ejpam-4951	66	18	the	the	DET
ejpam-4951	66	19	methods	method	NOUN
ejpam-4951	66	20	(	(	PUNCT
ejpam-4951	66	21	6)-(7	6)-(7	NOUN
ejpam-4951	66	22	)	)	PUNCT
ejpam-4951	66	23	,	,	PUNCT
ejpam-4951	66	24	the	the	DET
ejpam-4951	66	25	derivatives	derivative	NOUN
ejpam-4951	66	26	are	be	AUX
ejpam-4951	66	27	calculated	calculate	VERB
ejpam-4951	66	28	at	at	ADP
ejpam-4951	66	29	some	some	DET
ejpam-4951	66	30	convenient	convenient	ADJ
ejpam-4951	66	31	point	point	NOUN
ejpam-4951	66	32	.	.	PUNCT
ejpam-4951	67	1	as	as	ADP
ejpam-4951	67	2	the	the	DET
ejpam-4951	67	3	supreme	supreme	ADJ
ejpam-4951	67	4	goal	goal	NOUN
ejpam-4951	67	5	of	of	ADP
ejpam-4951	67	6	this	this	DET
ejpam-4951	67	7	paper	paper	NOUN
ejpam-4951	67	8	,	,	PUNCT
ejpam-4951	67	9	two	two	NUM
ejpam-4951	67	10	iterative	iterative	NOUN
ejpam-4951	67	11	methods	method	NOUN
ejpam-4951	67	12	are	be	AUX
ejpam-4951	67	13	constructed	construct	VERB
ejpam-4951	67	14	as	as	ADP
ejpam-4951	67	15	a	a	DET
ejpam-4951	67	16	variant	variant	NOUN
ejpam-4951	67	17	of	of	ADP
ejpam-4951	67	18	methods	method	NOUN
ejpam-4951	67	19	(	(	PUNCT
ejpam-4951	67	20	2	2	NUM
ejpam-4951	67	21	)	)	PUNCT
ejpam-4951	67	22	and	and	CCONJ
ejpam-4951	67	23	(	(	PUNCT
ejpam-4951	67	24	5	5	X
ejpam-4951	67	25	)	)	PUNCT
ejpam-4951	67	26	using	use	VERB
ejpam-4951	67	27	methods	method	NOUN
ejpam-4951	67	28	(	(	PUNCT
ejpam-4951	67	29	6)-(7	6)-(7	NOUN
ejpam-4951	67	30	)	)	PUNCT
ejpam-4951	67	31	.	.	PUNCT
ejpam-4951	68	1	also	also	ADV
ejpam-4951	68	2	,	,	PUNCT
ejpam-4951	68	3	it	it	PRON
ejpam-4951	68	4	has	have	VERB
ejpam-4951	68	5	to	to	PART
ejpam-4951	68	6	be	be	AUX
ejpam-4951	68	7	shown	show	VERB
ejpam-4951	68	8	that	that	SCONJ
ejpam-4951	68	9	both	both	DET
ejpam-4951	68	10	newly	newly	ADV
ejpam-4951	68	11	introduced	introduce	VERB
ejpam-4951	68	12	methods	method	NOUN
ejpam-4951	68	13	can	can	AUX
ejpam-4951	68	14	easily	easily	ADV
ejpam-4951	68	15	compete	compete	VERB
ejpam-4951	68	16	with	with	ADP
ejpam-4951	68	17	similar	similar	ADJ
ejpam-4951	68	18	existing	exist	VERB
ejpam-4951	68	19	methods	method	NOUN
ejpam-4951	68	20	.	.	PUNCT
ejpam-4951	69	1	2	2	X
ejpam-4951	69	2	.	.	X
ejpam-4951	69	3	methods	method	NOUN
ejpam-4951	69	4	with	with	ADP
ejpam-4951	69	5	convergence	convergence	NOUN
ejpam-4951	69	6	analysis	analysis	NOUN
ejpam-4951	69	7	at	at	ADP
ejpam-4951	69	8	first	first	ADV
ejpam-4951	69	9	,	,	PUNCT
ejpam-4951	69	10	we	we	PRON
ejpam-4951	69	11	present	present	VERB
ejpam-4951	69	12	the	the	DET
ejpam-4951	69	13	iterative	iterative	NOUN
ejpam-4951	69	14	method	method	NOUN
ejpam-4951	69	15	as	as	ADP
ejpam-4951	69	16	a	a	DET
ejpam-4951	69	17	variant	variant	NOUN
ejpam-4951	69	18	of	of	ADP
ejpam-4951	69	19	method	method	NOUN
ejpam-4951	69	20	(	(	PUNCT
ejpam-4951	69	21	2	2	X
ejpam-4951	69	22	)	)	PUNCT
ejpam-4951	69	23	using	use	VERB
ejpam-4951	69	24	the	the	DET
ejpam-4951	69	25	view	view	NOUN
ejpam-4951	69	26	of	of	ADP
ejpam-4951	69	27	method	method	NOUN
ejpam-4951	69	28	(	(	PUNCT
ejpam-4951	69	29	6)-(7	6)-(7	NOUN
ejpam-4951	69	30	)	)	PUNCT
ejpam-4951	69	31	as	as	SCONJ
ejpam-4951	69	32	given	give	VERB
ejpam-4951	69	33	below	below	ADV
ejpam-4951	69	34	:	:	PUNCT
ejpam-4951	69	35	if	if	SCONJ
ejpam-4951	69	36	x0	x0	PROPN
ejpam-4951	69	37	is	be	AUX
ejpam-4951	69	38	taken	take	VERB
ejpam-4951	69	39	as	as	ADP
ejpam-4951	69	40	the	the	DET
ejpam-4951	69	41	initial	initial	ADJ
ejpam-4951	69	42	approximate	approximate	ADJ
ejpam-4951	69	43	solution	solution	NOUN
ejpam-4951	69	44	,	,	PUNCT
ejpam-4951	69	45	x∗0	x∗0	NOUN
ejpam-4951	70	1	=	=	PUNCT
ejpam-4951	70	2	x0	x0	PROPN
ejpam-4951	70	3	x∗∗0	x∗∗0	PROPN
ejpam-4951	71	1	=	=	SYM
ejpam-4951	72	1	x0	x0	PROPN
ejpam-4951	72	2	−	−	PROPN
ejpam-4951	72	3	f(x0	f(x0	PROPN
ejpam-4951	72	4	)	)	PUNCT
ejpam-4951	73	1	f	f	PROPN
ejpam-4951	74	1	′	′	NUM
ejpam-4951	75	1	(	(	PUNCT
ejpam-4951	75	2	x0	x0	PROPN
ejpam-4951	75	3	+	+	CCONJ
ejpam-4951	75	4	x∗0	x∗0	NOUN
ejpam-4951	75	5	2	2	NUM
ejpam-4951	75	6	)	)	PUNCT
ejpam-4951	75	7	=	=	SYM
ejpam-4951	76	1	x0	x0	PROPN
ejpam-4951	76	2	−	−	PROPN
ejpam-4951	76	3	f(x0	f(x0	PROPN
ejpam-4951	76	4	)	)	PUNCT
ejpam-4951	76	5	f	f	PROPN
ejpam-4951	76	6	′(x0	′(x0	NOUN
ejpam-4951	76	7	)	)	PUNCT
ejpam-4951	77	1	x1	x1	PROPN
ejpam-4951	78	1	=	=	PUNCT
ejpam-4951	78	2	x∗∗0	x∗∗0	PROPN
ejpam-4951	79	1	−	−	PROPN
ejpam-4951	79	2	f(x∗∗0	f(x∗∗0	PROPN
ejpam-4951	79	3	)	)	PUNCT
ejpam-4951	79	4	f	f	PROPN
ejpam-4951	79	5	′(x∗∗0	′(x∗∗0	ADJ
ejpam-4951	79	6	)	)	PUNCT
ejpam-4951	79	7			NOUN
ejpam-4951	79	8	(	(	PUNCT
ejpam-4951	79	9	8)	8)	NUM
ejpam-4951	79	10	b.	b.	PROPN
ejpam-4951	79	11	sapkota	sapkota	PROPN
ejpam-4951	79	12	,	,	PUNCT
ejpam-4951	79	13	j.	j.	PROPN
ejpam-4951	79	14	jnawali	jnawali	PROPN
ejpam-4951	79	15	/	/	SYM
ejpam-4951	79	16	eur	eur	PROPN
ejpam-4951	79	17	.	.	PUNCT
ejpam-4951	80	1	j.	j.	PROPN
ejpam-4951	80	2	pure	pure	PROPN
ejpam-4951	80	3	appl	appl	PROPN
ejpam-4951	80	4	.	.	PROPN
ejpam-4951	80	5	math	math	PROPN
ejpam-4951	80	6	,	,	PUNCT
ejpam-4951	80	7	16	16	NUM
ejpam-4951	80	8	(	(	PUNCT
ejpam-4951	80	9	4	4	NUM
ejpam-4951	80	10	)	)	PUNCT
ejpam-4951	80	11	(	(	PUNCT
ejpam-4951	80	12	2023	2023	NUM
ejpam-4951	80	13	)	)	PUNCT
ejpam-4951	80	14	,	,	PUNCT
ejpam-4951	80	15	2419	2419	NUM
ejpam-4951	80	16	-	-	SYM
ejpam-4951	80	17	2430	2430	NUM
ejpam-4951	80	18	2422	2422	NUM
ejpam-4951	80	19	followed	follow	VERB
ejpam-4951	80	20	by	by	ADP
ejpam-4951	80	21	(	(	PUNCT
ejpam-4951	80	22	for	for	ADP
ejpam-4951	80	23	n	n	PRON
ejpam-4951	80	24	≥	≥	NOUN
ejpam-4951	80	25	1	1	NUM
ejpam-4951	80	26	)	)	PUNCT
ejpam-4951	80	27	x∗n	x∗n	X
ejpam-4951	81	1	=	=	PUNCT
ejpam-4951	81	2	xn	xn	PROPN
ejpam-4951	82	1	−	−	NUM
ejpam-4951	82	2	f(xn	f(xn	PROPN
ejpam-4951	82	3	)	)	PUNCT
ejpam-4951	82	4	f	f	NOUN
ejpam-4951	83	1	′	′	NUM
ejpam-4951	83	2	(	(	PUNCT
ejpam-4951	83	3	xn−1	xn−1	PROPN
ejpam-4951	83	4	+	+	CCONJ
ejpam-4951	83	5	x∗n−1	x∗n−1	PROPN
ejpam-4951	83	6	2	2	NUM
ejpam-4951	83	7	)	)	PUNCT
ejpam-4951	83	8	x∗∗n	x∗∗n	X
ejpam-4951	84	1	=	=	PUNCT
ejpam-4951	84	2	xn	xn	PROPN
ejpam-4951	85	1	−	−	NUM
ejpam-4951	85	2	f(xn	f(xn	PROPN
ejpam-4951	85	3	)	)	PUNCT
ejpam-4951	85	4	f	f	NOUN
ejpam-4951	86	1	′	′	NUM
ejpam-4951	86	2	(	(	PUNCT
ejpam-4951	86	3	xn	xn	PROPN
ejpam-4951	87	1	+	+	NUM
ejpam-4951	87	2	x∗n	x∗n	NUM
ejpam-4951	87	3	2	2	NUM
ejpam-4951	87	4	)	)	PUNCT
ejpam-4951	87	5	xn+1	xn+1	PROPN
ejpam-4951	87	6	=	=	SYM
ejpam-4951	87	7	x∗∗n	x∗∗n	NOUN
ejpam-4951	87	8	−	−	PROPN
ejpam-4951	87	9	f(x∗∗n	f(x∗∗n	NOUN
ejpam-4951	87	10	)	)	PUNCT
ejpam-4951	88	1	f	f	PROPN
ejpam-4951	88	2	′(x∗∗n	′(x∗∗n	NOUN
ejpam-4951	88	3	)	)	PUNCT
ejpam-4951	89	1			ADV
ejpam-4951	89	2	(	(	PUNCT
ejpam-4951	89	3	9	9	NUM
ejpam-4951	89	4	)	)	PUNCT
ejpam-4951	89	5	to	to	PART
ejpam-4951	89	6	analyze	analyze	VERB
ejpam-4951	89	7	it	it	PRON
ejpam-4951	89	8	’s	’	VERB
ejpam-4951	89	9	convergence	convergence	NOUN
ejpam-4951	89	10	,	,	PUNCT
ejpam-4951	89	11	we	we	PRON
ejpam-4951	89	12	prove	prove	VERB
ejpam-4951	89	13	:	:	PUNCT
ejpam-4951	89	14	theorem	theorem	NOUN
ejpam-4951	89	15	1	1	X
ejpam-4951	89	16	.	.	PUNCT
ejpam-4951	90	1	let	let	VERB
ejpam-4951	90	2	a	a	DET
ejpam-4951	90	3	sufficiently	sufficiently	ADV
ejpam-4951	90	4	differentiable	differentiable	ADJ
ejpam-4951	90	5	function	function	NOUN
ejpam-4951	90	6	f	f	NOUN
ejpam-4951	90	7	:	:	PUNCT
ejpam-4951	91	1	d	d	X
ejpam-4951	91	2	⊂	⊂	PROPN
ejpam-4951	91	3	r	r	NOUN
ejpam-4951	91	4	→	→	SYM
ejpam-4951	91	5	r	r	NOUN
ejpam-4951	91	6	has	have	VERB
ejpam-4951	91	7	a	a	DET
ejpam-4951	91	8	simple	simple	ADJ
ejpam-4951	91	9	root	root	NOUN
ejpam-4951	91	10	α	α	NOUN
ejpam-4951	91	11	in	in	ADP
ejpam-4951	91	12	the	the	DET
ejpam-4951	91	13	interval	interval	NOUN
ejpam-4951	91	14	d.	d.	NOUN
ejpam-4951	91	15	if	if	SCONJ
ejpam-4951	91	16	x0	x0	PROPN
ejpam-4951	91	17	is	be	AUX
ejpam-4951	91	18	sufficiently	sufficiently	ADV
ejpam-4951	91	19	close	close	ADJ
ejpam-4951	91	20	to	to	ADP
ejpam-4951	91	21	α	α	PRON
ejpam-4951	91	22	,	,	PUNCT
ejpam-4951	91	23	then	then	ADV
ejpam-4951	91	24	to	to	PART
ejpam-4951	91	25	solve	solve	VERB
ejpam-4951	91	26	the	the	DET
ejpam-4951	91	27	nonlinear	nonlinear	ADJ
ejpam-4951	91	28	equation	equation	NOUN
ejpam-4951	91	29	f(x	f(x	PROPN
ejpam-4951	91	30	)	)	PUNCT
ejpam-4951	92	1	=	=	SYM
ejpam-4951	92	2	0	0	NUM
ejpam-4951	92	3	,	,	PUNCT
ejpam-4951	92	4	(	(	PUNCT
ejpam-4951	92	5	8)-(9	8)-(9	NOUN
ejpam-4951	92	6	)	)	PUNCT
ejpam-4951	92	7	has	have	VERB
ejpam-4951	92	8	a	a	DET
ejpam-4951	92	9	convergence	convergence	NOUN
ejpam-4951	92	10	of	of	ADP
ejpam-4951	92	11	order	order	NOUN
ejpam-4951	92	12	4.45	4.45	NUM
ejpam-4951	92	13	.	.	PUNCT
ejpam-4951	93	1	proof	proof	NOUN
ejpam-4951	93	2	.	.	PUNCT
ejpam-4951	94	1	let	let	VERB
ejpam-4951	94	2	en	en	ADV
ejpam-4951	94	3	=	=	SYM
ejpam-4951	94	4	xn	xn	PROPN
ejpam-4951	95	1	−	−	PROPN
ejpam-4951	96	1	α	α	PRON
ejpam-4951	96	2	be	be	VERB
ejpam-4951	96	3	the	the	DET
ejpam-4951	96	4	error	error	NOUN
ejpam-4951	96	5	in	in	ADP
ejpam-4951	96	6	the	the	DET
ejpam-4951	96	7	nthiterationxn	nthiterationxn	NOUN
ejpam-4951	96	8	and	and	CCONJ
ejpam-4951	96	9	denote	denote	NOUN
ejpam-4951	96	10	cj	cj	NOUN
ejpam-4951	97	1	=	=	SYM
ejpam-4951	97	2	1	1	NUM
ejpam-4951	97	3	j	j	PROPN
ejpam-4951	97	4	!	!	PUNCT
ejpam-4951	97	5	.	.	PUNCT
ejpam-4951	98	1	fj(α	fj(α	NOUN
ejpam-4951	98	2	)	)	PUNCT
ejpam-4951	98	3	f	f	PROPN
ejpam-4951	98	4	′(α	′(α	PROPN
ejpam-4951	98	5	)	)	PUNCT
ejpam-4951	98	6	,	,	PUNCT
ejpam-4951	99	1	j	j	PROPN
ejpam-4951	99	2	=	=	SYM
ejpam-4951	99	3	2	2	NUM
ejpam-4951	99	4	,	,	PUNCT
ejpam-4951	99	5	3	3	NUM
ejpam-4951	99	6	,	,	PUNCT
ejpam-4951	99	7	4	4	NUM
ejpam-4951	99	8	....	....	PUNCT
ejpam-4951	100	1	it	it	PRON
ejpam-4951	100	2	is	be	AUX
ejpam-4951	100	3	standard	standard	ADJ
ejpam-4951	100	4	to	to	PART
ejpam-4951	100	5	work	work	VERB
ejpam-4951	100	6	out	out	ADP
ejpam-4951	100	7	that	that	SCONJ
ejpam-4951	100	8	the	the	DET
ejpam-4951	100	9	error	error	NOUN
ejpam-4951	100	10	equation	equation	NOUN
ejpam-4951	100	11	in	in	ADP
ejpam-4951	100	12	the	the	DET
ejpam-4951	100	13	newton	newton	PROPN
ejpam-4951	100	14	method	method	NOUN
ejpam-4951	100	15	1	1	NUM
ejpam-4951	100	16	:	:	SYM
ejpam-4951	100	17	en+1	en+1	ADJ
ejpam-4951	100	18	=	=	SYM
ejpam-4951	100	19	c2e	c2e	PROPN
ejpam-4951	100	20	2	2	NUM
ejpam-4951	100	21	n	n	CCONJ
ejpam-4951	100	22	,	,	PUNCT
ejpam-4951	100	23	(	(	PUNCT
ejpam-4951	100	24	10	10	NUM
ejpam-4951	100	25	)	)	PUNCT
ejpam-4951	100	26	where	where	SCONJ
ejpam-4951	100	27	the	the	DET
ejpam-4951	100	28	terms	term	NOUN
ejpam-4951	100	29	with	with	ADP
ejpam-4951	100	30	higher	high	ADJ
ejpam-4951	100	31	powers	power	NOUN
ejpam-4951	100	32	of	of	ADP
ejpam-4951	100	33	en	en	X
ejpam-4951	100	34	are	be	AUX
ejpam-4951	100	35	omitted	omit	VERB
ejpam-4951	100	36	.	.	PUNCT
ejpam-4951	101	1	let	let	VERB
ejpam-4951	101	2	us	we	PRON
ejpam-4951	101	3	go	go	VERB
ejpam-4951	101	4	on	on	ADP
ejpam-4951	101	5	to	to	PART
ejpam-4951	101	6	discuss	discuss	VERB
ejpam-4951	101	7	the	the	DET
ejpam-4951	101	8	convergence	convergence	NOUN
ejpam-4951	101	9	of	of	ADP
ejpam-4951	101	10	the	the	DET
ejpam-4951	101	11	methods	method	NOUN
ejpam-4951	101	12	(	(	PUNCT
ejpam-4951	101	13	8)-(9	8)-(9	NUM
ejpam-4951	101	14	)	)	PUNCT
ejpam-4951	101	15	.	.	PUNCT
ejpam-4951	102	1	let	let	VERB
ejpam-4951	102	2	e∗n	e∗n	VERB
ejpam-4951	102	3	,	,	PUNCT
ejpam-4951	102	4	e	e	X
ejpam-4951	102	5	∗∗	∗∗	PROPN
ejpam-4951	102	6	n	n	CCONJ
ejpam-4951	102	7	and	and	CCONJ
ejpam-4951	102	8	en	en	ADP
ejpam-4951	102	9	denote	denote	NOUN
ejpam-4951	102	10	errors	error	NOUN
ejpam-4951	102	11	at	at	ADP
ejpam-4951	102	12	iterates	iterate	NOUN
ejpam-4951	102	13	x∗n	x∗n	PRON
ejpam-4951	102	14	,	,	PUNCT
ejpam-4951	102	15	x	x	SYM
ejpam-4951	102	16	∗∗	∗∗	NOUN
ejpam-4951	102	17	n	n	CCONJ
ejpam-4951	102	18	and	and	CCONJ
ejpam-4951	102	19	xn	xn	NUM
ejpam-4951	102	20	respectively	respectively	ADV
ejpam-4951	102	21	.	.	PUNCT
ejpam-4951	103	1	then	then	ADV
ejpam-4951	103	2	clearly	clearly	ADV
ejpam-4951	103	3	e∗0	e∗0	NOUN
ejpam-4951	103	4	=	=	SYM
ejpam-4951	103	5	e0	e0	PROPN
ejpam-4951	103	6	and	and	CCONJ
ejpam-4951	103	7	in	in	ADP
ejpam-4951	103	8	the	the	DET
ejpam-4951	103	9	view	view	NOUN
ejpam-4951	103	10	of	of	ADP
ejpam-4951	103	11	(	(	PUNCT
ejpam-4951	103	12	10	10	NUM
ejpam-4951	103	13	)	)	PUNCT
ejpam-4951	103	14	,	,	PUNCT
ejpam-4951	103	15	from	from	ADP
ejpam-4951	103	16	(	(	PUNCT
ejpam-4951	103	17	8)	8)	NUM
ejpam-4951	103	18	,	,	PUNCT
ejpam-4951	103	19	we	we	PRON
ejpam-4951	103	20	get	get	VERB
ejpam-4951	103	21	the	the	DET
ejpam-4951	103	22	error	error	NOUN
ejpam-4951	103	23	equation	equation	NOUN
ejpam-4951	103	24	e∗∗0	e∗∗0	NOUN
ejpam-4951	104	1	=	=	SYM
ejpam-4951	104	2	c2e	c2e	NOUN
ejpam-4951	104	3	2	2	NUM
ejpam-4951	104	4	0	0	NUM
ejpam-4951	104	5	,	,	PUNCT
ejpam-4951	104	6	(	(	PUNCT
ejpam-4951	104	7	11	11	NUM
ejpam-4951	104	8	)	)	PUNCT
ejpam-4951	104	9	and	and	CCONJ
ejpam-4951	104	10	e1	e1	PROPN
ejpam-4951	104	11	=	=	SYM
ejpam-4951	104	12	c2(e	c2(e	NOUN
ejpam-4951	104	13	∗∗	∗∗	NOUN
ejpam-4951	104	14	0	0	NUM
ejpam-4951	104	15	)	)	SYM
ejpam-4951	104	16	2	2	NUM
ejpam-4951	104	17	=	=	SYM
ejpam-4951	104	18	c32e	c32e	VERB
ejpam-4951	104	19	4	4	NUM
ejpam-4951	104	20	0	0	NUM
ejpam-4951	104	21	(	(	PUNCT
ejpam-4951	104	22	12	12	NUM
ejpam-4951	104	23	)	)	PUNCT
ejpam-4951	104	24	here	here	ADV
ejpam-4951	104	25	,	,	PUNCT
ejpam-4951	104	26	x∗1	x∗1	VERB
ejpam-4951	104	27	=	=	PUNCT
ejpam-4951	105	1	x1	x1	PRON
ejpam-4951	105	2	−	−	PROPN
ejpam-4951	105	3	f(x1	f(x1	NOUN
ejpam-4951	105	4	)	)	PUNCT
ejpam-4951	106	1	f	f	PROPN
ejpam-4951	106	2	′[12(x0	′[12(x0	PROPN
ejpam-4951	106	3	+	+	CCONJ
ejpam-4951	106	4	x∗0	x∗0	PROPN
ejpam-4951	106	5	)	)	PUNCT
ejpam-4951	106	6	]	]	PUNCT
ejpam-4951	107	1	=	=	PUNCT
ejpam-4951	107	2	x1	x1	NUM
ejpam-4951	107	3	−	−	PROPN
ejpam-4951	107	4	f(x1	f(x1	ADJ
ejpam-4951	107	5	)	)	PUNCT
ejpam-4951	107	6	f	f	PROPN
ejpam-4951	107	7	′(x0	′(x0	NOUN
ejpam-4951	107	8	)	)	PUNCT
ejpam-4951	107	9	.	.	PUNCT
ejpam-4951	108	1	taylor	taylor	PROPN
ejpam-4951	108	2	series	series	PROPN
ejpam-4951	108	3	and	and	CCONJ
ejpam-4951	108	4	binomial	binomial	ADJ
ejpam-4951	108	5	expansion	expansion	NOUN
ejpam-4951	108	6	gives	give	VERB
ejpam-4951	108	7	the	the	DET
ejpam-4951	108	8	error	error	NOUN
ejpam-4951	108	9	equation	equation	NOUN
ejpam-4951	108	10	for	for	ADP
ejpam-4951	108	11	x∗1	x∗1	ADV
ejpam-4951	108	12	,	,	PUNCT
ejpam-4951	108	13	we	we	PRON
ejpam-4951	108	14	have	have	VERB
ejpam-4951	108	15	α+	α+	X
ejpam-4951	108	16	e∗1	e∗1	ADJ
ejpam-4951	108	17	=	=	SYM
ejpam-4951	108	18	α+	α+	PUNCT
ejpam-4951	108	19	e1	e1	PROPN
ejpam-4951	108	20	−	−	PROPN
ejpam-4951	108	21	f(α+	f(α+	NOUN
ejpam-4951	108	22	e1	e1	NOUN
ejpam-4951	108	23	)	)	PUNCT
ejpam-4951	108	24	f(α+	f(α+	NOUN
ejpam-4951	108	25	e0	e0	PROPN
ejpam-4951	108	26	)	)	PUNCT
ejpam-4951	108	27	e∗1	e∗1	ADJ
ejpam-4951	108	28	=	=	PUNCT
ejpam-4951	108	29	e1	e1	PROPN
ejpam-4951	108	30	−	−	PROPN
ejpam-4951	108	31	e1	e1	PROPN
ejpam-4951	108	32	+	+	CCONJ
ejpam-4951	109	1	c2e	c2e	NOUN
ejpam-4951	109	2	2	2	NUM
ejpam-4951	109	3	1	1	NUM
ejpam-4951	109	4	+	+	NUM
ejpam-4951	109	5	c3e	c3e	PROPN
ejpam-4951	109	6	3	3	NUM
ejpam-4951	109	7	1	1	NUM
ejpam-4951	109	8	+	+	NOUN
ejpam-4951	109	9	o(e41	o(e41	ADJ
ejpam-4951	109	10	)	)	PUNCT
ejpam-4951	109	11	1	1	NUM
ejpam-4951	110	1	+	+	NUM
ejpam-4951	110	2	2c2e0	2c2e0	NUM
ejpam-4951	110	3	+	+	CCONJ
ejpam-4951	110	4	3c3e20	3c3e20	NUM
ejpam-4951	110	5	+	+	NOUN
ejpam-4951	110	6	o(e30	o(e30	NOUN
ejpam-4951	110	7	)	)	PUNCT
ejpam-4951	110	8	=	=	SYM
ejpam-4951	110	9	e1	e1	PROPN
ejpam-4951	110	10	−	−	PROPN
ejpam-4951	110	11	(	(	PUNCT
ejpam-4951	110	12	e1	e1	PROPN
ejpam-4951	110	13	+	+	CCONJ
ejpam-4951	111	1	c2e	c2e	PROPN
ejpam-4951	111	2	2	2	NUM
ejpam-4951	111	3	1	1	NUM
ejpam-4951	111	4	+	+	NUM
ejpam-4951	111	5	c3e	c3e	PROPN
ejpam-4951	111	6	3	3	NUM
ejpam-4951	111	7	1	1	NUM
ejpam-4951	111	8	+	+	NOUN
ejpam-4951	111	9	o(e41	o(e41	ADJ
ejpam-4951	111	10	)	)	PUNCT
ejpam-4951	111	11	)	)	PUNCT
ejpam-4951	112	1	(	(	PUNCT
ejpam-4951	112	2	1−	1−	NUM
ejpam-4951	112	3	2c2e0	2c2e0	NUM
ejpam-4951	112	4	−	−	NOUN
ejpam-4951	112	5	3c3e	3c3e	NOUN
ejpam-4951	112	6	2	2	NUM
ejpam-4951	112	7	0	0	NUM
ejpam-4951	113	1	+	+	CCONJ
ejpam-4951	113	2	4c22e	4c22e	NOUN
ejpam-4951	113	3	2	2	NUM
ejpam-4951	113	4	0	0	NUM
ejpam-4951	113	5	+	+	NUM
ejpam-4951	113	6	o(e30	o(e30	NOUN
ejpam-4951	113	7	)	)	PUNCT
ejpam-4951	113	8	)	)	PUNCT
ejpam-4951	114	1	=	=	PUNCT
ejpam-4951	115	1	2c2e0e1	2c2e0e1	NUM
ejpam-4951	115	2	=	=	SYM
ejpam-4951	115	3	2c42e	2c42e	NUM
ejpam-4951	115	4	5	5	NUM
ejpam-4951	115	5	0	0	NUM
ejpam-4951	115	6	,	,	PUNCT
ejpam-4951	115	7	(	(	PUNCT
ejpam-4951	115	8	13	13	NUM
ejpam-4951	115	9	)	)	PUNCT
ejpam-4951	115	10	b.	b.	PROPN
ejpam-4951	115	11	sapkota	sapkota	PROPN
ejpam-4951	115	12	,	,	PUNCT
ejpam-4951	115	13	j.	j.	PROPN
ejpam-4951	115	14	jnawali	jnawali	PROPN
ejpam-4951	115	15	/	/	SYM
ejpam-4951	115	16	eur	eur	PROPN
ejpam-4951	115	17	.	.	PUNCT
ejpam-4951	116	1	j.	j.	PROPN
ejpam-4951	116	2	pure	pure	PROPN
ejpam-4951	116	3	appl	appl	PROPN
ejpam-4951	116	4	.	.	PROPN
ejpam-4951	116	5	math	math	PROPN
ejpam-4951	116	6	,	,	PUNCT
ejpam-4951	116	7	16	16	NUM
ejpam-4951	116	8	(	(	PUNCT
ejpam-4951	116	9	4	4	NUM
ejpam-4951	116	10	)	)	PUNCT
ejpam-4951	116	11	(	(	PUNCT
ejpam-4951	116	12	2023	2023	NUM
ejpam-4951	116	13	)	)	PUNCT
ejpam-4951	116	14	,	,	PUNCT
ejpam-4951	116	15	2419	2419	NUM
ejpam-4951	116	16	-	-	SYM
ejpam-4951	116	17	2430	2430	NUM
ejpam-4951	116	18	2423	2423	NUM
ejpam-4951	116	19	neglecting	neglect	VERB
ejpam-4951	116	20	the	the	DET
ejpam-4951	116	21	higher	high	ADJ
ejpam-4951	116	22	powers	power	NOUN
ejpam-4951	116	23	of	of	ADP
ejpam-4951	116	24	e0	e0	PROPN
ejpam-4951	116	25	.	.	PUNCT
ejpam-4951	117	1	next	next	ADV
ejpam-4951	117	2	,	,	PUNCT
ejpam-4951	117	3	the	the	DET
ejpam-4951	117	4	error	error	NOUN
ejpam-4951	117	5	in	in	ADP
ejpam-4951	117	6	x∗∗1	x∗∗1	PROPN
ejpam-4951	117	7	can	can	AUX
ejpam-4951	117	8	be	be	AUX
ejpam-4951	117	9	found	find	VERB
ejpam-4951	117	10	as	as	SCONJ
ejpam-4951	117	11	follows	follow	VERB
ejpam-4951	117	12	:	:	PUNCT
ejpam-4951	117	13	e∗∗1	e∗∗1	NOUN
ejpam-4951	117	14	=	=	NOUN
ejpam-4951	117	15	e1	e1	PROPN
ejpam-4951	117	16	−	−	PROPN
ejpam-4951	117	17	f(α+	f(α+	NOUN
ejpam-4951	117	18	e1	e1	NOUN
ejpam-4951	117	19	)	)	PUNCT
ejpam-4951	118	1	f	f	NOUN
ejpam-4951	118	2	′	′	NUM
ejpam-4951	118	3	(	(	PUNCT
ejpam-4951	118	4	α+	α+	X
ejpam-4951	118	5	e1+e∗1	e1+e∗1	PROPN
ejpam-4951	118	6	2	2	NUM
ejpam-4951	118	7	)	)	PUNCT
ejpam-4951	118	8	=	=	SYM
ejpam-4951	118	9	e1	e1	PROPN
ejpam-4951	118	10	−	−	PROPN
ejpam-4951	118	11	(	(	PUNCT
ejpam-4951	118	12	e+	e+	VERB
ejpam-4951	118	13	c2e	c2e	NOUN
ejpam-4951	118	14	2	2	NUM
ejpam-4951	118	15	1	1	NUM
ejpam-4951	118	16	+	+	NUM
ejpam-4951	118	17	c3e	c3e	PROPN
ejpam-4951	118	18	3	3	NUM
ejpam-4951	118	19	1	1	NUM
ejpam-4951	118	20	)	)	PUNCT
ejpam-4951	118	21	(	(	PUNCT
ejpam-4951	118	22	1	1	NUM
ejpam-4951	118	23	+	+	NUM
ejpam-4951	118	24	2c2	2c2	NUM
ejpam-4951	118	25	(	(	PUNCT
ejpam-4951	118	26	e1	e1	NOUN
ejpam-4951	118	27	+	+	CCONJ
ejpam-4951	118	28	e∗1	e∗1	ADJ
ejpam-4951	118	29	2	2	NUM
ejpam-4951	118	30	)	)	PUNCT
ejpam-4951	119	1	+	+	CCONJ
ejpam-4951	119	2	3c3	3c3	NUM
ejpam-4951	119	3	(	(	PUNCT
ejpam-4951	119	4	e1	e1	NOUN
ejpam-4951	119	5	+	+	CCONJ
ejpam-4951	119	6	e∗1	e∗1	ADJ
ejpam-4951	119	7	2	2	NUM
ejpam-4951	119	8	)	)	PUNCT
ejpam-4951	119	9	2	2	NUM
ejpam-4951	119	10	)	)	PUNCT
ejpam-4951	119	11	−1	−1	NOUN
ejpam-4951	119	12	=	=	SYM
ejpam-4951	119	13	c2e1e	c2e1e	NOUN
ejpam-4951	119	14	∗	∗	NOUN
ejpam-4951	119	15	1	1	NUM
ejpam-4951	119	16	=	=	SYM
ejpam-4951	119	17	2c52e	2c52e	NUM
ejpam-4951	119	18	9	9	NUM
ejpam-4951	119	19	0	0	NUM
ejpam-4951	119	20	(	(	PUNCT
ejpam-4951	119	21	14	14	NUM
ejpam-4951	119	22	)	)	PUNCT
ejpam-4951	119	23	by	by	ADP
ejpam-4951	119	24	using	use	VERB
ejpam-4951	119	25	(	(	PUNCT
ejpam-4951	119	26	12	12	NUM
ejpam-4951	119	27	)	)	PUNCT
ejpam-4951	119	28	and	and	CCONJ
ejpam-4951	119	29	(	(	PUNCT
ejpam-4951	119	30	13	13	NUM
ejpam-4951	119	31	)	)	PUNCT
ejpam-4951	119	32	.	.	PUNCT
ejpam-4951	120	1	also	also	ADV
ejpam-4951	120	2	,	,	PUNCT
ejpam-4951	120	3	from	from	ADP
ejpam-4951	120	4	the	the	DET
ejpam-4951	120	5	view	view	NOUN
ejpam-4951	120	6	of	of	ADP
ejpam-4951	120	7	the	the	DET
ejpam-4951	120	8	error	error	NOUN
ejpam-4951	120	9	equation	equation	NOUN
ejpam-4951	120	10	(	(	PUNCT
ejpam-4951	120	11	10	10	NUM
ejpam-4951	120	12	)	)	PUNCT
ejpam-4951	120	13	,	,	PUNCT
ejpam-4951	120	14	the	the	DET
ejpam-4951	120	15	error	error	NOUN
ejpam-4951	120	16	equation	equation	NOUN
ejpam-4951	120	17	for	for	ADP
ejpam-4951	120	18	x2	x2	PROPN
ejpam-4951	120	19	:	:	PUNCT
ejpam-4951	120	20	e2	e2	PROPN
ejpam-4951	120	21	=	=	PUNCT
ejpam-4951	120	22	c2(e	c2(e	NOUN
ejpam-4951	120	23	∗∗	∗∗	NOUN
ejpam-4951	120	24	1	1	NUM
ejpam-4951	120	25	)	)	SYM
ejpam-4951	120	26	2	2	NUM
ejpam-4951	120	27	=	=	SYM
ejpam-4951	120	28	22c112	22c112	NUM
ejpam-4951	120	29	e180	e180	PROPN
ejpam-4951	120	30	(	(	PUNCT
ejpam-4951	120	31	15	15	NUM
ejpam-4951	120	32	)	)	PUNCT
ejpam-4951	120	33	in	in	ADP
ejpam-4951	120	34	fact	fact	NOUN
ejpam-4951	120	35	,	,	PUNCT
ejpam-4951	120	36	for	for	ADP
ejpam-4951	120	37	n	n	PRON
ejpam-4951	120	38	≥	≥	NUM
ejpam-4951	120	39	2	2	NUM
ejpam-4951	120	40	,	,	PUNCT
ejpam-4951	120	41	the	the	DET
ejpam-4951	120	42	errors	error	NOUN
ejpam-4951	120	43	at	at	ADP
ejpam-4951	120	44	x∗n	x∗n	NUM
ejpam-4951	120	45	,	,	PUNCT
ejpam-4951	120	46	x	x	SYM
ejpam-4951	120	47	∗∗	∗∗	NOUN
ejpam-4951	120	48	n	n	CCONJ
ejpam-4951	120	49	and	and	CCONJ
ejpam-4951	120	50	xn	xn	PROPN
ejpam-4951	120	51	respectively	respectively	ADV
ejpam-4951	120	52	,	,	PUNCT
ejpam-4951	120	53	can	can	AUX
ejpam-4951	120	54	be	be	AUX
ejpam-4951	120	55	found	find	VERB
ejpam-4951	120	56	by	by	ADP
ejpam-4951	120	57	the	the	DET
ejpam-4951	120	58	relations	relation	NOUN
ejpam-4951	120	59	e∗n	e∗n	PROPN
ejpam-4951	120	60	=	=	SYM
ejpam-4951	120	61	c2enen−1	c2enen−1	PROPN
ejpam-4951	120	62	,	,	PUNCT
ejpam-4951	120	63	(	(	PUNCT
ejpam-4951	120	64	16	16	NUM
ejpam-4951	120	65	)	)	PUNCT
ejpam-4951	120	66	e∗∗n	e∗∗n	NOUN
ejpam-4951	120	67	=	=	PUNCT
ejpam-4951	121	1	c2ene	c2ene	NOUN
ejpam-4951	121	2	∗	∗	NOUN
ejpam-4951	121	3	n	n	NOUN
ejpam-4951	121	4	=	=	SYM
ejpam-4951	121	5	c22e	c22e	NOUN
ejpam-4951	121	6	2	2	NUM
ejpam-4951	121	7	nen−1	nen−1	PROPN
ejpam-4951	121	8	,	,	PUNCT
ejpam-4951	121	9	(	(	PUNCT
ejpam-4951	121	10	17	17	NUM
ejpam-4951	121	11	)	)	PUNCT
ejpam-4951	121	12	and	and	CCONJ
ejpam-4951	121	13	en+1	en+1	ADJ
ejpam-4951	121	14	=	=	SYM
ejpam-4951	121	15	c2e	c2e	ADJ
ejpam-4951	121	16	∗∗	∗∗	PROPN
ejpam-4951	121	17	n	n	CCONJ
ejpam-4951	121	18	2	2	NUM
ejpam-4951	121	19	=	=	NOUN
ejpam-4951	121	20	c52e	c52e	ADP
ejpam-4951	121	21	4	4	NUM
ejpam-4951	121	22	ne	ne	NOUN
ejpam-4951	121	23	2	2	NUM
ejpam-4951	121	24	n−1	n−1	PROPN
ejpam-4951	121	25	.	.	PUNCT
ejpam-4951	122	1	(	(	PUNCT
ejpam-4951	122	2	18	18	NUM
ejpam-4951	122	3	)	)	PUNCT
ejpam-4951	122	4	to	to	PART
ejpam-4951	122	5	calculate	calculate	VERB
ejpam-4951	122	6	the	the	DET
ejpam-4951	122	7	order	order	NOUN
ejpam-4951	122	8	of	of	ADP
ejpam-4951	122	9	convergence	convergence	NOUN
ejpam-4951	122	10	of	of	ADP
ejpam-4951	122	11	(	(	PUNCT
ejpam-4951	122	12	8)-(9	8)-(9	NOUN
ejpam-4951	122	13	)	)	PUNCT
ejpam-4951	122	14	,	,	PUNCT
ejpam-4951	122	15	the	the	DET
ejpam-4951	122	16	following	follow	VERB
ejpam-4951	122	17	relation	relation	NOUN
ejpam-4951	122	18	is	be	AUX
ejpam-4951	122	19	needed	need	VERB
ejpam-4951	122	20	:	:	PUNCT
ejpam-4951	122	21	en+1	en+1	ADJ
ejpam-4951	122	22	=	=	X
ejpam-4951	122	23	aepn	aepn	NOUN
ejpam-4951	122	24	(	(	PUNCT
ejpam-4951	122	25	19	19	NUM
ejpam-4951	122	26	)	)	PUNCT
ejpam-4951	122	27	thus	thus	ADV
ejpam-4951	122	28	,	,	PUNCT
ejpam-4951	122	29	en	en	X
ejpam-4951	122	30	=	=	SYM
ejpam-4951	122	31	aepn−1	aepn−1	PROPN
ejpam-4951	122	32	or	or	CCONJ
ejpam-4951	122	33	en−1	en−1	PROPN
ejpam-4951	122	34	=	=	PROPN
ejpam-4951	122	35	a	a	PRON
ejpam-4951	122	36	−	−	PROPN
ejpam-4951	122	37	1	1	NUM
ejpam-4951	122	38	p	p	NOUN
ejpam-4951	122	39	e	e	NOUN
ejpam-4951	122	40	1	1	NUM
ejpam-4951	122	41	p	p	NOUN
ejpam-4951	122	42	n	n	NOUN
ejpam-4951	122	43	.	.	PUNCT
ejpam-4951	123	1	(	(	PUNCT
ejpam-4951	123	2	20	20	NUM
ejpam-4951	123	3	)	)	PUNCT
ejpam-4951	123	4	from	from	ADP
ejpam-4951	123	5	(	(	PUNCT
ejpam-4951	123	6	16	16	NUM
ejpam-4951	123	7	)	)	PUNCT
ejpam-4951	123	8	,	,	PUNCT
ejpam-4951	123	9	(	(	PUNCT
ejpam-4951	123	10	17	17	NUM
ejpam-4951	123	11	)	)	PUNCT
ejpam-4951	123	12	and	and	CCONJ
ejpam-4951	123	13	(	(	PUNCT
ejpam-4951	123	14	18	18	NUM
ejpam-4951	123	15	)	)	PUNCT
ejpam-4951	123	16	,	,	PUNCT
ejpam-4951	123	17	we	we	PRON
ejpam-4951	123	18	have	have	VERB
ejpam-4951	123	19	aepn	aepn	NOUN
ejpam-4951	123	20	=	=	SYM
ejpam-4951	123	21	c52e	c52e	ADP
ejpam-4951	123	22	4	4	NUM
ejpam-4951	123	23	na	na	PART
ejpam-4951	123	24	−2	−2	PROPN
ejpam-4951	123	25	/	/	SYM
ejpam-4951	123	26	pe2	pe2	PROPN
ejpam-4951	123	27	/	/	SYM
ejpam-4951	123	28	pn	pn	PROPN
ejpam-4951	123	29	.	.	PUNCT
ejpam-4951	124	1	equating	equate	VERB
ejpam-4951	124	2	the	the	DET
ejpam-4951	124	3	power	power	NOUN
ejpam-4951	124	4	of	of	ADP
ejpam-4951	124	5	en	en	X
ejpam-4951	124	6	,	,	PUNCT
ejpam-4951	124	7	we	we	PRON
ejpam-4951	124	8	obtain	obtain	VERB
ejpam-4951	124	9	p	p	NOUN
ejpam-4951	124	10	=	=	NOUN
ejpam-4951	124	11	4	4	NUM
ejpam-4951	124	12	+	+	SYM
ejpam-4951	124	13	2	2	NUM
ejpam-4951	124	14	p	p	NOUN
ejpam-4951	124	15	or	or	CCONJ
ejpam-4951	124	16	,	,	PUNCT
ejpam-4951	124	17	p2	p2	PROPN
ejpam-4951	124	18	−	−	PROPN
ejpam-4951	125	1	4p−	4p−	NUM
ejpam-4951	125	2	2	2	NUM
ejpam-4951	125	3	=	=	SYM
ejpam-4951	125	4	0	0	NUM
ejpam-4951	125	5	or	or	CCONJ
ejpam-4951	125	6	,	,	PUNCT
ejpam-4951	125	7	p	p	X
ejpam-4951	125	8	=	=	PUNCT
ejpam-4951	125	9	4±	4±	PROPN
ejpam-4951	125	10	√	√	ADV
ejpam-4951	125	11	24	24	NUM
ejpam-4951	125	12	2	2	NUM
ejpam-4951	125	13	.	.	PUNCT
ejpam-4951	126	1	for	for	ADP
ejpam-4951	126	2	positive	positive	ADJ
ejpam-4951	126	3	sign	sign	NOUN
ejpam-4951	126	4	,	,	PUNCT
ejpam-4951	126	5	p	p	NOUN
ejpam-4951	126	6	=	=	SYM
ejpam-4951	126	7	2	2	NUM
ejpam-4951	126	8	+	+	CCONJ
ejpam-4951	126	9	√	√	NUM
ejpam-4951	126	10	6	6	NUM
ejpam-4951	127	1	≈	≈	PROPN
ejpam-4951	127	2	4.45	4.45	NUM
ejpam-4951	127	3	.	.	PUNCT
ejpam-4951	128	1	consequently	consequently	ADV
ejpam-4951	128	2	,	,	PUNCT
ejpam-4951	128	3	the	the	DET
ejpam-4951	128	4	convergence	convergence	NOUN
ejpam-4951	128	5	order	order	NOUN
ejpam-4951	128	6	of	of	ADP
ejpam-4951	128	7	methods	method	NOUN
ejpam-4951	128	8	(	(	PUNCT
ejpam-4951	128	9	8)-(9	8)-(9	NOUN
ejpam-4951	128	10	)	)	PUNCT
ejpam-4951	128	11	is	be	AUX
ejpam-4951	128	12	4.45	4.45	NUM
ejpam-4951	128	13	.	.	PUNCT
ejpam-4951	129	1	alternative	alternative	ADJ
ejpam-4951	129	2	proof	proof	NOUN
ejpam-4951	129	3	:	:	PUNCT
ejpam-4951	129	4	accumulating	accumulate	VERB
ejpam-4951	129	5	the	the	DET
ejpam-4951	129	6	relations	relation	NOUN
ejpam-4951	129	7	from	from	ADP
ejpam-4951	129	8	the	the	DET
ejpam-4951	129	9	proof	proof	NOUN
ejpam-4951	129	10	given	give	VERB
ejpam-4951	129	11	above	above	ADV
ejpam-4951	129	12	,	,	PUNCT
ejpam-4951	129	13	we	we	PRON
ejpam-4951	129	14	get	get	VERB
ejpam-4951	129	15	the	the	DET
ejpam-4951	129	16	errors	error	NOUN
ejpam-4951	129	17	at	at	ADP
ejpam-4951	129	18	xn	xn	PROPN
ejpam-4951	129	19	,	,	PUNCT
ejpam-4951	129	20	x∗n	x∗n	NUM
ejpam-4951	129	21	,	,	PUNCT
ejpam-4951	129	22	and	and	CCONJ
ejpam-4951	129	23	x∗∗n	x∗∗n	NOUN
ejpam-4951	129	24	stages	stage	NOUN
ejpam-4951	129	25	as	as	SCONJ
ejpam-4951	129	26	given	give	VERB
ejpam-4951	129	27	in	in	ADP
ejpam-4951	129	28	the	the	DET
ejpam-4951	129	29	following	follow	VERB
ejpam-4951	129	30	table-1	table-1	NUM
ejpam-4951	129	31	:	:	PUNCT
ejpam-4951	129	32	we	we	PRON
ejpam-4951	129	33	construct	construct	VERB
ejpam-4951	129	34	the	the	DET
ejpam-4951	129	35	table	table	NOUN
ejpam-4951	129	36	b.	b.	PROPN
ejpam-4951	129	37	sapkota	sapkota	PROPN
ejpam-4951	129	38	,	,	PUNCT
ejpam-4951	129	39	j.	j.	PROPN
ejpam-4951	129	40	jnawali	jnawali	PROPN
ejpam-4951	129	41	/	/	SYM
ejpam-4951	129	42	eur	eur	PROPN
ejpam-4951	129	43	.	.	PUNCT
ejpam-4951	130	1	j.	j.	PROPN
ejpam-4951	130	2	pure	pure	PROPN
ejpam-4951	130	3	appl	appl	PROPN
ejpam-4951	130	4	.	.	PROPN
ejpam-4951	130	5	math	math	PROPN
ejpam-4951	130	6	,	,	PUNCT
ejpam-4951	130	7	16	16	NUM
ejpam-4951	130	8	(	(	PUNCT
ejpam-4951	130	9	4	4	NUM
ejpam-4951	130	10	)	)	PUNCT
ejpam-4951	130	11	(	(	PUNCT
ejpam-4951	130	12	2023	2023	NUM
ejpam-4951	130	13	)	)	PUNCT
ejpam-4951	130	14	,	,	PUNCT
ejpam-4951	130	15	2419	2419	NUM
ejpam-4951	130	16	-	-	SYM
ejpam-4951	130	17	2430	2430	NUM
ejpam-4951	130	18	2424	2424	NUM
ejpam-4951	130	19	table	table	NOUN
ejpam-4951	130	20	1	1	NUM
ejpam-4951	130	21	:	:	PUNCT
ejpam-4951	130	22	successive	successive	ADJ
ejpam-4951	130	23	errors	error	NOUN
ejpam-4951	130	24	.	.	PUNCT
ejpam-4951	131	1	n	n	CCONJ
ejpam-4951	131	2	en	en	ADP
ejpam-4951	131	3	e∗n	e∗n	NUM
ejpam-4951	131	4	e∗∗n	e∗∗n	PROPN
ejpam-4951	131	5	0	0	NUM
ejpam-4951	131	6	e0	e0	PROPN
ejpam-4951	131	7	e0	e0	PROPN
ejpam-4951	131	8	c2e	c2e	NOUN
ejpam-4951	131	9	2	2	NUM
ejpam-4951	131	10	0	0	NUM
ejpam-4951	131	11	1	1	NUM
ejpam-4951	131	12	c32e	c32e	ADP
ejpam-4951	131	13	4	4	NUM
ejpam-4951	131	14	0	0	NUM
ejpam-4951	131	15	2c42e	2c42e	NUM
ejpam-4951	131	16	5	5	NUM
ejpam-4951	131	17	0	0	NUM
ejpam-4951	131	18	2c52e	2c52e	NUM
ejpam-4951	131	19	9	9	NUM
ejpam-4951	131	20	0	0	NUM
ejpam-4951	131	21	2	2	NUM
ejpam-4951	131	22	22c112	22c112	NUM
ejpam-4951	131	23	e180	e180	PROPN
ejpam-4951	131	24	22c142	22c142	NOUN
ejpam-4951	131	25	e220	e220	PROPN
ejpam-4951	131	26	24c262	24c262	NUM
ejpam-4951	131	27	e400	e400	NUM
ejpam-4951	131	28	3	3	NUM
ejpam-4951	131	29	28c532	28c532	NOUN
ejpam-4951	131	30	e800	e800	PROPN
ejpam-4951	131	31	210c652	210c652	NUM
ejpam-4951	132	1	e980	e980	PROPN
ejpam-4951	132	2	218c1192	218c1192	NUM
ejpam-4951	132	3	e1780	e1780	NUM
ejpam-4951	132	4	4	4	NUM
ejpam-4951	132	5	238c2392	238c2392	NUM
ejpam-4951	132	6	e3560	e3560	PROPN
ejpam-4951	132	7	246c2932	246c2932	NUM
ejpam-4951	132	8	e4360	e4360	ADJ
ejpam-4951	132	9	284c5332	284c5332	NUM
ejpam-4951	132	10	e7920	e7920	NOUN
ejpam-4951	132	11	5	5	NUM
ejpam-4951	132	12	2168c10672	2168c10672	NUM
ejpam-4951	132	13	e15840	e15840	NOUN
ejpam-4951	132	14	...	...	PUNCT
ejpam-4951	132	15	...	...	PUNCT
ejpam-4951	132	16	...	...	PUNCT
ejpam-4951	132	17	...	...	PUNCT
ejpam-4951	132	18	...	...	PUNCT
ejpam-4951	132	19	...	...	PUNCT
ejpam-4951	132	20	as	as	SCONJ
ejpam-4951	132	21	done	do	VERB
ejpam-4951	132	22	in	in	ADP
ejpam-4951	132	23	[	[	X
ejpam-4951	132	24	12	12	NUM
ejpam-4951	132	25	]	]	PUNCT
ejpam-4951	132	26	.	.	PUNCT
ejpam-4951	133	1	the	the	DET
ejpam-4951	133	2	sequence	sequence	NOUN
ejpam-4951	133	3	formed	form	VERB
ejpam-4951	133	4	by	by	ADP
ejpam-4951	133	5	the	the	DET
ejpam-4951	133	6	power	power	NOUN
ejpam-4951	133	7	of	of	ADP
ejpam-4951	133	8	e0	e0	PROPN
ejpam-4951	133	9	in	in	ADP
ejpam-4951	133	10	the	the	DET
ejpam-4951	133	11	errors	error	NOUN
ejpam-4951	133	12	at	at	ADP
ejpam-4951	133	13	each	each	DET
ejpam-4951	133	14	iteration	iteration	NOUN
ejpam-4951	133	15	is	be	AUX
ejpam-4951	133	16	4	4	NUM
ejpam-4951	133	17	,	,	PUNCT
ejpam-4951	133	18	18	18	NUM
ejpam-4951	133	19	,	,	PUNCT
ejpam-4951	133	20	80	80	NUM
ejpam-4951	133	21	,	,	PUNCT
ejpam-4951	133	22	356	356	NUM
ejpam-4951	133	23	,	,	PUNCT
ejpam-4951	133	24	1584	1584	NUM
ejpam-4951	133	25	,	,	PUNCT
ejpam-4951	133	26	·	·	PUNCT
ejpam-4951	133	27	·	·	PUNCT
ejpam-4951	133	28	·	·	PUNCT
ejpam-4951	133	29	(	(	PUNCT
ejpam-4951	133	30	21	21	NUM
ejpam-4951	133	31	)	)	PUNCT
ejpam-4951	133	32	the	the	DET
ejpam-4951	133	33	sequence	sequence	NOUN
ejpam-4951	133	34	of	of	ADP
ejpam-4951	133	35	their	their	PRON
ejpam-4951	133	36	successive	successive	ADJ
ejpam-4951	133	37	ratios	ratio	NOUN
ejpam-4951	133	38	is	be	AUX
ejpam-4951	133	39	18	18	NUM
ejpam-4951	133	40	4	4	NUM
ejpam-4951	133	41	,	,	PUNCT
ejpam-4951	133	42	80	80	NUM
ejpam-4951	133	43	18	18	NUM
ejpam-4951	133	44	,	,	PUNCT
ejpam-4951	133	45	356	356	NUM
ejpam-4951	133	46	80	80	NUM
ejpam-4951	133	47	,	,	PUNCT
ejpam-4951	133	48	1584	1584	NUM
ejpam-4951	133	49	356	356	NUM
ejpam-4951	133	50	,	,	PUNCT
ejpam-4951	133	51	·	·	PUNCT
ejpam-4951	133	52	·	·	PUNCT
ejpam-4951	133	53	·	·	PUNCT
ejpam-4951	133	54	or	or	CCONJ
ejpam-4951	133	55	4.5	4.5	NUM
ejpam-4951	133	56	,	,	PUNCT
ejpam-4951	133	57	4.44	4.44	NUM
ejpam-4951	133	58	,	,	PUNCT
ejpam-4951	133	59	4.45	4.45	NUM
ejpam-4951	133	60	,	,	PUNCT
ejpam-4951	133	61	4.45	4.45	NUM
ejpam-4951	133	62	,	,	PUNCT
ejpam-4951	133	63	·	·	PUNCT
ejpam-4951	133	64	·	·	PUNCT
ejpam-4951	133	65	·	·	PUNCT
ejpam-4951	133	66	.	.	PUNCT
ejpam-4951	134	1	if	if	SCONJ
ejpam-4951	134	2	{	{	PUNCT
ejpam-4951	134	3	ri	ri	NOUN
ejpam-4951	134	4	}	}	PUNCT
ejpam-4951	134	5	denotes	denote	VERB
ejpam-4951	134	6	the	the	DET
ejpam-4951	134	7	ith	ith	ADJ
ejpam-4951	134	8	term	term	NOUN
ejpam-4951	134	9	of	of	ADP
ejpam-4951	134	10	the	the	DET
ejpam-4951	134	11	sequence	sequence	NOUN
ejpam-4951	134	12	(	(	PUNCT
ejpam-4951	134	13	21	21	NUM
ejpam-4951	134	14	)	)	PUNCT
ejpam-4951	134	15	,	,	PUNCT
ejpam-4951	134	16	then	then	ADV
ejpam-4951	134	17	it	it	PRON
ejpam-4951	134	18	holds	hold	VERB
ejpam-4951	134	19	relation	relation	NOUN
ejpam-4951	134	20	ri	ri	NOUN
ejpam-4951	135	1	=	=	SYM
ejpam-4951	135	2	4ri−1	4ri−1	PROPN
ejpam-4951	135	3	+	+	CCONJ
ejpam-4951	135	4	2ri−2	2ri−2	NOUN
ejpam-4951	135	5	,	,	PUNCT
ejpam-4951	135	6	i	i	NOUN
ejpam-4951	135	7	=	=	NOUN
ejpam-4951	135	8	2	2	NUM
ejpam-4951	135	9	,	,	PUNCT
ejpam-4951	135	10	3	3	NUM
ejpam-4951	135	11	,	,	PUNCT
ejpam-4951	135	12	4	4	NUM
ejpam-4951	135	13	,	,	PUNCT
ejpam-4951	135	14	·	·	PUNCT
ejpam-4951	135	15	·	·	PUNCT
ejpam-4951	135	16	·	·	PUNCT
ejpam-4951	135	17	.	.	PUNCT
ejpam-4951	136	1	if	if	SCONJ
ejpam-4951	136	2	we	we	PRON
ejpam-4951	136	3	take	take	VERB
ejpam-4951	136	4	the	the	DET
ejpam-4951	136	5	limit	limit	NOUN
ejpam-4951	136	6	ri	ri	NOUN
ejpam-4951	136	7	ri−1	ri−1	PROPN
ejpam-4951	136	8	=	=	PUNCT
ejpam-4951	136	9	ri−1	ri−1	PROPN
ejpam-4951	136	10	ri−2	ri−2	NOUN
ejpam-4951	136	11	=	=	PROPN
ejpam-4951	136	12	p	p	X
ejpam-4951	136	13	then	then	ADV
ejpam-4951	136	14	,	,	PUNCT
ejpam-4951	136	15	we	we	PRON
ejpam-4951	136	16	get	get	VERB
ejpam-4951	136	17	p2	p2	PROPN
ejpam-4951	136	18	−	−	PROPN
ejpam-4951	137	1	4p−	4p−	NUM
ejpam-4951	137	2	2	2	NUM
ejpam-4951	137	3	=	=	SYM
ejpam-4951	137	4	0	0	NUM
ejpam-4951	137	5	,	,	PUNCT
ejpam-4951	137	6	(	(	PUNCT
ejpam-4951	137	7	22	22	NUM
ejpam-4951	137	8	)	)	PUNCT
ejpam-4951	137	9	which	which	PRON
ejpam-4951	137	10	gives	give	VERB
ejpam-4951	137	11	its	its	PRON
ejpam-4951	137	12	positive	positive	ADJ
ejpam-4951	137	13	root	root	NOUN
ejpam-4951	137	14	p	p	NOUN
ejpam-4951	137	15	=	=	NOUN
ejpam-4951	137	16	2	2	NUM
ejpam-4951	137	17	+	+	CCONJ
ejpam-4951	137	18	√	√	NUM
ejpam-4951	137	19	6	6	NUM
ejpam-4951	137	20	≈	≈	PROPN
ejpam-4951	137	21	4.45	4.45	NUM
ejpam-4951	137	22	.	.	PUNCT
ejpam-4951	138	1	consequently	consequently	ADV
ejpam-4951	138	2	,	,	PUNCT
ejpam-4951	138	3	convergence	convergence	NOUN
ejpam-4951	138	4	order	order	NOUN
ejpam-4951	138	5	of	of	ADP
ejpam-4951	138	6	the	the	DET
ejpam-4951	138	7	method	method	NOUN
ejpam-4951	138	8	(	(	PUNCT
ejpam-4951	138	9	8)-(9	8)-(9	NOUN
ejpam-4951	138	10	)	)	PUNCT
ejpam-4951	138	11	is	be	AUX
ejpam-4951	138	12	at	at	ADP
ejpam-4951	138	13	least	least	ADJ
ejpam-4951	138	14	4.45	4.45	NUM
ejpam-4951	138	15	.	.	PUNCT
ejpam-4951	139	1	□	□	PUNCT
ejpam-4951	139	2	next	next	ADV
ejpam-4951	139	3	,	,	PUNCT
ejpam-4951	139	4	we	we	PRON
ejpam-4951	139	5	modify	modify	VERB
ejpam-4951	139	6	method	method	NOUN
ejpam-4951	139	7	(	(	PUNCT
ejpam-4951	139	8	5	5	NUM
ejpam-4951	139	9	)	)	PUNCT
ejpam-4951	139	10	by	by	ADP
ejpam-4951	139	11	using	use	VERB
ejpam-4951	139	12	methods	method	NOUN
ejpam-4951	139	13	(	(	PUNCT
ejpam-4951	139	14	6)-7	6)-7	NUM
ejpam-4951	139	15	)	)	PUNCT
ejpam-4951	139	16	as	as	ADP
ejpam-4951	139	17	below	below	ADV
ejpam-4951	139	18	:	:	PUNCT
ejpam-4951	139	19	if	if	SCONJ
ejpam-4951	139	20	x0	x0	PROPN
ejpam-4951	139	21	is	be	AUX
ejpam-4951	139	22	the	the	DET
ejpam-4951	139	23	initial	initial	ADJ
ejpam-4951	139	24	approximation	approximation	NOUN
ejpam-4951	139	25	,	,	PUNCT
ejpam-4951	139	26	then	then	ADV
ejpam-4951	139	27	x∗0	x∗0	PROPN
ejpam-4951	139	28	=	=	SYM
ejpam-4951	139	29	x0	x0	PROPN
ejpam-4951	139	30	,	,	PUNCT
ejpam-4951	139	31	x1	x1	PROPN
ejpam-4951	139	32	=	=	PUNCT
ejpam-4951	139	33	x∗0	x∗0	PROPN
ejpam-4951	139	34	−	−	PROPN
ejpam-4951	139	35	f(x∗0	f(x∗0	NOUN
ejpam-4951	139	36	)	)	PUNCT
ejpam-4951	140	1	f	f	PROPN
ejpam-4951	141	1	′[12(x	′[12(x	PROPN
ejpam-4951	141	2	∗	∗	VERB
ejpam-4951	141	3	0	0	PUNCT
ejpam-4951	142	1	+	+	CCONJ
ejpam-4951	142	2	z1	z1	NOUN
ejpam-4951	142	3	)	)	PUNCT
ejpam-4951	142	4	]	]	PUNCT
ejpam-4951	142	5	,	,	PUNCT
ejpam-4951	142	6	with	with	ADP
ejpam-4951	142	7	z1	z1	NOUN
ejpam-4951	142	8	=	=	SYM
ejpam-4951	142	9	x0	x0	PROPN
ejpam-4951	142	10	−	−	PROPN
ejpam-4951	142	11	f(x0	f(x0	PROPN
ejpam-4951	142	12	)	)	PUNCT
ejpam-4951	143	1	f	f	NOUN
ejpam-4951	144	1	′	′	NUM
ejpam-4951	144	2	(	(	PUNCT
ejpam-4951	144	3	x0+x∗	x0+x∗	PROPN
ejpam-4951	144	4	0	0	NUM
ejpam-4951	144	5	2	2	NUM
ejpam-4951	144	6	)	)	PUNCT
ejpam-4951	144	7	.	.	PUNCT
ejpam-4951	145	1			PROPN
ejpam-4951	145	2	(	(	PUNCT
ejpam-4951	145	3	23	23	NUM
ejpam-4951	145	4	)	)	PUNCT
ejpam-4951	145	5	x∗1	x∗1	VERB
ejpam-4951	146	1	=	=	PUNCT
ejpam-4951	147	1	x1	x1	PRON
ejpam-4951	147	2	−	−	PROPN
ejpam-4951	147	3	f(x1	f(x1	NOUN
ejpam-4951	148	1	)	)	PUNCT
ejpam-4951	148	2	f	f	PROPN
ejpam-4951	149	1	′[12(x1	′[12(x1	PROPN
ejpam-4951	149	2	+	+	NUM
ejpam-4951	149	3	z∗1	z∗1	NOUN
ejpam-4951	149	4	)	)	PUNCT
ejpam-4951	149	5	]	]	PUNCT
ejpam-4951	149	6	,	,	PUNCT
ejpam-4951	149	7	with	with	ADP
ejpam-4951	149	8	z∗1	z∗1	NOUN
ejpam-4951	149	9	=	=	PUNCT
ejpam-4951	149	10	x1	x1	PROPN
ejpam-4951	149	11	−	−	PROPN
ejpam-4951	149	12	f(x1	f(x1	NOUN
ejpam-4951	149	13	)	)	PUNCT
ejpam-4951	149	14	f	f	NOUN
ejpam-4951	150	1	′	′	NUM
ejpam-4951	150	2	(	(	PUNCT
ejpam-4951	150	3	x0+x∗	x0+x∗	PROPN
ejpam-4951	150	4	0	0	NUM
ejpam-4951	150	5	2	2	NUM
ejpam-4951	150	6	)	)	PUNCT
ejpam-4951	150	7	.	.	PUNCT
ejpam-4951	151	1	}	}	PUNCT
ejpam-4951	151	2	(	(	PUNCT
ejpam-4951	151	3	24	24	NUM
ejpam-4951	151	4	)	)	PUNCT
ejpam-4951	151	5	b.	b.	PROPN
ejpam-4951	151	6	sapkota	sapkota	PROPN
ejpam-4951	151	7	,	,	PUNCT
ejpam-4951	151	8	j.	j.	PROPN
ejpam-4951	151	9	jnawali	jnawali	PROPN
ejpam-4951	151	10	/	/	SYM
ejpam-4951	151	11	eur	eur	PROPN
ejpam-4951	151	12	.	.	PUNCT
ejpam-4951	152	1	j.	j.	PROPN
ejpam-4951	152	2	pure	pure	PROPN
ejpam-4951	152	3	appl	appl	PROPN
ejpam-4951	152	4	.	.	PROPN
ejpam-4951	152	5	math	math	PROPN
ejpam-4951	152	6	,	,	PUNCT
ejpam-4951	152	7	16	16	NUM
ejpam-4951	152	8	(	(	PUNCT
ejpam-4951	152	9	4	4	NUM
ejpam-4951	152	10	)	)	PUNCT
ejpam-4951	152	11	(	(	PUNCT
ejpam-4951	152	12	2023	2023	NUM
ejpam-4951	152	13	)	)	PUNCT
ejpam-4951	152	14	,	,	PUNCT
ejpam-4951	152	15	2419	2419	NUM
ejpam-4951	152	16	-	-	SYM
ejpam-4951	152	17	2430	2430	NUM
ejpam-4951	152	18	2425	2425	NUM
ejpam-4951	152	19	for	for	ADP
ejpam-4951	152	20	n	n	X
ejpam-4951	152	21	≥	≥	NOUN
ejpam-4951	152	22	1	1	NUM
ejpam-4951	152	23	,	,	PUNCT
ejpam-4951	152	24	we	we	PRON
ejpam-4951	152	25	get	get	VERB
ejpam-4951	152	26	the	the	DET
ejpam-4951	152	27	following	follow	VERB
ejpam-4951	152	28	iterations	iteration	NOUN
ejpam-4951	152	29	:	:	PUNCT
ejpam-4951	152	30	x∗n	x∗n	PUNCT
ejpam-4951	153	1	=	=	SYM
ejpam-4951	153	2	xn	xn	PROPN
ejpam-4951	154	1	−	−	NUM
ejpam-4951	154	2	f(xn	f(xn	PROPN
ejpam-4951	154	3	)	)	PUNCT
ejpam-4951	154	4	f	f	PROPN
ejpam-4951	154	5	′[12(xn	′[12(xn	NOUN
ejpam-4951	155	1	+	+	CCONJ
ejpam-4951	155	2	z∗n	z∗n	NUM
ejpam-4951	155	3	)	)	PUNCT
ejpam-4951	155	4	]	]	PUNCT
ejpam-4951	155	5	,	,	PUNCT
ejpam-4951	155	6	where	where	SCONJ
ejpam-4951	155	7	z∗n	z∗n	NUM
ejpam-4951	155	8	=	=	SYM
ejpam-4951	155	9	xn	xn	PROPN
ejpam-4951	155	10	−	−	NUM
ejpam-4951	155	11	f(xn	f(xn	PROPN
ejpam-4951	155	12	)	)	PUNCT
ejpam-4951	155	13	f	f	NOUN
ejpam-4951	156	1	′	′	NUM
ejpam-4951	156	2	(	(	PUNCT
ejpam-4951	156	3	xn−1+x∗	xn−1+x∗	PROPN
ejpam-4951	156	4	n−1	n−1	PROPN
ejpam-4951	156	5	2	2	NUM
ejpam-4951	156	6	)	)	PUNCT
ejpam-4951	156	7	xn+1	xn+1	PROPN
ejpam-4951	156	8	=	=	SYM
ejpam-4951	156	9	x∗n	x∗n	PUNCT
ejpam-4951	156	10	−	−	NUM
ejpam-4951	156	11	f(x∗n	f(x∗n	NOUN
ejpam-4951	156	12	)	)	PUNCT
ejpam-4951	157	1	f	f	X
ejpam-4951	158	1	′	′	NUM
ejpam-4951	158	2	(	(	PUNCT
ejpam-4951	158	3	x∗	x∗	PROPN
ejpam-4951	158	4	n+zn+1	n+zn+1	PROPN
ejpam-4951	158	5	2	2	NUM
ejpam-4951	158	6	)	)	PUNCT
ejpam-4951	158	7	,	,	PUNCT
ejpam-4951	158	8	where	where	SCONJ
ejpam-4951	158	9	zn+1	zn+1	VERB
ejpam-4951	158	10	=	=	SYM
ejpam-4951	158	11	xn	xn	PROPN
ejpam-4951	158	12	−	−	NUM
ejpam-4951	158	13	f(xn	f(xn	PROPN
ejpam-4951	158	14	)	)	PUNCT
ejpam-4951	158	15	f	f	NOUN
ejpam-4951	159	1	′	′	NUM
ejpam-4951	159	2	(	(	PUNCT
ejpam-4951	159	3	xn+x∗	xn+x∗	PROPN
ejpam-4951	159	4	n	n	PRON
ejpam-4951	159	5	2	2	NUM
ejpam-4951	159	6	)	)	PUNCT
ejpam-4951	159	7	.	.	PUNCT
ejpam-4951	160	1			NOUN
ejpam-4951	160	2	(	(	PUNCT
ejpam-4951	160	3	25	25	NUM
ejpam-4951	160	4	)	)	PUNCT
ejpam-4951	160	5	the	the	DET
ejpam-4951	160	6	proof	proof	NOUN
ejpam-4951	160	7	of	of	ADP
ejpam-4951	160	8	the	the	DET
ejpam-4951	160	9	convergence	convergence	NOUN
ejpam-4951	160	10	results	result	NOUN
ejpam-4951	160	11	of	of	ADP
ejpam-4951	160	12	the	the	DET
ejpam-4951	160	13	above	above	ADJ
ejpam-4951	160	14	theorem	theorem	NOUN
ejpam-4951	160	15	is	be	AUX
ejpam-4951	160	16	given	give	VERB
ejpam-4951	160	17	below	below	ADV
ejpam-4951	160	18	.	.	PUNCT
ejpam-4951	161	1	theorem	theorem	NOUN
ejpam-4951	161	2	2	2	NUM
ejpam-4951	161	3	.	.	PUNCT
ejpam-4951	162	1	let	let	VERB
ejpam-4951	162	2	a	a	DET
ejpam-4951	162	3	sufficiently	sufficiently	ADV
ejpam-4951	162	4	differentiable	differentiable	ADJ
ejpam-4951	162	5	function	function	NOUN
ejpam-4951	162	6	f	f	NOUN
ejpam-4951	162	7	:	:	PUNCT
ejpam-4951	163	1	d	d	X
ejpam-4951	163	2	⊂	⊂	PROPN
ejpam-4951	163	3	r	r	NOUN
ejpam-4951	163	4	→	→	SYM
ejpam-4951	163	5	r	r	NOUN
ejpam-4951	163	6	has	have	VERB
ejpam-4951	163	7	a	a	DET
ejpam-4951	163	8	simple	simple	ADJ
ejpam-4951	163	9	root	root	NOUN
ejpam-4951	163	10	α	α	NOUN
ejpam-4951	163	11	in	in	ADP
ejpam-4951	163	12	the	the	DET
ejpam-4951	163	13	interval	interval	NOUN
ejpam-4951	163	14	d.	d.	NOUN
ejpam-4951	163	15	if	if	SCONJ
ejpam-4951	163	16	x0	x0	PROPN
ejpam-4951	163	17	is	be	AUX
ejpam-4951	163	18	sufficiently	sufficiently	ADV
ejpam-4951	163	19	close	close	ADJ
ejpam-4951	163	20	to	to	ADP
ejpam-4951	163	21	α	α	PRON
ejpam-4951	163	22	,	,	PUNCT
ejpam-4951	163	23	then	then	ADV
ejpam-4951	163	24	the	the	DET
ejpam-4951	163	25	methods	method	NOUN
ejpam-4951	163	26	(	(	PUNCT
ejpam-4951	163	27	23)-(25	23)-(25	NUM
ejpam-4951	163	28	)	)	PUNCT
ejpam-4951	163	29	to	to	PART
ejpam-4951	163	30	solve	solve	VERB
ejpam-4951	163	31	the	the	DET
ejpam-4951	163	32	nonlinear	nonlinear	ADJ
ejpam-4951	163	33	equation	equation	NOUN
ejpam-4951	163	34	f(x	f(x	PROPN
ejpam-4951	163	35	)	)	PUNCT
ejpam-4951	164	1	=	=	SYM
ejpam-4951	164	2	0	0	NUM
ejpam-4951	164	3	,	,	PUNCT
ejpam-4951	164	4	have	have	VERB
ejpam-4951	164	5	convergence	convergence	NOUN
ejpam-4951	164	6	order	order	NOUN
ejpam-4951	164	7	5.1925	5.1925	NUM
ejpam-4951	164	8	.	.	PUNCT
ejpam-4951	165	1	proof	proof	NOUN
ejpam-4951	165	2	.	.	PUNCT
ejpam-4951	166	1	let	let	VERB
ejpam-4951	166	2	en	en	ADV
ejpam-4951	166	3	and	and	CCONJ
ejpam-4951	166	4	e∗n	e∗n	PRON
ejpam-4951	166	5	be	be	AUX
ejpam-4951	166	6	the	the	DET
ejpam-4951	166	7	errors	error	NOUN
ejpam-4951	166	8	in	in	ADP
ejpam-4951	166	9	xn	xn	PROPN
ejpam-4951	166	10	and	and	CCONJ
ejpam-4951	166	11	x∗n	x∗n	NUM
ejpam-4951	166	12	,	,	PUNCT
ejpam-4951	166	13	respectively	respectively	ADV
ejpam-4951	166	14	.	.	PUNCT
ejpam-4951	167	1	again	again	ADV
ejpam-4951	167	2	,	,	PUNCT
ejpam-4951	167	3	suppose	suppose	VERB
ejpam-4951	167	4	ck	ck	INTJ
ejpam-4951	167	5	=	=	SYM
ejpam-4951	167	6	fk(α	fk(α	X
ejpam-4951	167	7	)	)	PUNCT
ejpam-4951	167	8	k!f	k!f	PROPN
ejpam-4951	167	9	′(α	′(α	NUM
ejpam-4951	167	10	)	)	PUNCT
ejpam-4951	167	11	,	,	PUNCT
ejpam-4951	168	1	k	k	X
ejpam-4951	168	2	=	=	SYM
ejpam-4951	168	3	2	2	NUM
ejpam-4951	168	4	,	,	PUNCT
ejpam-4951	168	5	3	3	NUM
ejpam-4951	168	6	,	,	PUNCT
ejpam-4951	168	7	4	4	NUM
ejpam-4951	168	8	....	....	PUNCT
ejpam-4951	168	9	the	the	DET
ejpam-4951	168	10	error	error	NOUN
ejpam-4951	168	11	equation	equation	NOUN
ejpam-4951	168	12	of	of	ADP
ejpam-4951	168	13	method	method	NOUN
ejpam-4951	168	14	(	(	PUNCT
ejpam-4951	168	15	5	5	NUM
ejpam-4951	168	16	)	)	PUNCT
ejpam-4951	168	17	as	as	SCONJ
ejpam-4951	168	18	obtained	obtain	VERB
ejpam-4951	168	19	by	by	ADP
ejpam-4951	168	20	özban	özban	PROPN
ejpam-4951	169	1	[	[	X
ejpam-4951	169	2	13	13	NUM
ejpam-4951	169	3	]	]	PUNCT
ejpam-4951	169	4	:	:	PUNCT
ejpam-4951	169	5	en+1	en+1	PROPN
ejpam-4951	169	6	=	=	SYM
ejpam-4951	169	7	ae3n	ae3n	PROPN
ejpam-4951	169	8	,	,	PUNCT
ejpam-4951	169	9	(	(	PUNCT
ejpam-4951	169	10	26	26	NUM
ejpam-4951	169	11	)	)	PUNCT
ejpam-4951	169	12	where	where	SCONJ
ejpam-4951	169	13	a	a	DET
ejpam-4951	169	14	=	=	NOUN
ejpam-4951	169	15	c22	c22	NOUN
ejpam-4951	169	16	−	−	PROPN
ejpam-4951	169	17	1	1	NUM
ejpam-4951	169	18	4c3	4c3	NUM
ejpam-4951	169	19	and	and	CCONJ
ejpam-4951	169	20	the	the	DET
ejpam-4951	169	21	higher	high	ADJ
ejpam-4951	169	22	powers	power	NOUN
ejpam-4951	169	23	of	of	ADP
ejpam-4951	169	24	en	en	X
ejpam-4951	169	25	being	be	AUX
ejpam-4951	169	26	neglected	neglect	VERB
ejpam-4951	169	27	.	.	PUNCT
ejpam-4951	170	1	in	in	ADP
ejpam-4951	170	2	the	the	DET
ejpam-4951	170	3	same	same	ADJ
ejpam-4951	170	4	line	line	NOUN
ejpam-4951	170	5	of	of	ADP
ejpam-4951	170	6	proof	proof	NOUN
ejpam-4951	170	7	of	of	ADP
ejpam-4951	170	8	above	above	ADP
ejpam-4951	170	9	result	result	NOUN
ejpam-4951	170	10	,	,	PUNCT
ejpam-4951	170	11	e∗0	e∗0	NOUN
ejpam-4951	170	12	and	and	CCONJ
ejpam-4951	170	13	e1	e1	NOUN
ejpam-4951	170	14	,	,	PUNCT
ejpam-4951	170	15	in	in	ADP
ejpam-4951	170	16	x∗0	x∗0	NOUN
ejpam-4951	170	17	and	and	CCONJ
ejpam-4951	170	18	x1	x1	NUM
ejpam-4951	170	19	in	in	ADP
ejpam-4951	170	20	(	(	PUNCT
ejpam-4951	170	21	23)-(25	23)-(25	NUM
ejpam-4951	170	22	)	)	PUNCT
ejpam-4951	170	23	are	be	AUX
ejpam-4951	170	24	given	give	VERB
ejpam-4951	170	25	by	by	ADP
ejpam-4951	170	26	e∗0	e∗0	NOUN
ejpam-4951	170	27	=	=	SYM
ejpam-4951	170	28	e0	e0	PROPN
ejpam-4951	170	29	e1	e1	PROPN
ejpam-4951	170	30	=	=	PUNCT
ejpam-4951	170	31	ae30	ae30	PROPN
ejpam-4951	170	32	,	,	PUNCT
ejpam-4951	170	33	(	(	PUNCT
ejpam-4951	170	34	27	27	NUM
ejpam-4951	170	35	)	)	PUNCT
ejpam-4951	170	36	where	where	SCONJ
ejpam-4951	170	37	higher	high	ADJ
ejpam-4951	170	38	powers	power	NOUN
ejpam-4951	170	39	of	of	ADP
ejpam-4951	170	40	small	small	ADJ
ejpam-4951	170	41	quantity	quantity	NOUN
ejpam-4951	170	42	are	be	AUX
ejpam-4951	170	43	neglected	neglect	VERB
ejpam-4951	170	44	.	.	PUNCT
ejpam-4951	171	1	next	next	ADV
ejpam-4951	171	2	,	,	PUNCT
ejpam-4951	171	3	we	we	PRON
ejpam-4951	171	4	find	find	VERB
ejpam-4951	171	5	e∗1	e∗1	ADJ
ejpam-4951	171	6	in	in	ADP
ejpam-4951	171	7	x∗1	x∗1	PROPN
ejpam-4951	171	8	.	.	PUNCT
ejpam-4951	172	1	taylor	taylor	PROPN
ejpam-4951	172	2	and	and	CCONJ
ejpam-4951	172	3	binomial	binomial	PROPN
ejpam-4951	172	4	series	series	NOUN
ejpam-4951	172	5	expansion	expansion	NOUN
ejpam-4951	172	6	gives	give	VERB
ejpam-4951	172	7	:	:	PUNCT
ejpam-4951	172	8	f(x1	f(x1	ADJ
ejpam-4951	172	9	)	)	PUNCT
ejpam-4951	172	10	f	f	NOUN
ejpam-4951	172	11	′(x0	′(x0	NOUN
ejpam-4951	172	12	)	)	PUNCT
ejpam-4951	172	13	=	=	SYM
ejpam-4951	172	14	f(α+	f(α+	NUM
ejpam-4951	172	15	e1	e1	PROPN
ejpam-4951	172	16	)	)	PUNCT
ejpam-4951	172	17	f	f	PROPN
ejpam-4951	172	18	′(α+	′(α+	NOUN
ejpam-4951	172	19	e0	e0	PROPN
ejpam-4951	172	20	)	)	PUNCT
ejpam-4951	173	1	=	=	PRON
ejpam-4951	173	2	(	(	PUNCT
ejpam-4951	173	3	e1	e1	PROPN
ejpam-4951	173	4	+	+	CCONJ
ejpam-4951	173	5	c2e	c2e	PROPN
ejpam-4951	173	6	2	2	NUM
ejpam-4951	173	7	1	1	NUM
ejpam-4951	173	8	+	+	NUM
ejpam-4951	173	9	c3e	c3e	PROPN
ejpam-4951	173	10	3	3	NUM
ejpam-4951	173	11	1	1	NUM
ejpam-4951	173	12	+	+	NOUN
ejpam-4951	173	13	o(e41	o(e41	ADJ
ejpam-4951	173	14	)	)	PUNCT
ejpam-4951	173	15	)	)	PUNCT
ejpam-4951	173	16	(	(	PUNCT
ejpam-4951	173	17	1	1	NUM
ejpam-4951	173	18	+	+	NUM
ejpam-4951	173	19	2c2e0	2c2e0	NUM
ejpam-4951	174	1	+	+	CCONJ
ejpam-4951	174	2	3c3e	3c3e	NOUN
ejpam-4951	174	3	2	2	NUM
ejpam-4951	174	4	0	0	NUM
ejpam-4951	174	5	+	+	NOUN
ejpam-4951	174	6	o(e30	o(e30	NOUN
ejpam-4951	174	7	)	)	PUNCT
ejpam-4951	174	8	)	)	PUNCT
ejpam-4951	174	9	−1	−1	NOUN
ejpam-4951	174	10	=	=	NOUN
ejpam-4951	174	11	e1	e1	PROPN
ejpam-4951	174	12	−	−	PROPN
ejpam-4951	174	13	2c2e0e1	2c2e0e1	NUM
ejpam-4951	175	1	+	+	NOUN
ejpam-4951	175	2	o(e50	o(e50	NUM
ejpam-4951	175	3	)	)	PUNCT
ejpam-4951	175	4	,	,	PUNCT
ejpam-4951	175	5	and	and	CCONJ
ejpam-4951	175	6	hence	hence	ADV
ejpam-4951	175	7	z∗1	z∗1	NOUN
ejpam-4951	175	8	=	=	PUNCT
ejpam-4951	176	1	x1	x1	PROPN
ejpam-4951	176	2	−	−	PROPN
ejpam-4951	176	3	f(x1	f(x1	ADJ
ejpam-4951	176	4	)	)	PUNCT
ejpam-4951	176	5	f	f	NOUN
ejpam-4951	176	6	′(x0	′(x0	NOUN
ejpam-4951	176	7	)	)	PUNCT
ejpam-4951	177	1	=	=	PUNCT
ejpam-4951	177	2	α+	α+	X
ejpam-4951	177	3	2c2e0e1	2c2e0e1	NUM
ejpam-4951	177	4	+	+	NOUN
ejpam-4951	177	5	o(e50	o(e50	NUM
ejpam-4951	177	6	)	)	PUNCT
ejpam-4951	177	7	.	.	PUNCT
ejpam-4951	178	1	also	also	ADV
ejpam-4951	178	2	,	,	PUNCT
ejpam-4951	178	3	x1	x1	PROPN
ejpam-4951	178	4	+	+	NUM
ejpam-4951	178	5	z∗1	z∗1	NOUN
ejpam-4951	178	6	2	2	NUM
ejpam-4951	178	7	=	=	SYM
ejpam-4951	178	8	α+	α+	PUNCT
ejpam-4951	178	9	e1	e1	PROPN
ejpam-4951	178	10	+	+	CCONJ
ejpam-4951	178	11	2c2e0e1	2c2e0e1	NUM
ejpam-4951	178	12	+	+	CCONJ
ejpam-4951	178	13	...	...	SYM
ejpam-4951	178	14	2	2	NUM
ejpam-4951	178	15	,	,	PUNCT
ejpam-4951	178	16	and	and	CCONJ
ejpam-4951	178	17	f	f	PROPN
ejpam-4951	178	18	′(x1	′(x1	PROPN
ejpam-4951	178	19	+	+	NUM
ejpam-4951	178	20	z∗1	z∗1	NOUN
ejpam-4951	178	21	2	2	NUM
ejpam-4951	178	22	)	)	PUNCT
ejpam-4951	178	23	=	=	SYM
ejpam-4951	178	24	f	f	PROPN
ejpam-4951	178	25	′(α	′(α	NOUN
ejpam-4951	178	26	)	)	PUNCT
ejpam-4951	179	1	(	(	PUNCT
ejpam-4951	179	2	1	1	NUM
ejpam-4951	179	3	+	+	CCONJ
ejpam-4951	179	4	c2e1	c2e1	NOUN
ejpam-4951	179	5	+	+	CCONJ
ejpam-4951	179	6	2c22e0e1	2c22e0e1	NUM
ejpam-4951	179	7	+	+	NOUN
ejpam-4951	179	8	o(e50	o(e50	NUM
ejpam-4951	179	9	)	)	PUNCT
ejpam-4951	179	10	)	)	PUNCT
ejpam-4951	179	11	.	.	PUNCT
ejpam-4951	180	1	(	(	PUNCT
ejpam-4951	180	2	28	28	NUM
ejpam-4951	180	3	)	)	PUNCT
ejpam-4951	180	4	b.	b.	PROPN
ejpam-4951	180	5	sapkota	sapkota	PROPN
ejpam-4951	180	6	,	,	PUNCT
ejpam-4951	180	7	j.	j.	PROPN
ejpam-4951	180	8	jnawali	jnawali	PROPN
ejpam-4951	180	9	/	/	SYM
ejpam-4951	180	10	eur	eur	PROPN
ejpam-4951	180	11	.	.	PUNCT
ejpam-4951	181	1	j.	j.	PROPN
ejpam-4951	181	2	pure	pure	PROPN
ejpam-4951	181	3	appl	appl	PROPN
ejpam-4951	181	4	.	.	PROPN
ejpam-4951	181	5	math	math	PROPN
ejpam-4951	181	6	,	,	PUNCT
ejpam-4951	181	7	16	16	NUM
ejpam-4951	181	8	(	(	PUNCT
ejpam-4951	181	9	4	4	NUM
ejpam-4951	181	10	)	)	PUNCT
ejpam-4951	181	11	(	(	PUNCT
ejpam-4951	181	12	2023	2023	NUM
ejpam-4951	181	13	)	)	PUNCT
ejpam-4951	181	14	,	,	PUNCT
ejpam-4951	181	15	2419	2419	NUM
ejpam-4951	181	16	-	-	SYM
ejpam-4951	181	17	2430	2430	NUM
ejpam-4951	181	18	2426	2426	NUM
ejpam-4951	181	19	consequently	consequently	ADV
ejpam-4951	181	20	,	,	PUNCT
ejpam-4951	181	21	using	use	VERB
ejpam-4951	181	22	(	(	PUNCT
ejpam-4951	181	23	27	27	NUM
ejpam-4951	181	24	)	)	PUNCT
ejpam-4951	181	25	and	and	CCONJ
ejpam-4951	181	26	(	(	PUNCT
ejpam-4951	181	27	28	28	NUM
ejpam-4951	181	28	)	)	PUNCT
ejpam-4951	181	29	,	,	PUNCT
ejpam-4951	181	30	e∗1	e∗1	ADJ
ejpam-4951	181	31	in	in	ADP
ejpam-4951	181	32	x∗1	x∗1	PROPN
ejpam-4951	181	33	at	at	ADP
ejpam-4951	181	34	the	the	DET
ejpam-4951	181	35	equation	equation	NOUN
ejpam-4951	181	36	(	(	PUNCT
ejpam-4951	181	37	24	24	NUM
ejpam-4951	181	38	)	)	PUNCT
ejpam-4951	181	39	is	be	AUX
ejpam-4951	181	40	given	give	VERB
ejpam-4951	181	41	by	by	ADP
ejpam-4951	181	42	e∗1	e∗1	ADJ
ejpam-4951	181	43	=	=	SYM
ejpam-4951	181	44	e1	e1	PROPN
ejpam-4951	181	45	−	−	PROPN
ejpam-4951	181	46	(	(	PUNCT
ejpam-4951	181	47	e1	e1	PROPN
ejpam-4951	181	48	+	+	CCONJ
ejpam-4951	181	49	c2e	c2e	PROPN
ejpam-4951	181	50	2	2	NUM
ejpam-4951	181	51	1	1	NUM
ejpam-4951	181	52	+	+	NOUN
ejpam-4951	181	53	o(e31	o(e31	NUM
ejpam-4951	181	54	)	)	PUNCT
ejpam-4951	181	55	)	)	PUNCT
ejpam-4951	182	1	(	(	PUNCT
ejpam-4951	182	2	1	1	NUM
ejpam-4951	182	3	+	+	CCONJ
ejpam-4951	182	4	c2e1	c2e1	NOUN
ejpam-4951	182	5	+	+	CCONJ
ejpam-4951	182	6	2c22e0e1	2c22e0e1	NUM
ejpam-4951	182	7	+	+	NOUN
ejpam-4951	182	8	o(e50	o(e50	NUM
ejpam-4951	182	9	)	)	PUNCT
ejpam-4951	182	10	)	)	PUNCT
ejpam-4951	182	11	−1	−1	NOUN
ejpam-4951	182	12	=	=	SYM
ejpam-4951	182	13	2c22e0e	2c22e0e	NOUN
ejpam-4951	182	14	2	2	NUM
ejpam-4951	182	15	1	1	NUM
ejpam-4951	182	16	=	=	SYM
ejpam-4951	182	17	be70	be70	PROPN
ejpam-4951	182	18	,	,	PUNCT
ejpam-4951	182	19	where	where	SCONJ
ejpam-4951	182	20	b	b	X
ejpam-4951	182	21	=	=	SYM
ejpam-4951	182	22	2c22a	2c22a	NUM
ejpam-4951	182	23	2	2	NUM
ejpam-4951	182	24	.	.	PUNCT
ejpam-4951	182	25	from	from	ADP
ejpam-4951	182	26	(	(	PUNCT
ejpam-4951	182	27	25	25	NUM
ejpam-4951	182	28	)	)	PUNCT
ejpam-4951	182	29	,	,	PUNCT
ejpam-4951	182	30	using	use	VERB
ejpam-4951	182	31	e∗1	e∗1	NOUN
ejpam-4951	182	32	,	,	PUNCT
ejpam-4951	182	33	we	we	PRON
ejpam-4951	182	34	now	now	ADV
ejpam-4951	182	35	find	find	VERB
ejpam-4951	182	36	e2	e2	PROPN
ejpam-4951	182	37	in	in	ADP
ejpam-4951	182	38	x2	x2	PROPN
ejpam-4951	182	39	=	=	PUNCT
ejpam-4951	182	40	x∗1	x∗1	PROPN
ejpam-4951	183	1	−	−	PROPN
ejpam-4951	183	2	f(x∗1	f(x∗1	ADJ
ejpam-4951	183	3	)	)	PUNCT
ejpam-4951	183	4	f	f	NOUN
ejpam-4951	183	5	′	′	NUM
ejpam-4951	183	6	(	(	PUNCT
ejpam-4951	183	7	x∗	x∗	PROPN
ejpam-4951	183	8	1+z2	1+z2	NUM
ejpam-4951	183	9	2	2	NUM
ejpam-4951	183	10	)	)	PUNCT
ejpam-4951	183	11	,	,	PUNCT
ejpam-4951	183	12	where	where	SCONJ
ejpam-4951	183	13	z2	z2	PROPN
ejpam-4951	183	14	=	=	SYM
ejpam-4951	183	15	x1	x1	PROPN
ejpam-4951	183	16	−	−	PROPN
ejpam-4951	183	17	f(x1	f(x1	NOUN
ejpam-4951	184	1	)	)	PUNCT
ejpam-4951	184	2	f	f	NOUN
ejpam-4951	185	1	′	′	NUM
ejpam-4951	185	2	(	(	PUNCT
ejpam-4951	185	3	x1+x∗	x1+x∗	PROPN
ejpam-4951	185	4	1	1	NUM
ejpam-4951	185	5	2	2	NUM
ejpam-4951	185	6	)	)	PUNCT
ejpam-4951	185	7	.	.	PUNCT
ejpam-4951	186	1	now	now	ADV
ejpam-4951	186	2	,	,	PUNCT
ejpam-4951	186	3	f	f	PROPN
ejpam-4951	186	4	′(x1	′(x1	PROPN
ejpam-4951	186	5	+	+	CCONJ
ejpam-4951	186	6	x∗1	x∗1	ADV
ejpam-4951	186	7	2	2	NUM
ejpam-4951	186	8	)	)	PUNCT
ejpam-4951	187	1	=	=	SYM
ejpam-4951	187	2	f	f	PROPN
ejpam-4951	187	3	′(α+	′(α+	NOUN
ejpam-4951	187	4	e1	e1	VERB
ejpam-4951	187	5	+	+	CCONJ
ejpam-4951	187	6	e∗1	e∗1	ADJ
ejpam-4951	187	7	2	2	NUM
ejpam-4951	187	8	)	)	PUNCT
ejpam-4951	188	1	=	=	SYM
ejpam-4951	188	2	f	f	PROPN
ejpam-4951	188	3	′(α	′(α	NOUN
ejpam-4951	188	4	)	)	PUNCT
ejpam-4951	188	5	(	(	PUNCT
ejpam-4951	188	6	1	1	NUM
ejpam-4951	188	7	+	+	CCONJ
ejpam-4951	188	8	c2e1	c2e1	X
ejpam-4951	188	9	+	+	CCONJ
ejpam-4951	188	10	c2e	c2e	NOUN
ejpam-4951	188	11	∗	∗	NOUN
ejpam-4951	188	12	1	1	NUM
ejpam-4951	188	13	+	+	CCONJ
ejpam-4951	188	14	3	3	NUM
ejpam-4951	188	15	4	4	NUM
ejpam-4951	188	16	c3e	c3e	NOUN
ejpam-4951	188	17	2	2	NUM
ejpam-4951	188	18	1	1	NUM
ejpam-4951	188	19	+	+	NOUN
ejpam-4951	188	20	o(e90	o(e90	NOUN
ejpam-4951	188	21	)	)	PUNCT
ejpam-4951	188	22	)	)	PUNCT
ejpam-4951	188	23	in	in	ADP
ejpam-4951	188	24	turn	turn	NOUN
ejpam-4951	188	25	,	,	PUNCT
ejpam-4951	188	26	f(x1	f(x1	ADJ
ejpam-4951	188	27	)	)	PUNCT
ejpam-4951	188	28	f	f	NOUN
ejpam-4951	189	1	′	′	NUM
ejpam-4951	189	2	(	(	PUNCT
ejpam-4951	189	3	x1+x∗	x1+x∗	PROPN
ejpam-4951	189	4	1	1	NUM
ejpam-4951	189	5	2	2	NUM
ejpam-4951	189	6	)	)	PUNCT
ejpam-4951	189	7	=	=	SYM
ejpam-4951	189	8	(	(	PUNCT
ejpam-4951	189	9	e1	e1	PROPN
ejpam-4951	189	10	+	+	CCONJ
ejpam-4951	189	11	c2e	c2e	PROPN
ejpam-4951	189	12	2	2	NUM
ejpam-4951	189	13	1	1	NUM
ejpam-4951	189	14	+	+	NOUN
ejpam-4951	189	15	o(e31	o(e31	NUM
ejpam-4951	189	16	)	)	PUNCT
ejpam-4951	189	17	)	)	PUNCT
ejpam-4951	190	1	(	(	PUNCT
ejpam-4951	190	2	1	1	NUM
ejpam-4951	190	3	+	+	CCONJ
ejpam-4951	190	4	c2e1	c2e1	X
ejpam-4951	190	5	+	+	CCONJ
ejpam-4951	190	6	c2e	c2e	NOUN
ejpam-4951	190	7	∗	∗	NOUN
ejpam-4951	190	8	1	1	NUM
ejpam-4951	190	9	+	+	CCONJ
ejpam-4951	190	10	3	3	NUM
ejpam-4951	190	11	4	4	NUM
ejpam-4951	190	12	c3e	c3e	NOUN
ejpam-4951	190	13	2	2	NUM
ejpam-4951	190	14	1	1	NUM
ejpam-4951	190	15	+	+	NOUN
ejpam-4951	190	16	o(e90	o(e90	NOUN
ejpam-4951	190	17	)	)	PUNCT
ejpam-4951	190	18	)	)	PUNCT
ejpam-4951	190	19	−1	−1	NOUN
ejpam-4951	190	20	=	=	SYM
ejpam-4951	190	21	e1	e1	NOUN
ejpam-4951	190	22	+	+	CCONJ
ejpam-4951	190	23	1	1	NUM
ejpam-4951	190	24	4	4	NUM
ejpam-4951	190	25	c3e	c3e	NOUN
ejpam-4951	190	26	3	3	NUM
ejpam-4951	190	27	1	1	NUM
ejpam-4951	190	28	−	−	NOUN
ejpam-4951	190	29	c2e1e	c2e1e	NUM
ejpam-4951	190	30	∗	∗	NOUN
ejpam-4951	190	31	1	1	NUM
ejpam-4951	190	32	+	+	CCONJ
ejpam-4951	190	33	...	...	PUNCT
ejpam-4951	190	34	and	and	CCONJ
ejpam-4951	190	35	therefore	therefore	ADV
ejpam-4951	190	36	z2	z2	PROPN
ejpam-4951	190	37	=	=	PUNCT
ejpam-4951	190	38	α−	α−	ADP
ejpam-4951	190	39	1	1	NUM
ejpam-4951	190	40	4	4	NUM
ejpam-4951	190	41	c3e	c3e	NOUN
ejpam-4951	190	42	3	3	NUM
ejpam-4951	190	43	1	1	NUM
ejpam-4951	190	44	+	+	NUM
ejpam-4951	190	45	c2e1e	c2e1e	NOUN
ejpam-4951	190	46	∗	∗	NOUN
ejpam-4951	190	47	1	1	NUM
ejpam-4951	190	48	+	+	CCONJ
ejpam-4951	190	49	....	....	PUNCT
ejpam-4951	190	50	here	here	ADV
ejpam-4951	190	51	,	,	PUNCT
ejpam-4951	190	52	x∗1	x∗1	VERB
ejpam-4951	191	1	+	+	X
ejpam-4951	191	2	z2	z2	PROPN
ejpam-4951	191	3	2	2	NUM
ejpam-4951	191	4	=	=	SYM
ejpam-4951	191	5	α+	α+	PUNCT
ejpam-4951	191	6	1	1	NUM
ejpam-4951	191	7	2	2	NUM
ejpam-4951	191	8	(	(	PUNCT
ejpam-4951	191	9	e∗1	e∗1	ADJ
ejpam-4951	191	10	−	−	PROPN
ejpam-4951	191	11	1	1	NUM
ejpam-4951	191	12	4	4	NUM
ejpam-4951	191	13	c3e	c3e	NOUN
ejpam-4951	191	14	3	3	NUM
ejpam-4951	191	15	1	1	NUM
ejpam-4951	191	16	+	+	NUM
ejpam-4951	191	17	c2e1e	c2e1e	NOUN
ejpam-4951	191	18	∗	∗	NOUN
ejpam-4951	191	19	1	1	NUM
ejpam-4951	191	20	+	+	CCONJ
ejpam-4951	191	21	...	...	PUNCT
ejpam-4951	191	22	)	)	PUNCT
ejpam-4951	191	23	,	,	PUNCT
ejpam-4951	191	24	and	and	CCONJ
ejpam-4951	191	25	f	f	PROPN
ejpam-4951	191	26	′(x∗1	′(x∗1	VERB
ejpam-4951	191	27	+	+	PROPN
ejpam-4951	191	28	z2	z2	NOUN
ejpam-4951	191	29	2	2	NUM
ejpam-4951	191	30	)	)	PUNCT
ejpam-4951	191	31	=	=	SYM
ejpam-4951	191	32	f	f	PROPN
ejpam-4951	191	33	′(α	′(α	NOUN
ejpam-4951	191	34	)	)	PUNCT
ejpam-4951	191	35	(	(	PUNCT
ejpam-4951	191	36	1	1	NUM
ejpam-4951	191	37	+	+	CCONJ
ejpam-4951	191	38	c2e	c2e	NOUN
ejpam-4951	191	39	∗	∗	NOUN
ejpam-4951	191	40	1	1	NUM
ejpam-4951	191	41	−	−	NUM
ejpam-4951	191	42	1	1	NUM
ejpam-4951	191	43	4	4	NUM
ejpam-4951	191	44	c2c3e1	c2c3e1	NOUN
ejpam-4951	191	45	3	3	NUM
ejpam-4951	191	46	+	+	CCONJ
ejpam-4951	191	47	c22e1e	c22e1e	NOUN
ejpam-4951	191	48	∗	∗	NOUN
ejpam-4951	191	49	1	1	NUM
ejpam-4951	191	50	+	+	CCONJ
ejpam-4951	191	51	...	...	PUNCT
ejpam-4951	191	52	)	)	PUNCT
ejpam-4951	192	1	thus	thus	ADV
ejpam-4951	192	2	,	,	PUNCT
ejpam-4951	192	3	the	the	DET
ejpam-4951	192	4	error	error	NOUN
ejpam-4951	192	5	e2	e2	NOUN
ejpam-4951	192	6	in	in	ADP
ejpam-4951	192	7	x2	x2	PROPN
ejpam-4951	192	8	is	be	AUX
ejpam-4951	192	9	:	:	PUNCT
ejpam-4951	192	10	e2	e2	PROPN
ejpam-4951	192	11	=	=	PUNCT
ejpam-4951	192	12	ce31e	ce31e	NOUN
ejpam-4951	192	13	∗	∗	NOUN
ejpam-4951	192	14	1	1	NUM
ejpam-4951	192	15	,	,	PUNCT
ejpam-4951	192	16	where	where	SCONJ
ejpam-4951	192	17	c	c	NOUN
ejpam-4951	192	18	=	=	SYM
ejpam-4951	192	19	−1	−1	NOUN
ejpam-4951	192	20	4c2c3	4c2c3	NOUN
ejpam-4951	192	21	and	and	CCONJ
ejpam-4951	192	22	higher	high	ADJ
ejpam-4951	192	23	powers	power	NOUN
ejpam-4951	192	24	of	of	ADP
ejpam-4951	192	25	small	small	ADJ
ejpam-4951	192	26	quantities	quantity	NOUN
ejpam-4951	192	27	are	be	AUX
ejpam-4951	192	28	neglected	neglect	VERB
ejpam-4951	192	29	.	.	PUNCT
ejpam-4951	193	1	consequently	consequently	ADV
ejpam-4951	193	2	,	,	PUNCT
ejpam-4951	193	3	for	for	ADP
ejpam-4951	193	4	n	n	PRON
ejpam-4951	193	5	≥	≥	NUM
ejpam-4951	193	6	1	1	NUM
ejpam-4951	193	7	,	,	PUNCT
ejpam-4951	193	8	we	we	PRON
ejpam-4951	193	9	get	get	VERB
ejpam-4951	193	10	:	:	PUNCT
ejpam-4951	193	11	en+1	en+1	ADJ
ejpam-4951	193	12	=	=	SYM
ejpam-4951	193	13	ce3ne	ce3ne	NOUN
ejpam-4951	193	14	∗	∗	NOUN
ejpam-4951	193	15	n.	n.	NOUN
ejpam-4951	193	16	(	(	PUNCT
ejpam-4951	193	17	29	29	NUM
ejpam-4951	193	18	)	)	PUNCT
ejpam-4951	193	19	to	to	PART
ejpam-4951	193	20	compute	compute	VERB
ejpam-4951	193	21	en+1	en+1	NOUN
ejpam-4951	193	22	explicitly	explicitly	ADV
ejpam-4951	193	23	,	,	PUNCT
ejpam-4951	193	24	the	the	DET
ejpam-4951	193	25	values	value	NOUN
ejpam-4951	193	26	of	of	ADP
ejpam-4951	193	27	e∗n	e∗n	PROPN
ejpam-4951	193	28	are	be	AUX
ejpam-4951	193	29	needed	need	VERB
ejpam-4951	193	30	.	.	PUNCT
ejpam-4951	194	1	the	the	DET
ejpam-4951	194	2	value	value	NOUN
ejpam-4951	194	3	of	of	ADP
ejpam-4951	194	4	e∗1	e∗1	PROPN
ejpam-4951	194	5	is	be	AUX
ejpam-4951	194	6	already	already	ADV
ejpam-4951	194	7	known	know	VERB
ejpam-4951	194	8	.	.	PUNCT
ejpam-4951	195	1	like	like	INTJ
ejpam-4951	195	2	above	above	ADV
ejpam-4951	195	3	,	,	PUNCT
ejpam-4951	195	4	e∗2	e∗2	VERB
ejpam-4951	195	5	in	in	ADP
ejpam-4951	195	6	x∗2	x∗2	PROPN
ejpam-4951	195	7	can	can	AUX
ejpam-4951	195	8	be	be	AUX
ejpam-4951	195	9	found	find	VERB
ejpam-4951	195	10	,	,	PUNCT
ejpam-4951	195	11	and	and	CCONJ
ejpam-4951	195	12	its	its	PRON
ejpam-4951	195	13	value	value	NOUN
ejpam-4951	195	14	is	be	AUX
ejpam-4951	195	15	given	give	VERB
ejpam-4951	195	16	by	by	ADP
ejpam-4951	195	17	e∗2	e∗2	NOUN
ejpam-4951	195	18	=	=	PUNCT
ejpam-4951	195	19	de1e	de1e	NOUN
ejpam-4951	195	20	2	2	NUM
ejpam-4951	195	21	2	2	NUM
ejpam-4951	195	22	,	,	PUNCT
ejpam-4951	195	23	b.	b.	PROPN
ejpam-4951	195	24	sapkota	sapkota	PROPN
ejpam-4951	195	25	,	,	PUNCT
ejpam-4951	195	26	j.	j.	PROPN
ejpam-4951	195	27	jnawali	jnawali	PROPN
ejpam-4951	195	28	/	/	SYM
ejpam-4951	195	29	eur	eur	PROPN
ejpam-4951	195	30	.	.	PUNCT
ejpam-4951	196	1	j.	j.	PROPN
ejpam-4951	196	2	pure	pure	PROPN
ejpam-4951	196	3	appl	appl	PROPN
ejpam-4951	196	4	.	.	PROPN
ejpam-4951	196	5	math	math	PROPN
ejpam-4951	196	6	,	,	PUNCT
ejpam-4951	196	7	16	16	NUM
ejpam-4951	196	8	(	(	PUNCT
ejpam-4951	196	9	4	4	NUM
ejpam-4951	196	10	)	)	PUNCT
ejpam-4951	196	11	(	(	PUNCT
ejpam-4951	196	12	2023	2023	NUM
ejpam-4951	196	13	)	)	PUNCT
ejpam-4951	196	14	,	,	PUNCT
ejpam-4951	196	15	2419	2419	NUM
ejpam-4951	196	16	-	-	SYM
ejpam-4951	196	17	2430	2430	NUM
ejpam-4951	196	18	2427	2427	NUM
ejpam-4951	196	19	where	where	SCONJ
ejpam-4951	196	20	d	d	PROPN
ejpam-4951	196	21	=	=	SYM
ejpam-4951	196	22	c22	c22	PROPN
ejpam-4951	196	23	and	and	CCONJ
ejpam-4951	196	24	,	,	PUNCT
ejpam-4951	196	25	again	again	ADV
ejpam-4951	196	26	,	,	PUNCT
ejpam-4951	196	27	for	for	ADP
ejpam-4951	196	28	n	n	PRON
ejpam-4951	196	29	≥	≥	NUM
ejpam-4951	196	30	2	2	NUM
ejpam-4951	196	31	,	,	PUNCT
ejpam-4951	196	32	the	the	DET
ejpam-4951	196	33	following	follow	VERB
ejpam-4951	196	34	formula	formula	NOUN
ejpam-4951	196	35	can	can	AUX
ejpam-4951	196	36	be	be	AUX
ejpam-4951	196	37	obtained	obtain	VERB
ejpam-4951	196	38	:	:	PUNCT
ejpam-4951	196	39	e∗n	e∗n	PROPN
ejpam-4951	196	40	=	=	SYM
ejpam-4951	196	41	den−1e	den−1e	PROPN
ejpam-4951	196	42	2	2	NUM
ejpam-4951	196	43	n.	n.	NOUN
ejpam-4951	196	44	(	(	PUNCT
ejpam-4951	196	45	30	30	NUM
ejpam-4951	196	46	)	)	PUNCT
ejpam-4951	196	47	to	to	PART
ejpam-4951	196	48	investigate	investigate	VERB
ejpam-4951	196	49	the	the	DET
ejpam-4951	196	50	convergence	convergence	NOUN
ejpam-4951	196	51	order	order	NOUN
ejpam-4951	196	52	of	of	ADP
ejpam-4951	196	53	methods	method	NOUN
ejpam-4951	196	54	(	(	PUNCT
ejpam-4951	196	55	23)-(25	23)-(25	NUM
ejpam-4951	196	56	)	)	PUNCT
ejpam-4951	196	57	,	,	PUNCT
ejpam-4951	196	58	the	the	DET
ejpam-4951	196	59	following	follow	VERB
ejpam-4951	196	60	form	form	NOUN
ejpam-4951	196	61	should	should	AUX
ejpam-4951	196	62	be	be	AUX
ejpam-4951	196	63	obtained	obtain	VERB
ejpam-4951	196	64	:	:	PUNCT
ejpam-4951	196	65	en+1	en+1	ADJ
ejpam-4951	196	66	=	=	PROPN
ejpam-4951	196	67	aepn	aepn	NOUN
ejpam-4951	196	68	.	.	PUNCT
ejpam-4951	197	1	(	(	PUNCT
ejpam-4951	197	2	31	31	NUM
ejpam-4951	197	3	)	)	PUNCT
ejpam-4951	197	4	also	also	ADV
ejpam-4951	197	5	,	,	PUNCT
ejpam-4951	197	6	en	en	X
ejpam-4951	197	7	=	=	SYM
ejpam-4951	197	8	aepn−1	aepn−1	PROPN
ejpam-4951	197	9	or	or	CCONJ
ejpam-4951	197	10	en−1	en−1	PROPN
ejpam-4951	197	11	=	=	PROPN
ejpam-4951	198	1	a	a	DET
ejpam-4951	198	2	−	−	PROPN
ejpam-4951	198	3	1	1	NUM
ejpam-4951	198	4	p	p	NOUN
ejpam-4951	198	5	e	e	NOUN
ejpam-4951	198	6	1	1	NUM
ejpam-4951	198	7	p	p	NOUN
ejpam-4951	198	8	n	n	NOUN
ejpam-4951	198	9	.	.	PUNCT
ejpam-4951	199	1	(	(	PUNCT
ejpam-4951	199	2	32	32	NUM
ejpam-4951	199	3	)	)	PUNCT
ejpam-4951	199	4	from	from	ADP
ejpam-4951	199	5	relations	relation	NOUN
ejpam-4951	199	6	(	(	PUNCT
ejpam-4951	199	7	29	29	NUM
ejpam-4951	199	8	)	)	PUNCT
ejpam-4951	199	9	,	,	PUNCT
ejpam-4951	199	10	(	(	PUNCT
ejpam-4951	199	11	30	30	NUM
ejpam-4951	199	12	)	)	PUNCT
ejpam-4951	199	13	and	and	CCONJ
ejpam-4951	199	14	(	(	PUNCT
ejpam-4951	199	15	31	31	NUM
ejpam-4951	199	16	)	)	PUNCT
ejpam-4951	199	17	,	,	PUNCT
ejpam-4951	199	18	we	we	PRON
ejpam-4951	199	19	have	have	VERB
ejpam-4951	199	20	aepn	aepn	NOUN
ejpam-4951	199	21	=	=	SYM
ejpam-4951	199	22	en+1	en+1	ADJ
ejpam-4951	199	23	=	=	SYM
ejpam-4951	199	24	ce3ne	ce3ne	NOUN
ejpam-4951	199	25	∗	∗	NOUN
ejpam-4951	199	26	n	n	NOUN
ejpam-4951	199	27	=	=	SYM
ejpam-4951	199	28	ce3nden−1e	ce3nden−1e	ADP
ejpam-4951	199	29	2	2	NUM
ejpam-4951	199	30	n	n	NOUN
ejpam-4951	199	31	=	=	PUNCT
ejpam-4951	200	1	cde5na	cde5na	PRON
ejpam-4951	200	2	−	−	ADP
ejpam-4951	200	3	1	1	NUM
ejpam-4951	200	4	p	p	NOUN
ejpam-4951	200	5	e	e	NOUN
ejpam-4951	200	6	1	1	NUM
ejpam-4951	200	7	p	p	NOUN
ejpam-4951	200	8	equating	equate	VERB
ejpam-4951	200	9	the	the	DET
ejpam-4951	200	10	power	power	NOUN
ejpam-4951	200	11	of	of	ADP
ejpam-4951	200	12	en	en	X
ejpam-4951	200	13	,	,	PUNCT
ejpam-4951	200	14	we	we	PRON
ejpam-4951	200	15	get	get	VERB
ejpam-4951	200	16	p	p	NOUN
ejpam-4951	200	17	=	=	NOUN
ejpam-4951	200	18	5	5	NUM
ejpam-4951	200	19	+	+	SYM
ejpam-4951	200	20	1	1	NUM
ejpam-4951	200	21	p	p	NOUN
ejpam-4951	200	22	or	or	CCONJ
ejpam-4951	200	23	,	,	PUNCT
ejpam-4951	200	24	p2	p2	PROPN
ejpam-4951	200	25	−	−	PROPN
ejpam-4951	201	1	5p+	5p+	NUM
ejpam-4951	201	2	1	1	NUM
ejpam-4951	201	3	=	=	SYM
ejpam-4951	201	4	0	0	NUM
ejpam-4951	202	1	∴	∴	PROPN
ejpam-4951	202	2	p	p	PROPN
ejpam-4951	202	3	=	=	PUNCT
ejpam-4951	202	4	5±	5±	NUM
ejpam-4951	202	5	√	√	ADV
ejpam-4951	202	6	29	29	NUM
ejpam-4951	202	7	2	2	NUM
ejpam-4951	202	8	hence	hence	ADV
ejpam-4951	202	9	,	,	PUNCT
ejpam-4951	202	10	the	the	DET
ejpam-4951	202	11	convergence	convergence	NOUN
ejpam-4951	202	12	order	order	NOUN
ejpam-4951	202	13	of	of	ADP
ejpam-4951	202	14	method	method	NOUN
ejpam-4951	202	15	(	(	PUNCT
ejpam-4951	202	16	23)-(25)is	23)-(25)is	NUM
ejpam-4951	202	17	5	5	NUM
ejpam-4951	202	18	+	+	NUM
ejpam-4951	202	19	√	√	NUM
ejpam-4951	202	20	29	29	NUM
ejpam-4951	202	21	2	2	NUM
ejpam-4951	202	22	≈	≈	PROPN
ejpam-4951	202	23	5.1925	5.1925	NUM
ejpam-4951	202	24	note	note	NOUN
ejpam-4951	202	25	:	:	PUNCT
ejpam-4951	202	26	the	the	DET
ejpam-4951	202	27	above	above	ADJ
ejpam-4951	202	28	theorem	theorem	NOUN
ejpam-4951	202	29	can	can	AUX
ejpam-4951	202	30	also	also	ADV
ejpam-4951	202	31	be	be	AUX
ejpam-4951	202	32	proved	prove	VERB
ejpam-4951	202	33	in	in	ADP
ejpam-4951	202	34	the	the	DET
ejpam-4951	202	35	same	same	ADJ
ejpam-4951	202	36	line	line	NOUN
ejpam-4951	202	37	of	of	ADP
ejpam-4951	202	38	alternative	alternative	ADJ
ejpam-4951	202	39	proof	proof	NOUN
ejpam-4951	202	40	of	of	ADP
ejpam-4951	202	41	theorem	theorem	NOUN
ejpam-4951	202	42	1	1	NUM
ejpam-4951	202	43	.	.	NOUN
ejpam-4951	203	1	3	3	NUM
ejpam-4951	203	2	.	.	NOUN
ejpam-4951	203	3	numerical	numerical	ADJ
ejpam-4951	203	4	examples	example	NOUN
ejpam-4951	203	5	here	here	ADV
ejpam-4951	203	6	,	,	PUNCT
ejpam-4951	203	7	we	we	PRON
ejpam-4951	203	8	will	will	AUX
ejpam-4951	203	9	be	be	AUX
ejpam-4951	203	10	discussing	discuss	VERB
ejpam-4951	203	11	some	some	DET
ejpam-4951	203	12	numerical	numerical	ADJ
ejpam-4951	203	13	examples	example	NOUN
ejpam-4951	203	14	to	to	PART
ejpam-4951	203	15	exhibit	exhibit	VERB
ejpam-4951	203	16	the	the	DET
ejpam-4951	203	17	performance	performance	NOUN
ejpam-4951	203	18	of	of	ADP
ejpam-4951	203	19	the	the	DET
ejpam-4951	203	20	newly	newly	ADV
ejpam-4951	203	21	developed	develop	VERB
ejpam-4951	203	22	methods	method	NOUN
ejpam-4951	203	23	.	.	PUNCT
ejpam-4951	204	1	we	we	PRON
ejpam-4951	204	2	will	will	AUX
ejpam-4951	204	3	compare	compare	VERB
ejpam-4951	204	4	these	these	DET
ejpam-4951	204	5	methods	method	NOUN
ejpam-4951	204	6	with	with	ADP
ejpam-4951	204	7	newton	newton	PROPN
ejpam-4951	204	8	’s	’s	PART
ejpam-4951	204	9	method	method	NOUN
ejpam-4951	204	10	(	(	PUNCT
ejpam-4951	204	11	1	1	NUM
ejpam-4951	204	12	)	)	PUNCT
ejpam-4951	204	13	,	,	PUNCT
ejpam-4951	204	14	mcdougall	mcdougall	NOUN
ejpam-4951	204	15	and	and	CCONJ
ejpam-4951	204	16	wotherspoon	wotherspoon	ADV
ejpam-4951	204	17	(	(	PUNCT
ejpam-4951	204	18	8-(9	8-(9	NOUN
ejpam-4951	204	19	)	)	PUNCT
ejpam-4951	204	20	,	,	PUNCT
ejpam-4951	204	21	midpoint	midpoint	PROPN
ejpam-4951	204	22	newton	newton	PROPN
ejpam-4951	204	23	’s	’s	PART
ejpam-4951	204	24	method	method	NOUN
ejpam-4951	204	25	(	(	PUNCT
ejpam-4951	204	26	5	5	NUM
ejpam-4951	204	27	)	)	PUNCT
ejpam-4951	204	28	,	,	PUNCT
ejpam-4951	204	29	and	and	CCONJ
ejpam-4951	204	30	double	double	PROPN
ejpam-4951	204	31	newton	newton	PROPN
ejpam-4951	204	32	’s	’s	PART
ejpam-4951	204	33	method	method	NOUN
ejpam-4951	204	34	(	(	PUNCT
ejpam-4951	204	35	2	2	NUM
ejpam-4951	204	36	)	)	PUNCT
ejpam-4951	204	37	.	.	PUNCT
ejpam-4951	205	1	for	for	ADP
ejpam-4951	205	2	the	the	DET
ejpam-4951	205	3	numerical	numerical	PROPN
ejpam-4951	205	4	computations	computations	PROPN
ejpam-4951	205	5	,	,	PUNCT
ejpam-4951	205	6	matlab	matlab	PROPN
ejpam-4951	205	7	software	software	NOUN
ejpam-4951	205	8	is	be	AUX
ejpam-4951	205	9	used	use	VERB
ejpam-4951	205	10	under	under	ADP
ejpam-4951	205	11	the	the	DET
ejpam-4951	205	12	stopping	stopping	NOUN
ejpam-4951	205	13	criteria	criterion	NOUN
ejpam-4951	205	14	|xn+1	|xn+1	NOUN
ejpam-4951	205	15	−	−	PROPN
ejpam-4951	206	1	xn|	xn|	PROPN
ejpam-4951	206	2	<	<	X
ejpam-4951	206	3	10−15	10−15	PROPN
ejpam-4951	206	4	or	or	CCONJ
ejpam-4951	206	5	|f(xn)|	|f(xn)|	ADP
ejpam-4951	206	6	<	<	X
ejpam-4951	206	7	10−15	10−15	PROPN
ejpam-4951	206	8	.	.	PUNCT
ejpam-4951	207	1	to	to	PART
ejpam-4951	207	2	determine	determine	VERB
ejpam-4951	207	3	the	the	DET
ejpam-4951	207	4	initial	initial	ADJ
ejpam-4951	207	5	approximation	approximation	NOUN
ejpam-4951	207	6	,	,	PUNCT
ejpam-4951	207	7	intermediate	intermediate	ADJ
ejpam-4951	207	8	value	value	NOUN
ejpam-4951	207	9	theorem	theorem	NOUN
ejpam-4951	207	10	or	or	CCONJ
ejpam-4951	207	11	graphical	graphical	ADJ
ejpam-4951	207	12	method	method	NOUN
ejpam-4951	207	13	can	can	AUX
ejpam-4951	207	14	be	be	AUX
ejpam-4951	207	15	used	use	VERB
ejpam-4951	207	16	.	.	PUNCT
ejpam-4951	208	1	for	for	ADP
ejpam-4951	208	2	the	the	DET
ejpam-4951	208	3	comparison	comparison	NOUN
ejpam-4951	208	4	,	,	PUNCT
ejpam-4951	208	5	the	the	DET
ejpam-4951	208	6	following	follow	VERB
ejpam-4951	208	7	function	function	NOUN
ejpam-4951	208	8	has	have	AUX
ejpam-4951	208	9	been	be	AUX
ejpam-4951	208	10	used	use	VERB
ejpam-4951	208	11	:	:	PUNCT
ejpam-4951	208	12	(	(	PUNCT
ejpam-4951	208	13	i	i	NOUN
ejpam-4951	208	14	)	)	PUNCT
ejpam-4951	208	15	f1	f1	NOUN
ejpam-4951	209	1	=	=	SYM
ejpam-4951	209	2	x3	x3	PROPN
ejpam-4951	210	1	+	+	CCONJ
ejpam-4951	210	2	4x2	4x2	NUM
ejpam-4951	210	3	−	−	NOUN
ejpam-4951	210	4	10	10	NUM
ejpam-4951	210	5	(	(	PUNCT
ejpam-4951	210	6	ii	ii	NOUN
ejpam-4951	210	7	)	)	PUNCT
ejpam-4951	210	8	f2	f2	PROPN
ejpam-4951	210	9	=	=	SYM
ejpam-4951	210	10	x6	x6	PROPN
ejpam-4951	210	11	−	−	PROPN
ejpam-4951	210	12	x−	x−	PROPN
ejpam-4951	210	13	1	1	NUM
ejpam-4951	210	14	(	(	PUNCT
ejpam-4951	210	15	iii	iii	NOUN
ejpam-4951	210	16	)	)	PUNCT
ejpam-4951	210	17	f3	f3	NOUN
ejpam-4951	210	18	=	=	SYM
ejpam-4951	210	19	sin2	sin2	PROPN
ejpam-4951	210	20	x−	x−	PROPN
ejpam-4951	211	1	x2	x2	PROPN
ejpam-4951	212	1	+	+	CCONJ
ejpam-4951	212	2	1	1	NUM
ejpam-4951	212	3	(	(	PUNCT
ejpam-4951	212	4	iv	iv	X
ejpam-4951	212	5	)	)	PUNCT
ejpam-4951	212	6	f4	f4	PROPN
ejpam-4951	212	7	=	=	SYM
ejpam-4951	212	8	xex	xex	PROPN
ejpam-4951	212	9	2	2	NUM
ejpam-4951	212	10	−	−	PROPN
ejpam-4951	212	11	sin2	sin2	NOUN
ejpam-4951	212	12	x+	x+	PUNCT
ejpam-4951	212	13	3	3	NUM
ejpam-4951	212	14	cosx+	cosx+	NOUN
ejpam-4951	212	15	5	5	NUM
ejpam-4951	212	16	(	(	PUNCT
ejpam-4951	212	17	v	v	NOUN
ejpam-4951	212	18	)	)	PUNCT
ejpam-4951	212	19	f5	f5	PROPN
ejpam-4951	212	20	=	=	SYM
ejpam-4951	212	21	cosx−	cosx−	PROPN
ejpam-4951	212	22	xex	xex	PROPN
ejpam-4951	213	1	+	+	CCONJ
ejpam-4951	213	2	x2	x2	PROPN
ejpam-4951	213	3	(	(	PUNCT
ejpam-4951	213	4	vi	vi	NOUN
ejpam-4951	213	5	)	)	PUNCT
ejpam-4951	213	6	f6	f6	NOUN
ejpam-4951	213	7	=	=	PUNCT
ejpam-4951	213	8	ex	ex	X
ejpam-4951	213	9	2	2	NUM
ejpam-4951	213	10	+	+	NOUN
ejpam-4951	213	11	7x−30	7x−30	NUM
ejpam-4951	213	12	−	−	NOUN
ejpam-4951	213	13	1	1	NUM
ejpam-4951	213	14	(	(	PUNCT
ejpam-4951	213	15	vii	vii	PROPN
ejpam-4951	213	16	)	)	PUNCT
ejpam-4951	213	17	f7	f7	PROPN
ejpam-4951	214	1	=	=	PUNCT
ejpam-4951	214	2	ex	ex	X
ejpam-4951	214	3	sinx+	sinx+	PROPN
ejpam-4951	214	4	ln(x2	ln(x2	NOUN
ejpam-4951	214	5	+	+	CCONJ
ejpam-4951	214	6	1	1	NUM
ejpam-4951	214	7	)	)	PUNCT
ejpam-4951	214	8	(	(	PUNCT
ejpam-4951	214	9	viii	viii	NOUN
ejpam-4951	214	10	)	)	PUNCT
ejpam-4951	214	11	f8	f8	PROPN
ejpam-4951	214	12	=	=	SYM
ejpam-4951	214	13	(	(	PUNCT
ejpam-4951	214	14	x−	x−	PROPN
ejpam-4951	214	15	2)23	2)23	NUM
ejpam-4951	214	16	−	−	NOUN
ejpam-4951	214	17	1	1	NUM
ejpam-4951	214	18	where	where	SCONJ
ejpam-4951	214	19	,	,	PUNCT
ejpam-4951	214	20	nm	nm	PROPN
ejpam-4951	214	21	,	,	PUNCT
ejpam-4951	214	22	mwm	mwm	NOUN
ejpam-4951	214	23	,	,	PUNCT
ejpam-4951	214	24	mnm	mnm	PROPN
ejpam-4951	214	25	,	,	PUNCT
ejpam-4951	214	26	dnm	dnm	PROPN
ejpam-4951	214	27	denote	denote	PROPN
ejpam-4951	214	28	newton	newton	PROPN
ejpam-4951	214	29	’s	’s	PART
ejpam-4951	214	30	method	method	NOUN
ejpam-4951	214	31	,	,	PUNCT
ejpam-4951	214	32	mcdougall	mcdougall	NOUN
ejpam-4951	214	33	and	and	CCONJ
ejpam-4951	214	34	wotherspoon	wotherspoon	NOUN
ejpam-4951	214	35	method	method	NOUN
ejpam-4951	214	36	,	,	PUNCT
ejpam-4951	214	37	mid	mid	ADJ
ejpam-4951	214	38	-	-	NOUN
ejpam-4951	214	39	point	point	ADJ
ejpam-4951	214	40	newton	newton	PROPN
ejpam-4951	214	41	’s	’s	PART
ejpam-4951	214	42	method	method	NOUN
ejpam-4951	214	43	and	and	CCONJ
ejpam-4951	214	44	double	double	PROPN
ejpam-4951	214	45	newton	newton	PROPN
ejpam-4951	214	46	’s	’s	PART
ejpam-4951	214	47	method	method	NOUN
ejpam-4951	214	48	respectively	respectively	ADV
ejpam-4951	214	49	.	.	PUNCT
ejpam-4951	215	1	b.	b.	PROPN
ejpam-4951	215	2	sapkota	sapkota	PROPN
ejpam-4951	215	3	,	,	PUNCT
ejpam-4951	215	4	j.	j.	PROPN
ejpam-4951	215	5	jnawali	jnawali	PROPN
ejpam-4951	215	6	/	/	SYM
ejpam-4951	215	7	eur	eur	PROPN
ejpam-4951	215	8	.	.	PUNCT
ejpam-4951	216	1	j.	j.	PROPN
ejpam-4951	216	2	pure	pure	PROPN
ejpam-4951	216	3	appl	appl	PROPN
ejpam-4951	216	4	.	.	PROPN
ejpam-4951	216	5	math	math	PROPN
ejpam-4951	216	6	,	,	PUNCT
ejpam-4951	216	7	16	16	NUM
ejpam-4951	216	8	(	(	PUNCT
ejpam-4951	216	9	4	4	NUM
ejpam-4951	216	10	)	)	PUNCT
ejpam-4951	216	11	(	(	PUNCT
ejpam-4951	216	12	2023	2023	NUM
ejpam-4951	216	13	)	)	PUNCT
ejpam-4951	216	14	,	,	PUNCT
ejpam-4951	216	15	2419	2419	NUM
ejpam-4951	216	16	-	-	SYM
ejpam-4951	216	17	2430	2430	NUM
ejpam-4951	216	18	2428	2428	NUM
ejpam-4951	216	19	table	table	NOUN
ejpam-4951	216	20	2	2	NUM
ejpam-4951	216	21	:	:	PUNCT
ejpam-4951	216	22	comparison	comparison	NOUN
ejpam-4951	216	23	of	of	ADP
ejpam-4951	216	24	various	various	ADJ
ejpam-4951	216	25	methods	method	NOUN
ejpam-4951	216	26	with	with	ADP
ejpam-4951	216	27	distinct	distinct	ADJ
ejpam-4951	216	28	initial	initial	ADJ
ejpam-4951	216	29	approximation	approximation	NOUN
ejpam-4951	216	30	x0	x0	PROPN
ejpam-4951	216	31	.	.	PUNCT
ejpam-4951	217	1	function	function	VERB
ejpam-4951	217	2	x0	x0	PROPN
ejpam-4951	217	3	number	number	NOUN
ejpam-4951	217	4	of	of	ADP
ejpam-4951	217	5	iterations	iteration	NOUN
ejpam-4951	217	6	root	root	VERB
ejpam-4951	217	7	nm	nm	PRON
ejpam-4951	217	8	mwm	mwm	NOUN
ejpam-4951	217	9	mnm	mnm	PROPN
ejpam-4951	217	10	dnm	dnm	PROPN
ejpam-4951	217	11	method	method	NOUN
ejpam-4951	217	12	method	method	NOUN
ejpam-4951	217	13	(	(	PUNCT
ejpam-4951	217	14	8)-(9	8)-(9	NUM
ejpam-4951	217	15	)	)	PUNCT
ejpam-4951	217	16	(	(	PUNCT
ejpam-4951	217	17	23)-(25	23)-(25	NUM
ejpam-4951	217	18	)	)	PUNCT
ejpam-4951	217	19	3	3	NUM
ejpam-4951	217	20	6	6	NUM
ejpam-4951	217	21	5	5	NUM
ejpam-4951	217	22	4	4	NUM
ejpam-4951	217	23	3	3	NUM
ejpam-4951	217	24	3	3	NUM
ejpam-4951	217	25	3	3	NUM
ejpam-4951	217	26	1.365230013414097	1.365230013414097	NUM
ejpam-4951	217	27	f1	f1	NOUN
ejpam-4951	217	28	1	1	NUM
ejpam-4951	217	29	5	5	NUM
ejpam-4951	217	30	4	4	NUM
ejpam-4951	217	31	3	3	NUM
ejpam-4951	217	32	3	3	NUM
ejpam-4951	217	33	3	3	NUM
ejpam-4951	217	34	3	3	NUM
ejpam-4951	217	35	-1	-1	SYM
ejpam-4951	217	36	24	24	NUM
ejpam-4951	217	37	32	32	NUM
ejpam-4951	217	38	9	9	NUM
ejpam-4951	217	39	12	12	NUM
ejpam-4951	217	40	5	5	NUM
ejpam-4951	217	41	7	7	NUM
ejpam-4951	217	42	3	3	NUM
ejpam-4951	217	43	10	10	NUM
ejpam-4951	217	44	9	9	NUM
ejpam-4951	217	45	7	7	NUM
ejpam-4951	217	46	5	5	NUM
ejpam-4951	217	47	5	5	NUM
ejpam-4951	217	48	5	5	NUM
ejpam-4951	217	49	1.34724138401519	1.34724138401519	NUM
ejpam-4951	217	50	f2	f2	ADJ
ejpam-4951	217	51	1	1	NUM
ejpam-4951	217	52	6	6	NUM
ejpam-4951	217	53	5	5	NUM
ejpam-4951	217	54	4	4	NUM
ejpam-4951	217	55	3	3	NUM
ejpam-4951	217	56	3	3	NUM
ejpam-4951	217	57	3	3	NUM
ejpam-4951	217	58	0	0	NUM
ejpam-4951	217	59	7	7	NUM
ejpam-4951	217	60	7	7	NUM
ejpam-4951	217	61	4	4	NUM
ejpam-4951	217	62	4	4	NUM
ejpam-4951	217	63	4	4	NUM
ejpam-4951	217	64	3	3	NUM
ejpam-4951	217	65	-0.778089598678601	-0.778089598678601	ADP
ejpam-4951	217	66	10	10	NUM
ejpam-4951	217	67	8	8	NUM
ejpam-4951	217	68	7	7	NUM
ejpam-4951	217	69	5	5	NUM
ejpam-4951	217	70	4	4	NUM
ejpam-4951	217	71	4	4	NUM
ejpam-4951	217	72	4	4	NUM
ejpam-4951	217	73	1.404491648215341	1.404491648215341	NUM
ejpam-4951	217	74	f3	f3	NOUN
ejpam-4951	217	75	4	4	NUM
ejpam-4951	217	76	6	6	NUM
ejpam-4951	217	77	5	5	NUM
ejpam-4951	217	78	4	4	NUM
ejpam-4951	217	79	3	3	NUM
ejpam-4951	217	80	3	3	NUM
ejpam-4951	217	81	3	3	NUM
ejpam-4951	217	82	-3	-3	SYM
ejpam-4951	217	83	6	6	NUM
ejpam-4951	217	84	5	5	NUM
ejpam-4951	217	85	4	4	NUM
ejpam-4951	217	86	3	3	NUM
ejpam-4951	217	87	3	3	NUM
ejpam-4951	217	88	3	3	NUM
ejpam-4951	217	89	-1.404491648215341	-1.404491648215341	NOUN
ejpam-4951	217	90	1	1	NUM
ejpam-4951	217	91	8	8	NUM
ejpam-4951	217	92	7	7	NUM
ejpam-4951	217	93	div	div	NOUN
ejpam-4951	217	94	5	5	NUM
ejpam-4951	217	95	11	11	NUM
ejpam-4951	217	96	80	80	NUM
ejpam-4951	217	97	-1.207647827130919	-1.207647827130919	NOUN
ejpam-4951	217	98	f4	f4	ADP
ejpam-4951	217	99	-2	-2	NOUN
ejpam-4951	217	100	9	9	NUM
ejpam-4951	217	101	8	8	NUM
ejpam-4951	217	102	6	6	NUM
ejpam-4951	217	103	5	5	NUM
ejpam-4951	217	104	5	5	NUM
ejpam-4951	217	105	5	5	NUM
ejpam-4951	217	106	-1.5	-1.5	SYM
ejpam-4951	217	107	7	7	NUM
ejpam-4951	217	108	6	6	NUM
ejpam-4951	217	109	5	5	NUM
ejpam-4951	217	110	4	4	NUM
ejpam-4951	217	111	4	4	NUM
ejpam-4951	217	112	4	4	NUM
ejpam-4951	217	113	-1.5	-1.5	SYM
ejpam-4951	217	114	7	7	NUM
ejpam-4951	217	115	5	5	NUM
ejpam-4951	217	116	5	5	NUM
ejpam-4951	217	117	4	4	NUM
ejpam-4951	217	118	4	4	NUM
ejpam-4951	217	119	4	4	NUM
ejpam-4951	217	120	0.639154096332008	0.639154096332008	NUM
ejpam-4951	217	121	f5	f5	NOUN
ejpam-4951	217	122	5	5	NUM
ejpam-4951	217	123	11	11	NUM
ejpam-4951	217	124	9	9	NUM
ejpam-4951	217	125	7	7	NUM
ejpam-4951	217	126	6	6	NUM
ejpam-4951	217	127	6	6	NUM
ejpam-4951	217	128	5	5	NUM
ejpam-4951	217	129	10	10	NUM
ejpam-4951	217	130	17	17	NUM
ejpam-4951	217	131	14	14	NUM
ejpam-4951	217	132	10	10	NUM
ejpam-4951	217	133	9	9	NUM
ejpam-4951	217	134	8	8	NUM
ejpam-4951	217	135	7	7	NUM
ejpam-4951	217	136	6	6	NUM
ejpam-4951	217	137	53	53	NUM
ejpam-4951	217	138	46	46	NUM
ejpam-4951	217	139	34	34	NUM
ejpam-4951	217	140	27	27	NUM
ejpam-4951	217	141	26	26	NUM
ejpam-4951	217	142	22	22	NUM
ejpam-4951	217	143	3	3	NUM
ejpam-4951	217	144	f6	f6	PROPN
ejpam-4951	217	145	5	5	NUM
ejpam-4951	217	146	35	35	NUM
ejpam-4951	217	147	29	29	NUM
ejpam-4951	217	148	22	22	NUM
ejpam-4951	217	149	18	18	NUM
ejpam-4951	217	150	17	17	NUM
ejpam-4951	217	151	15	15	NUM
ejpam-4951	217	152	4	4	NUM
ejpam-4951	217	153	19	19	NUM
ejpam-4951	217	154	16	16	NUM
ejpam-4951	217	155	12	12	NUM
ejpam-4951	217	156	10	10	NUM
ejpam-4951	217	157	10	10	NUM
ejpam-4951	217	158	8	8	NUM
ejpam-4951	217	159	0.5	0.5	NUM
ejpam-4951	217	160	6	6	NUM
ejpam-4951	217	161	5	5	NUM
ejpam-4951	217	162	4	4	NUM
ejpam-4951	217	163	3	3	NUM
ejpam-4951	217	164	3	3	NUM
ejpam-4951	217	165	3	3	NUM
ejpam-4951	217	166	0	0	NUM
ejpam-4951	217	167	f7	f7	PROPN
ejpam-4951	217	168	1	1	NUM
ejpam-4951	217	169	7	7	NUM
ejpam-4951	217	170	6	6	NUM
ejpam-4951	217	171	5	5	NUM
ejpam-4951	217	172	4	4	NUM
ejpam-4951	217	173	4	4	NUM
ejpam-4951	217	174	3	3	NUM
ejpam-4951	217	175	2	2	NUM
ejpam-4951	217	176	6	6	NUM
ejpam-4951	217	177	6	6	NUM
ejpam-4951	217	178	5	5	NUM
ejpam-4951	217	179	4	4	NUM
ejpam-4951	217	180	3	3	NUM
ejpam-4951	217	181	3	3	NUM
ejpam-4951	217	182	3.5	3.5	NUM
ejpam-4951	217	183	14	14	NUM
ejpam-4951	217	184	12	12	NUM
ejpam-4951	217	185	9	9	NUM
ejpam-4951	217	186	7	7	NUM
ejpam-4951	217	187	7	7	NUM
ejpam-4951	217	188	6	6	NUM
ejpam-4951	217	189	3	3	NUM
ejpam-4951	217	190	f8	f8	PROPN
ejpam-4951	217	191	4	4	NUM
ejpam-4951	217	192	21	21	NUM
ejpam-4951	217	193	17	17	NUM
ejpam-4951	217	194	13	13	NUM
ejpam-4951	217	195	11	11	NUM
ejpam-4951	217	196	10	10	NUM
ejpam-4951	217	197	9	9	NUM
ejpam-4951	217	198	4.5	4.5	NUM
ejpam-4951	217	199	26	26	NUM
ejpam-4951	217	200	21	21	NUM
ejpam-4951	217	201	16	16	NUM
ejpam-4951	217	202	13	13	NUM
ejpam-4951	217	203	13	13	NUM
ejpam-4951	217	204	11	11	NUM
ejpam-4951	217	205	4	4	NUM
ejpam-4951	217	206	.	.	PUNCT
ejpam-4951	217	207	conclusion	conclusion	NOUN
ejpam-4951	217	208	here	here	ADV
ejpam-4951	217	209	,	,	PUNCT
ejpam-4951	217	210	we	we	PRON
ejpam-4951	217	211	explored	explore	VERB
ejpam-4951	217	212	two	two	NUM
ejpam-4951	217	213	modified	modified	ADJ
ejpam-4951	217	214	double	double	PROPN
ejpam-4951	217	215	newton	newton	PROPN
ejpam-4951	217	216	’s	’s	PART
ejpam-4951	217	217	type	type	NOUN
ejpam-4951	217	218	iterative	iterative	NOUN
ejpam-4951	217	219	methods	method	NOUN
ejpam-4951	217	220	(	(	PUNCT
ejpam-4951	217	221	8)-(9	8)-(9	NOUN
ejpam-4951	217	222	)	)	PUNCT
ejpam-4951	217	223	and	and	CCONJ
ejpam-4951	217	224	(	(	PUNCT
ejpam-4951	217	225	23)-(25	23)-(25	NUM
ejpam-4951	217	226	)	)	PUNCT
ejpam-4951	217	227	of	of	ADP
ejpam-4951	217	228	convergence	convergence	NOUN
ejpam-4951	217	229	of	of	ADP
ejpam-4951	217	230	order	order	NOUN
ejpam-4951	217	231	4	4	NUM
ejpam-4951	217	232	and	and	CCONJ
ejpam-4951	217	233	modified	modify	VERB
ejpam-4951	217	234	midpoint	midpoint	PROPN
ejpam-4951	217	235	newton	newton	PROPN
ejpam-4951	217	236	’s	’s	PART
ejpam-4951	217	237	methods	method	NOUN
ejpam-4951	217	238	of	of	ADP
ejpam-4951	217	239	convergence	convergence	NOUN
ejpam-4951	217	240	order	order	NOUN
ejpam-4951	217	241	3	3	NUM
ejpam-4951	217	242	as	as	ADP
ejpam-4951	217	243	iterative	iterative	PROPN
ejpam-4951	217	244	newton	newton	PROPN
ejpam-4951	217	245	’s	’s	PART
ejpam-4951	217	246	type	type	NOUN
ejpam-4951	217	247	methods	method	NOUN
ejpam-4951	217	248	,	,	PUNCT
ejpam-4951	217	249	respectively	respectively	ADV
ejpam-4951	217	250	.	.	PUNCT
ejpam-4951	218	1	in	in	ADP
ejpam-4951	218	2	theorem-1	theorem-1	PROPN
ejpam-4951	218	3	,	,	PUNCT
ejpam-4951	218	4	we	we	PRON
ejpam-4951	218	5	established	establish	VERB
ejpam-4951	218	6	that	that	SCONJ
ejpam-4951	218	7	the	the	DET
ejpam-4951	218	8	technique	technique	NOUN
ejpam-4951	218	9	(	(	PUNCT
ejpam-4951	218	10	8)-(9	8)-(9	NOUN
ejpam-4951	218	11	)	)	PUNCT
ejpam-4951	218	12	has	have	VERB
ejpam-4951	218	13	a	a	DET
ejpam-4951	218	14	convergence	convergence	NOUN
ejpam-4951	218	15	order	order	NOUN
ejpam-4951	218	16	of	of	ADP
ejpam-4951	218	17	4.45	4.45	NUM
ejpam-4951	218	18	when	when	SCONJ
ejpam-4951	218	19	evaluating	evaluate	VERB
ejpam-4951	218	20	the	the	DET
ejpam-4951	218	21	same	same	ADJ
ejpam-4951	218	22	number	number	NOUN
ejpam-4951	218	23	of	of	ADP
ejpam-4951	218	24	functions	function	NOUN
ejpam-4951	218	25	per	per	ADP
ejpam-4951	218	26	iteration	iteration	NOUN
ejpam-4951	218	27	.	.	PUNCT
ejpam-4951	219	1	as	as	ADP
ejpam-4951	219	2	a	a	DET
ejpam-4951	219	3	result	result	NOUN
ejpam-4951	219	4	,	,	PUNCT
ejpam-4951	219	5	this	this	DET
ejpam-4951	219	6	newly	newly	ADV
ejpam-4951	219	7	discovered	discover	VERB
ejpam-4951	219	8	method	method	NOUN
ejpam-4951	219	9	’s	’s	PART
ejpam-4951	219	10	convergence	convergence	NOUN
ejpam-4951	219	11	order	order	NOUN
ejpam-4951	219	12	and	and	CCONJ
ejpam-4951	219	13	efficiency	efficiency	NOUN
ejpam-4951	219	14	index	index	NOUN
ejpam-4951	219	15	are	be	AUX
ejpam-4951	219	16	higher	high	ADJ
ejpam-4951	219	17	than	than	ADP
ejpam-4951	219	18	those	those	PRON
ejpam-4951	219	19	of	of	ADP
ejpam-4951	219	20	the	the	DET
ejpam-4951	219	21	double	double	PROPN
ejpam-4951	219	22	newton	newton	PROPN
ejpam-4951	219	23	’s	’s	PART
ejpam-4951	219	24	approach	approach	NOUN
ejpam-4951	219	25	.	.	PUNCT
ejpam-4951	220	1	additionally	additionally	ADV
ejpam-4951	220	2	,	,	PUNCT
ejpam-4951	220	3	the	the	DET
ejpam-4951	220	4	modified	modify	VERB
ejpam-4951	220	5	method	method	NOUN
ejpam-4951	220	6	’s	’s	PART
ejpam-4951	220	7	order	order	NOUN
ejpam-4951	220	8	of	of	ADP
ejpam-4951	220	9	convergence	convergence	NOUN
ejpam-4951	220	10	(	(	PUNCT
ejpam-4951	220	11	23)-(25	23)-(25	NUM
ejpam-4951	220	12	)	)	PUNCT
ejpam-4951	220	13	is	be	AUX
ejpam-4951	220	14	greater	great	ADJ
ejpam-4951	220	15	than	than	ADP
ejpam-4951	220	16	newton	newton	PROPN
ejpam-4951	220	17	’s	’s	PART
ejpam-4951	220	18	method	method	PROPN
ejpam-4951	220	19	’s	’s	PART
ejpam-4951	220	20	mid	mid	NOUN
ejpam-4951	220	21	-	-	NOUN
ejpam-4951	220	22	point	point	NOUN
ejpam-4951	220	23	;	;	PUNCT
ejpam-4951	220	24	however	however	ADV
ejpam-4951	220	25	,	,	PUNCT
ejpam-4951	220	26	after	after	ADP
ejpam-4951	220	27	the	the	DET
ejpam-4951	220	28	initial	initial	ADJ
ejpam-4951	220	29	iteration	iteration	NOUN
ejpam-4951	220	30	,	,	PUNCT
ejpam-4951	220	31	we	we	PRON
ejpam-4951	220	32	have	have	VERB
ejpam-4951	220	33	to	to	PART
ejpam-4951	220	34	evaluate	evaluate	VERB
ejpam-4951	220	35	two	two	NUM
ejpam-4951	220	36	more	more	ADJ
ejpam-4951	220	37	functions	function	NOUN
ejpam-4951	220	38	.	.	PUNCT
ejpam-4951	221	1	the	the	DET
ejpam-4951	221	2	computational	computational	ADJ
ejpam-4951	221	3	result	result	NOUN
ejpam-4951	221	4	shown	show	VERB
ejpam-4951	221	5	in	in	ADP
ejpam-4951	221	6	table-2	table-2	NUM
ejpam-4951	221	7	compares	compare	VERB
ejpam-4951	221	8	the	the	DET
ejpam-4951	221	9	practical	practical	ADJ
ejpam-4951	221	10	performance	performance	NOUN
ejpam-4951	221	11	of	of	ADP
ejpam-4951	221	12	the	the	DET
ejpam-4951	221	13	recently	recently	ADV
ejpam-4951	221	14	investigated	investigate	VERB
ejpam-4951	221	15	approaches	approach	NOUN
ejpam-4951	221	16	.	.	PUNCT
ejpam-4951	222	1	references	reference	NOUN
ejpam-4951	222	2	2429	2429	NUM
ejpam-4951	222	3	references	reference	NOUN
ejpam-4951	222	4	[	[	X
ejpam-4951	222	5	1	1	NUM
ejpam-4951	222	6	]	]	PUNCT
ejpam-4951	222	7	h	h	NOUN
ejpam-4951	222	8	anton	anton	NOUN
ejpam-4951	222	9	and	and	CCONJ
ejpam-4951	222	10	c	c	PROPN
ejpam-4951	222	11	dan	dan	PROPN
ejpam-4951	222	12	rorres	rorre	VERB
ejpam-4951	222	13	.	.	PUNCT
ejpam-4951	223	1	elementary	elementary	ADJ
ejpam-4951	223	2	linear	linear	PROPN
ejpam-4951	223	3	algebra	algebra	PROPN
ejpam-4951	223	4	.	.	PUNCT
ejpam-4951	224	1	john	john	PROPN
ejpam-4951	224	2	wiley	wiley	PROPN
ejpam-4951	224	3	and	and	CCONJ
ejpam-4951	224	4	sons	son	NOUN
ejpam-4951	224	5	,	,	PUNCT
ejpam-4951	224	6	hoboken	hoboken	PROPN
ejpam-4951	224	7	,	,	PUNCT
ejpam-4951	224	8	usa	usa	PROPN
ejpam-4951	224	9	,	,	PUNCT
ejpam-4951	224	10	2013	2013	NUM
ejpam-4951	224	11	.	.	PUNCT
ejpam-4951	225	1	[	[	X
ejpam-4951	225	2	2	2	NUM
ejpam-4951	225	3	]	]	SYM
ejpam-4951	225	4	r	r	NOUN
ejpam-4951	225	5	l	l	NOUN
ejpam-4951	225	6	burdan	burdan	NOUN
ejpam-4951	225	7	and	and	CCONJ
ejpam-4951	225	8	j	j	PROPN
ejpam-4951	225	9	d	d	PROPN
ejpam-4951	225	10	faires	faire	NOUN
ejpam-4951	225	11	.	.	PUNCT
ejpam-4951	226	1	numerical	numerical	ADJ
ejpam-4951	226	2	analysis	analysis	NOUN
ejpam-4951	226	3	.	.	PUNCT
ejpam-4951	227	1	cenage	cenage	ADJ
ejpam-4951	227	2	learning	learning	PROPN
ejpam-4951	227	3	,	,	PUNCT
ejpam-4951	227	4	usa	usa	PROPN
ejpam-4951	227	5	,	,	PUNCT
ejpam-4951	227	6	2010	2010	NUM
ejpam-4951	227	7	.	.	PUNCT
ejpam-4951	228	1	[	[	X
ejpam-4951	228	2	3	3	X
ejpam-4951	228	3	]	]	X
ejpam-4951	228	4	m	m	VERB
ejpam-4951	228	5	dehghan	dehghan	ADJ
ejpam-4951	228	6	and	and	CCONJ
ejpam-4951	228	7	m	m	NOUN
ejpam-4951	228	8	hajarian	hajarian	PROPN
ejpam-4951	228	9	.	.	PUNCT
ejpam-4951	229	1	new	new	ADJ
ejpam-4951	229	2	iterative	iterative	NOUN
ejpam-4951	229	3	method	method	NOUN
ejpam-4951	229	4	for	for	ADP
ejpam-4951	229	5	solving	solve	VERB
ejpam-4951	229	6	non	non	ADJ
ejpam-4951	229	7	-	-	ADJ
ejpam-4951	229	8	linear	linear	ADJ
ejpam-4951	229	9	equations	equation	NOUN
ejpam-4951	229	10	with	with	ADP
ejpam-4951	229	11	fourth	fourth	ADJ
ejpam-4951	229	12	-	-	PUNCT
ejpam-4951	229	13	order	order	NOUN
ejpam-4951	229	14	convergence	convergence	NOUN
ejpam-4951	229	15	.	.	PUNCT
ejpam-4951	230	1	international	international	ADJ
ejpam-4951	230	2	journal	journal	PROPN
ejpam-4951	230	3	of	of	ADP
ejpam-4951	230	4	computer	computer	NOUN
ejpam-4951	230	5	mathematics	mathematic	NOUN
ejpam-4951	230	6	,	,	PUNCT
ejpam-4951	230	7	87:834–839	87:834–839	PROPN
ejpam-4951	230	8	,	,	PUNCT
ejpam-4951	230	9	2010	2010	NUM
ejpam-4951	230	10	.	.	PUNCT
ejpam-4951	231	1	[	[	X
ejpam-4951	231	2	4	4	X
ejpam-4951	231	3	]	]	SYM
ejpam-4951	231	4	v	v	ADP
ejpam-4951	231	5	hasanovand	hasanovand	NOUN
ejpam-4951	231	6	,	,	PUNCT
ejpam-4951	231	7	i	i	PRON
ejpam-4951	231	8	ivanov	ivanov	VERB
ejpam-4951	231	9	,	,	PUNCT
ejpam-4951	231	10	and	and	CCONJ
ejpam-4951	231	11	g	g	PROPN
ejpam-4951	231	12	nedjibov	nedjibov	PROPN
ejpam-4951	231	13	.	.	PUNCT
ejpam-4951	232	1	a	a	DET
ejpam-4951	232	2	new	new	ADJ
ejpam-4951	232	3	modification	modification	NOUN
ejpam-4951	232	4	of	of	ADP
ejpam-4951	232	5	newton	newton	PROPN
ejpam-4951	232	6	’s	’s	PART
ejpam-4951	232	7	method	method	NOUN
ejpam-4951	232	8	.	.	PUNCT
ejpam-4951	233	1	application	application	NOUN
ejpam-4951	233	2	of	of	ADP
ejpam-4951	233	3	mathematics	mathematic	NOUN
ejpam-4951	233	4	in	in	ADP
ejpam-4951	233	5	engineering	engineering	NOUN
ejpam-4951	233	6	.	.	PUNCT
ejpam-4951	233	7	,	,	PUNCT
ejpam-4951	233	8	27(3):278–286	27(3):278–286	PROPN
ejpam-4951	233	9	.	.	PROPN
ejpam-4951	233	10	,	,	PUNCT
ejpam-4951	233	11	2002	2002	NUM
ejpam-4951	233	12	.	.	PUNCT
ejpam-4951	234	1	[	[	X
ejpam-4951	234	2	5	5	NUM
ejpam-4951	234	3	]	]	PUNCT
ejpam-4951	234	4	h	h	NOUN
ejpam-4951	234	5	h	h	NOUN
ejpam-4951	234	6	h	h	PROPN
ejpam-4951	234	7	homeier	homeier	PROPN
ejpam-4951	234	8	.	.	PUNCT
ejpam-4951	235	1	on	on	ADP
ejpam-4951	235	2	newton	newton	PROPN
ejpam-4951	235	3	’s	’s	PART
ejpam-4951	235	4	type	type	NOUN
ejpam-4951	235	5	methods	method	NOUN
ejpam-4951	235	6	with	with	ADP
ejpam-4951	235	7	cubic	cubic	ADJ
ejpam-4951	235	8	convergence	convergence	NOUN
ejpam-4951	235	9	.	.	PUNCT
ejpam-4951	236	1	j.	j.	PROPN
ejpam-4951	236	2	comput	comput	PROPN
ejpam-4951	236	3	.	.	PUNCT
ejpam-4951	237	1	appl	appl	PROPN
ejpam-4951	237	2	.	.	PROPN
ejpam-4951	237	3	math	math	PROPN
ejpam-4951	237	4	.	.	PUNCT
ejpam-4951	237	5	,	,	PUNCT
ejpam-4951	237	6	176:425–432	176:425–432	NUM
ejpam-4951	237	7	,	,	PUNCT
ejpam-4951	237	8	2005	2005	NUM
ejpam-4951	237	9	.	.	PUNCT
ejpam-4951	238	1	[	[	X
ejpam-4951	238	2	6	6	NUM
ejpam-4951	238	3	]	]	X
ejpam-4951	238	4	d	d	X
ejpam-4951	238	5	jain	jain	PROPN
ejpam-4951	238	6	.	.	PUNCT
ejpam-4951	239	1	families	family	NOUN
ejpam-4951	239	2	of	of	ADP
ejpam-4951	239	3	newton	newton	PROPN
ejpam-4951	239	4	-	-	PUNCT
ejpam-4951	239	5	like	like	ADJ
ejpam-4951	239	6	methods	method	NOUN
ejpam-4951	239	7	with	with	ADP
ejpam-4951	239	8	fourth	fourth	ADJ
ejpam-4951	239	9	-	-	PUNCT
ejpam-4951	239	10	order	order	NOUN
ejpam-4951	239	11	convergence	convergence	NOUN
ejpam-4951	239	12	.	.	PUNCT
ejpam-4951	240	1	int	int	NOUN
ejpam-4951	240	2	.	.	PUNCT
ejpam-4951	241	1	j.	j.	PROPN
ejpam-4951	241	2	comp	comp	PROPN
ejpam-4951	241	3	.	.	PUNCT
ejpam-4951	242	1	math	math	PROPN
ejpam-4951	242	2	.	.	PUNCT
ejpam-4951	242	3	,	,	PUNCT
ejpam-4951	242	4	90:1072–1082	90:1072–1082	PROPN
ejpam-4951	242	5	,	,	PUNCT
ejpam-4951	242	6	2013	2013	NUM
ejpam-4951	242	7	.	.	PUNCT
ejpam-4951	243	1	[	[	X
ejpam-4951	243	2	7	7	X
ejpam-4951	243	3	]	]	X
ejpam-4951	243	4	p	p	X
ejpam-4951	243	5	jain	jain	NOUN
ejpam-4951	243	6	,	,	PUNCT
ejpam-4951	243	7	c	c	PROPN
ejpam-4951	243	8	r	r	NOUN
ejpam-4951	243	9	bhatta	bhatta	NOUN
ejpam-4951	243	10	,	,	PUNCT
ejpam-4951	243	11	and	and	CCONJ
ejpam-4951	243	12	j	j	PROPN
ejpam-4951	243	13	jnawali	jnawali	PROPN
ejpam-4951	243	14	.	.	PUNCT
ejpam-4951	244	1	modified	modified	PROPN
ejpam-4951	244	2	newton	newton	PROPN
ejpam-4951	244	3	-	-	PUNCT
ejpam-4951	244	4	type	type	NOUN
ejpam-4951	244	5	methods	method	NOUN
ejpam-4951	244	6	with	with	ADP
ejpam-4951	244	7	higher	high	ADJ
ejpam-4951	244	8	order	order	NOUN
ejpam-4951	244	9	of	of	ADP
ejpam-4951	244	10	convergence	convergence	NOUN
ejpam-4951	244	11	.	.	PUNCT
ejpam-4951	245	1	jordan	jordan	PROPN
ejpam-4951	245	2	j.	j.	PROPN
ejpam-4951	245	3	math	math	PROPN
ejpam-4951	245	4	.	.	PUNCT
ejpam-4951	246	1	stat	stat	PROPN
ejpam-4951	246	2	.	.	PUNCT
ejpam-4951	246	3	,	,	PUNCT
ejpam-4951	246	4	8:327–341	8:327–341	NUM
ejpam-4951	246	5	,	,	PUNCT
ejpam-4951	246	6	2015	2015	NUM
ejpam-4951	246	7	.	.	PUNCT
ejpam-4951	247	1	[	[	X
ejpam-4951	247	2	8	8	X
ejpam-4951	247	3	]	]	X
ejpam-4951	247	4	p	p	X
ejpam-4951	247	5	jain	jain	NOUN
ejpam-4951	247	6	,	,	PUNCT
ejpam-4951	247	7	c	c	PROPN
ejpam-4951	247	8	r	r	NOUN
ejpam-4951	247	9	bhatta	bhatta	NOUN
ejpam-4951	247	10	,	,	PUNCT
ejpam-4951	247	11	and	and	CCONJ
ejpam-4951	247	12	j	j	PROPN
ejpam-4951	247	13	jnawali	jnawali	PROPN
ejpam-4951	247	14	.	.	PUNCT
ejpam-4951	248	1	newton	newton	PROPN
ejpam-4951	248	2	type	type	NOUN
ejpam-4951	248	3	iterative	iterative	NOUN
ejpam-4951	248	4	methods	method	NOUN
ejpam-4951	248	5	with	with	ADP
ejpam-4951	248	6	higher	high	ADJ
ejpam-4951	248	7	order	order	NOUN
ejpam-4951	248	8	of	of	ADP
ejpam-4951	248	9	convergence	convergence	NOUN
ejpam-4951	248	10	.	.	PUNCT
ejpam-4951	249	1	j.	j.	PROPN
ejpam-4951	249	2	numer	numer	PROPN
ejpam-4951	249	3	.	.	PUNCT
ejpam-4951	250	1	anal	anal	PROPN
ejpam-4951	250	2	.	.	PUNCT
ejpam-4951	251	1	approx	approx	PROPN
ejpam-4951	251	2	.	.	PUNCT
ejpam-4951	252	1	theory	theory	NOUN
ejpam-4951	252	2	.	.	PUNCT
ejpam-4951	252	3	,	,	PUNCT
ejpam-4951	252	4	45:14–26	45:14–26	PROPN
ejpam-4951	252	5	,	,	PUNCT
ejpam-4951	252	6	2016	2016	NUM
ejpam-4951	252	7	.	.	PUNCT
ejpam-4951	253	1	[	[	X
ejpam-4951	253	2	9	9	NUM
ejpam-4951	253	3	]	]	X
ejpam-4951	253	4	k	k	NOUN
ejpam-4951	253	5	jisheing	jisheing	NOUN
ejpam-4951	253	6	,	,	PUNCT
ejpam-4951	253	7	l	l	NOUN
ejpam-4951	253	8	yitian	yitian	NOUN
ejpam-4951	253	9	,	,	PUNCT
ejpam-4951	253	10	and	and	CCONJ
ejpam-4951	253	11	w	w	PROPN
ejpam-4951	253	12	xiuhua	xiuhua	PROPN
ejpam-4951	253	13	.	.	PUNCT
ejpam-4951	254	1	third	third	ADJ
ejpam-4951	254	2	-	-	PUNCT
ejpam-4951	254	3	order	order	NOUN
ejpam-4951	254	4	modification	modification	NOUN
ejpam-4951	254	5	of	of	ADP
ejpam-4951	254	6	newton	newton	PROPN
ejpam-4951	254	7	’s	’s	PART
ejpam-4951	254	8	method	method	NOUN
ejpam-4951	254	9	.	.	PUNCT
ejpam-4951	255	1	j.	j.	PROPN
ejpam-4951	255	2	comput	comput	PROPN
ejpam-4951	255	3	.	.	PUNCT
ejpam-4951	256	1	appl	appl	PROPN
ejpam-4951	256	2	.	.	PROPN
ejpam-4951	256	3	math	math	PROPN
ejpam-4951	256	4	.	.	PUNCT
ejpam-4951	256	5	,	,	PUNCT
ejpam-4951	256	6	205:1–5	205:1–5	NUM
ejpam-4951	256	7	,	,	PUNCT
ejpam-4951	256	8	2007	2007	NUM
ejpam-4951	256	9	.	.	PUNCT
ejpam-4951	257	1	[	[	X
ejpam-4951	257	2	10	10	NUM
ejpam-4951	257	3	]	]	X
ejpam-4951	257	4	j	j	PROPN
ejpam-4951	257	5	jnawali	jnawali	PROPN
ejpam-4951	257	6	.	.	PUNCT
ejpam-4951	258	1	some	some	DET
ejpam-4951	258	2	iterative	iterative	NOUN
ejpam-4951	258	3	methods	method	NOUN
ejpam-4951	258	4	to	to	PART
ejpam-4951	258	5	solve	solve	VERB
ejpam-4951	258	6	nonlinear	nonlinear	ADJ
ejpam-4951	258	7	equations	equation	NOUN
ejpam-4951	258	8	having	have	VERB
ejpam-4951	258	9	faster	fast	ADJ
ejpam-4951	258	10	convergence	convergence	NOUN
ejpam-4951	258	11	.	.	PUNCT
ejpam-4951	259	1	punjab	punjab	PROPN
ejpam-4951	259	2	university	university	PROPN
ejpam-4951	259	3	journal	journal	NOUN
ejpam-4951	259	4	of	of	ADP
ejpam-4951	259	5	mathematics	mathematics	PROPN
ejpam-4951	259	6	.	.	PUNCT
ejpam-4951	259	7	,	,	PUNCT
ejpam-4951	259	8	52:57–72	52:57–72	NUM
ejpam-4951	259	9	,	,	PUNCT
ejpam-4951	259	10	2020	2020	NUM
ejpam-4951	259	11	.	.	PUNCT
ejpam-4951	260	1	[	[	X
ejpam-4951	260	2	11	11	NUM
ejpam-4951	260	3	]	]	X
ejpam-4951	260	4	s	s	PROPN
ejpam-4951	260	5	k	k	PROPN
ejpam-4951	260	6	khatri	khatri	PROPN
ejpam-4951	260	7	.	.	PUNCT
ejpam-4951	261	1	how	how	SCONJ
ejpam-4951	261	2	to	to	PART
ejpam-4951	261	3	develop	develop	VERB
ejpam-4951	261	4	fourth	fourth	ADJ
ejpam-4951	261	5	and	and	CCONJ
ejpam-4951	261	6	seventh	seventh	ADJ
ejpam-4951	261	7	order	order	NOUN
ejpam-4951	261	8	iterative	iterative	NOUN
ejpam-4951	261	9	methods	method	NOUN
ejpam-4951	261	10	.	.	PUNCT
ejpam-4951	262	1	novi	novi	PROPN
ejpam-4951	262	2	sad	sad	PROPN
ejpam-4951	262	3	j.	j.	PROPN
ejpam-4951	262	4	maths	maths	PROPN
ejpam-4951	262	5	.	.	PROPN
ejpam-4951	262	6	,	,	PUNCT
ejpam-4951	262	7	40:61–67	40:61–67	NUM
ejpam-4951	262	8	,	,	PUNCT
ejpam-4951	262	9	2010	2010	NUM
ejpam-4951	262	10	.	.	PUNCT
ejpam-4951	263	1	[	[	X
ejpam-4951	263	2	12	12	NUM
ejpam-4951	263	3	]	]	PUNCT
ejpam-4951	263	4	t	t	PROPN
ejpam-4951	263	5	j	j	PROPN
ejpam-4951	263	6	mcdougall	mcdougall	PROPN
ejpam-4951	263	7	and	and	CCONJ
ejpam-4951	263	8	s	s	PROPN
ejpam-4951	263	9	j	j	PROPN
ejpam-4951	263	10	wotherspoon	wotherspoon	ADV
ejpam-4951	263	11	.	.	PUNCT
ejpam-4951	264	1	a	a	DET
ejpam-4951	264	2	simple	simple	ADJ
ejpam-4951	264	3	modification	modification	NOUN
ejpam-4951	264	4	of	of	ADP
ejpam-4951	264	5	newton	newton	PROPN
ejpam-4951	264	6	’s	’s	PART
ejpam-4951	264	7	method	method	NOUN
ejpam-4951	264	8	to	to	PART
ejpam-4951	264	9	achieve	achieve	VERB
ejpam-4951	264	10	convergence	convergence	NOUN
ejpam-4951	264	11	of	of	ADP
ejpam-4951	264	12	order	order	NOUN
ejpam-4951	264	13	1	1	NUM
ejpam-4951	264	14	+	+	CCONJ
ejpam-4951	264	15	√	√	NUM
ejpam-4951	264	16	2	2	NUM
ejpam-4951	264	17	.	.	PUNCT
ejpam-4951	264	18	appl	appl	PROPN
ejpam-4951	264	19	.	.	PROPN
ejpam-4951	264	20	math	math	PROPN
ejpam-4951	264	21	.	.	PUNCT
ejpam-4951	265	1	lett	lett	PROPN
ejpam-4951	265	2	.	.	PROPN
ejpam-4951	265	3	,	,	PUNCT
ejpam-4951	265	4	29:20–25	29:20–25	NUM
ejpam-4951	265	5	,	,	PUNCT
ejpam-4951	265	6	2014	2014	NUM
ejpam-4951	265	7	.	.	PUNCT
ejpam-4951	266	1	[	[	X
ejpam-4951	266	2	13	13	NUM
ejpam-4951	266	3	]	]	PUNCT
ejpam-4951	266	4	a	a	DET
ejpam-4951	266	5	y	y	PROPN
ejpam-4951	266	6	ozban	ozban	NOUN
ejpam-4951	266	7	.	.	PUNCT
ejpam-4951	267	1	some	some	DET
ejpam-4951	267	2	new	new	ADJ
ejpam-4951	267	3	variants	variant	NOUN
ejpam-4951	267	4	of	of	ADP
ejpam-4951	267	5	newton	newton	PROPN
ejpam-4951	267	6	’s	’s	PART
ejpam-4951	267	7	method	method	NOUN
ejpam-4951	267	8	.	.	PUNCT
ejpam-4951	268	1	applied	apply	VERB
ejpam-4951	268	2	mathematics	mathematics	NOUN
ejpam-4951	268	3	letters	letter	NOUN
ejpam-4951	268	4	,	,	PUNCT
ejpam-4951	268	5	17:677–682	17:677–682	ADV
ejpam-4951	268	6	,	,	PUNCT
ejpam-4951	268	7	2007	2007	NUM
ejpam-4951	268	8	.	.	PUNCT
ejpam-4951	269	1	[	[	X
ejpam-4951	269	2	14	14	NUM
ejpam-4951	269	3	]	]	X
ejpam-4951	269	4	m	m	VERB
ejpam-4951	269	5	k	k	X
ejpam-4951	269	6	singh	singh	PROPN
ejpam-4951	269	7	.	.	PUNCT
ejpam-4951	270	1	a	a	DET
ejpam-4951	270	2	six	six	NUM
ejpam-4951	270	3	-	-	PUNCT
ejpam-4951	270	4	order	order	NOUN
ejpam-4951	270	5	variant	variant	NOUN
ejpam-4951	270	6	of	of	ADP
ejpam-4951	270	7	newton	newton	PROPN
ejpam-4951	270	8	’s	’s	PART
ejpam-4951	270	9	method	method	NOUN
ejpam-4951	270	10	for	for	ADP
ejpam-4951	270	11	solving	solve	VERB
ejpam-4951	270	12	nonlinear	nonlinear	ADJ
ejpam-4951	270	13	equations	equation	NOUN
ejpam-4951	270	14	.	.	PUNCT
ejpam-4951	271	1	cmst	cmst	PROPN
ejpam-4951	271	2	,	,	PUNCT
ejpam-4951	271	3	usa	usa	PROPN
ejpam-4951	271	4	,	,	PUNCT
ejpam-4951	271	5	2009	2009	NUM
ejpam-4951	271	6	.	.	PUNCT
ejpam-4951	272	1	[	[	X
ejpam-4951	272	2	15	15	NUM
ejpam-4951	272	3	]	]	X
ejpam-4951	272	4	j	j	PROPN
ejpam-4951	272	5	f	f	PROPN
ejpam-4951	272	6	traub	traub	PROPN
ejpam-4951	272	7	.	.	PUNCT
ejpam-4951	272	8	iterative	iterative	NOUN
ejpam-4951	272	9	methods	method	NOUN
ejpam-4951	272	10	for	for	ADP
ejpam-4951	272	11	the	the	DET
ejpam-4951	272	12	solution	solution	NOUN
ejpam-4951	272	13	of	of	ADP
ejpam-4951	272	14	equations	equation	NOUN
ejpam-4951	272	15	.	.	PUNCT
ejpam-4951	273	1	chelsea	chelsea	PROPN
ejpam-4951	273	2	publishing	publishing	PROPN
ejpam-4951	273	3	company	company	NOUN
ejpam-4951	273	4	,	,	PUNCT
ejpam-4951	273	5	isbn	isbn	ADJ
ejpam-4951	273	6	0	0	NUM
ejpam-4951	273	7	-	-	PUNCT
ejpam-4951	273	8	8284	8284	NUM
ejpam-4951	273	9	-	-	PUNCT
ejpam-4951	273	10	0312	0312	NUM
ejpam-4951	273	11	-	-	PUNCT
ejpam-4951	273	12	0	0	NUM
ejpam-4951	273	13	,	,	PUNCT
ejpam-4951	273	14	new	new	PROPN
ejpam-4951	273	15	york	york	PROPN
ejpam-4951	273	16	,	,	PUNCT
ejpam-4951	273	17	usa	usa	PROPN
ejpam-4951	273	18	,	,	PUNCT
ejpam-4951	273	19	1977	1977	NUM
ejpam-4951	273	20	.	.	PUNCT
ejpam-4951	274	1	[	[	X
ejpam-4951	274	2	16	16	NUM
ejpam-4951	274	3	]	]	X
ejpam-4951	274	4	p	p	X
ejpam-4951	274	5	wang	wang	PROPN
ejpam-4951	274	6	.	.	PUNCT
ejpam-4951	275	1	a	a	DET
ejpam-4951	275	2	third	third	ADJ
ejpam-4951	275	3	-	-	PUNCT
ejpam-4951	275	4	order	order	NOUN
ejpam-4951	275	5	family	family	NOUN
ejpam-4951	275	6	of	of	ADP
ejpam-4951	275	7	newton	newton	PROPN
ejpam-4951	275	8	-	-	PUNCT
ejpam-4951	275	9	like	like	ADJ
ejpam-4951	275	10	iteration	iteration	NOUN
ejpam-4951	275	11	methods	method	NOUN
ejpam-4951	275	12	for	for	ADP
ejpam-4951	275	13	solving	solve	VERB
ejpam-4951	275	14	nonlinear	nonlinear	ADJ
ejpam-4951	275	15	equations	equation	NOUN
ejpam-4951	275	16	.	.	PUNCT
ejpam-4951	276	1	journal	journal	PROPN
ejpam-4951	276	2	of	of	ADP
ejpam-4951	276	3	numerical	numerical	ADJ
ejpam-4951	276	4	mathematics	mathematics	PROPN
ejpam-4951	276	5	and	and	CCONJ
ejpam-4951	276	6	stochastics	stochastic	NOUN
ejpam-4951	276	7	.	.	PUNCT
ejpam-4951	276	8	,	,	PUNCT
ejpam-4951	276	9	3(1):13–19	3(1):13–19	NUM
ejpam-4951	276	10	,	,	PUNCT
ejpam-4951	276	11	2011	2011	NUM
ejpam-4951	276	12	.	.	PUNCT
ejpam-4951	277	1	references	reference	NOUN
ejpam-4951	277	2	2430	2430	NUM
ejpam-4951	278	1	[	[	X
ejpam-4951	278	2	17	17	NUM
ejpam-4951	278	3	]	]	PUNCT
ejpam-4951	278	4	s	s	PART
ejpam-4951	278	5	weerakoon	weerakoon	NOUN
ejpam-4951	278	6	and	and	CCONJ
ejpam-4951	278	7	t	t	PROPN
ejpam-4951	278	8	g	g	PROPN
ejpam-4951	279	1	i	i	PROPN
ejpam-4951	279	2	fernando	fernando	PROPN
ejpam-4951	279	3	.	.	PUNCT
ejpam-4951	280	1	a	a	DET
ejpam-4951	280	2	variant	variant	NOUN
ejpam-4951	280	3	of	of	ADP
ejpam-4951	280	4	newton	newton	PROPN
ejpam-4951	280	5	’s	’s	PART
ejpam-4951	280	6	method	method	NOUN
ejpam-4951	280	7	with	with	ADP
ejpam-4951	280	8	accelerated	accelerate	VERB
ejpam-4951	280	9	third	third	ADJ
ejpam-4951	280	10	-	-	PUNCT
ejpam-4951	280	11	order	order	NOUN
ejpam-4951	280	12	convergence	convergence	NOUN
ejpam-4951	280	13	.	.	PUNCT
ejpam-4951	281	1	applied	apply	VERB
ejpam-4951	281	2	mathematics	mathematics	NOUN
ejpam-4951	281	3	letters	letter	NOUN
ejpam-4951	281	4	,	,	PUNCT
ejpam-4951	281	5	13(8):87–93	13(8):87–93	NUM
ejpam-4951	281	6	,	,	PUNCT
ejpam-4951	281	7	2000	2000	NUM
ejpam-4951	281	8	.	.	PUNCT