id	sid	tid	token	lemma	pos
ma-386	1	1	2025	2025	NUM
ma-386	1	2	ada	ada	PROPN
ma-386	1	3	academica	academica	PROPN
ma-386	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-386	1	5	.	.	PUNCT
ma-386	2	1	j.	j.	PROPN
ma-386	2	2	math	math	PROPN
ma-386	2	3	.	.	PUNCT
ma-386	3	1	anal	anal	ADJ
ma-386	3	2	.	.	PUNCT
ma-386	4	1	5	5	NUM
ma-386	4	2	(	(	PUNCT
ma-386	4	3	2025	2025	NUM
ma-386	4	4	)	)	PUNCT
ma-386	4	5	18doi	18doi	NUM
ma-386	4	6	:	:	PUNCT
ma-386	4	7	10.28924	10.28924	NUM
ma-386	4	8	/	/	SYM
ma-386	4	9	ada	ada	PROPN
ma-386	4	10	/	/	SYM
ma-386	4	11	ma.5.18	ma.5.18	PROPN
ma-386	4	12	on	on	ADP
ma-386	4	13	local	local	ADJ
ma-386	4	14	and	and	CCONJ
ma-386	4	15	semi	semi	ADJ
ma-386	4	16	-	-	ADJ
ma-386	4	17	local	local	ADJ
ma-386	4	18	convergence	convergence	NOUN
ma-386	4	19	analysis	analysis	NOUN
ma-386	4	20	of	of	ADP
ma-386	4	21	a	a	DET
ma-386	4	22	high	high	ADJ
ma-386	4	23	-	-	PUNCT
ma-386	4	24	order	order	NOUN
ma-386	4	25	iterative	iterative	NOUN
ma-386	4	26	method	method	NOUN
ma-386	4	27	for	for	ADP
ma-386	4	28	solving	solve	VERB
ma-386	4	29	nonlinear	nonlinear	ADJ
ma-386	4	30	systems	system	NOUN
ma-386	4	31	without	without	ADP
ma-386	4	32	high	high	ADJ
ma-386	4	33	derivatives	derivative	NOUN
ma-386	4	34	ioannis	ioannis	PROPN
ma-386	4	35	k.	k.	PROPN
ma-386	4	36	argyros1,∗	argyros1,∗	PROPN
ma-386	4	37	,	,	PUNCT
ma-386	4	38	stepan	stepan	PROPN
ma-386	4	39	shakhno2	shakhno2	PROPN
ma-386	4	40	,	,	PUNCT
ma-386	4	41	yurii	yurii	PROPN
ma-386	4	42	shunkin2	shunkin2	PROPN
ma-386	4	43	,	,	PUNCT
ma-386	4	44	samundra	samundra	VERB
ma-386	4	45	regmi3,christopher	regmi3,christopher	ADJ
ma-386	4	46	i.	i.	PROPN
ma-386	4	47	argyros4	argyros4	PROPN
ma-386	5	1	1department	1department	NUM
ma-386	5	2	of	of	ADP
ma-386	5	3	computing	computing	NOUN
ma-386	5	4	and	and	CCONJ
ma-386	5	5	mathematical	mathematical	ADJ
ma-386	5	6	sciences	sciences	PROPN
ma-386	5	7	,	,	PUNCT
ma-386	5	8	cameron	cameron	PROPN
ma-386	5	9	university	university	PROPN
ma-386	5	10	,	,	PUNCT
ma-386	5	11	lawton	lawton	PROPN
ma-386	5	12	,	,	PUNCT
ma-386	5	13	ok	ok	PROPN
ma-386	5	14	73505	73505	NUM
ma-386	5	15	,	,	PUNCT
ma-386	5	16	usa	usa	PROPN
ma-386	5	17	iargyros@cameron.edu	iargyros@cameron.edu	PROPN
ma-386	6	1	2department	2department	NUM
ma-386	6	2	of	of	ADP
ma-386	6	3	theory	theory	NOUN
ma-386	6	4	of	of	ADP
ma-386	6	5	optimal	optimal	ADJ
ma-386	6	6	processes	process	NOUN
ma-386	6	7	,	,	PUNCT
ma-386	6	8	ivan	ivan	PROPN
ma-386	6	9	franko	franko	PROPN
ma-386	6	10	national	national	PROPN
ma-386	6	11	university	university	PROPN
ma-386	6	12	of	of	ADP
ma-386	6	13	lviv	lviv	PROPN
ma-386	6	14	,	,	PUNCT
ma-386	6	15	universytetska	universytetska	PROPN
ma-386	6	16	str	str	PROPN
ma-386	6	17	.	.	PROPN
ma-386	7	1	1	1	NUM
ma-386	7	2	,	,	PUNCT
ma-386	7	3	79000	79000	NUM
ma-386	7	4	lviv	lviv	PROPN
ma-386	7	5	,	,	PUNCT
ma-386	7	6	ukraine	ukraine	PROPN
ma-386	7	7	stepan.shakhno@lnu.edu.ua	stepan.shakhno@lnu.edu.ua	PROPN
ma-386	7	8	,	,	PUNCT
ma-386	7	9	yuriy.shunkin@lnu.edu.ua	yuriy.shunkin@lnu.edu.ua	PROPN
ma-386	7	10	3department	3department	NUM
ma-386	7	11	of	of	ADP
ma-386	7	12	mathematics	mathematic	NOUN
ma-386	7	13	,	,	PUNCT
ma-386	7	14	university	university	PROPN
ma-386	7	15	of	of	ADP
ma-386	7	16	houston	houston	PROPN
ma-386	7	17	,	,	PUNCT
ma-386	7	18	houston	houston	PROPN
ma-386	7	19	,	,	PUNCT
ma-386	7	20	tx	tx	PROPN
ma-386	7	21	77014	77014	NUM
ma-386	7	22	,	,	PUNCT
ma-386	7	23	usa	usa	PROPN
ma-386	7	24	sregmi5@uh.edu	sregmi5@uh.edu	PROPN
ma-386	7	25	4georgia	4georgia	NUM
ma-386	7	26	institute	institute	NOUN
ma-386	7	27	of	of	ADP
ma-386	7	28	technology	technology	NOUN
ma-386	7	29	,	,	PUNCT
ma-386	7	30	225	225	NUM
ma-386	7	31	north	north	PROPN
ma-386	7	32	avenue	avenue	PROPN
ma-386	7	33	nw	nw	PROPN
ma-386	7	34	,	,	PUNCT
ma-386	7	35	atlanta	atlanta	PROPN
ma-386	7	36	,	,	PUNCT
ma-386	7	37	ga	ga	PROPN
ma-386	7	38	30313	30313	NUM
ma-386	7	39	,	,	PUNCT
ma-386	7	40	usa	usa	PROPN
ma-386	7	41	cargyros3@gatech.edu	cargyros3@gatech.edu	PROPN
ma-386	7	42	∗correspondence	∗correspondence	NOUN
ma-386	7	43	:	:	PUNCT
ma-386	7	44	iargyros@cameron.edu	iargyros@cameron.edu	X
ma-386	8	1	abstract	abstract	ADJ
ma-386	8	2	.	.	PUNCT
ma-386	9	1	in	in	ADP
ma-386	9	2	this	this	DET
ma-386	9	3	paper	paper	NOUN
ma-386	9	4	,	,	PUNCT
ma-386	9	5	we	we	PRON
ma-386	9	6	study	study	VERB
ma-386	9	7	a	a	DET
ma-386	9	8	general	general	ADJ
ma-386	9	9	high	high	ADJ
ma-386	9	10	-	-	PUNCT
ma-386	9	11	order	order	NOUN
ma-386	9	12	iterative	iterative	NOUN
ma-386	9	13	method	method	NOUN
ma-386	9	14	for	for	ADP
ma-386	9	15	solving	solve	VERB
ma-386	9	16	nonlinear	nonlinear	ADJ
ma-386	9	17	sys	sy	NOUN
ma-386	9	18	-	-	NOUN
ma-386	9	19	tems	tem	NOUN
ma-386	9	20	in	in	ADP
ma-386	9	21	banach	banach	NOUN
ma-386	9	22	spaces	space	NOUN
ma-386	9	23	without	without	ADP
ma-386	9	24	requiring	require	VERB
ma-386	9	25	higher	high	ADJ
ma-386	9	26	-	-	PUNCT
ma-386	9	27	order	order	NOUN
ma-386	9	28	derivatives	derivative	NOUN
ma-386	9	29	.	.	PUNCT
ma-386	10	1	the	the	DET
ma-386	10	2	proposed	propose	VERB
ma-386	10	3	method	method	NOUN
ma-386	10	4	constructseach	constructseach	NOUN
ma-386	10	5	iteration	iteration	NOUN
ma-386	10	6	by	by	ADP
ma-386	10	7	combining	combine	VERB
ma-386	10	8	evaluations	evaluation	NOUN
ma-386	10	9	of	of	ADP
ma-386	10	10	the	the	DET
ma-386	10	11	operator	operator	NOUN
ma-386	10	12	and	and	CCONJ
ma-386	10	13	its	its	PRON
ma-386	10	14	derivative	derivative	NOUN
ma-386	10	15	,	,	PUNCT
ma-386	10	16	together	together	ADV
ma-386	10	17	with	with	ADP
ma-386	10	18	an	an	DET
ma-386	10	19	adaptedcorrection	adaptedcorrection	NOUN
ma-386	10	20	scheme	scheme	NOUN
ma-386	10	21	.	.	PUNCT
ma-386	11	1	a	a	DET
ma-386	11	2	detailed	detailed	ADJ
ma-386	11	3	local	local	ADJ
ma-386	11	4	convergence	convergence	NOUN
ma-386	11	5	analysis	analysis	NOUN
ma-386	11	6	under	under	ADP
ma-386	11	7	majorant	majorant	NOUN
ma-386	11	8	conditions	condition	NOUN
ma-386	11	9	is	be	AUX
ma-386	11	10	provided	provide	VERB
ma-386	11	11	,	,	PUNCT
ma-386	11	12	es	es	DET
ma-386	11	13	-	-	PUNCT
ma-386	11	14	tablishing	tablishing	NOUN
ma-386	11	15	the	the	DET
ma-386	11	16	convergence	convergence	NOUN
ma-386	11	17	to	to	ADP
ma-386	11	18	the	the	DET
ma-386	11	19	solution	solution	NOUN
ma-386	11	20	.	.	PUNCT
ma-386	12	1	we	we	PRON
ma-386	12	2	also	also	ADV
ma-386	12	3	show	show	VERB
ma-386	12	4	a	a	DET
ma-386	12	5	semi	semi	ADJ
ma-386	12	6	-	-	ADJ
ma-386	12	7	local	local	ADJ
ma-386	12	8	convergence	convergence	NOUN
ma-386	12	9	by	by	ADP
ma-386	12	10	introducingnew	introducingnew	ADJ
ma-386	12	11	majorizing	majorize	VERB
ma-386	12	12	sequences	sequence	NOUN
ma-386	12	13	.	.	PUNCT
ma-386	13	1	the	the	DET
ma-386	13	2	theoretical	theoretical	ADJ
ma-386	13	3	results	result	NOUN
ma-386	13	4	are	be	AUX
ma-386	13	5	illustrated	illustrate	VERB
ma-386	13	6	with	with	ADP
ma-386	13	7	examples	example	NOUN
ma-386	13	8	,	,	PUNCT
ma-386	13	9	and	and	CCONJ
ma-386	13	10	confirm	confirm	VERB
ma-386	13	11	thetheoretical	thetheoretical	ADJ
ma-386	13	12	predictions	prediction	NOUN
ma-386	13	13	.	.	PUNCT
ma-386	14	1	1	1	X
ma-386	14	2	.	.	X
ma-386	14	3	introduction	introduction	NOUN
ma-386	14	4	numerous	numerous	ADJ
ma-386	14	5	problems	problem	NOUN
ma-386	14	6	in	in	ADP
ma-386	14	7	applied	applied	ADJ
ma-386	14	8	mathematics	mathematic	NOUN
ma-386	14	9	,	,	PUNCT
ma-386	14	10	scientific	scientific	ADJ
ma-386	14	11	computing	computing	NOUN
ma-386	14	12	,	,	PUNCT
ma-386	14	13	and	and	CCONJ
ma-386	14	14	engineering	engineering	NOUN
ma-386	14	15	are	be	AUX
ma-386	14	16	modeledby	modeledby	ADJ
ma-386	14	17	nonlinear	nonlinear	ADJ
ma-386	14	18	systems	system	NOUN
ma-386	14	19	of	of	ADP
ma-386	14	20	the	the	DET
ma-386	14	21	form	form	NOUN
ma-386	14	22	g	g	NOUN
ma-386	14	23	:	:	PUNCT
ma-386	14	24	d	d	PROPN
ma-386	14	25	⊂	⊂	PROPN
ma-386	14	26	b0	b0	PROPN
ma-386	14	27	→	→	SYM
ma-386	14	28	b	b	PROPN
ma-386	14	29	,	,	PUNCT
ma-386	14	30	where	where	SCONJ
ma-386	14	31	d	d	NOUN
ma-386	14	32	is	be	AUX
ma-386	14	33	an	an	DET
ma-386	14	34	open	open	ADJ
ma-386	14	35	and	and	CCONJ
ma-386	14	36	convex	convex	NOUN
ma-386	14	37	subset	subset	NOUN
ma-386	14	38	of	of	ADP
ma-386	14	39	the	the	DET
ma-386	14	40	banach	banach	NOUN
ma-386	14	41	space	space	NOUN
ma-386	14	42	b0	b0	NOUN
ma-386	14	43	,	,	PUNCT
ma-386	14	44	and	and	CCONJ
ma-386	14	45	b	b	NOUN
ma-386	14	46	is	be	AUX
ma-386	14	47	another	another	DET
ma-386	14	48	banach	banach	NOUN
ma-386	14	49	space.the	space.the	DET
ma-386	14	50	goal	goal	NOUN
ma-386	14	51	is	be	AUX
ma-386	14	52	to	to	PART
ma-386	14	53	find	find	VERB
ma-386	14	54	x∗	x∗	PROPN
ma-386	14	55	∈	∈	PROPN
ma-386	15	1	d	d	X
ma-386	15	2	satisfying	satisfy	VERB
ma-386	15	3	g(x	g(x	NOUN
ma-386	15	4	)	)	PUNCT
ma-386	15	5	=	=	SYM
ma-386	16	1	0	0	X
ma-386	16	2	.	.	PUNCT
ma-386	17	1	(	(	PUNCT
ma-386	17	2	1	1	X
ma-386	17	3	)	)	PUNCT
ma-386	17	4	received	receive	VERB
ma-386	17	5	:	:	PUNCT
ma-386	17	6	1	1	NUM
ma-386	17	7	jun	jun	PROPN
ma-386	17	8	2025	2025	NUM
ma-386	17	9	.	.	PUNCT
ma-386	18	1	key	key	ADJ
ma-386	18	2	words	word	NOUN
ma-386	18	3	and	and	CCONJ
ma-386	18	4	phrases	phrase	NOUN
ma-386	18	5	.	.	PUNCT
ma-386	19	1	high	high	ADJ
ma-386	19	2	-	-	PUNCT
ma-386	19	3	order	order	NOUN
ma-386	19	4	methods	method	NOUN
ma-386	19	5	;	;	PUNCT
ma-386	19	6	nonlinear	nonlinear	ADJ
ma-386	19	7	systems	system	NOUN
ma-386	19	8	;	;	PUNCT
ma-386	19	9	semi	semi	ADJ
ma-386	19	10	-	-	ADJ
ma-386	19	11	local	local	ADJ
ma-386	19	12	convergence	convergence	NOUN
ma-386	19	13	;	;	PUNCT
ma-386	19	14	iterative	iterative	NOUN
ma-386	19	15	schemes.1	schemes.1	PROPN
ma-386	19	16	https://adac.ee	https://adac.ee	PROPN
ma-386	19	17	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	19	18	eur	eur	PROPN
ma-386	19	19	.	.	PUNCT
ma-386	20	1	j.	j.	PROPN
ma-386	20	2	math	math	PROPN
ma-386	20	3	.	.	PUNCT
ma-386	21	1	anal	anal	PROPN
ma-386	21	2	.	.	PUNCT
ma-386	22	1	10.28924	10.28924	NUM
ma-386	22	2	/	/	SYM
ma-386	22	3	ada	ada	NOUN
ma-386	22	4	/	/	SYM
ma-386	22	5	ma.5.18	ma.5.18	NOUN
ma-386	22	6	2finding	2finding	NUM
ma-386	22	7	exact	exact	ADJ
ma-386	22	8	analytical	analytical	ADJ
ma-386	22	9	solutions	solution	NOUN
ma-386	22	10	to	to	ADP
ma-386	22	11	such	such	ADJ
ma-386	22	12	nonlinear	nonlinear	ADJ
ma-386	22	13	systems	system	NOUN
ma-386	22	14	is	be	AUX
ma-386	22	15	typically	typically	ADV
ma-386	22	16	difficult	difficult	ADJ
ma-386	22	17	or	or	CCONJ
ma-386	22	18	impossible.consequently	impossible.consequently	ADV
ma-386	22	19	,	,	PUNCT
ma-386	22	20	iterative	iterative	ADJ
ma-386	22	21	methods	method	NOUN
ma-386	22	22	are	be	AUX
ma-386	22	23	commonly	commonly	ADV
ma-386	22	24	employed	employ	VERB
ma-386	22	25	.	.	PUNCT
ma-386	23	1	newton	newton	PROPN
ma-386	23	2	’s	’s	PART
ma-386	23	3	method	method	NOUN
ma-386	23	4	,	,	PUNCT
ma-386	23	5	defined	define	VERB
ma-386	23	6	by	by	ADP
ma-386	23	7	xn+1	xn+1	PROPN
ma-386	23	8	=	=	SYM
ma-386	23	9	xn	xn	PROPN
ma-386	23	10	−	−	PROPN
ma-386	23	11	g′(xn)−1g(xn	g′(xn)−1g(xn	NOUN
ma-386	23	12	)	)	PUNCT
ma-386	23	13	,	,	PUNCT
ma-386	23	14	is	be	AUX
ma-386	23	15	among	among	ADP
ma-386	23	16	the	the	DET
ma-386	23	17	most	most	ADV
ma-386	23	18	classical	classical	ADJ
ma-386	23	19	and	and	CCONJ
ma-386	23	20	efficient	efficient	ADJ
ma-386	23	21	iterative	iterative	NOUN
ma-386	23	22	schemes	scheme	NOUN
ma-386	23	23	,	,	PUNCT
ma-386	23	24	offering	offer	VERB
ma-386	23	25	quadratic	quadratic	ADJ
ma-386	23	26	convergence	convergence	NOUN
ma-386	23	27	undersuitable	undersuitable	ADJ
ma-386	23	28	conditions	condition	NOUN
ma-386	23	29	.	.	PUNCT
ma-386	24	1	however	however	ADV
ma-386	24	2	,	,	PUNCT
ma-386	24	3	many	many	ADJ
ma-386	24	4	real	real	ADJ
ma-386	24	5	-	-	PUNCT
ma-386	24	6	world	world	NOUN
ma-386	24	7	problems	problem	NOUN
ma-386	24	8	demand	demand	VERB
ma-386	24	9	faster	fast	ADJ
ma-386	24	10	convergence	convergence	NOUN
ma-386	24	11	with	with	ADP
ma-386	24	12	lowercomputational	lowercomputational	ADJ
ma-386	24	13	cost	cost	NOUN
ma-386	24	14	,	,	PUNCT
ma-386	24	15	motivating	motivate	VERB
ma-386	24	16	the	the	DET
ma-386	24	17	development	development	NOUN
ma-386	24	18	of	of	ADP
ma-386	24	19	high	high	ADJ
ma-386	24	20	-	-	PUNCT
ma-386	24	21	order	order	NOUN
ma-386	24	22	methods.following	methods.followe	VERB
ma-386	24	23	this	this	DET
ma-386	24	24	line	line	NOUN
ma-386	24	25	,	,	PUNCT
ma-386	24	26	we	we	PRON
ma-386	24	27	study	study	VERB
ma-386	24	28	a	a	DET
ma-386	24	29	general	general	ADJ
ma-386	24	30	high	high	ADJ
ma-386	24	31	-	-	PUNCT
ma-386	24	32	order	order	NOUN
ma-386	24	33	iterative	iterative	NOUN
ma-386	24	34	method	method	NOUN
ma-386	24	35	,	,	PUNCT
ma-386	24	36	which	which	PRON
ma-386	24	37	extends	extend	VERB
ma-386	24	38	classicalschemes	classicalscheme	NOUN
ma-386	24	39	by	by	ADP
ma-386	24	40	incorporating	incorporate	VERB
ma-386	24	41	additional	additional	ADJ
ma-386	24	42	correction	correction	NOUN
ma-386	24	43	steps	step	NOUN
ma-386	24	44	while	while	SCONJ
ma-386	24	45	using	use	VERB
ma-386	24	46	only	only	ADJ
ma-386	24	47	evaluations	evaluation	NOUN
ma-386	24	48	of	of	ADP
ma-386	24	49	g	g	NOUN
ma-386	24	50	and	and	CCONJ
ma-386	24	51	g′(without	g′(without	VERB
ma-386	24	52	requiring	require	VERB
ma-386	24	53	higher	high	ADJ
ma-386	24	54	derivatives	derivative	NOUN
ma-386	24	55	)	)	PUNCT
ma-386	24	56	.	.	PUNCT
ma-386	25	1	inspired	inspire	VERB
ma-386	25	2	by	by	ADP
ma-386	25	3	the	the	DET
ma-386	25	4	high	high	ADJ
ma-386	25	5	-	-	PUNCT
ma-386	25	6	order	order	NOUN
ma-386	25	7	framework	framework	NOUN
ma-386	25	8	of	of	ADP
ma-386	25	9	behl	behl	PROPN
ma-386	25	10	et	et	PROPN
ma-386	25	11	al	al	PROPN
ma-386	25	12	.	.	PUNCT
ma-386	26	1	[	[	X
ma-386	26	2	9	9	NUM
ma-386	26	3	]	]	PUNCT
ma-386	26	4	,	,	PUNCT
ma-386	26	5	whichattains	whichattain	NOUN
ma-386	26	6	order	order	NOUN
ma-386	26	7	3(k−1	3(k−1	NUM
ma-386	26	8	)	)	PUNCT
ma-386	26	9	for	for	ADP
ma-386	26	10	systems	system	NOUN
ma-386	26	11	in	in	ADP
ma-386	26	12	rm	rm	NOUN
ma-386	26	13	by	by	ADP
ma-386	26	14	reusing	reuse	VERB
ma-386	26	15	a	a	DET
ma-386	26	16	frozen	frozen	ADJ
ma-386	26	17	inverse	inverse	NOUN
ma-386	26	18	jacobian	jacobian	NOUN
ma-386	26	19	and	and	CCONJ
ma-386	26	20	relying	rely	VERB
ma-386	26	21	solely	solely	ADV
ma-386	26	22	onfirst	onfirst	ADJ
ma-386	26	23	-	-	PUNCT
ma-386	26	24	order	order	NOUN
ma-386	26	25	information	information	NOUN
ma-386	26	26	,	,	PUNCT
ma-386	26	27	the	the	DET
ma-386	26	28	present	present	ADJ
ma-386	26	29	study	study	NOUN
ma-386	26	30	generalizes	generalize	VERB
ma-386	26	31	that	that	SCONJ
ma-386	26	32	scheme	scheme	NOUN
ma-386	26	33	to	to	PART
ma-386	26	34	banach	banach	NOUN
ma-386	26	35	spaces	space	NOUN
ma-386	26	36	,	,	PUNCT
ma-386	26	37	discards	discard	VERB
ma-386	26	38	theseventh	theseventh	NOUN
ma-386	26	39	-	-	PUNCT
ma-386	26	40	derivative	derivative	ADJ
ma-386	26	41	assumptions	assumption	NOUN
ma-386	26	42	underpinning	underpin	VERB
ma-386	26	43	their	their	PRON
ma-386	26	44	local	local	ADJ
ma-386	26	45	taylor	taylor	NOUN
ma-386	26	46	analysis	analysis	NOUN
ma-386	26	47	,	,	PUNCT
ma-386	26	48	and	and	CCONJ
ma-386	26	49	furnishes	furnish	VERB
ma-386	26	50	a	a	DET
ma-386	26	51	unifiedlocal	unifiedlocal	ADJ
ma-386	26	52	and	and	CCONJ
ma-386	26	53	semi	semi	ADJ
ma-386	26	54	-	-	ADJ
ma-386	26	55	local	local	ADJ
ma-386	26	56	convergence	convergence	NOUN
ma-386	26	57	theory	theory	NOUN
ma-386	26	58	with	with	ADP
ma-386	26	59	computable	computable	ADJ
ma-386	26	60	error	error	NOUN
ma-386	26	61	bounds	bound	NOUN
ma-386	26	62	,	,	PUNCT
ma-386	26	63	larger	large	ADJ
ma-386	26	64	attraction	attraction	NOUN
ma-386	26	65	regions	region	NOUN
ma-386	26	66	,	,	PUNCT
ma-386	26	67	and	and	CCONJ
ma-386	26	68	sharpened	sharpen	VERB
ma-386	26	69	uniqueness	uniqueness	NOUN
ma-386	26	70	criteria	criterion	NOUN
ma-386	26	71	—	—	PUNCT
ma-386	26	72	thereby	thereby	ADV
ma-386	26	73	achieving	achieve	VERB
ma-386	26	74	broader	broad	ADJ
ma-386	26	75	applicability.let	applicability.let	X
ma-386	26	76	k	k	X
ma-386	26	77	≥	≥	PROPN
ma-386	26	78	3	3	NUM
ma-386	26	79	be	be	AUX
ma-386	26	80	a	a	DET
ma-386	26	81	natural	natural	ADJ
ma-386	26	82	number	number	NOUN
ma-386	26	83	and	and	CCONJ
ma-386	26	84	x0	x0	PROPN
ma-386	26	85	∈	∈	PROPN
ma-386	27	1	d	d	X
ma-386	27	2	an	an	DET
ma-386	27	3	initial	initial	ADJ
ma-386	27	4	point	point	NOUN
ma-386	27	5	.	.	PUNCT
ma-386	28	1	then	then	ADV
ma-386	28	2	,	,	PUNCT
ma-386	28	3	the	the	DET
ma-386	28	4	method	method	NOUN
ma-386	28	5	is	be	AUX
ma-386	28	6	defined	define	VERB
ma-386	28	7	for	for	ADP
ma-386	28	8	each	each	DET
ma-386	28	9	n	n	NOUN
ma-386	28	10	=	=	SYM
ma-386	28	11	0	0	NUM
ma-386	28	12	,	,	PUNCT
ma-386	28	13	1	1	NUM
ma-386	28	14	,	,	PUNCT
ma-386	28	15	2	2	NUM
ma-386	28	16	,	,	PUNCT
ma-386	28	17	.	.	PUNCT
ma-386	28	18	.	.	PUNCT
ma-386	28	19	.	.	PUNCT
ma-386	29	1	by	by	ADP
ma-386	29	2	y	y	PROPN
ma-386	29	3	(	(	PUNCT
ma-386	29	4	1	1	NUM
ma-386	29	5	)	)	PUNCT
ma-386	29	6	n	n	NOUN
ma-386	29	7	=	=	SYM
ma-386	29	8	xn	xn	PROPN
ma-386	30	1	−	−	PROPN
ma-386	31	1	g′(xn)−1g(xn	g′(xn)−1g(xn	NOUN
ma-386	31	2	)	)	PUNCT
ma-386	31	3	,	,	PUNCT
ma-386	31	4	y	y	PROPN
ma-386	31	5	(	(	PUNCT
ma-386	31	6	2	2	NUM
ma-386	31	7	)	)	PUNCT
ma-386	31	8	n	n	NOUN
ma-386	31	9	=	=	SYM
ma-386	31	10	xn	xn	PROPN
ma-386	32	1	−	−	PROPN
ma-386	32	2	2t−1g(xn	2t−1g(xn	NUM
ma-386	32	3	)	)	PUNCT
ma-386	32	4	,	,	PUNCT
ma-386	32	5	y	y	PROPN
ma-386	32	6	(	(	PUNCT
ma-386	32	7	3	3	NUM
ma-386	32	8	)	)	PUNCT
ma-386	32	9	n	n	NOUN
ma-386	32	10	=	=	SYM
ma-386	32	11	y	y	PROPN
ma-386	32	12	(	(	PUNCT
ma-386	32	13	2	2	NUM
ma-386	32	14	)	)	PUNCT
ma-386	32	15	n	n	CCONJ
ma-386	32	16	−mg(y	−mg(y	ADJ
ma-386	32	17	(	(	PUNCT
ma-386	32	18	2	2	NUM
ma-386	32	19	)	)	PUNCT
ma-386	32	20	)	)	PUNCT
ma-386	32	21	n	n	CCONJ
ma-386	32	22	,	,	PUNCT
ma-386	32	23	·	·	PUNCT
ma-386	32	24	·	·	PUNCT
ma-386	32	25	·	·	PUNCT
ma-386	32	26	xn+1	xn+1	PUNCT
ma-386	33	1	=	=	SYM
ma-386	33	2	y	y	PROPN
ma-386	33	3	(	(	PUNCT
ma-386	33	4	k	k	NOUN
ma-386	33	5	)	)	PUNCT
ma-386	33	6	n	n	PROPN
ma-386	33	7	=	=	SYM
ma-386	33	8	y	y	PROPN
ma-386	33	9	(	(	PUNCT
ma-386	33	10	k−1	k−1	PROPN
ma-386	33	11	)	)	PUNCT
ma-386	33	12	n	n	CCONJ
ma-386	33	13	−mg(y	−mg(y	PROPN
ma-386	33	14	(	(	PUNCT
ma-386	33	15	k−1	k−1	PROPN
ma-386	33	16	)	)	PUNCT
ma-386	33	17	n	n	CCONJ
ma-386	33	18	)	)	PUNCT
ma-386	33	19	,	,	PUNCT
ma-386	33	20	(	(	PUNCT
ma-386	33	21	2	2	X
ma-386	33	22	)	)	PUNCT
ma-386	33	23	where	where	SCONJ
ma-386	33	24	the	the	DET
ma-386	33	25	operators	operator	NOUN
ma-386	33	26	t	t	PROPN
ma-386	33	27	,	,	PUNCT
ma-386	33	28	l	l	PROPN
ma-386	33	29	,	,	PUNCT
ma-386	33	30	and	and	CCONJ
ma-386	33	31	m	m	PROPN
ma-386	33	32	are	be	AUX
ma-386	33	33	given	give	VERB
ma-386	33	34	by	by	ADP
ma-386	33	35	t	t	PROPN
ma-386	33	36	=	=	SYM
ma-386	33	37	tn	tn	PROPN
ma-386	33	38	=	=	SYM
ma-386	33	39	g′(xn	g′(xn	PROPN
ma-386	33	40	)	)	PUNCT
ma-386	34	1	+	+	CCONJ
ma-386	34	2	g′(y	g′(y	X
ma-386	34	3	(	(	PUNCT
ma-386	34	4	1	1	NUM
ma-386	34	5	)	)	PUNCT
ma-386	34	6	)	)	PUNCT
ma-386	35	1	n	n	X
ma-386	35	2	,	,	PUNCT
ma-386	35	3	l	l	NOUN
ma-386	35	4	=	=	PUNCT
ma-386	35	5	ln	ln	NOUN
ma-386	35	6	=	=	PUNCT
ma-386	35	7	3f	3f	PROPN
ma-386	35	8	′(y	′(y	X
ma-386	35	9	(	(	PUNCT
ma-386	35	10	2	2	NUM
ma-386	35	11	)	)	PUNCT
ma-386	35	12	)	)	PUNCT
ma-386	36	1	n	n	CCONJ
ma-386	36	2	−	−	PROPN
ma-386	36	3	g′(xn	g′(xn	NOUN
ma-386	36	4	)	)	PUNCT
ma-386	36	5	,	,	PUNCT
ma-386	36	6	m	m	VERB
ma-386	36	7	=	=	SYM
ma-386	36	8	mn	mn	PROPN
ma-386	36	9	=	=	SYM
ma-386	36	10	l−1tg′(xn)−1	l−1tg′(xn)−1	PROPN
ma-386	36	11	.	.	PUNCT
ma-386	37	1	the	the	DET
ma-386	37	2	method	method	NOUN
ma-386	37	3	(	(	PUNCT
ma-386	37	4	2	2	X
ma-386	37	5	)	)	PUNCT
ma-386	37	6	is	be	AUX
ma-386	37	7	shown	show	VERB
ma-386	37	8	in	in	ADP
ma-386	37	9	[	[	X
ma-386	37	10	9	9	NUM
ma-386	37	11	]	]	PUNCT
ma-386	37	12	to	to	PART
ma-386	37	13	possess	possess	VERB
ma-386	37	14	convergence	convergence	NOUN
ma-386	37	15	order	order	NOUN
ma-386	37	16	3(j	3(j	NUM
ma-386	37	17	−	−	NOUN
ma-386	37	18	1	1	NUM
ma-386	37	19	)	)	PUNCT
ma-386	37	20	for	for	ADP
ma-386	37	21	j	j	PROPN
ma-386	37	22	=	=	SYM
ma-386	37	23	3	3	PROPN
ma-386	37	24	,	,	PUNCT
ma-386	37	25	.	.	PUNCT
ma-386	37	26	.	.	PUNCT
ma-386	37	27	.	.	PUNCT
ma-386	38	1	,	,	PUNCT
ma-386	38	2	k	k	PROPN
ma-386	38	3	usingtaylor	usingtaylor	NOUN
ma-386	38	4	expansions	expansion	NOUN
ma-386	38	5	when	when	SCONJ
ma-386	38	6	b0	b0	NOUN
ma-386	38	7	=	=	SYM
ma-386	38	8	b	b	PROPN
ma-386	38	9	=	=	SYM
ma-386	38	10	rm	rm	PROPN
ma-386	38	11	(	(	PUNCT
ma-386	38	12	m	m	PROPN
ma-386	38	13	natural	natural	ADJ
ma-386	38	14	number	number	NOUN
ma-386	38	15	)	)	PUNCT
ma-386	38	16	,	,	PUNCT
ma-386	38	17	assuming	assume	VERB
ma-386	38	18	the	the	DET
ma-386	38	19	existence	existence	NOUN
ma-386	38	20	of	of	ADP
ma-386	38	21	at	at	ADV
ma-386	38	22	least	least	ADJ
ma-386	38	23	theseventh	theseventh	NOUN
ma-386	38	24	derivative	derivative	ADJ
ma-386	38	25	g(7	g(7	PROPN
ma-386	38	26	)	)	PUNCT
ma-386	38	27	,	,	PUNCT
ma-386	38	28	although	although	SCONJ
ma-386	38	29	the	the	DET
ma-386	38	30	derivatives	derivative	NOUN
ma-386	38	31	g′′	g′′	NOUN
ma-386	38	32	,	,	PUNCT
ma-386	38	33	g(3	g(3	PROPN
ma-386	38	34	)	)	PUNCT
ma-386	38	35	,	,	PUNCT
ma-386	38	36	...	...	PUNCT
ma-386	38	37	,	,	PUNCT
ma-386	38	38	g(7	g(7	PROPN
ma-386	38	39	)	)	PUNCT
ma-386	38	40	are	be	AUX
ma-386	38	41	not	not	PART
ma-386	38	42	explicitly	explicitly	ADV
ma-386	38	43	required	require	VERB
ma-386	38	44	in	in	ADP
ma-386	38	45	theiteration	theiteration	NOUN
ma-386	38	46	steps.unlike	steps.unlike	ADP
ma-386	38	47	many	many	ADJ
ma-386	38	48	classical	classical	ADJ
ma-386	38	49	methods	method	NOUN
ma-386	38	50	that	that	PRON
ma-386	38	51	impose	impose	VERB
ma-386	38	52	strong	strong	ADJ
ma-386	38	53	smoothness	smoothness	ADJ
ma-386	38	54	assumptions	assumption	NOUN
ma-386	38	55	,	,	PUNCT
ma-386	38	56	this	this	DET
ma-386	38	57	method	method	NOUN
ma-386	38	58	is	be	AUX
ma-386	38	59	de	de	ADJ
ma-386	38	60	-	-	VERB
ma-386	38	61	signed	sign	VERB
ma-386	38	62	to	to	PART
ma-386	38	63	work	work	VERB
ma-386	38	64	under	under	ADP
ma-386	38	65	weaker	weak	ADJ
ma-386	38	66	differentiability	differentiability	NOUN
ma-386	38	67	conditions	condition	NOUN
ma-386	38	68	.	.	PUNCT
ma-386	39	1	it	it	PRON
ma-386	39	2	builds	build	VERB
ma-386	39	3	upon	upon	SCONJ
ma-386	39	4	ideas	idea	NOUN
ma-386	39	5	from	from	ADP
ma-386	39	6	previous	previous	ADJ
ma-386	39	7	studies	study	NOUN
ma-386	39	8	,	,	PUNCT
ma-386	39	9	including	include	VERB
ma-386	39	10	parhi	parhi	NOUN
ma-386	39	11	and	and	CCONJ
ma-386	39	12	gupta	gupta	PROPN
ma-386	39	13	[	[	X
ma-386	39	14	14	14	NUM
ma-386	39	15	]	]	PUNCT
ma-386	39	16	,	,	PUNCT
ma-386	39	17	wang	wang	PROPN
ma-386	39	18	et	et	PROPN
ma-386	39	19	al	al	PROPN
ma-386	39	20	.	.	PUNCT
ma-386	40	1	[	[	X
ma-386	40	2	18	18	NUM
ma-386	40	3	]	]	PUNCT
ma-386	40	4	,	,	PUNCT
ma-386	40	5	and	and	CCONJ
ma-386	40	6	cordero	cordero	PROPN
ma-386	40	7	et	et	PROPN
ma-386	40	8	al	al	PROPN
ma-386	40	9	.	.	PUNCT
ma-386	41	1	[	[	X
ma-386	41	2	10	10	NUM
ma-386	41	3	]	]	PUNCT
ma-386	41	4	,	,	PUNCT
ma-386	41	5	while	while	SCONJ
ma-386	41	6	aiming	aim	VERB
ma-386	41	7	for	for	ADP
ma-386	41	8	a	a	DET
ma-386	41	9	betterbalance	betterbalance	NOUN
ma-386	41	10	between	between	ADP
ma-386	41	11	convergence	convergence	NOUN
ma-386	41	12	speed	speed	NOUN
ma-386	41	13	,	,	PUNCT
ma-386	41	14	computational	computational	ADJ
ma-386	41	15	cost	cost	NOUN
ma-386	41	16	,	,	PUNCT
ma-386	41	17	and	and	CCONJ
ma-386	41	18	robustness	robustness	NOUN
ma-386	41	19	.	.	PUNCT
ma-386	42	1	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	42	2	eur	eur	PROPN
ma-386	42	3	.	.	PUNCT
ma-386	43	1	j.	j.	PROPN
ma-386	43	2	math	math	PROPN
ma-386	43	3	.	.	PUNCT
ma-386	44	1	anal	anal	PROPN
ma-386	44	2	.	.	PUNCT
ma-386	45	1	10.28924	10.28924	NUM
ma-386	45	2	/	/	SYM
ma-386	45	3	ada	ada	PROPN
ma-386	45	4	/	/	SYM
ma-386	45	5	ma.5.18	ma.5.18	PROPN
ma-386	45	6	3to	3to	PROPN
ma-386	45	7	illustrate	illustrate	VERB
ma-386	45	8	the	the	DET
ma-386	45	9	need	need	NOUN
ma-386	45	10	for	for	ADP
ma-386	45	11	such	such	DET
ma-386	45	12	an	an	DET
ma-386	45	13	approach	approach	NOUN
ma-386	45	14	,	,	PUNCT
ma-386	45	15	consider	consider	VERB
ma-386	45	16	the	the	DET
ma-386	45	17	scalar	scalar	ADJ
ma-386	45	18	function	function	NOUN
ma-386	45	19	g	g	NOUN
ma-386	45	20	:	:	PUNCT
ma-386	46	1	d	d	X
ma-386	46	2	→	→	SYM
ma-386	46	3	r	r	NOUN
ma-386	46	4	defined	define	VERB
ma-386	46	5	by	by	ADP
ma-386	46	6	g(t	g(t	PROPN
ma-386	46	7	)	)	PUNCT
ma-386	47	1	=	=	PUNCT
ma-386	47	2	b1t7	b1t7	PROPN
ma-386	47	3	log	log	NOUN
ma-386	47	4	t	t	PROPN
ma-386	48	1	+	+	CCONJ
ma-386	48	2	b1	b1	PROPN
ma-386	48	3	t	t	PROPN
ma-386	48	4	8	8	NUM
ma-386	48	5	+	+	NUM
ma-386	48	6	b2	b2	NOUN
ma-386	48	7	t	t	NOUN
ma-386	48	8	9	9	NUM
ma-386	48	9	,	,	PUNCT
ma-386	48	10	t	t	PROPN
ma-386	48	11	6=	6=	PROPN
ma-386	48	12	0	0	NUM
ma-386	48	13	,	,	PUNCT
ma-386	48	14	0	0	NUM
ma-386	48	15	,	,	PUNCT
ma-386	48	16	t	t	NOUN
ma-386	48	17	=	=	SYM
ma-386	48	18	0	0	NUM
ma-386	48	19	,	,	PUNCT
ma-386	48	20	where	where	SCONJ
ma-386	48	21	d	d	NOUN
ma-386	48	22	=	=	PUNCT
ma-386	49	1	[	[	X
ma-386	49	2	−2	−2	X
ma-386	49	3	,	,	PUNCT
ma-386	49	4	2	2	NUM
ma-386	49	5	)	)	PUNCT
ma-386	49	6	,	,	PUNCT
ma-386	49	7	and	and	CCONJ
ma-386	49	8	b1	b1	NOUN
ma-386	49	9	,	,	PUNCT
ma-386	49	10	b2	b2	NOUN
ma-386	49	11	are	be	AUX
ma-386	49	12	real	real	ADJ
ma-386	49	13	constants	constant	NOUN
ma-386	49	14	with	with	ADP
ma-386	49	15	b1	b1	PROPN
ma-386	49	16	6=	6=	PRON
ma-386	49	17	0	0	NUM
ma-386	49	18	and	and	CCONJ
ma-386	49	19	b1	b1	NOUN
ma-386	49	20	+	+	CCONJ
ma-386	49	21	b2	b2	NOUN
ma-386	49	22	=	=	SYM
ma-386	49	23	0	0	NUM
ma-386	49	24	.	.	PUNCT
ma-386	50	1	although	although	SCONJ
ma-386	50	2	g	g	PROPN
ma-386	50	3	hasa	hasa	PROPN
ma-386	50	4	zero	zero	NUM
ma-386	50	5	at	at	ADP
ma-386	50	6	t∗	t∗	NOUN
ma-386	50	7	=	=	SYM
ma-386	50	8	1	1	NUM
ma-386	50	9	,	,	PUNCT
ma-386	50	10	the	the	DET
ma-386	50	11	seventh	seventh	ADJ
ma-386	50	12	derivative	derivative	ADJ
ma-386	50	13	g(7)(t	g(7)(t	NOUN
ma-386	50	14	)	)	PUNCT
ma-386	50	15	does	do	AUX
ma-386	50	16	not	not	PART
ma-386	50	17	exist	exist	VERB
ma-386	50	18	at	at	ADP
ma-386	50	19	t	t	NOUN
ma-386	50	20	=	=	SYM
ma-386	50	21	0	0	NUM
ma-386	50	22	,	,	PUNCT
ma-386	50	23	showing	show	VERB
ma-386	50	24	that	that	SCONJ
ma-386	50	25	classicalconvergence	classicalconvergence	NOUN
ma-386	50	26	assumptions	assumption	NOUN
ma-386	50	27	based	base	VERB
ma-386	50	28	on	on	ADP
ma-386	50	29	higher	high	ADJ
ma-386	50	30	derivatives	derivative	NOUN
ma-386	50	31	are	be	AUX
ma-386	50	32	not	not	PART
ma-386	50	33	satisfied.this	satisfied.this	NUM
ma-386	50	34	observation	observation	NOUN
ma-386	50	35	motivates	motivate	VERB
ma-386	50	36	the	the	DET
ma-386	50	37	use	use	NOUN
ma-386	50	38	of	of	ADP
ma-386	50	39	generalized	generalized	ADJ
ma-386	50	40	majorant	majorant	NOUN
ma-386	50	41	conditions	condition	NOUN
ma-386	50	42	rather	rather	ADV
ma-386	50	43	than	than	ADP
ma-386	50	44	strict	strict	ADJ
ma-386	50	45	smooth	smooth	ADJ
ma-386	50	46	-	-	PUNCT
ma-386	50	47	ness	ness	ADJ
ma-386	50	48	hypotheses	hypothesis	NOUN
ma-386	50	49	.	.	PUNCT
ma-386	51	1	moreover	moreover	ADV
ma-386	51	2	,	,	PUNCT
ma-386	51	3	method	method	VERB
ma-386	51	4	not	not	PART
ma-386	51	5	only	only	ADV
ma-386	51	6	achieves	achieve	VERB
ma-386	51	7	high	high	ADJ
ma-386	51	8	-	-	PUNCT
ma-386	51	9	order	order	NOUN
ma-386	51	10	local	local	ADJ
ma-386	51	11	convergence	convergence	NOUN
ma-386	51	12	but	but	CCONJ
ma-386	51	13	also	also	ADV
ma-386	51	14	pro	pro	ADJ
ma-386	51	15	-	-	NOUN
ma-386	51	16	vides	vide	NOUN
ma-386	51	17	a	a	DET
ma-386	51	18	semi	semi	ADJ
ma-386	51	19	-	-	ADJ
ma-386	51	20	local	local	ADJ
ma-386	51	21	convergence	convergence	NOUN
ma-386	51	22	analysis	analysis	NOUN
ma-386	51	23	by	by	ADP
ma-386	51	24	constructing	construct	VERB
ma-386	51	25	suitable	suitable	ADJ
ma-386	51	26	majorizing	majorize	VERB
ma-386	51	27	sequences.the	sequences.the	DET
ma-386	51	28	main	main	ADJ
ma-386	51	29	contributions	contribution	NOUN
ma-386	51	30	of	of	ADP
ma-386	51	31	this	this	DET
ma-386	51	32	paper	paper	NOUN
ma-386	51	33	are	be	AUX
ma-386	51	34	as	as	SCONJ
ma-386	51	35	follows	follow	VERB
ma-386	51	36	:	:	PUNCT
ma-386	51	37	•	•	ADP
ma-386	51	38	a	a	DET
ma-386	51	39	local	local	ADJ
ma-386	51	40	convergence	convergence	NOUN
ma-386	51	41	analysis	analysis	NOUN
ma-386	51	42	is	be	AUX
ma-386	51	43	established	establish	VERB
ma-386	51	44	that	that	PRON
ma-386	51	45	depends	depend	VERB
ma-386	51	46	only	only	ADV
ma-386	51	47	on	on	ADP
ma-386	51	48	g	g	PROPN
ma-386	51	49	,	,	PUNCT
ma-386	51	50	g′	g′	NOUN
ma-386	51	51	,	,	PUNCT
ma-386	51	52	and	and	CCONJ
ma-386	51	53	suitablyconstructed	suitablyconstructe	VERB
ma-386	51	54	auxiliary	auxiliary	ADJ
ma-386	51	55	operators	operator	NOUN
ma-386	51	56	,	,	PUNCT
ma-386	51	57	thereby	thereby	ADV
ma-386	51	58	eliminating	eliminate	VERB
ma-386	51	59	any	any	DET
ma-386	51	60	need	need	NOUN
ma-386	51	61	for	for	ADP
ma-386	51	62	higher	high	ADJ
ma-386	51	63	-	-	PUNCT
ma-386	51	64	order	order	NOUN
ma-386	51	65	derivatives	derivative	NOUN
ma-386	51	66	.	.	PUNCT
ma-386	52	1	•	•	NUM
ma-386	52	2	semi	semi	ADJ
ma-386	52	3	-	-	ADJ
ma-386	52	4	local	local	ADJ
ma-386	52	5	convergence	convergence	NOUN
ma-386	52	6	results	result	NOUN
ma-386	52	7	are	be	AUX
ma-386	52	8	provided	provide	VERB
ma-386	52	9	through	through	ADP
ma-386	52	10	the	the	DET
ma-386	52	11	use	use	NOUN
ma-386	52	12	of	of	ADP
ma-386	52	13	majorizing	majorize	VERB
ma-386	52	14	sequences	sequence	NOUN
ma-386	52	15	,	,	PUNCT
ma-386	52	16	guar	guar	NOUN
ma-386	52	17	-	-	PUNCT
ma-386	52	18	anteeing	anteee	VERB
ma-386	52	19	convergence	convergence	NOUN
ma-386	52	20	even	even	ADV
ma-386	52	21	when	when	SCONJ
ma-386	52	22	the	the	DET
ma-386	52	23	initial	initial	ADJ
ma-386	52	24	guess	guess	NOUN
ma-386	52	25	is	be	AUX
ma-386	52	26	relatively	relatively	ADV
ma-386	52	27	far	far	ADV
ma-386	52	28	from	from	ADP
ma-386	52	29	the	the	DET
ma-386	52	30	solution	solution	NOUN
ma-386	52	31	.	.	PUNCT
ma-386	53	1	•	•	NUM
ma-386	53	2	computable	computable	ADJ
ma-386	53	3	radii	radius	NOUN
ma-386	53	4	of	of	ADP
ma-386	53	5	convergence	convergence	NOUN
ma-386	53	6	and	and	CCONJ
ma-386	53	7	explicit	explicit	ADJ
ma-386	53	8	error	error	NOUN
ma-386	53	9	bounds	bound	NOUN
ma-386	53	10	are	be	AUX
ma-386	53	11	derived	derive	VERB
ma-386	53	12	,	,	PUNCT
ma-386	53	13	permitting	permit	VERB
ma-386	53	14	a	a	DET
ma-386	53	15	prioriestimates	prioriestimate	NOUN
ma-386	53	16	of	of	ADP
ma-386	53	17	the	the	DET
ma-386	53	18	number	number	NOUN
ma-386	53	19	of	of	ADP
ma-386	53	20	iterations	iteration	NOUN
ma-386	53	21	required	require	VERB
ma-386	53	22	to	to	PART
ma-386	53	23	achieve	achieve	VERB
ma-386	53	24	a	a	DET
ma-386	53	25	prescribed	prescribed	ADJ
ma-386	53	26	accuracy	accuracy	NOUN
ma-386	53	27	.	.	PUNCT
ma-386	54	1	•	•	NOUN
ma-386	54	2	conditions	condition	NOUN
ma-386	54	3	are	be	AUX
ma-386	54	4	specified	specify	VERB
ma-386	54	5	that	that	PRON
ma-386	54	6	ensure	ensure	VERB
ma-386	54	7	the	the	DET
ma-386	54	8	uniqueness	uniqueness	NOUN
ma-386	54	9	of	of	ADP
ma-386	54	10	the	the	DET
ma-386	54	11	solution	solution	NOUN
ma-386	54	12	within	within	ADP
ma-386	54	13	a	a	DET
ma-386	54	14	neighborhoodof	neighborhoodof	NOUN
ma-386	54	15	the	the	DET
ma-386	54	16	limit	limit	NOUN
ma-386	54	17	point.the	point.the	DET
ma-386	54	18	remainder	remainder	NOUN
ma-386	54	19	of	of	ADP
ma-386	54	20	the	the	DET
ma-386	54	21	paper	paper	NOUN
ma-386	54	22	is	be	AUX
ma-386	54	23	organized	organize	VERB
ma-386	54	24	as	as	SCONJ
ma-386	54	25	follows	follow	VERB
ma-386	54	26	.	.	PUNCT
ma-386	55	1	in	in	ADP
ma-386	55	2	section	section	NOUN
ma-386	55	3	2	2	NUM
ma-386	55	4	,	,	PUNCT
ma-386	55	5	we	we	PRON
ma-386	55	6	introduce	introduce	VERB
ma-386	55	7	the	the	DET
ma-386	55	8	assumptionsand	assumptionsand	NOUN
ma-386	55	9	establish	establish	VERB
ma-386	55	10	the	the	DET
ma-386	55	11	local	local	ADJ
ma-386	55	12	convergence	convergence	NOUN
ma-386	55	13	theorems	theorem	NOUN
ma-386	55	14	,	,	PUNCT
ma-386	55	15	including	include	VERB
ma-386	55	16	uniqueness	uniqueness	NOUN
ma-386	55	17	and	and	CCONJ
ma-386	55	18	error	error	NOUN
ma-386	55	19	estimates	estimate	NOUN
ma-386	55	20	.	.	PUNCT
ma-386	56	1	sec	sec	PROPN
ma-386	56	2	-	-	PUNCT
ma-386	56	3	tion	tion	NOUN
ma-386	56	4	3	3	NUM
ma-386	56	5	presents	present	VERB
ma-386	56	6	the	the	DET
ma-386	56	7	semi	semi	ADJ
ma-386	56	8	-	-	ADJ
ma-386	56	9	local	local	ADJ
ma-386	56	10	convergence	convergence	NOUN
ma-386	56	11	analysis	analysis	NOUN
ma-386	56	12	via	via	ADP
ma-386	56	13	majorizing	majorize	VERB
ma-386	56	14	sequences	sequence	NOUN
ma-386	56	15	.	.	PUNCT
ma-386	57	1	section	section	NOUN
ma-386	57	2	4	4	NUM
ma-386	57	3	discussesexamples	discussesexample	NOUN
ma-386	57	4	and	and	CCONJ
ma-386	57	5	practical	practical	ADJ
ma-386	57	6	aspects	aspect	NOUN
ma-386	57	7	.	.	PUNCT
ma-386	58	1	finally	finally	ADV
ma-386	58	2	,	,	PUNCT
ma-386	58	3	conclusions	conclusion	NOUN
ma-386	58	4	are	be	AUX
ma-386	58	5	drawn	draw	VERB
ma-386	58	6	in	in	ADP
ma-386	58	7	section	section	NOUN
ma-386	58	8	5	5	NUM
ma-386	58	9	.	.	NOUN
ma-386	58	10	2	2	NUM
ma-386	58	11	.	.	X
ma-386	58	12	convergence	convergence	NOUN
ma-386	58	13	analysis	analysis	NOUN
ma-386	58	14	2.1	2.1	NUM
ma-386	58	15	.	.	PUNCT
ma-386	59	1	local	local	ADJ
ma-386	59	2	.	.	PUNCT
ma-386	60	1	some	some	DET
ma-386	60	2	real	real	ADJ
ma-386	60	3	functions	function	NOUN
ma-386	60	4	which	which	PRON
ma-386	60	5	are	be	AUX
ma-386	60	6	defined	define	VERB
ma-386	60	7	on	on	ADP
ma-386	60	8	the	the	DET
ma-386	60	9	interval	interval	NOUN
ma-386	60	10	a	a	PRON
ma-386	60	11	=	=	X
ma-386	61	1	[	[	X
ma-386	61	2	0,+∞	0,+∞	NUM
ma-386	61	3	)	)	PUNCT
ma-386	61	4	play	play	VERB
ma-386	61	5	a	a	DET
ma-386	61	6	crucial	crucial	ADJ
ma-386	61	7	rolein	rolein	NOUN
ma-386	61	8	the	the	DET
ma-386	61	9	local	local	ADJ
ma-386	61	10	convergence	convergence	NOUN
ma-386	61	11	analysis	analysis	NOUN
ma-386	61	12	of	of	ADP
ma-386	61	13	the	the	DET
ma-386	61	14	method	method	NOUN
ma-386	61	15	(	(	PUNCT
ma-386	61	16	2).suppose	2).suppose	NUM
ma-386	61	17	(	(	PUNCT
ma-386	61	18	h1	h1	PROPN
ma-386	61	19	)	)	PUNCT
ma-386	61	20	there	there	PRON
ma-386	61	21	exists	exist	VERB
ma-386	61	22	a	a	DET
ma-386	61	23	nondecreasing	nondecreasing	ADJ
ma-386	61	24	and	and	CCONJ
ma-386	61	25	continuous	continuous	ADJ
ma-386	61	26	function	function	NOUN
ma-386	61	27	φ0	φ0	NOUN
ma-386	61	28	:	:	PUNCT
ma-386	61	29	a	a	PRON
ma-386	61	30	→	→	X
ma-386	61	31	a	a	DET
ma-386	61	32	such	such	ADJ
ma-386	61	33	that	that	SCONJ
ma-386	61	34	the	the	DET
ma-386	61	35	function	function	NOUN
ma-386	61	36	1	1	NUM
ma-386	61	37	−	−	NOUN
ma-386	61	38	φ0(t	φ0(t	PROPN
ma-386	61	39	)	)	PUNCT
ma-386	61	40	has	have	AUX
ma-386	61	41	a	a	DET
ma-386	61	42	smallest	small	ADJ
ma-386	61	43	positive	positive	ADJ
ma-386	61	44	zero	zero	NUM
ma-386	61	45	in	in	ADP
ma-386	61	46	a	a	PRON
ma-386	61	47	,	,	PUNCT
ma-386	61	48	which	which	PRON
ma-386	61	49	is	be	AUX
ma-386	61	50	denoted	denote	VERB
ma-386	61	51	by	by	ADP
ma-386	61	52	s0	s0	PROPN
ma-386	61	53	.	.	PUNCT
ma-386	62	1	define	define	VERB
ma-386	62	2	the	the	DET
ma-386	62	3	interval	interval	NOUN
ma-386	62	4	a0	a0	NOUN
ma-386	62	5	=	=	PUNCT
ma-386	63	1	[	[	X
ma-386	63	2	0	0	NUM
ma-386	63	3	,	,	PUNCT
ma-386	63	4	s0	s0	PROPN
ma-386	63	5	)	)	PUNCT
ma-386	63	6	.	.	PUNCT
ma-386	64	1	(	(	PUNCT
ma-386	64	2	h2	h2	NOUN
ma-386	64	3	)	)	PUNCT
ma-386	64	4	there	there	PRON
ma-386	64	5	exists	exist	VERB
ma-386	64	6	a	a	DET
ma-386	64	7	nondecreasing	nondecreasing	ADJ
ma-386	64	8	and	and	CCONJ
ma-386	64	9	continuous	continuous	ADJ
ma-386	64	10	function	function	NOUN
ma-386	64	11	φ	φ	NOUN
ma-386	64	12	:	:	PUNCT
ma-386	64	13	a0	a0	PROPN
ma-386	64	14	→	→	PUNCT
ma-386	64	15	a	a	DET
ma-386	64	16	such	such	ADJ
ma-386	64	17	that	that	PRON
ma-386	64	18	for	for	ADP
ma-386	64	19	h1	h1	PROPN
ma-386	64	20	:	:	PUNCT
ma-386	64	21	a0	a0	PROPN
ma-386	64	22	→	→	SYM
ma-386	64	23	adefined	adefine	VERB
ma-386	64	24	by	by	ADP
ma-386	64	25	h1(t	h1(t	PROPN
ma-386	64	26	)	)	PUNCT
ma-386	64	27	=	=	PUNCT
ma-386	65	1	1∫	1∫	NUM
ma-386	65	2	0	0	NUM
ma-386	65	3	φ((t	φ((t	NOUN
ma-386	65	4	−	−	PROPN
ma-386	65	5	η)t)dη	η)t)dη	PROPN
ma-386	65	6	(	(	PUNCT
ma-386	65	7	3	3	NUM
ma-386	65	8	)	)	PUNCT
ma-386	65	9	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	NOUN
ma-386	65	10	eur	eur	PROPN
ma-386	65	11	.	.	PUNCT
ma-386	66	1	j.	j.	PROPN
ma-386	66	2	math	math	PROPN
ma-386	66	3	.	.	PUNCT
ma-386	67	1	anal	anal	PROPN
ma-386	67	2	.	.	PUNCT
ma-386	68	1	10.28924	10.28924	NUM
ma-386	68	2	/	/	SYM
ma-386	68	3	ada	ada	NOUN
ma-386	68	4	/	/	SYM
ma-386	68	5	ma.5.18	ma.5.18	PROPN
ma-386	68	6	4the	4the	NUM
ma-386	68	7	function	function	NOUN
ma-386	68	8	1−	1−	NUM
ma-386	68	9	h1(t	h1(t	X
ma-386	68	10	)	)	PUNCT
ma-386	68	11	has	have	VERB
ma-386	68	12	a	a	DET
ma-386	68	13	smallest	small	ADJ
ma-386	68	14	positive	positive	ADJ
ma-386	68	15	zero	zero	NUM
ma-386	68	16	in	in	ADP
ma-386	68	17	the	the	DET
ma-386	68	18	interval	interval	NOUN
ma-386	68	19	a0	a0	NOUN
ma-386	68	20	,	,	PUNCT
ma-386	68	21	which	which	PRON
ma-386	68	22	is	be	AUX
ma-386	68	23	denoted	denote	VERB
ma-386	68	24	by	by	ADP
ma-386	68	25	r1	r1	PROPN
ma-386	68	26	.	.	PUNCT
ma-386	69	1	(	(	PUNCT
ma-386	69	2	h3	h3	NOUN
ma-386	69	3	)	)	PUNCT
ma-386	69	4	for	for	ADP
ma-386	69	5	p	p	NOUN
ma-386	69	6	:	:	PUNCT
ma-386	69	7	a0	a0	PROPN
ma-386	69	8	→	→	PUNCT
ma-386	69	9	a	a	PRON
ma-386	69	10	defined	define	VERB
ma-386	69	11	by	by	ADP
ma-386	69	12	p(t	p(t	NOUN
ma-386	69	13	)	)	PUNCT
ma-386	69	14	=	=	SYM
ma-386	69	15	1	1	NUM
ma-386	69	16	2	2	NUM
ma-386	69	17	(	(	PUNCT
ma-386	69	18	φ0(t	φ0(t	ADJ
ma-386	69	19	)	)	PUNCT
ma-386	69	20	+	+	NUM
ma-386	69	21	φ0(h1(t)t	φ0(h1(t)t	NOUN
ma-386	69	22	)	)	PUNCT
ma-386	69	23	)	)	PUNCT
ma-386	69	24	(	(	PUNCT
ma-386	69	25	4	4	X
ma-386	69	26	)	)	PUNCT
ma-386	69	27	the	the	DET
ma-386	69	28	function	function	NOUN
ma-386	69	29	1	1	NUM
ma-386	69	30	−	−	NOUN
ma-386	69	31	p(t	p(t	NOUN
ma-386	69	32	)	)	PUNCT
ma-386	69	33	has	have	VERB
ma-386	69	34	a	a	DET
ma-386	69	35	smallest	small	ADJ
ma-386	69	36	positive	positive	ADJ
ma-386	69	37	zero	zero	NUM
ma-386	69	38	in	in	ADP
ma-386	69	39	the	the	DET
ma-386	69	40	interval	interval	NOUN
ma-386	69	41	a0	a0	NOUN
ma-386	69	42	,	,	PUNCT
ma-386	69	43	which	which	PRON
ma-386	69	44	is	be	AUX
ma-386	69	45	denoted	denote	VERB
ma-386	69	46	by	by	ADP
ma-386	69	47	s1	s1	PROPN
ma-386	69	48	.	.	PUNCT
ma-386	70	1	define	define	VERB
ma-386	70	2	the	the	DET
ma-386	70	3	interval	interval	NOUN
ma-386	70	4	a1	a1	NOUN
ma-386	70	5	=	=	PUNCT
ma-386	71	1	[	[	X
ma-386	71	2	0	0	NUM
ma-386	71	3	,	,	PUNCT
ma-386	71	4	s1	s1	NOUN
ma-386	71	5	)	)	PUNCT
ma-386	71	6	.	.	PUNCT
ma-386	72	1	(	(	PUNCT
ma-386	72	2	h4	h4	PROPN
ma-386	72	3	)	)	PUNCT
ma-386	72	4	for	for	ADP
ma-386	72	5	φ	φ	PRON
ma-386	72	6	:	:	PUNCT
ma-386	72	7	a1	a1	NOUN
ma-386	72	8	→	→	SYM
ma-386	72	9	a	a	DET
ma-386	72	10	,	,	PUNCT
ma-386	72	11	h2	h2	NOUN
ma-386	72	12	:	:	PUNCT
ma-386	72	13	a1	a1	NOUN
ma-386	72	14	→	→	SYM
ma-386	72	15	a	a	NOUN
ma-386	72	16	,	,	PUNCT
ma-386	72	17	p	p	X
ma-386	72	18	:	:	PUNCT
ma-386	72	19	a1	a1	NOUN
ma-386	72	20	→	→	SYM
ma-386	72	21	a	a	PRON
ma-386	72	22	,	,	PUNCT
ma-386	72	23	defined	define	VERB
ma-386	72	24	by	by	ADP
ma-386	72	25	φ(t	φ(t	PROPN
ma-386	72	26	)	)	PUNCT
ma-386	72	27	=	=	PUNCT
ma-386	73	1			PROPN
ma-386	73	2	φ((1	φ((1	PROPN
ma-386	73	3	+	+	PROPN
ma-386	73	4	h1(t))t	h1(t))t	PROPN
ma-386	73	5	)	)	PUNCT
ma-386	73	6	or	or	CCONJ
ma-386	73	7	φ0(t	φ0(t	NOUN
ma-386	73	8	)	)	PUNCT
ma-386	73	9	+	+	NUM
ma-386	73	10	φ0(h1(t)t	φ0(h1(t)t	NOUN
ma-386	73	11	)	)	PUNCT
ma-386	73	12	,	,	PUNCT
ma-386	73	13	p(t	p(t	NOUN
ma-386	73	14	)	)	PUNCT
ma-386	73	15	=	=	SYM
ma-386	73	16	1	1	NUM
ma-386	73	17	2	2	NUM
ma-386	73	18	(	(	PUNCT
ma-386	73	19	φ0(t	φ0(t	ADJ
ma-386	73	20	)	)	PUNCT
ma-386	73	21	+	+	NUM
ma-386	73	22	φ0(h1(t)t	φ0(h1(t)t	NOUN
ma-386	73	23	)	)	PUNCT
ma-386	73	24	)	)	PUNCT
ma-386	73	25	,	,	PUNCT
ma-386	73	26	and	and	CCONJ
ma-386	73	27	h2(t	h2(t	NOUN
ma-386	73	28	)	)	PUNCT
ma-386	73	29	=	=	PUNCT
ma-386	74	1	1∫	1∫	NUM
ma-386	74	2	0	0	NUM
ma-386	74	3	φ0((1−	φ0((1−	PROPN
ma-386	74	4	η)t)dη	η)t)dη	PROPN
ma-386	74	5	1−	1−	NUM
ma-386	74	6	φ0(t	φ0(t	PROPN
ma-386	74	7	)	)	PUNCT
ma-386	74	8	+	+	SYM
ma-386	74	9	φ(t	φ(t	PROPN
ma-386	74	10	)	)	PUNCT
ma-386	74	11	(	(	PUNCT
ma-386	74	12	1	1	NUM
ma-386	74	13	+	+	CCONJ
ma-386	74	14	1∫	1∫	NUM
ma-386	74	15	0	0	NUM
ma-386	74	16	φ0(ηt)dη	φ0(ηt)dη	NOUN
ma-386	74	17	)	)	PUNCT
ma-386	75	1	2(1−	2(1−	X
ma-386	75	2	φ0(t))(1−	φ0(t))(1−	PROPN
ma-386	75	3	p(t	p(t	NOUN
ma-386	75	4	)	)	PUNCT
ma-386	75	5	)	)	PUNCT
ma-386	76	1	,	,	PUNCT
ma-386	76	2	the	the	DET
ma-386	76	3	function	function	NOUN
ma-386	76	4	1−	1−	NUM
ma-386	76	5	h2(t	h2(t	NOUN
ma-386	76	6	)	)	PUNCT
ma-386	76	7	has	have	VERB
ma-386	76	8	a	a	DET
ma-386	76	9	smallest	small	ADJ
ma-386	76	10	positive	positive	ADJ
ma-386	76	11	zero	zero	NUM
ma-386	76	12	in	in	ADP
ma-386	76	13	the	the	DET
ma-386	76	14	interval	interval	NOUN
ma-386	76	15	a1	a1	NOUN
ma-386	76	16	,	,	PUNCT
ma-386	76	17	which	which	PRON
ma-386	76	18	is	be	AUX
ma-386	76	19	denoted	denote	VERB
ma-386	76	20	by	by	ADP
ma-386	76	21	r2	r2	PROPN
ma-386	76	22	.	.	PUNCT
ma-386	77	1	(	(	PUNCT
ma-386	77	2	h5	h5	PROPN
ma-386	77	3	)	)	PUNCT
ma-386	77	4	for	for	ADP
ma-386	77	5	q	q	NOUN
ma-386	77	6	:	:	PUNCT
ma-386	77	7	a1	a1	NOUN
ma-386	77	8	→	→	SYM
ma-386	78	1	a	a	DET
ma-386	78	2	defined	define	VERB
ma-386	78	3	by	by	ADP
ma-386	78	4	q(t	q(t	NOUN
ma-386	78	5	)	)	PUNCT
ma-386	78	6	=	=	SYM
ma-386	78	7	1	1	NUM
ma-386	78	8	2	2	NUM
ma-386	78	9	(	(	PUNCT
ma-386	78	10	φ0(t	φ0(t	ADJ
ma-386	78	11	)	)	PUNCT
ma-386	78	12	+	+	NUM
ma-386	78	13	3φ0(h1(t)t	3φ0(h1(t)t	NUM
ma-386	78	14	)	)	PUNCT
ma-386	78	15	)	)	PUNCT
ma-386	79	1	the	the	DET
ma-386	79	2	function	function	NOUN
ma-386	79	3	1	1	NUM
ma-386	79	4	−	−	NOUN
ma-386	79	5	q(t	q(t	PROPN
ma-386	79	6	)	)	PUNCT
ma-386	79	7	has	have	VERB
ma-386	79	8	a	a	DET
ma-386	79	9	smallest	small	ADJ
ma-386	79	10	positive	positive	ADJ
ma-386	79	11	zero	zero	NUM
ma-386	79	12	,	,	PUNCT
ma-386	79	13	which	which	PRON
ma-386	79	14	is	be	AUX
ma-386	79	15	denoted	denote	VERB
ma-386	79	16	by	by	ADP
ma-386	79	17	s2	s2	PROPN
ma-386	79	18	.	.	PUNCT
ma-386	80	1	define	define	VERB
ma-386	80	2	theinterval	theinterval	PROPN
ma-386	80	3	a2	a2	PROPN
ma-386	80	4	=	=	PUNCT
ma-386	81	1	[	[	X
ma-386	81	2	0	0	NUM
ma-386	81	3	,	,	PUNCT
ma-386	81	4	s2	s2	PROPN
ma-386	81	5	)	)	PUNCT
ma-386	81	6	.	.	PUNCT
ma-386	82	1	(	(	PUNCT
ma-386	82	2	h6	h6	PROPN
ma-386	82	3	)	)	PUNCT
ma-386	82	4	for	for	ADP
ma-386	82	5	j	j	PROPN
ma-386	82	6	=	=	SYM
ma-386	82	7	3	3	PROPN
ma-386	82	8	,	,	PUNCT
ma-386	82	9	.	.	PUNCT
ma-386	82	10	.	.	PUNCT
ma-386	82	11	.	.	PUNCT
ma-386	83	1	,	,	PUNCT
ma-386	83	2	k	k	NOUN
ma-386	83	3	,	,	PUNCT
ma-386	83	4	aj−1	aj−1	X
ma-386	83	5	=	=	PUNCT
ma-386	84	1	[	[	X
ma-386	84	2	0	0	NUM
ma-386	84	3	,	,	PUNCT
ma-386	84	4	sj−1	sj−1	NOUN
ma-386	84	5	)	)	PUNCT
ma-386	84	6	,	,	PUNCT
ma-386	84	7	hj	hj	PROPN
ma-386	84	8	:	:	PUNCT
ma-386	84	9	aj−1	aj−1	NOUN
ma-386	84	10	→	→	SYM
ma-386	84	11	athe	athe	ADJ
ma-386	84	12	functions	function	NOUN
ma-386	84	13	1−	1−	NUM
ma-386	84	14	φ0(hj−1(t)t	φ0(hj−1(t)t	NOUN
ma-386	84	15	)	)	PUNCT
ma-386	84	16	and	and	CCONJ
ma-386	84	17	1−	1−	NUM
ma-386	84	18	hj(t	hj(t	X
ma-386	84	19	)	)	PUNCT
ma-386	84	20	have	have	VERB
ma-386	84	21	smallest	small	ADJ
ma-386	84	22	positive	positive	ADJ
ma-386	84	23	zeros	zero	NOUN
ma-386	84	24	in	in	ADP
ma-386	84	25	the	the	DET
ma-386	84	26	interval	interval	NOUN
ma-386	84	27	aj−1	aj−1	NOUN
ma-386	84	28	,	,	PUNCT
ma-386	84	29	which	which	PRON
ma-386	84	30	are	be	AUX
ma-386	84	31	denoted	denote	VERB
ma-386	84	32	by	by	ADP
ma-386	84	33	sj−1	sj−1	NOUN
ma-386	84	34	and	and	CCONJ
ma-386	84	35	rj	rj	PROPN
ma-386	84	36	,	,	PUNCT
ma-386	84	37	respectively	respectively	ADV
ma-386	84	38	,	,	PUNCT
ma-386	84	39	where	where	SCONJ
ma-386	84	40	hj(t	hj(t	PUNCT
ma-386	84	41	)	)	PUNCT
ma-386	84	42	=	=	SYM
ma-386	85	1			NOUN
ma-386	86	1	1∫	1∫	NUM
ma-386	86	2	0	0	NUM
ma-386	86	3	φ0((1−	φ0((1−	PROPN
ma-386	86	4	η)hj−1(t)t)dη	η)hj−1(t)t)dη	PROPN
ma-386	86	5	1−	1−	NUM
ma-386	86	6	φ0(hj−1(t)t	φ0(hj−1(t)t	NOUN
ma-386	86	7	)	)	PUNCT
ma-386	86	8	+	+	CCONJ
ma-386	86	9	(	(	PUNCT
ma-386	86	10	1	1	NUM
ma-386	86	11	+	+	NUM
ma-386	86	12	φ0(h1(t)t	φ0(h1(t)t	NOUN
ma-386	86	13	)	)	PUNCT
ma-386	86	14	)	)	PUNCT
ma-386	86	15	(	(	PUNCT
ma-386	86	16	1	1	NUM
ma-386	86	17	+	+	CCONJ
ma-386	86	18	1∫	1∫	NUM
ma-386	86	19	0	0	NUM
ma-386	86	20	φ0(ηhj−1(t)t)dη	φ0(ηhj−1(t)t)dη	NUM
ma-386	86	21	)	)	PUNCT
ma-386	86	22	2(1−	2(1−	X
ma-386	86	23	φ0(t))(1−	φ0(t))(1−	PROPN
ma-386	86	24	q(t	q(t	PROPN
ma-386	86	25	)	)	PUNCT
ma-386	86	26	)	)	PUNCT
ma-386	86	27			NOUN
ma-386	86	28	hj−1(t	hj−1(t	NOUN
ma-386	86	29	)	)	PUNCT
ma-386	86	30	define	define	VERB
ma-386	86	31	r∗	r∗	NOUN
ma-386	86	32	=	=	SYM
ma-386	86	33	min{rj	min{rj	NOUN
ma-386	86	34	}	}	PUNCT
ma-386	86	35	,	,	PUNCT
ma-386	86	36	m	m	VERB
ma-386	86	37	=	=	NOUN
ma-386	86	38	1	1	NUM
ma-386	86	39	,	,	PUNCT
ma-386	86	40	2	2	NUM
ma-386	86	41	,	,	PUNCT
ma-386	86	42	.	.	PUNCT
ma-386	86	43	.	.	PUNCT
ma-386	87	1	.	.	PUNCT
ma-386	88	1	,	,	PUNCT
ma-386	88	2	k	k	PROPN
ma-386	88	3	and	and	CCONJ
ma-386	88	4	a∗	a∗	PROPN
ma-386	88	5	=	=	PUNCT
ma-386	89	1	[	[	X
ma-386	89	2	0	0	NUM
ma-386	89	3	,	,	PUNCT
ma-386	89	4	r∗	r∗	PROPN
ma-386	89	5	)	)	PUNCT
ma-386	89	6	(	(	PUNCT
ma-386	89	7	5	5	X
ma-386	89	8	)	)	PUNCT
ma-386	89	9	it	it	PRON
ma-386	89	10	follows	follow	VERB
ma-386	89	11	by	by	ADP
ma-386	89	12	these	these	DET
ma-386	89	13	definitions	definition	NOUN
ma-386	89	14	and	and	CCONJ
ma-386	89	15	conditions	condition	NOUN
ma-386	89	16	(	(	PUNCT
ma-386	89	17	h1)−	h1)−	PROPN
ma-386	89	18	(	(	PUNCT
ma-386	89	19	h6	h6	PROPN
ma-386	89	20	)	)	PUNCT
ma-386	89	21	that	that	SCONJ
ma-386	89	22	for	for	ADP
ma-386	89	23	each	each	DET
ma-386	89	24	t	t	PROPN
ma-386	89	25	∈	∈	PROPN
ma-386	89	26	a∗	a∗	PROPN
ma-386	89	27	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	89	28	eur	eur	PROPN
ma-386	89	29	.	.	PUNCT
ma-386	90	1	j.	j.	PROPN
ma-386	90	2	math	math	PROPN
ma-386	90	3	.	.	PUNCT
ma-386	91	1	anal	anal	PROPN
ma-386	91	2	.	.	PUNCT
ma-386	92	1	10.28924	10.28924	NUM
ma-386	92	2	/	/	SYM
ma-386	92	3	ada	ada	PROPN
ma-386	92	4	/	/	SYM
ma-386	92	5	ma.5.18	ma.5.18	NOUN
ma-386	92	6	5	5	NUM
ma-386	92	7	0	0	NUM
ma-386	92	8	≤	≤	NUM
ma-386	92	9	φ0(t	φ0(t	PROPN
ma-386	92	10	)	)	PUNCT
ma-386	92	11	<	<	X
ma-386	92	12	1	1	NUM
ma-386	92	13	,	,	PUNCT
ma-386	92	14	(	(	PUNCT
ma-386	92	15	6	6	NUM
ma-386	92	16	)	)	PUNCT
ma-386	92	17	0	0	NUM
ma-386	92	18	≤	≤	NUM
ma-386	92	19	p(t	p(t	NOUN
ma-386	92	20	)	)	PUNCT
ma-386	92	21	<	<	X
ma-386	92	22	1	1	NUM
ma-386	92	23	,	,	PUNCT
ma-386	92	24	(	(	PUNCT
ma-386	92	25	7	7	NUM
ma-386	92	26	)	)	PUNCT
ma-386	92	27	0	0	NUM
ma-386	93	1	≤	≤	NUM
ma-386	94	1	q(t	q(t	PROPN
ma-386	94	2	)	)	PUNCT
ma-386	94	3	<	<	X
ma-386	94	4	1	1	NUM
ma-386	94	5	,	,	PUNCT
ma-386	94	6	(	(	PUNCT
ma-386	94	7	8)	8)	NUM
ma-386	94	8	0	0	NUM
ma-386	94	9	≤	≤	NOUN
ma-386	94	10	φ0(hj−1(t)t	φ0(hj−1(t)t	NOUN
ma-386	94	11	)	)	PUNCT
ma-386	94	12	<	<	X
ma-386	94	13	1	1	NUM
ma-386	94	14	,	,	PUNCT
ma-386	94	15	(	(	PUNCT
ma-386	94	16	9)and	9)and	NUM
ma-386	94	17	(	(	PUNCT
ma-386	94	18	10	10	NUM
ma-386	94	19	)	)	PUNCT
ma-386	94	20	0	0	NUM
ma-386	94	21	≤	≤	NUM
ma-386	94	22	hj(t	hj(t	PRON
ma-386	94	23	)	)	PUNCT
ma-386	94	24	<	<	X
ma-386	94	25	1	1	X
ma-386	94	26	.	.	PUNCT
ma-386	94	27	(	(	PUNCT
ma-386	94	28	11	11	NUM
ma-386	94	29	)	)	PUNCT
ma-386	94	30	notice	notice	NOUN
ma-386	94	31	also	also	ADV
ma-386	94	32	that	that	SCONJ
ma-386	94	33	the	the	DET
ma-386	94	34	parameter	parameter	NOUN
ma-386	94	35	r	r	NOUN
ma-386	94	36	is	be	AUX
ma-386	94	37	shown	show	VERB
ma-386	94	38	to	to	PART
ma-386	94	39	be	be	AUX
ma-386	94	40	a	a	DET
ma-386	94	41	radius	radius	NOUN
ma-386	94	42	of	of	ADP
ma-386	94	43	convergence	convergence	NOUN
ma-386	94	44	for	for	ADP
ma-386	94	45	the	the	DET
ma-386	94	46	method(2	method(2	NOUN
ma-386	94	47	)	)	PUNCT
ma-386	94	48	(	(	PUNCT
ma-386	94	49	see	see	VERB
ma-386	94	50	theorem	theorem	ADJ
ma-386	94	51	1).next	1).next	NUM
ma-386	94	52	,	,	PUNCT
ma-386	94	53	we	we	PRON
ma-386	94	54	relate	relate	VERB
ma-386	94	55	functions	function	NOUN
ma-386	94	56	φ0	φ0	PROPN
ma-386	94	57	and	and	CCONJ
ma-386	94	58	φ	φ	NOUN
ma-386	94	59	to	to	ADP
ma-386	94	60	the	the	DET
ma-386	94	61	operators	operator	NOUN
ma-386	94	62	in	in	ADP
ma-386	94	63	the	the	DET
ma-386	94	64	method	method	NOUN
ma-386	94	65	(	(	PUNCT
ma-386	94	66	2	2	NUM
ma-386	94	67	)	)	PUNCT
ma-386	94	68	.	.	PUNCT
ma-386	95	1	(	(	PUNCT
ma-386	95	2	h7	h7	PROPN
ma-386	95	3	)	)	PUNCT
ma-386	95	4	there	there	PRON
ma-386	95	5	exists	exist	VERB
ma-386	95	6	a	a	DET
ma-386	95	7	solution	solution	NOUN
ma-386	95	8	x∗	x∗	PROPN
ma-386	95	9	∈	∈	PROPN
ma-386	95	10	d	d	PROPN
ma-386	95	11	and	and	CCONJ
ma-386	95	12	a	a	DET
ma-386	95	13	linear	linear	ADJ
ma-386	95	14	operator	operator	NOUN
ma-386	95	15	e	e	NOUN
ma-386	95	16	∈	∈	PROPN
ma-386	95	17	l(b0	l(b0	PROPN
ma-386	95	18	,	,	PUNCT
ma-386	95	19	b	b	NOUN
ma-386	95	20	)	)	PUNCT
ma-386	95	21	which	which	PRON
ma-386	95	22	is	be	AUX
ma-386	95	23	invertible	invertible	ADJ
ma-386	95	24	suchthat	suchthat	PROPN
ma-386	95	25	for	for	ADP
ma-386	95	26	each	each	DET
ma-386	95	27	z	z	NOUN
ma-386	95	28	∈	∈	PROPN
ma-386	96	1	d	d	X
ma-386	96	2	‖e−1(g(z)−	‖e−1(g(z)−	NOUN
ma-386	96	3	e)‖	e)‖	ADP
ma-386	96	4	≤	≤	PROPN
ma-386	97	1	φ0(‖z	φ0(‖z	ADV
ma-386	97	2	−	−	PROPN
ma-386	98	1	x∗‖	x∗‖	NUM
ma-386	98	2	)	)	PUNCT
ma-386	98	3	.	.	PUNCT
ma-386	99	1	define	define	VERB
ma-386	99	2	the	the	DET
ma-386	99	3	region	region	NOUN
ma-386	99	4	d0	d0	NOUN
ma-386	99	5	=	=	SYM
ma-386	99	6	d∩u(x∗	d∩u(x∗	PROPN
ma-386	99	7	,	,	PUNCT
ma-386	99	8	s0	s0	PROPN
ma-386	99	9	)	)	PUNCT
ma-386	99	10	,	,	PUNCT
ma-386	99	11	where	where	SCONJ
ma-386	99	12	u(x	u(x	NOUN
ma-386	99	13	,	,	PUNCT
ma-386	99	14	s	s	PART
ma-386	99	15	)	)	PUNCT
ma-386	99	16	stands	stand	VERB
ma-386	99	17	for	for	ADP
ma-386	99	18	an	an	DET
ma-386	99	19	open	open	ADJ
ma-386	99	20	ball	ball	NOUN
ma-386	99	21	in	in	ADP
ma-386	99	22	b0	b0	NOUN
ma-386	99	23	centeredat	centeredat	PROPN
ma-386	99	24	x	x	X
ma-386	99	25	and	and	CCONJ
ma-386	99	26	of	of	ADP
ma-386	99	27	some	some	DET
ma-386	99	28	radius	radius	NOUN
ma-386	99	29	s	s	PROPN
ma-386	99	30	>	>	X
ma-386	99	31	0	0	NUM
ma-386	99	32	.	.	PUNCT
ma-386	100	1	the	the	DET
ma-386	100	2	set	set	NOUN
ma-386	100	3	u[x	u[x	PROPN
ma-386	100	4	,	,	PUNCT
ma-386	100	5	s	s	PART
ma-386	100	6	]	]	X
ma-386	100	7	denotes	denote	VERB
ma-386	100	8	the	the	DET
ma-386	100	9	closure	closure	NOUN
ma-386	100	10	of	of	ADP
ma-386	100	11	u(x	u(x	NOUN
ma-386	100	12	,	,	PUNCT
ma-386	100	13	s	s	NOUN
ma-386	100	14	)	)	PUNCT
ma-386	100	15	,	,	PUNCT
ma-386	100	16	which	which	PRON
ma-386	100	17	is	be	AUX
ma-386	100	18	aclosed	aclose	VERB
ma-386	100	19	set	set	VERB
ma-386	100	20	.	.	PUNCT
ma-386	101	1	(	(	PUNCT
ma-386	101	2	h8	h8	PROPN
ma-386	101	3	)	)	PUNCT
ma-386	102	1	‖e−1(g′(z2)−	‖e−1(g′(z2)−	PROPN
ma-386	102	2	g′(z1))‖	g′(z1))‖	VERB
ma-386	102	3	≤	≤	NUM
ma-386	102	4	φ(‖z2	φ(‖z2	NOUN
ma-386	102	5	−	−	PROPN
ma-386	102	6	z1‖	z1‖	NOUN
ma-386	102	7	)	)	PUNCT
ma-386	102	8	for	for	ADP
ma-386	102	9	each	each	DET
ma-386	102	10	z1	z1	NOUN
ma-386	102	11	,	,	PUNCT
ma-386	102	12	z2	z2	PROPN
ma-386	102	13	∈	∈	PROPN
ma-386	102	14	d0	d0	NOUN
ma-386	102	15	.	.	PUNCT
ma-386	103	1	(	(	PUNCT
ma-386	103	2	h9	h9	NOUN
ma-386	103	3	)	)	PUNCT
ma-386	103	4	u[x∗	u[x∗	PROPN
ma-386	103	5	,	,	PUNCT
ma-386	103	6	r∗	r∗	PROPN
ma-386	103	7	]	]	PUNCT
ma-386	103	8	⊂	⊂	PROPN
ma-386	103	9	d.	d.	PROPN
ma-386	103	10	remark	remark	VERB
ma-386	103	11	1	1	NUM
ma-386	103	12	.	.	PUNCT
ma-386	104	1	some	some	DET
ma-386	104	2	possible	possible	ADJ
ma-386	104	3	selections	selection	NOUN
ma-386	104	4	for	for	ADP
ma-386	104	5	the	the	DET
ma-386	104	6	linear	linear	ADJ
ma-386	104	7	operator	operator	NOUN
ma-386	104	8	e	e	NOUN
ma-386	104	9	can	can	AUX
ma-386	104	10	be	be	AUX
ma-386	104	11	e	e	NOUN
ma-386	104	12	=	=	SYM
ma-386	104	13	i	i	PROPN
ma-386	104	14	,	,	PUNCT
ma-386	104	15	the	the	DET
ma-386	104	16	identity	identity	NOUN
ma-386	104	17	operator	operator	NOUN
ma-386	104	18	,	,	PUNCT
ma-386	104	19	or	or	CCONJ
ma-386	104	20	e	e	NOUN
ma-386	104	21	=	=	SYM
ma-386	104	22	g′(z̄	g′(z̄	PROPN
ma-386	104	23	)	)	PUNCT
ma-386	104	24	for	for	ADP
ma-386	104	25	some	some	DET
ma-386	104	26	z̄	z̄	NOUN
ma-386	104	27	∈	∈	PROPN
ma-386	104	28	d	d	NOUN
ma-386	104	29	with	with	ADP
ma-386	104	30	z̄	z̄	PROPN
ma-386	104	31	6=	6=	NUM
ma-386	104	32	x∗	x∗	PROPN
ma-386	104	33	or	or	CCONJ
ma-386	104	34	e	e	NOUN
ma-386	104	35	=	=	SYM
ma-386	104	36	g′(x∗	g′(x∗	PROPN
ma-386	104	37	)	)	PUNCT
ma-386	104	38	.	.	PUNCT
ma-386	105	1	the	the	DET
ma-386	105	2	last	last	ADJ
ma-386	105	3	choice	choice	NOUN
ma-386	105	4	of	of	ADP
ma-386	105	5	e	e	PROPN
ma-386	105	6	implies	imply	VERB
ma-386	105	7	x∗	x∗	PROPN
ma-386	105	8	is	be	AUX
ma-386	105	9	asimple	asimple	ADJ
ma-386	105	10	solution	solution	NOUN
ma-386	105	11	of	of	ADP
ma-386	105	12	the	the	DET
ma-386	105	13	equation	equation	NOUN
ma-386	105	14	g(x	g(x	NOUN
ma-386	105	15	)	)	PUNCT
ma-386	106	1	=	=	SYM
ma-386	106	2	0	0	X
ma-386	106	3	.	.	PUNCT
ma-386	107	1	it	it	PRON
ma-386	107	2	is	be	AUX
ma-386	107	3	worth	worth	ADJ
ma-386	107	4	noting	note	VERB
ma-386	107	5	,	,	PUNCT
ma-386	107	6	though	though	ADV
ma-386	107	7	,	,	PUNCT
ma-386	107	8	that	that	SCONJ
ma-386	107	9	such	such	DET
ma-386	107	10	an	an	DET
ma-386	107	11	assumption	assumption	NOUN
ma-386	107	12	isnot	isnot	ADV
ma-386	107	13	made	make	VERB
ma-386	107	14	or	or	CCONJ
ma-386	107	15	implied	imply	VERB
ma-386	107	16	by	by	ADP
ma-386	107	17	the	the	DET
ma-386	107	18	conditions	condition	NOUN
ma-386	107	19	(	(	PUNCT
ma-386	107	20	h1)–(h9	h1)–(h9	NOUN
ma-386	107	21	)	)	PUNCT
ma-386	107	22	.	.	PUNCT
ma-386	108	1	the	the	DET
ma-386	108	2	local	local	ADJ
ma-386	108	3	convergence	convergence	NOUN
ma-386	108	4	analysis	analysis	NOUN
ma-386	108	5	of	of	ADP
ma-386	108	6	the	the	DET
ma-386	108	7	method	method	NOUN
ma-386	108	8	(	(	PUNCT
ma-386	108	9	2	2	X
ma-386	108	10	)	)	PUNCT
ma-386	108	11	is	be	AUX
ma-386	108	12	provided	provide	VERB
ma-386	108	13	in	in	ADP
ma-386	108	14	the	the	DET
ma-386	108	15	next	next	ADJ
ma-386	108	16	result	result	NOUN
ma-386	108	17	.	.	PUNCT
ma-386	109	1	let	let	VERB
ma-386	109	2	u0	u0	ADJ
ma-386	109	3	=	=	PROPN
ma-386	109	4	u(x∗	u(x∗	PROPN
ma-386	109	5	,	,	PUNCT
ma-386	109	6	r∗)−	r∗)−	NOUN
ma-386	109	7	{	{	PUNCT
ma-386	109	8	x∗	x∗	PROPN
ma-386	109	9	}	}	PUNCT
ma-386	109	10	.	.	PUNCT
ma-386	110	1	theorem	theorem	NOUN
ma-386	110	2	1	1	NUM
ma-386	110	3	.	.	PUNCT
ma-386	110	4	suppose	suppose	VERB
ma-386	110	5	that	that	SCONJ
ma-386	110	6	the	the	DET
ma-386	110	7	conditions	condition	NOUN
ma-386	110	8	(	(	PUNCT
ma-386	110	9	h1)–(h9	h1)–(h9	NOUN
ma-386	110	10	)	)	PUNCT
ma-386	110	11	hold	hold	NOUN
ma-386	110	12	.	.	PUNCT
ma-386	111	1	then	then	ADV
ma-386	111	2	,	,	PUNCT
ma-386	111	3	the	the	DET
ma-386	111	4	sequence	sequence	NOUN
ma-386	111	5	{	{	PUNCT
ma-386	111	6	xn	xn	PROPN
ma-386	111	7	}	}	PUNCT
ma-386	111	8	generated	generate	VERB
ma-386	111	9	for	for	ADP
ma-386	111	10	the	the	DET
ma-386	111	11	starting	starting	NOUN
ma-386	111	12	point	point	NOUN
ma-386	111	13	x0	x0	PROPN
ma-386	111	14	∈	∈	PROPN
ma-386	111	15	u0	u0	PROPN
ma-386	111	16	is	be	AUX
ma-386	111	17	convergent	convergent	ADJ
ma-386	111	18	to	to	ADP
ma-386	111	19	the	the	DET
ma-386	111	20	solution	solution	NOUN
ma-386	111	21	x∗	x∗	PROPN
ma-386	111	22	of	of	ADP
ma-386	111	23	the	the	DET
ma-386	111	24	equation	equation	NOUN
ma-386	111	25	g(x	g(x	NOUN
ma-386	111	26	)	)	PUNCT
ma-386	112	1	=	=	SYM
ma-386	112	2	0	0	X
ma-386	112	3	.	.	PUNCT
ma-386	113	1	proof	proof	NOUN
ma-386	113	2	.	.	PUNCT
ma-386	114	1	the	the	DET
ma-386	114	2	following	follow	VERB
ma-386	114	3	assertions	assertion	NOUN
ma-386	114	4	shall	shall	AUX
ma-386	114	5	be	be	AUX
ma-386	114	6	established	establish	VERB
ma-386	114	7	using	use	VERB
ma-386	114	8	induction	induction	NOUN
ma-386	114	9	on	on	ADP
ma-386	114	10	n	n	PROPN
ma-386	114	11	=	=	SYM
ma-386	114	12	0	0	NUM
ma-386	114	13	,	,	PUNCT
ma-386	114	14	1	1	NUM
ma-386	114	15	,	,	PUNCT
ma-386	114	16	2	2	NUM
ma-386	114	17	,	,	PUNCT
ma-386	114	18	.	.	PUNCT
ma-386	114	19	.	.	PUNCT
ma-386	114	20	.	.	PUNCT
ma-386	115	1	‖y	‖y	PUNCT
ma-386	116	1	(	(	PUNCT
ma-386	116	2	1)n	1)n	NUM
ma-386	116	3	−	−	PROPN
ma-386	116	4	x∗‖	x∗‖	PROPN
ma-386	116	5	≤	≤	PROPN
ma-386	116	6	g1(‖xn	g1(‖xn	PROPN
ma-386	116	7	−	−	PROPN
ma-386	116	8	x∗‖)‖xn	x∗‖)‖xn	PUNCT
ma-386	117	1	−	−	PROPN
ma-386	117	2	x∗‖	x∗‖	PROPN
ma-386	117	3	≤	≤	NOUN
ma-386	118	1	‖xn	‖xn	PROPN
ma-386	118	2	−	−	PROPN
ma-386	118	3	x∗‖	x∗‖	PROPN
ma-386	118	4	<	<	X
ma-386	118	5	r∗	r∗	PROPN
ma-386	118	6	,	,	PUNCT
ma-386	118	7	(	(	PUNCT
ma-386	118	8	12	12	NUM
ma-386	118	9	)	)	PUNCT
ma-386	118	10	‖y	‖y	PUNCT
ma-386	118	11	(	(	PUNCT
ma-386	118	12	2)n	2)n	NUM
ma-386	118	13	−	−	PROPN
ma-386	118	14	x∗‖	x∗‖	PROPN
ma-386	118	15	≤	≤	PROPN
ma-386	118	16	g2(‖xn	g2(‖xn	PROPN
ma-386	118	17	−	−	PROPN
ma-386	118	18	x∗‖)‖xn	x∗‖)‖xn	PUNCT
ma-386	119	1	−	−	PROPN
ma-386	119	2	x∗‖	x∗‖	PROPN
ma-386	119	3	≤	≤	NOUN
ma-386	119	4	‖xn	‖xn	PUNCT
ma-386	119	5	−	−	PROPN
ma-386	119	6	x∗‖	x∗‖	PROPN
ma-386	119	7	,	,	PUNCT
ma-386	119	8	(	(	PUNCT
ma-386	119	9	13	13	NUM
ma-386	119	10	)	)	PUNCT
ma-386	119	11	‖y	‖y	PUNCT
ma-386	120	1	(	(	PUNCT
ma-386	120	2	j)n	j)n	NOUN
ma-386	120	3	−	−	PROPN
ma-386	120	4	x∗‖	x∗‖	PROPN
ma-386	120	5	≤	≤	NUM
ma-386	120	6	gj(‖xn	gj(‖xn	PROPN
ma-386	120	7	−	−	PROPN
ma-386	120	8	x∗‖)‖xn	x∗‖)‖xn	PUNCT
ma-386	121	1	−	−	PROPN
ma-386	121	2	x∗‖	x∗‖	PROPN
ma-386	121	3	≤	≤	NOUN
ma-386	122	1	‖xn	‖xn	PUNCT
ma-386	122	2	−	−	PROPN
ma-386	122	3	x∗‖	x∗‖	PROPN
ma-386	122	4	,	,	PUNCT
ma-386	122	5	(	(	PUNCT
ma-386	122	6	14	14	NUM
ma-386	122	7	)	)	PUNCT
ma-386	122	8	·	·	PUNCT
ma-386	122	9	·	·	PUNCT
ma-386	122	10	·	·	PUNCT
ma-386	122	11	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	122	12	eur	eur	PROPN
ma-386	122	13	.	.	PUNCT
ma-386	123	1	j.	j.	PROPN
ma-386	123	2	math	math	PROPN
ma-386	123	3	.	.	PUNCT
ma-386	124	1	anal	anal	PROPN
ma-386	124	2	.	.	PUNCT
ma-386	125	1	10.28924	10.28924	NUM
ma-386	125	2	/	/	SYM
ma-386	125	3	ada	ada	PROPN
ma-386	125	4	/	/	SYM
ma-386	125	5	ma.5.18	ma.5.18	PROPN
ma-386	125	6	6	6	NUM
ma-386	125	7	‖xn+1	‖xn+1	NOUN
ma-386	125	8	−	−	PROPN
ma-386	125	9	x∗‖	x∗‖	PROPN
ma-386	125	10	=	=	SYM
ma-386	126	1	‖y	‖y	PROPN
ma-386	126	2	(	(	PUNCT
ma-386	126	3	k)n	k)n	PROPN
ma-386	126	4	−	−	PROPN
ma-386	126	5	x∗‖	x∗‖	PROPN
ma-386	126	6	≤	≤	PROPN
ma-386	126	7	gk(‖xn	gk(‖xn	PROPN
ma-386	126	8	−	−	PROPN
ma-386	126	9	x∗‖)‖xn	x∗‖)‖xn	PUNCT
ma-386	127	1	−	−	PROPN
ma-386	127	2	x∗‖	x∗‖	PROPN
ma-386	127	3	≤	≤	NOUN
ma-386	128	1	‖xn	‖xn	PROPN
ma-386	128	2	−	−	PROPN
ma-386	128	3	x∗‖.	x∗‖.	PROPN
ma-386	128	4	(	(	PUNCT
ma-386	128	5	15	15	NUM
ma-386	128	6	)	)	PUNCT
ma-386	128	7	pick	pick	VERB
ma-386	128	8	u	u	NOUN
ma-386	128	9	∈	∈	PROPN
ma-386	128	10	u0	u0	NOUN
ma-386	128	11	.	.	PUNCT
ma-386	129	1	it	it	PRON
ma-386	129	2	follows	follow	VERB
ma-386	129	3	by	by	ADP
ma-386	129	4	conditions	condition	NOUN
ma-386	129	5	(	(	PUNCT
ma-386	129	6	h1	h1	PROPN
ma-386	129	7	)	)	PUNCT
ma-386	129	8	,	,	PUNCT
ma-386	129	9	(	(	PUNCT
ma-386	129	10	h7	h7	NOUN
ma-386	129	11	)	)	PUNCT
ma-386	129	12	,	,	PUNCT
ma-386	129	13	and	and	CCONJ
ma-386	129	14	(	(	PUNCT
ma-386	129	15	5	5	NUM
ma-386	129	16	)	)	PUNCT
ma-386	129	17	,	,	PUNCT
ma-386	129	18	(	(	PUNCT
ma-386	129	19	6	6	X
ma-386	129	20	)	)	PUNCT
ma-386	129	21	‖e−1(g′(u)−	‖e−1(g′(u)−	PROPN
ma-386	129	22	e)‖	e)‖	ADJ
ma-386	129	23	≤	≤	NOUN
ma-386	129	24	φ0(‖u	φ0(‖u	NOUN
ma-386	129	25	−	−	PROPN
ma-386	129	26	x∗‖	x∗‖	NUM
ma-386	129	27	)	)	PUNCT
ma-386	129	28	≤	≤	NOUN
ma-386	129	29	φ0(r∗	φ0(r∗	X
ma-386	129	30	)	)	PUNCT
ma-386	129	31	<	<	X
ma-386	130	1	1	1	X
ma-386	130	2	.	.	PUNCT
ma-386	130	3	(	(	PUNCT
ma-386	130	4	16	16	NUM
ma-386	130	5	)	)	PUNCT
ma-386	130	6	so	so	ADV
ma-386	130	7	,	,	PUNCT
ma-386	130	8	the	the	DET
ma-386	130	9	linear	linear	ADJ
ma-386	130	10	operator	operator	NOUN
ma-386	130	11	g′(u	g′(u	PROPN
ma-386	130	12	)	)	PUNCT
ma-386	130	13	is	be	AUX
ma-386	130	14	invertible	invertible	ADJ
ma-386	130	15	by	by	ADP
ma-386	130	16	the	the	DET
ma-386	130	17	lemma	lemma	PROPN
ma-386	130	18	due	due	ADP
ma-386	130	19	to	to	PART
ma-386	130	20	banach	banach	NOUN
ma-386	130	21	[	[	X
ma-386	130	22	13	13	NUM
ma-386	130	23	]	]	PUNCT
ma-386	130	24	and	and	CCONJ
ma-386	130	25	‖g′(u)−1e‖	‖g′(u)−1e‖	X
ma-386	130	26	≤	≤	NUM
ma-386	130	27	1	1	NUM
ma-386	130	28	1−	1−	NUM
ma-386	130	29	φ0(‖u	φ0(‖u	NOUN
ma-386	130	30	−	−	PROPN
ma-386	130	31	x∗‖	x∗‖	NUM
ma-386	130	32	)	)	PUNCT
ma-386	130	33	.	.	PUNCT
ma-386	131	1	(	(	PUNCT
ma-386	131	2	17	17	NUM
ma-386	131	3	)	)	PUNCT
ma-386	131	4	in	in	ADP
ma-386	131	5	particular	particular	ADJ
ma-386	131	6	,	,	PUNCT
ma-386	131	7	if	if	SCONJ
ma-386	131	8	u	u	NOUN
ma-386	131	9	=	=	PROPN
ma-386	131	10	x0	x0	PROPN
ma-386	131	11	,	,	PUNCT
ma-386	131	12	the	the	DET
ma-386	131	13	iterate	iterate	NOUN
ma-386	131	14	y	y	PROPN
ma-386	131	15	(	(	PUNCT
ma-386	131	16	1)0	1)0	PROPN
ma-386	131	17	exists	exist	VERB
ma-386	131	18	by	by	ADP
ma-386	131	19	the	the	DET
ma-386	131	20	first	first	ADJ
ma-386	131	21	substep	substep	NOUN
ma-386	131	22	of	of	ADP
ma-386	131	23	the	the	DET
ma-386	131	24	method	method	NOUN
ma-386	131	25	(	(	PUNCT
ma-386	131	26	2	2	NUM
ma-386	131	27	)	)	PUNCT
ma-386	131	28	for	for	ADP
ma-386	131	29	n	n	NOUN
ma-386	131	30	=	=	SYM
ma-386	131	31	0,and	0,and	NUM
ma-386	131	32	we	we	PRON
ma-386	131	33	can	can	AUX
ma-386	131	34	write	write	VERB
ma-386	131	35	y	y	PROPN
ma-386	131	36	(	(	PUNCT
ma-386	131	37	1	1	NUM
ma-386	131	38	)	)	PUNCT
ma-386	131	39	0	0	NUM
ma-386	132	1	−	−	NOUN
ma-386	132	2	x	x	SYM
ma-386	132	3	∗	∗	NOUN
ma-386	132	4	=	=	PUNCT
ma-386	133	1	x0	x0	NUM
ma-386	133	2	−	−	PROPN
ma-386	133	3	x∗	x∗	PROPN
ma-386	133	4	−	−	PROPN
ma-386	133	5	g′(x0)−1g(x0	g′(x0)−1g(x0	NOUN
ma-386	133	6	)	)	PUNCT
ma-386	134	1	=	=	PUNCT
ma-386	134	2	[	[	PUNCT
ma-386	134	3	g′(x0	g′(x0	NOUN
ma-386	134	4	)	)	PUNCT
ma-386	134	5	−1e	−1e	X
ma-386	134	6	]	]	PUNCT
ma-386	135	1			PROPN
ma-386	135	2	1∫	1∫	NUM
ma-386	135	3	0	0	NUM
ma-386	135	4	e−1(g′(x0	e−1(g′(x0	PROPN
ma-386	135	5	+	+	CCONJ
ma-386	135	6	η(x∗	η(x∗	NOUN
ma-386	135	7	−	−	PROPN
ma-386	135	8	x0))−	x0))−	PROPN
ma-386	136	1	g′(x0))dη(x0	g′(x0))dη(x0	PROPN
ma-386	136	2	−	−	PROPN
ma-386	136	3	x∗	x∗	NOUN
ma-386	136	4	)	)	PUNCT
ma-386	136	5			PROPN
ma-386	136	6	(	(	PUNCT
ma-386	136	7	18	18	NUM
ma-386	136	8	)	)	PUNCT
ma-386	136	9	using	use	VERB
ma-386	136	10	the	the	DET
ma-386	136	11	condition	condition	NOUN
ma-386	136	12	(	(	PUNCT
ma-386	136	13	h8	h8	PROPN
ma-386	136	14	)	)	PUNCT
ma-386	136	15	,	,	PUNCT
ma-386	136	16	(	(	PUNCT
ma-386	136	17	5	5	NUM
ma-386	136	18	)	)	PUNCT
ma-386	136	19	,	,	PUNCT
ma-386	136	20	(	(	PUNCT
ma-386	136	21	11	11	NUM
ma-386	136	22	)	)	PUNCT
ma-386	136	23	(	(	PUNCT
ma-386	136	24	for	for	ADP
ma-386	136	25	i	i	PRON
ma-386	136	26	=	=	NOUN
ma-386	136	27	1	1	NUM
ma-386	136	28	)	)	PUNCT
ma-386	136	29	,	,	PUNCT
ma-386	136	30	(	(	PUNCT
ma-386	136	31	17	17	NUM
ma-386	136	32	)	)	PUNCT
ma-386	136	33	,	,	PUNCT
ma-386	136	34	and	and	CCONJ
ma-386	136	35	(	(	PUNCT
ma-386	136	36	18	18	NUM
ma-386	136	37	)	)	PUNCT
ma-386	136	38	,	,	PUNCT
ma-386	136	39	we	we	PRON
ma-386	136	40	get	get	VERB
ma-386	136	41	from	from	ADP
ma-386	136	42	(	(	PUNCT
ma-386	136	43	18	18	NUM
ma-386	136	44	)	)	PUNCT
ma-386	136	45	‖y	‖y	PUNCT
ma-386	137	1	(	(	PUNCT
ma-386	137	2	1)0	1)0	NUM
ma-386	137	3	−x	−x	NOUN
ma-386	137	4	∗‖	∗‖	PROPN
ma-386	137	5	≤	≤	NOUN
ma-386	138	1	1∫	1∫	NUM
ma-386	138	2	0	0	NUM
ma-386	138	3	φ((1−	φ((1−	NUM
ma-386	138	4	η)‖x0	η)‖x0	NOUN
ma-386	138	5	−	−	PROPN
ma-386	139	1	x∗‖)dη‖x0	x∗‖)dη‖x0	PROPN
ma-386	140	1	−	−	PROPN
ma-386	140	2	x∗‖	x∗‖	X
ma-386	140	3	1−	1−	NUM
ma-386	141	1	φ0(‖x0	φ0(‖x0	PROPN
ma-386	141	2	−	−	PROPN
ma-386	141	3	x∗‖	x∗‖	NUM
ma-386	141	4	)	)	PUNCT
ma-386	141	5	≤	≤	PUNCT
ma-386	142	1	q1(‖x0−x∗‖)‖x0−x∗‖	q1(‖x0−x∗‖)‖x0−x∗‖	ADP
ma-386	142	2	≤	≤	NUM
ma-386	142	3	‖x0−x∗‖	‖x0−x∗‖	ADP
ma-386	142	4	<	<	X
ma-386	142	5	r∗.	r∗.	NOUN
ma-386	142	6	(	(	PUNCT
ma-386	142	7	19	19	NUM
ma-386	142	8	)	)	PUNCT
ma-386	142	9	thus	thus	ADV
ma-386	142	10	,	,	PUNCT
ma-386	142	11	the	the	DET
ma-386	142	12	assertion	assertion	NOUN
ma-386	142	13	(	(	PUNCT
ma-386	142	14	12	12	NUM
ma-386	142	15	)	)	PUNCT
ma-386	142	16	holds	hold	VERB
ma-386	142	17	if	if	SCONJ
ma-386	142	18	n	n	NOUN
ma-386	142	19	=	=	SYM
ma-386	142	20	0	0	NUM
ma-386	142	21	and	and	CCONJ
ma-386	142	22	the	the	DET
ma-386	142	23	iterate	iterate	NOUN
ma-386	142	24	y	y	PROPN
ma-386	142	25	(	(	PUNCT
ma-386	142	26	1)0	1)0	PROPN
ma-386	142	27	∈	∈	PROPN
ma-386	142	28	u0	u0	NOUN
ma-386	142	29	.	.	PUNCT
ma-386	143	1	next	next	ADV
ma-386	143	2	,	,	PUNCT
ma-386	143	3	we	we	PRON
ma-386	143	4	show	show	VERB
ma-386	143	5	t0	t0	PROPN
ma-386	143	6	is	be	AUX
ma-386	143	7	alsoinvertible	alsoinvertible	ADJ
ma-386	143	8	.	.	PUNCT
ma-386	144	1	in	in	ADP
ma-386	144	2	view	view	NOUN
ma-386	144	3	of	of	ADP
ma-386	144	4	the	the	DET
ma-386	144	5	conditions	condition	NOUN
ma-386	144	6	(	(	PUNCT
ma-386	144	7	h7	h7	PROPN
ma-386	144	8	)	)	PUNCT
ma-386	144	9	,	,	PUNCT
ma-386	144	10	(	(	PUNCT
ma-386	144	11	5	5	NUM
ma-386	144	12	)	)	PUNCT
ma-386	144	13	,	,	PUNCT
ma-386	144	14	(	(	PUNCT
ma-386	144	15	7	7	NUM
ma-386	144	16	)	)	PUNCT
ma-386	144	17	,	,	PUNCT
ma-386	144	18	and	and	CCONJ
ma-386	144	19	(	(	PUNCT
ma-386	144	20	19	19	NUM
ma-386	144	21	)	)	PUNCT
ma-386	144	22	,	,	PUNCT
ma-386	144	23	we	we	PRON
ma-386	144	24	can	can	AUX
ma-386	144	25	have	have	VERB
ma-386	144	26	‖(2e)−1(t0	‖(2e)−1(t0	NOUN
ma-386	144	27	−	−	PROPN
ma-386	145	1	2e)‖	2e)‖	NUM
ma-386	145	2	≤	≤	NUM
ma-386	145	3	1	1	NUM
ma-386	145	4	2	2	NUM
ma-386	145	5	(	(	PUNCT
ma-386	145	6	φ0(‖x0	φ0(‖x0	PROPN
ma-386	145	7	−	−	PROPN
ma-386	145	8	x∗‖	x∗‖	NUM
ma-386	145	9	)	)	PUNCT
ma-386	146	1	+	+	CCONJ
ma-386	146	2	φ0(‖y	φ0(‖y	NOUN
ma-386	146	3	(	(	PUNCT
ma-386	146	4	1)0	1)0	NUM
ma-386	146	5	−	−	PROPN
ma-386	146	6	x	x	SYM
ma-386	146	7	∗‖	∗‖	PROPN
ma-386	146	8	)	)	PUNCT
ma-386	146	9	)	)	PUNCT
ma-386	146	10	≤	≤	NUM
ma-386	146	11	1	1	NUM
ma-386	146	12	2	2	NUM
ma-386	146	13	(	(	PUNCT
ma-386	146	14	φ0(‖x0	φ0(‖x0	PROPN
ma-386	146	15	−	−	PROPN
ma-386	146	16	x∗‖	x∗‖	NUM
ma-386	146	17	)	)	PUNCT
ma-386	147	1	+	+	CCONJ
ma-386	148	1	φ0	φ0	PROPN
ma-386	148	2	(	(	PUNCT
ma-386	148	3	g1(‖x0	g1(‖x0	PROPN
ma-386	148	4	−	−	PROPN
ma-386	148	5	x∗‖)‖x0	x∗‖)‖x0	NOUN
ma-386	148	6	−	−	PROPN
ma-386	148	7	x∗‖	x∗‖	PROPN
ma-386	148	8	)	)	PUNCT
ma-386	148	9	)	)	PUNCT
ma-386	149	1	=	=	SYM
ma-386	149	2	p0	p0	NOUN
ma-386	149	3	<	<	X
ma-386	149	4	1	1	NUM
ma-386	149	5	.	.	PUNCT
ma-386	150	1	thus	thus	ADV
ma-386	150	2	,	,	PUNCT
ma-386	150	3	the	the	DET
ma-386	150	4	linear	linear	ADJ
ma-386	150	5	operator	operator	NOUN
ma-386	150	6	t0	t0	PROPN
ma-386	150	7	is	be	AUX
ma-386	150	8	invertible	invertible	ADJ
ma-386	150	9	and	and	CCONJ
ma-386	150	10	‖t−10	‖t−10	PRON
ma-386	150	11	e‖	e‖	ADJ
ma-386	150	12	≤	≤	ADJ
ma-386	150	13	1	1	NUM
ma-386	150	14	2(1−	2(1−	NUM
ma-386	150	15	p0	p0	NOUN
ma-386	150	16	)	)	PUNCT
ma-386	150	17	.	.	PUNCT
ma-386	151	1	(	(	PUNCT
ma-386	151	2	20	20	NUM
ma-386	151	3	)	)	PUNCT
ma-386	151	4	moreover	moreover	ADV
ma-386	151	5	,	,	PUNCT
ma-386	151	6	the	the	DET
ma-386	151	7	iterate	iterate	NOUN
ma-386	151	8	y	y	PROPN
ma-386	151	9	(	(	PUNCT
ma-386	151	10	2)0	2)0	PROPN
ma-386	151	11	is	be	AUX
ma-386	151	12	well	well	ADV
ma-386	151	13	defined	define	VERB
ma-386	151	14	by	by	ADP
ma-386	151	15	the	the	DET
ma-386	151	16	second	second	ADJ
ma-386	151	17	substep	substep	NOUN
ma-386	151	18	of	of	ADP
ma-386	151	19	method	method	NOUN
ma-386	151	20	(	(	PUNCT
ma-386	151	21	2	2	NUM
ma-386	151	22	)	)	PUNCT
ma-386	151	23	,	,	PUNCT
ma-386	151	24	from	from	ADP
ma-386	151	25	which	which	PRON
ma-386	151	26	wecan	wecan	VERB
ma-386	151	27	also	also	ADV
ma-386	151	28	write	write	VERB
ma-386	151	29	y	y	PROPN
ma-386	151	30	(	(	PUNCT
ma-386	151	31	2	2	NUM
ma-386	151	32	)	)	PUNCT
ma-386	151	33	0	0	NUM
ma-386	152	1	−	−	NOUN
ma-386	152	2	x	x	SYM
ma-386	152	3	∗	∗	NOUN
ma-386	152	4	=	=	PUNCT
ma-386	153	1	x0	x0	NUM
ma-386	153	2	−	−	PROPN
ma-386	153	3	x∗	x∗	PROPN
ma-386	153	4	−	−	PROPN
ma-386	153	5	g′(x0)−1g(x0	g′(x0)−1g(x0	NOUN
ma-386	153	6	)	)	PUNCT
ma-386	154	1	+	+	CCONJ
ma-386	154	2	(	(	PUNCT
ma-386	154	3	g′(x0	g′(x0	NOUN
ma-386	154	4	)	)	PUNCT
ma-386	154	5	−1	−1	NOUN
ma-386	154	6	−	−	NOUN
ma-386	154	7	2t−10	2t−10	NUM
ma-386	154	8	)	)	PUNCT
ma-386	154	9	g(x0	g(x0	NOUN
ma-386	154	10	)	)	PUNCT
ma-386	154	11	=	=	SYM
ma-386	155	1	x0	x0	PROPN
ma-386	155	2	−	−	PROPN
ma-386	155	3	x∗	x∗	PROPN
ma-386	156	1	−	−	PROPN
ma-386	156	2	g′(x0)−1g(x0)−	g′(x0)−1g(x0)−	PROPN
ma-386	156	3	(	(	PUNCT
ma-386	156	4	2t−10	2t−10	NUM
ma-386	156	5	−	−	NOUN
ma-386	156	6	g	g	NOUN
ma-386	156	7	′(x0	′(x0	NOUN
ma-386	156	8	)	)	PUNCT
ma-386	156	9	−1)g(x0	−1)g(x0	NUM
ma-386	156	10	)	)	PUNCT
ma-386	156	11	=	=	SYM
ma-386	157	1	x0	x0	PROPN
ma-386	157	2	−	−	PROPN
ma-386	157	3	x∗	x∗	PROPN
ma-386	158	1	−	−	PROPN
ma-386	158	2	g′(x0)−1g(x0)−	g′(x0)−1g(x0)−	PROPN
ma-386	158	3	t−10	t−10	PROPN
ma-386	158	4	(	(	PUNCT
ma-386	158	5	g′(x0)−	g′(x0)−	X
ma-386	158	6	g′(y	g′(y	PROPN
ma-386	158	7	(	(	PUNCT
ma-386	158	8	1)0	1)0	NUM
ma-386	158	9	)	)	PUNCT
ma-386	158	10	g′(x0))−1g(x0	g′(x0))−1g(x0	PROPN
ma-386	158	11	)	)	PUNCT
ma-386	158	12	=	=	SYM
ma-386	159	1	x0	x0	PROPN
ma-386	159	2	−	−	PROPN
ma-386	159	3	x∗	x∗	PROPN
ma-386	159	4	−	−	PROPN
ma-386	159	5	g′(x0)−1g(x0	g′(x0)−1g(x0	NOUN
ma-386	159	6	)	)	PUNCT
ma-386	160	1	+	+	CCONJ
ma-386	160	2	[	[	X
ma-386	160	3	t−10	t−10	X
ma-386	160	4	e][e−1(g′(y	e][e−1(g′(y	NOUN
ma-386	160	5	(	(	PUNCT
ma-386	160	6	1	1	NUM
ma-386	160	7	)	)	PUNCT
ma-386	160	8	0	0	NUM
ma-386	160	9	)	)	PUNCT
ma-386	160	10	−	−	PROPN
ma-386	160	11	g′(x0))]g′(x0	g′(x0))]g′(x0	PROPN
ma-386	160	12	)	)	PUNCT
ma-386	160	13	−1g(x0	−1g(x0	PROPN
ma-386	160	14	)	)	PUNCT
ma-386	160	15	(	(	PUNCT
ma-386	160	16	21	21	NUM
ma-386	160	17	)	)	PUNCT
ma-386	160	18	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	160	19	eur	eur	PROPN
ma-386	160	20	.	.	PUNCT
ma-386	161	1	j.	j.	PROPN
ma-386	161	2	math	math	PROPN
ma-386	161	3	.	.	PUNCT
ma-386	162	1	anal	anal	PROPN
ma-386	162	2	.	.	PUNCT
ma-386	163	1	10.28924	10.28924	NUM
ma-386	163	2	/	/	SYM
ma-386	163	3	ada	ada	PROPN
ma-386	163	4	/	/	SYM
ma-386	163	5	ma.5.18	ma.5.18	PROPN
ma-386	163	6	7by	7by	NOUN
ma-386	163	7	the	the	DET
ma-386	163	8	conditions	condition	NOUN
ma-386	163	9	(	(	PUNCT
ma-386	163	10	h1	h1	PROPN
ma-386	163	11	)	)	PUNCT
ma-386	163	12	,	,	PUNCT
ma-386	163	13	(	(	PUNCT
ma-386	163	14	h7	h7	PROPN
ma-386	163	15	)	)	PUNCT
ma-386	163	16	,	,	PUNCT
ma-386	163	17	(	(	PUNCT
ma-386	163	18	h8	h8	PROPN
ma-386	163	19	)	)	PUNCT
ma-386	163	20	,	,	PUNCT
ma-386	163	21	(	(	PUNCT
ma-386	163	22	17	17	NUM
ma-386	163	23	)	)	PUNCT
ma-386	163	24	(	(	PUNCT
ma-386	163	25	for	for	ADP
ma-386	163	26	u	u	NOUN
ma-386	163	27	=	=	NOUN
ma-386	163	28	x0	x0	PROPN
ma-386	163	29	)	)	PUNCT
ma-386	163	30	,	,	PUNCT
ma-386	163	31	(	(	PUNCT
ma-386	163	32	19	19	NUM
ma-386	163	33	)	)	PUNCT
ma-386	163	34	,	,	PUNCT
ma-386	163	35	(	(	PUNCT
ma-386	163	36	11	11	NUM
ma-386	163	37	)	)	PUNCT
ma-386	163	38	(	(	PUNCT
ma-386	163	39	for	for	ADP
ma-386	163	40	i	i	PRON
ma-386	163	41	=	=	NOUN
ma-386	163	42	2	2	NUM
ma-386	163	43	)	)	PUNCT
ma-386	163	44	,	,	PUNCT
ma-386	163	45	(	(	PUNCT
ma-386	163	46	20	20	NUM
ma-386	163	47	)	)	PUNCT
ma-386	163	48	and	and	CCONJ
ma-386	163	49	(	(	PUNCT
ma-386	163	50	21	21	NUM
ma-386	163	51	)	)	PUNCT
ma-386	163	52	,	,	PUNCT
ma-386	163	53	weobtain	weobtain	NOUN
ma-386	163	54	‖y	‖y	PUNCT
ma-386	164	1	(	(	PUNCT
ma-386	164	2	2)0	2)0	NUM
ma-386	164	3	−	−	NOUN
ma-386	165	1	x	x	SYM
ma-386	165	2	∗‖	∗‖	PROPN
ma-386	165	3	≤	≤	PUNCT
ma-386	165	4			PROPN
ma-386	166	1	1∫	1∫	NUM
ma-386	166	2	0	0	NUM
ma-386	166	3	φ((1−	φ((1−	NUM
ma-386	166	4	η)‖x0	η)‖x0	NOUN
ma-386	166	5	−	−	PUNCT
ma-386	166	6	x∗‖)dη	x∗‖)dη	PROPN
ma-386	166	7	1−	1−	NUM
ma-386	167	1	φ0(‖x0	φ0(‖x0	PROPN
ma-386	167	2	−	−	PROPN
ma-386	167	3	x∗‖	x∗‖	NUM
ma-386	167	4	)	)	PUNCT
ma-386	168	1	+	+	CCONJ
ma-386	168	2	φ0(1	φ0(1	ADJ
ma-386	168	3	+	+	CCONJ
ma-386	168	4	1∫	1∫	NUM
ma-386	168	5	0	0	NUM
ma-386	168	6	φ0(η‖x0	φ0(η‖x0	NOUN
ma-386	168	7	−	−	PROPN
ma-386	168	8	x∗‖)dη	x∗‖)dη	PROPN
ma-386	168	9	)	)	PUNCT
ma-386	168	10	2(1−	2(1−	X
ma-386	169	1	φ0(‖x0	φ0(‖x0	X
ma-386	169	2	−	−	PROPN
ma-386	169	3	x∗‖))(1−	x∗‖))(1−	ADJ
ma-386	169	4	p0	p0	PROPN
ma-386	169	5	)	)	PUNCT
ma-386	169	6			PROPN
ma-386	169	7	‖x0	‖x0	NOUN
ma-386	170	1	−	−	PROPN
ma-386	170	2	x∗‖	x∗‖	PROPN
ma-386	170	3	≤	≤	PROPN
ma-386	171	1	g2(‖x0	g2(‖x0	PROPN
ma-386	171	2	−	−	PROPN
ma-386	172	1	x∗‖)‖x0	x∗‖)‖x0	NOUN
ma-386	172	2	−	−	PROPN
ma-386	172	3	x∗‖	x∗‖	PROPN
ma-386	172	4	≤	≤	PROPN
ma-386	173	1	‖x0	‖x0	NOUN
ma-386	173	2	−	−	PROPN
ma-386	173	3	x∗‖.	x∗‖.	PROPN
ma-386	173	4	(	(	PUNCT
ma-386	173	5	22	22	NUM
ma-386	173	6	)	)	PUNCT
ma-386	173	7	hence	hence	ADV
ma-386	174	1	,	,	PUNCT
ma-386	174	2	the	the	DET
ma-386	174	3	assertion	assertion	NOUN
ma-386	174	4	(	(	PUNCT
ma-386	174	5	13	13	NUM
ma-386	174	6	)	)	PUNCT
ma-386	174	7	holds	hold	VERB
ma-386	174	8	if	if	SCONJ
ma-386	174	9	n	n	NOUN
ma-386	174	10	=	=	SYM
ma-386	174	11	0	0	NUM
ma-386	174	12	and	and	CCONJ
ma-386	174	13	the	the	DET
ma-386	174	14	iterate	iterate	NOUN
ma-386	174	15	y	y	PROPN
ma-386	174	16	(	(	PUNCT
ma-386	174	17	2)0	2)0	PROPN
ma-386	174	18	∈	∈	PROPN
ma-386	174	19	u0	u0	NOUN
ma-386	174	20	.	.	PUNCT
ma-386	175	1	similarly	similarly	ADV
ma-386	175	2	,	,	PUNCT
ma-386	175	3	from	from	ADP
ma-386	175	4	(	(	PUNCT
ma-386	175	5	8)	8)	NUM
ma-386	175	6	and	and	CCONJ
ma-386	175	7	(	(	PUNCT
ma-386	175	8	h7)we	h7)we	PROPN
ma-386	175	9	can	can	AUX
ma-386	175	10	have	have	VERB
ma-386	175	11	‖(2e−1)(l−	‖(2e−1)(l−	ADJ
ma-386	175	12	2e)‖	2e)‖	NUM
ma-386	175	13	=	=	SYM
ma-386	175	14	1	1	NUM
ma-386	175	15	2	2	NUM
ma-386	175	16	‖e−1	‖e−1	NOUN
ma-386	175	17	(	(	PUNCT
ma-386	175	18	3(g′(y	3(g′(y	NUM
ma-386	175	19	(	(	PUNCT
ma-386	175	20	1	1	NUM
ma-386	175	21	)	)	PUNCT
ma-386	175	22	)	)	PUNCT
ma-386	175	23	0	0	NUM
ma-386	176	1	−	−	PROPN
ma-386	176	2	e	e	X
ma-386	176	3	)	)	PUNCT
ma-386	176	4	+	+	CCONJ
ma-386	176	5	(	(	PUNCT
ma-386	176	6	g′(x0)−	g′(x0)−	X
ma-386	176	7	e	e	NOUN
ma-386	176	8	)	)	PUNCT
ma-386	176	9	)	)	PUNCT
ma-386	177	1	‖	‖	PROPN
ma-386	177	2	≤	≤	NUM
ma-386	177	3	1	1	NUM
ma-386	177	4	2	2	NUM
ma-386	177	5	(	(	PUNCT
ma-386	177	6	3φ0(‖y	3φ0(‖y	NUM
ma-386	177	7	(	(	PUNCT
ma-386	177	8	1)0	1)0	NOUN
ma-386	177	9	−	−	PROPN
ma-386	177	10	x	x	SYM
ma-386	177	11	∗‖	∗‖	PROPN
ma-386	177	12	)	)	PUNCT
ma-386	178	1	+	+	CCONJ
ma-386	179	1	φ0(‖x0	φ0(‖x0	PROPN
ma-386	179	2	−	−	PROPN
ma-386	179	3	x∗‖	x∗‖	NUM
ma-386	179	4	)	)	PUNCT
ma-386	179	5	)	)	PUNCT
ma-386	179	6	≤	≤	NOUN
ma-386	179	7	q0	q0	VERB
ma-386	179	8	<	<	X
ma-386	179	9	1,so	1,so	NUM
ma-386	179	10	‖l−1e‖	‖l−1e‖	PROPN
ma-386	179	11	≤	≤	NUM
ma-386	179	12	1	1	NUM
ma-386	179	13	2(1−	2(1−	NUM
ma-386	179	14	q0	q0	PROPN
ma-386	179	15	)	)	PUNCT
ma-386	179	16	.	.	PUNCT
ma-386	180	1	(	(	PUNCT
ma-386	180	2	23	23	NUM
ma-386	180	3	)	)	PUNCT
ma-386	180	4	thus	thus	ADV
ma-386	180	5	,	,	PUNCT
ma-386	180	6	the	the	DET
ma-386	180	7	iterates	iterate	NOUN
ma-386	180	8	y	y	PROPN
ma-386	180	9	(	(	PUNCT
ma-386	180	10	3)0	3)0	PROPN
ma-386	180	11	,	,	PUNCT
ma-386	180	12	.	.	PUNCT
ma-386	180	13	.	.	PUNCT
ma-386	181	1	.	.	PUNCT
ma-386	182	1	,	,	PUNCT
ma-386	182	2	y	y	PROPN
ma-386	182	3	(	(	PUNCT
ma-386	182	4	k	k	NOUN
ma-386	182	5	)	)	PUNCT
ma-386	182	6	0	0	NUM
ma-386	183	1	=	=	SYM
ma-386	183	2	x1	x1	NUM
ma-386	183	3	exist	exist	VERB
ma-386	183	4	,	,	PUNCT
ma-386	183	5	since	since	SCONJ
ma-386	183	6	l	l	NOUN
ma-386	183	7	is	be	AUX
ma-386	183	8	invertible	invertible	ADJ
ma-386	183	9	and	and	CCONJ
ma-386	183	10	we	we	PRON
ma-386	183	11	can	can	AUX
ma-386	183	12	write	write	VERB
ma-386	183	13	for	for	ADP
ma-386	183	14	j	j	PROPN
ma-386	183	15	=	=	SYM
ma-386	183	16	3	3	NUM
ma-386	183	17	,	,	PUNCT
ma-386	183	18	4	4	NUM
ma-386	183	19	,	,	PUNCT
ma-386	183	20	.	.	PUNCT
ma-386	183	21	.	.	PUNCT
ma-386	183	22	.	.	PUNCT
ma-386	184	1	,	,	PUNCT
ma-386	184	2	k	k	PROPN
ma-386	184	3	y	y	PROPN
ma-386	184	4	(	(	PUNCT
ma-386	184	5	j	j	PROPN
ma-386	184	6	)	)	PUNCT
ma-386	184	7	0	0	NUM
ma-386	185	1	−	−	NOUN
ma-386	185	2	x	x	SYM
ma-386	185	3	∗	∗	NOUN
ma-386	185	4	=	=	SYM
ma-386	185	5	y	y	PROPN
ma-386	185	6	(	(	PUNCT
ma-386	185	7	j−1	j−1	PROPN
ma-386	185	8	)	)	PUNCT
ma-386	185	9	0	0	NUM
ma-386	186	1	−	−	PROPN
ma-386	186	2	x∗	x∗	PROPN
ma-386	186	3	−	−	PROPN
ma-386	187	1	g′(y	g′(y	PROPN
ma-386	187	2	(	(	PUNCT
ma-386	187	3	j−1)0	j−1)0	NOUN
ma-386	187	4	)	)	PUNCT
ma-386	187	5	−1g(y	−1g(y	PROPN
ma-386	187	6	(	(	PUNCT
ma-386	187	7	j−1	j−1	PROPN
ma-386	187	8	)	)	PUNCT
ma-386	187	9	0	0	NUM
ma-386	187	10	)	)	PUNCT
ma-386	188	1	+	+	CCONJ
ma-386	188	2	(	(	PUNCT
ma-386	188	3	i	i	PRON
ma-386	188	4	−m0)g(y	−m0)g(y	VERB
ma-386	188	5	(	(	PUNCT
ma-386	188	6	j−1	j−1	PROPN
ma-386	188	7	)	)	PUNCT
ma-386	188	8	0	0	NUM
ma-386	188	9	)	)	PUNCT
ma-386	189	1	=	=	SYM
ma-386	189	2	y	y	PROPN
ma-386	189	3	(	(	PUNCT
ma-386	189	4	j−1	j−1	PROPN
ma-386	189	5	)	)	PUNCT
ma-386	189	6	0	0	NUM
ma-386	190	1	−	−	PROPN
ma-386	190	2	x∗	x∗	PROPN
ma-386	190	3	−	−	PROPN
ma-386	191	1	g′(y	g′(y	PROPN
ma-386	191	2	(	(	PUNCT
ma-386	191	3	j−1)0	j−1)0	NOUN
ma-386	191	4	)	)	PUNCT
ma-386	191	5	−1g(y	−1g(y	PROPN
ma-386	191	6	(	(	PUNCT
ma-386	191	7	j−1	j−1	PROPN
ma-386	191	8	)	)	PUNCT
ma-386	191	9	0	0	NUM
ma-386	191	10	)	)	PUNCT
ma-386	191	11	−	−	NOUN
ma-386	192	1	l−1g′(y	l−1g′(y	NOUN
ma-386	192	2	(	(	PUNCT
ma-386	192	3	j−1)0	j−1)0	NOUN
ma-386	192	4	)	)	PUNCT
ma-386	192	5	g′(x0	g′(x0	NOUN
ma-386	192	6	)	)	PUNCT
ma-386	192	7	−1g(y	−1g(y	NOUN
ma-386	192	8	(	(	PUNCT
ma-386	192	9	2	2	NUM
ma-386	192	10	)	)	PUNCT
ma-386	192	11	0	0	NUM
ma-386	192	12	)	)	PUNCT
ma-386	192	13	(	(	PUNCT
ma-386	192	14	24	24	NUM
ma-386	192	15	)	)	PUNCT
ma-386	192	16	which	which	PRON
ma-386	192	17	can	can	AUX
ma-386	192	18	be	be	AUX
ma-386	192	19	implied	imply	VERB
ma-386	192	20	by	by	ADP
ma-386	192	21	(	(	PUNCT
ma-386	192	22	5	5	NUM
ma-386	192	23	)	)	PUNCT
ma-386	192	24	,	,	PUNCT
ma-386	192	25	(	(	PUNCT
ma-386	192	26	11	11	NUM
ma-386	192	27	)	)	PUNCT
ma-386	192	28	,	,	PUNCT
ma-386	192	29	(	(	PUNCT
ma-386	192	30	22	22	NUM
ma-386	192	31	)	)	PUNCT
ma-386	192	32	,	,	PUNCT
ma-386	192	33	and	and	CCONJ
ma-386	192	34	(	(	PUNCT
ma-386	192	35	23	23	NUM
ma-386	192	36	)	)	PUNCT
ma-386	192	37	‖y	‖y	PUNCT
ma-386	193	1	(	(	PUNCT
ma-386	193	2	j)0	j)0	NOUN
ma-386	193	3	−	−	PROPN
ma-386	194	1	x	x	SYM
ma-386	194	2	∗‖	∗‖	PROPN
ma-386	194	3	≤	≤	PUNCT
ma-386	194	4			PROPN
ma-386	195	1	1∫	1∫	NUM
ma-386	195	2	0	0	NUM
ma-386	195	3	φ0((1−	φ0((1−	PROPN
ma-386	195	4	η)‖y	η)‖y	NOUN
ma-386	195	5	(	(	PUNCT
ma-386	195	6	j−1)0	j−1)0	PROPN
ma-386	195	7	−	−	PROPN
ma-386	195	8	x∗‖)dη	x∗‖)dη	PROPN
ma-386	195	9	1−	1−	NUM
ma-386	195	10	φ0(‖y	φ0(‖y	NOUN
ma-386	195	11	(	(	PUNCT
ma-386	195	12	j−1)0	j−1)0	PROPN
ma-386	195	13	−	−	PROPN
ma-386	195	14	x∗‖	x∗‖	PROPN
ma-386	195	15	)	)	PUNCT
ma-386	195	16	+	+	CCONJ
ma-386	195	17	(	(	PUNCT
ma-386	195	18	1	1	NUM
ma-386	195	19	+	+	NUM
ma-386	195	20	φ0(‖y	φ0(‖y	NOUN
ma-386	195	21	(	(	PUNCT
ma-386	195	22	j−1	j−1	PROPN
ma-386	195	23	)	)	PUNCT
ma-386	195	24	0	0	NUM
ma-386	196	1	−	−	PROPN
ma-386	196	2	x∗‖))(1	x∗‖))(1	PROPN
ma-386	197	1	+	+	CCONJ
ma-386	198	1	1∫	1∫	NUM
ma-386	198	2	0	0	NUM
ma-386	198	3	φ0(η‖y	φ0(η‖y	NOUN
ma-386	198	4	(	(	PUNCT
ma-386	198	5	j−1)0	j−1)0	PROPN
ma-386	198	6	−	−	PROPN
ma-386	198	7	x∗‖)dη	x∗‖)dη	PROPN
ma-386	198	8	)	)	PUNCT
ma-386	198	9	2(1−	2(1−	X
ma-386	199	1	φ0(‖x0	φ0(‖x0	PROPN
ma-386	199	2	−	−	PROPN
ma-386	199	3	x∗‖))(1−	x∗‖))(1−	X
ma-386	199	4	q0	q0	PROPN
ma-386	199	5	)	)	PUNCT
ma-386	199	6			PROPN
ma-386	199	7	‖y	‖y	PUNCT
ma-386	200	1	(	(	PUNCT
ma-386	200	2	j−1)0	j−1)0	PROPN
ma-386	200	3	−	−	PROPN
ma-386	200	4	x∗‖	x∗‖	PROPN
ma-386	200	5	≤	≤	NUM
ma-386	200	6	gj(‖y	gj(‖y	PROPN
ma-386	200	7	(	(	PUNCT
ma-386	200	8	j−1)0	j−1)0	PROPN
ma-386	200	9	−	−	PROPN
ma-386	200	10	x∗‖)‖y	x∗‖)‖y	NOUN
ma-386	200	11	(	(	PUNCT
ma-386	200	12	j−1)0	j−1)0	PROPN
ma-386	200	13	−	−	PROPN
ma-386	200	14	x∗‖	x∗‖	PROPN
ma-386	200	15	≤	≤	PROPN
ma-386	200	16	‖x0	‖x0	NOUN
ma-386	200	17	−	−	PROPN
ma-386	200	18	x∗‖	x∗‖	PROPN
ma-386	200	19	(	(	PUNCT
ma-386	200	20	25	25	NUM
ma-386	200	21	)	)	PUNCT
ma-386	200	22	where	where	SCONJ
ma-386	200	23	we	we	PRON
ma-386	200	24	have	have	AUX
ma-386	200	25	also	also	ADV
ma-386	200	26	used	use	VERB
ma-386	200	27	the	the	DET
ma-386	200	28	estimates	estimate	NOUN
ma-386	200	29	‖e−1(g′(y	‖e−1(g′(y	PROPN
ma-386	200	30	(	(	PUNCT
ma-386	200	31	j)0	j)0	PROPN
ma-386	200	32	)	)	PUNCT
ma-386	200	33	−	−	PROPN
ma-386	201	1	g′(x0))‖	g′(x0))‖	PROPN
ma-386	201	2	≤	≤	PART
ma-386	201	3	φ(‖y	φ(‖y	NOUN
ma-386	201	4	(	(	PUNCT
ma-386	201	5	1)0	1)0	NUM
ma-386	201	6	−	−	NOUN
ma-386	201	7	x0‖	x0‖	PROPN
ma-386	201	8	)	)	PUNCT
ma-386	201	9	≤	≤	NUM
ma-386	201	10	φ(‖y	φ(‖y	NOUN
ma-386	201	11	(	(	PUNCT
ma-386	201	12	1)0	1)0	NUM
ma-386	201	13	−	−	NOUN
ma-386	201	14	x	x	SYM
ma-386	201	15	∗‖+	∗‖+	PROPN
ma-386	201	16	‖x0	‖x0	NOUN
ma-386	201	17	−	−	PROPN
ma-386	201	18	x∗‖	x∗‖	PROPN
ma-386	201	19	)	)	PUNCT
ma-386	201	20	≤	≤	NOUN
ma-386	201	21	φ0or	φ0or	X
ma-386	202	1	‖e−1(g′(y	‖e−1(g′(y	PROPN
ma-386	202	2	(	(	PUNCT
ma-386	202	3	1)0	1)0	NUM
ma-386	202	4	)	)	PUNCT
ma-386	202	5	−	−	PROPN
ma-386	203	1	g′(x0))‖	g′(x0))‖	PROPN
ma-386	203	2	≤	≤	PROPN
ma-386	203	3	‖e−1(g′(y	‖e−1(g′(y	PROPN
ma-386	203	4	(	(	PUNCT
ma-386	203	5	1)0	1)0	NUM
ma-386	203	6	)	)	PUNCT
ma-386	203	7	−	−	PROPN
ma-386	203	8	g′(x∗))‖+	g′(x∗))‖+	PROPN
ma-386	203	9	‖e−1(g′(x0)−	‖e−1(g′(x0)−	PROPN
ma-386	203	10	g′(x∗))‖	g′(x∗))‖	NOUN
ma-386	203	11	≤	≤	ADJ
ma-386	203	12	φ0(‖y	φ0(‖y	NOUN
ma-386	203	13	(	(	PUNCT
ma-386	203	14	1)0	1)0	NUM
ma-386	203	15	−	−	PROPN
ma-386	203	16	x	x	SYM
ma-386	203	17	∗‖	∗‖	PROPN
ma-386	203	18	)	)	PUNCT
ma-386	204	1	+	+	CCONJ
ma-386	204	2	φ0(‖x0	φ0(‖x0	PROPN
ma-386	204	3	−	−	PROPN
ma-386	204	4	x∗‖	x∗‖	NUM
ma-386	204	5	)	)	PUNCT
ma-386	205	1	≤	≤	NOUN
ma-386	205	2	φ0	φ0	PROPN
ma-386	205	3	,	,	PUNCT
ma-386	205	4	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	205	5	eur	eur	PROPN
ma-386	205	6	.	.	PUNCT
ma-386	206	1	j.	j.	PROPN
ma-386	206	2	math	math	PROPN
ma-386	206	3	.	.	PUNCT
ma-386	207	1	anal	anal	PROPN
ma-386	207	2	.	.	PUNCT
ma-386	208	1	10.28924	10.28924	NUM
ma-386	208	2	/	/	SYM
ma-386	208	3	ada	ada	PROPN
ma-386	208	4	/	/	SYM
ma-386	208	5	ma.5.18	ma.5.18	PROPN
ma-386	208	6	8	8	NUM
ma-386	208	7	‖e−1g(y	‖e−1g(y	PROPN
ma-386	208	8	(	(	PUNCT
ma-386	208	9	1	1	NUM
ma-386	208	10	)	)	PUNCT
ma-386	208	11	0	0	NUM
ma-386	208	12	)	)	PUNCT
ma-386	209	1	‖	‖	PROPN
ma-386	209	2	=	=	SYM
ma-386	209	3	‖e−1(g(y	‖e−1(g(y	NOUN
ma-386	209	4	(	(	PUNCT
ma-386	209	5	1	1	NUM
ma-386	209	6	)	)	PUNCT
ma-386	209	7	0	0	NUM
ma-386	209	8	)	)	PUNCT
ma-386	209	9	−	−	NOUN
ma-386	210	1	e	e	X
ma-386	210	2	+	+	CCONJ
ma-386	210	3	e)‖	e)‖	VERB
ma-386	210	4	≤	≤	NUM
ma-386	210	5	1	1	NUM
ma-386	210	6	+	+	NUM
ma-386	210	7	‖e−1(g′(y	‖e−1(g′(y	PROPN
ma-386	210	8	(	(	PUNCT
ma-386	210	9	1)0	1)0	NUM
ma-386	210	10	)	)	PUNCT
ma-386	210	11	−	−	PROPN
ma-386	210	12	e)‖	e)‖	ADJ
ma-386	210	13	≤	≤	NUM
ma-386	210	14	1	1	NUM
ma-386	210	15	+	+	NUM
ma-386	210	16	φ0(‖y	φ0(‖y	NOUN
ma-386	210	17	(	(	PUNCT
ma-386	210	18	1)0	1)0	NUM
ma-386	210	19	−	−	PROPN
ma-386	210	20	x	x	SYM
ma-386	210	21	∗‖	∗‖	PROPN
ma-386	210	22	)	)	PUNCT
ma-386	210	23	,	,	PUNCT
ma-386	210	24	and	and	CCONJ
ma-386	210	25	‖e−1g(y	‖e−1g(y	PROPN
ma-386	210	26	(	(	PUNCT
ma-386	210	27	1	1	NUM
ma-386	210	28	)	)	PUNCT
ma-386	210	29	0	0	NUM
ma-386	210	30	)	)	PUNCT
ma-386	210	31	‖	‖	PROPN
ma-386	210	32	=	=	SYM
ma-386	210	33	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ma-386	211	1	1∫	1∫	NUM
ma-386	211	2	0	0	NUM
ma-386	211	3	e−1(g′(x∗	e−1(g′(x∗	PROPN
ma-386	211	4	+	+	CCONJ
ma-386	211	5	η(y	η(y	PROPN
ma-386	211	6	(	(	PUNCT
ma-386	211	7	1	1	NUM
ma-386	211	8	)	)	PUNCT
ma-386	211	9	0	0	NUM
ma-386	212	1	−	−	NOUN
ma-386	212	2	x	x	SYM
ma-386	212	3	∗)))dη(y	∗)))dη(y	PROPN
ma-386	212	4	(	(	PUNCT
ma-386	212	5	1	1	NUM
ma-386	212	6	)	)	PUNCT
ma-386	212	7	0	0	NUM
ma-386	213	1	−	−	NOUN
ma-386	213	2	x	x	SYM
ma-386	213	3	∗	∗	PROPN
ma-386	213	4	)	)	PUNCT
ma-386	213	5	∥∥∥∥∥∥	∥∥∥∥∥∥	PUNCT
ma-386	214	1	=	=	SYM
ma-386	214	2	∥∥∥∥∥∥	∥∥∥∥∥∥	PROPN
ma-386	215	1	1∫	1∫	NUM
ma-386	215	2	0	0	NUM
ma-386	215	3	e−1(g′(x∗	e−1(g′(x∗	PROPN
ma-386	215	4	+	+	CCONJ
ma-386	215	5	η(y	η(y	PROPN
ma-386	215	6	(	(	PUNCT
ma-386	215	7	1	1	NUM
ma-386	215	8	)	)	PUNCT
ma-386	215	9	0	0	NUM
ma-386	216	1	−	−	NOUN
ma-386	216	2	x	x	PUNCT
ma-386	216	3	∗))−	∗))−	PROPN
ma-386	216	4	e	e	NOUN
ma-386	216	5	+	+	CCONJ
ma-386	216	6	e)dη(y	e)dη(y	PROPN
ma-386	216	7	(	(	PUNCT
ma-386	216	8	1	1	NUM
ma-386	216	9	)	)	PUNCT
ma-386	216	10	0	0	NUM
ma-386	217	1	−	−	NOUN
ma-386	217	2	x	x	SYM
ma-386	217	3	∗	∗	NOUN
ma-386	217	4	)	)	PUNCT
ma-386	217	5	∥∥∥∥∥∥	∥∥∥∥∥∥	NUM
ma-386	218	1	≤	≤	NOUN
ma-386	218	2	(	(	PUNCT
ma-386	218	3	1	1	NUM
ma-386	218	4	+	+	NUM
ma-386	218	5	∫	∫	PROPN
ma-386	218	6	1	1	NUM
ma-386	218	7	0	0	NUM
ma-386	219	1	φ0(η‖y	φ0(η‖y	NOUN
ma-386	219	2	(	(	PUNCT
ma-386	219	3	1)0	1)0	NOUN
ma-386	219	4	−	−	PROPN
ma-386	219	5	x	x	SYM
ma-386	219	6	∗‖)dη	∗‖)dη	PROPN
ma-386	219	7	)	)	PUNCT
ma-386	219	8	‖y	‖y	PUNCT
ma-386	220	1	(	(	PUNCT
ma-386	220	2	1)0	1)0	NUM
ma-386	220	3	−	−	PROPN
ma-386	220	4	x	x	SYM
ma-386	221	1	∗‖.	∗‖.	PROPN
ma-386	221	2	therefore	therefore	ADV
ma-386	221	3	,	,	PUNCT
ma-386	221	4	the	the	DET
ma-386	221	5	assertions	assertion	NOUN
ma-386	221	6	(	(	PUNCT
ma-386	221	7	14	14	NUM
ma-386	221	8	)	)	PUNCT
ma-386	221	9	and	and	CCONJ
ma-386	221	10	(	(	PUNCT
ma-386	221	11	15	15	X
ma-386	221	12	)	)	PUNCT
ma-386	221	13	hold	hold	VERB
ma-386	221	14	if	if	SCONJ
ma-386	221	15	n	n	NOUN
ma-386	221	16	=	=	SYM
ma-386	221	17	0	0	NUM
ma-386	221	18	and	and	CCONJ
ma-386	221	19	the	the	DET
ma-386	221	20	iterate	iterate	NOUN
ma-386	221	21	y	y	PROPN
ma-386	221	22	(	(	PUNCT
ma-386	221	23	j,)0	j,)0	PROPN
ma-386	221	24	x1	x1	PROPN
ma-386	221	25	∈	∈	PROPN
ma-386	221	26	u0.the	u0.the	DET
ma-386	221	27	induction	induction	NOUN
ma-386	221	28	for	for	ADP
ma-386	221	29	assertions	assertion	NOUN
ma-386	221	30	(	(	PUNCT
ma-386	221	31	12)–(15	12)–(15	NUM
ma-386	221	32	)	)	PUNCT
ma-386	221	33	is	be	AUX
ma-386	221	34	completed	complete	VERB
ma-386	221	35	if	if	SCONJ
ma-386	221	36	x0	x0	PROPN
ma-386	221	37	,	,	PUNCT
ma-386	221	38	y	y	PROPN
ma-386	221	39	(	(	PUNCT
ma-386	221	40	1	1	NUM
ma-386	221	41	,	,	PUNCT
ma-386	221	42	)	)	PUNCT
ma-386	221	43	0	0	PUNCT
ma-386	222	1	y	y	PROPN
ma-386	222	2	(	(	PUNCT
ma-386	222	3	2	2	NUM
ma-386	222	4	,	,	PUNCT
ma-386	222	5	)	)	PUNCT
ma-386	222	6	0	0	PUNCT
ma-386	223	1	y	y	PROPN
ma-386	223	2	(	(	PUNCT
ma-386	223	3	j	j	PROPN
ma-386	223	4	)	)	PUNCT
ma-386	223	5	0	0	NUM
ma-386	223	6	are	be	AUX
ma-386	223	7	replaced	replace	VERB
ma-386	223	8	by	by	ADP
ma-386	223	9	xj	xj	PROPN
ma-386	223	10	,	,	PUNCT
ma-386	223	11	y	y	PROPN
ma-386	223	12	(	(	PUNCT
ma-386	223	13	1	1	NUM
ma-386	223	14	,	,	PUNCT
ma-386	223	15	)	)	PUNCT
ma-386	224	1	j	j	PROPN
ma-386	224	2	y	y	PROPN
ma-386	224	3	(	(	PUNCT
ma-386	224	4	2	2	NUM
ma-386	224	5	,	,	PUNCT
ma-386	224	6	)	)	PUNCT
ma-386	224	7	j	j	PROPN
ma-386	224	8	y	y	PROPN
ma-386	224	9	(	(	PUNCT
ma-386	224	10	j	j	PROPN
ma-386	224	11	)	)	PUNCT
ma-386	224	12	j	j	PROPN
ma-386	224	13	respectively.furthermore	respectively.furthermore	NOUN
ma-386	224	14	,	,	PUNCT
ma-386	224	15	by	by	ADP
ma-386	224	16	estimate	estimate	NOUN
ma-386	224	17	(	(	PUNCT
ma-386	224	18	15	15	NUM
ma-386	224	19	)	)	PUNCT
ma-386	224	20	and	and	CCONJ
ma-386	224	21	dk	dk	PROPN
ma-386	224	22	=	=	PROPN
ma-386	224	23	gk(‖x0	gk(‖x0	PROPN
ma-386	224	24	−	−	PROPN
ma-386	224	25	x∗‖	x∗‖	PROPN
ma-386	224	26	)	)	PUNCT
ma-386	224	27	∈	∈	PROPN
ma-386	225	1	[	[	X
ma-386	225	2	0	0	NUM
ma-386	225	3	,	,	PUNCT
ma-386	225	4	1	1	NUM
ma-386	225	5	)	)	PUNCT
ma-386	225	6	,	,	PUNCT
ma-386	225	7	we	we	PRON
ma-386	225	8	can	can	AUX
ma-386	225	9	get	get	VERB
ma-386	225	10	‖xn+1	‖xn+1	NOUN
ma-386	225	11	−	−	PROPN
ma-386	225	12	x∗‖	x∗‖	PROPN
ma-386	225	13	=	=	SYM
ma-386	225	14	‖y	‖y	PROPN
ma-386	225	15	(	(	PUNCT
ma-386	225	16	k)n	k)n	PROPN
ma-386	225	17	−	−	PROPN
ma-386	225	18	x∗‖	x∗‖	PROPN
ma-386	225	19	≤	≤	PROPN
ma-386	225	20	dk‖y	dk‖y	PROPN
ma-386	225	21	(	(	PUNCT
ma-386	225	22	k−1)n	k−1)n	PROPN
ma-386	225	23	−	−	PROPN
ma-386	225	24	x∗‖	x∗‖	PROPN
ma-386	225	25	≤	≤	NUM
ma-386	225	26	dkdk−1‖y	dkdk−1‖y	PROPN
ma-386	225	27	(	(	PUNCT
ma-386	225	28	k−2)n	k−2)n	PROPN
ma-386	225	29	−	−	PROPN
ma-386	225	30	x∗‖	x∗‖	PROPN
ma-386	225	31	≤	≤	X
ma-386	225	32	·	·	PUNCT
ma-386	225	33	·	·	PUNCT
ma-386	225	34	·	·	PUNCT
ma-386	226	1	≤	≤	NUM
ma-386	226	2	dkdk−1	dkdk−1	NOUN
ma-386	226	3	·	·	PUNCT
ma-386	226	4	·	·	PUNCT
ma-386	226	5	·	·	PUNCT
ma-386	227	1	d3‖y	d3‖y	NUM
ma-386	227	2	(	(	PUNCT
ma-386	227	3	2)n	2)n	NUM
ma-386	227	4	−	−	PROPN
ma-386	227	5	x∗‖	x∗‖	SYM
ma-386	227	6	≤	≤	NUM
ma-386	227	7	dkdk−1	dkdk−1	PROPN
ma-386	227	8	·	·	PUNCT
ma-386	227	9	·	·	PUNCT
ma-386	227	10	·	·	PUNCT
ma-386	228	1	d2‖xn	d2‖xn	ADJ
ma-386	228	2	−	−	PROPN
ma-386	228	3	x∗‖.	x∗‖.	PROPN
ma-386	228	4	(	(	PUNCT
ma-386	228	5	26	26	NUM
ma-386	228	6	)	)	PUNCT
ma-386	228	7	it	it	PRON
ma-386	228	8	follows	follow	VERB
ma-386	228	9	by	by	ADP
ma-386	228	10	the	the	DET
ma-386	228	11	definition	definition	NOUN
ma-386	228	12	of	of	ADP
ma-386	228	13	dk	dk	PROPN
ma-386	228	14	that	that	SCONJ
ma-386	228	15	there	there	PRON
ma-386	228	16	exists	exist	VERB
ma-386	228	17	d	d	X
ma-386	228	18	∈	∈	PROPN
ma-386	229	1	[	[	X
ma-386	229	2	0	0	NUM
ma-386	229	3	,	,	PUNCT
ma-386	229	4	1	1	NUM
ma-386	229	5	)	)	PUNCT
ma-386	229	6	such	such	ADJ
ma-386	229	7	that	that	DET
ma-386	229	8	d2	d2	PROPN
ma-386	229	9	,	,	PUNCT
ma-386	229	10	d3	d3	PROPN
ma-386	229	11	,	,	PUNCT
ma-386	229	12	.	.	PUNCT
ma-386	229	13	.	.	PUNCT
ma-386	230	1	.	.	PUNCT
ma-386	231	1	,	,	PUNCT
ma-386	231	2	dk	dk	PROPN
ma-386	231	3	≤	≤	PROPN
ma-386	231	4	d	d	PROPN
ma-386	231	5	(	(	PUNCT
ma-386	231	6	27	27	NUM
ma-386	231	7	)	)	PUNCT
ma-386	231	8	so	so	ADV
ma-386	231	9	,	,	PUNCT
ma-386	231	10	by	by	ADP
ma-386	231	11	(	(	PUNCT
ma-386	231	12	26	26	NUM
ma-386	231	13	)	)	PUNCT
ma-386	231	14	and	and	CCONJ
ma-386	231	15	(	(	PUNCT
ma-386	231	16	27	27	NUM
ma-386	231	17	)	)	PUNCT
ma-386	231	18	,	,	PUNCT
ma-386	231	19	we	we	PRON
ma-386	231	20	get	get	VERB
ma-386	231	21	‖xn+1	‖xn+1	VERB
ma-386	231	22	−	−	PROPN
ma-386	232	1	x∗‖	x∗‖	PROPN
ma-386	232	2	≤	≤	NOUN
ma-386	232	3	dk−1‖xn	dk−1‖xn	PROPN
ma-386	232	4	−	−	PROPN
ma-386	232	5	x∗‖	x∗‖	PROPN
ma-386	232	6	≤	≤	NUM
ma-386	233	1	d	d	X
ma-386	233	2	(	(	PUNCT
ma-386	233	3	k−1)(n+1)‖x0	k−1)(n+1)‖x0	PROPN
ma-386	233	4	−	−	PROPN
ma-386	233	5	x∗‖	x∗‖	PROPN
ma-386	233	6	<	<	X
ma-386	233	7	r∗.	r∗.	NOUN
ma-386	233	8	(	(	PUNCT
ma-386	233	9	28	28	NUM
ma-386	233	10	)	)	PUNCT
ma-386	233	11	finally	finally	ADV
ma-386	233	12	,	,	PUNCT
ma-386	233	13	if	if	SCONJ
ma-386	233	14	we	we	PRON
ma-386	233	15	let	let	VERB
ma-386	233	16	n	n	X
ma-386	233	17	→	→	SYM
ma-386	233	18	+	+	NUM
ma-386	233	19	∞	∞	PROPN
ma-386	233	20	in	in	ADP
ma-386	233	21	(	(	PUNCT
ma-386	233	22	28	28	NUM
ma-386	233	23	)	)	PUNCT
ma-386	233	24	,	,	PUNCT
ma-386	233	25	we	we	PRON
ma-386	233	26	conclude	conclude	VERB
ma-386	233	27	that	that	SCONJ
ma-386	233	28	lim	lim	PROPN
ma-386	233	29	n→+∞	n→+∞	VERB
ma-386	233	30	xn	xn	PROPN
ma-386	233	31	=	=	SYM
ma-386	233	32	x∗	x∗	PROPN
ma-386	233	33	,	,	PUNCT
ma-386	233	34	and	and	CCONJ
ma-386	233	35	all	all	DET
ma-386	233	36	the	the	DET
ma-386	233	37	iterates	iterate	NOUN
ma-386	233	38	{	{	PUNCT
ma-386	233	39	xn	xn	NOUN
ma-386	233	40	}	}	PUNCT
ma-386	233	41	⊆	⊆	NUM
ma-386	233	42	u0	u0	NOUN
ma-386	233	43	.	.	PUNCT
ma-386	234	1	�	�	PROPN
ma-386	234	2	the	the	DET
ma-386	234	3	uniqueness	uniqueness	NOUN
ma-386	234	4	of	of	ADP
ma-386	234	5	the	the	DET
ma-386	234	6	solution	solution	NOUN
ma-386	234	7	x∗	x∗	PROPN
ma-386	234	8	is	be	AUX
ma-386	234	9	established	establish	VERB
ma-386	234	10	in	in	ADP
ma-386	234	11	a	a	DET
ma-386	234	12	neighborhood	neighborhood	NOUN
ma-386	234	13	of	of	ADP
ma-386	234	14	it	it	PRON
ma-386	234	15	next	next	ADV
ma-386	234	16	.	.	PUNCT
ma-386	235	1	proposition	proposition	NOUN
ma-386	235	2	1	1	NUM
ma-386	235	3	.	.	PUNCT
ma-386	235	4	suppose	suppose	VERB
ma-386	235	5	that	that	SCONJ
ma-386	235	6	the	the	DET
ma-386	235	7	condition	condition	NOUN
ma-386	235	8	(	(	PUNCT
ma-386	235	9	h7	h7	PROPN
ma-386	235	10	)	)	PUNCT
ma-386	235	11	holds	hold	VERB
ma-386	235	12	in	in	ADP
ma-386	235	13	the	the	DET
ma-386	235	14	ball	ball	NOUN
ma-386	235	15	u(x∗	u(x∗	NOUN
ma-386	235	16	,	,	PUNCT
ma-386	235	17	r1	r1	PROPN
ma-386	235	18	)	)	PUNCT
ma-386	235	19	,	,	PUNCT
ma-386	235	20	for	for	ADP
ma-386	235	21	some	some	DET
ma-386	235	22	r1	r1	PROPN
ma-386	235	23	>	>	X
ma-386	235	24	0	0	PUNCT
ma-386	236	1	and	and	CCONJ
ma-386	236	2	there	there	PRON
ma-386	236	3	exists	exist	VERB
ma-386	236	4	r2	r2	PROPN
ma-386	236	5	≥	≥	PROPN
ma-386	236	6	r1	r1	PROPN
ma-386	237	1	such	such	ADJ
ma-386	237	2	that	that	SCONJ
ma-386	237	3	1∫	1∫	NUM
ma-386	237	4	0	0	NUM
ma-386	237	5	φ0(ηr2)dη	φ0(ηr2)dη	NOUN
ma-386	237	6	<	<	NOUN
ma-386	237	7	1	1	NUM
ma-386	237	8	.	.	PUNCT
ma-386	237	9	(	(	PUNCT
ma-386	237	10	29	29	NUM
ma-386	237	11	)	)	PUNCT
ma-386	237	12	define	define	VERB
ma-386	237	13	the	the	DET
ma-386	237	14	region	region	NOUN
ma-386	237	15	d1	d1	NOUN
ma-386	237	16	=	=	PUNCT
ma-386	238	1	d	d	PROPN
ma-386	238	2	∩	∩	X
ma-386	238	3	u[x∗	u[x∗	PROPN
ma-386	238	4	,	,	PUNCT
ma-386	238	5	r2	r2	PROPN
ma-386	238	6	]	]	PUNCT
ma-386	238	7	.	.	PUNCT
ma-386	239	1	then	then	ADV
ma-386	239	2	,	,	PUNCT
ma-386	239	3	x∗	x∗	PROPN
ma-386	239	4	is	be	AUX
ma-386	239	5	the	the	DET
ma-386	239	6	only	only	ADJ
ma-386	239	7	solution	solution	NOUN
ma-386	239	8	of	of	ADP
ma-386	239	9	the	the	DET
ma-386	239	10	equation	equation	NOUN
ma-386	239	11	g(x	g(x	NOUN
ma-386	239	12	)	)	PUNCT
ma-386	240	1	=	=	SYM
ma-386	240	2	0	0	NUM
ma-386	241	1	in	in	ADP
ma-386	241	2	the	the	DET
ma-386	241	3	region	region	NOUN
ma-386	241	4	d1	d1	PROPN
ma-386	241	5	.	.	PUNCT
ma-386	242	1	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	242	2	eur	eur	PROPN
ma-386	242	3	.	.	PUNCT
ma-386	243	1	j.	j.	PROPN
ma-386	243	2	math	math	PROPN
ma-386	243	3	.	.	PUNCT
ma-386	244	1	anal	anal	PROPN
ma-386	244	2	.	.	PUNCT
ma-386	245	1	10.28924	10.28924	NUM
ma-386	245	2	/	/	SYM
ma-386	245	3	ada	ada	PROPN
ma-386	245	4	/	/	SYM
ma-386	245	5	ma.5.18	ma.5.18	NOUN
ma-386	245	6	9	9	NUM
ma-386	245	7	proof	proof	NOUN
ma-386	245	8	.	.	PUNCT
ma-386	245	9	suppose	suppose	VERB
ma-386	245	10	that	that	SCONJ
ma-386	245	11	there	there	PRON
ma-386	245	12	exists	exist	VERB
ma-386	245	13	a	a	DET
ma-386	245	14	solution	solution	NOUN
ma-386	245	15	z∗	z∗	NOUN
ma-386	245	16	∈	∈	NOUN
ma-386	245	17	d1	d1	NOUN
ma-386	245	18	of	of	ADP
ma-386	245	19	the	the	DET
ma-386	245	20	equation	equation	NOUN
ma-386	245	21	g(x	g(x	NOUN
ma-386	245	22	)	)	PUNCT
ma-386	246	1	=	=	SYM
ma-386	246	2	0	0	NUM
ma-386	246	3	such	such	ADJ
ma-386	246	4	that	that	DET
ma-386	246	5	z∗	z∗	PROPN
ma-386	246	6	6=	6=	PRON
ma-386	247	1	x∗.then	x∗.then	PROPN
ma-386	247	2	,	,	PUNCT
ma-386	247	3	define	define	VERB
ma-386	247	4	the	the	DET
ma-386	247	5	linear	linear	ADJ
ma-386	247	6	operator	operator	NOUN
ma-386	247	7	e1	e1	NOUN
ma-386	247	8	=	=	PUNCT
ma-386	248	1	1∫	1∫	NUM
ma-386	248	2	0	0	X
ma-386	249	1	g′(x∗	g′(x∗	NOUN
ma-386	249	2	+	+	NUM
ma-386	249	3	η(z∗	η(z∗	PRON
ma-386	249	4	−	−	PROPN
ma-386	249	5	x∗))dη	x∗))dη	PROPN
ma-386	249	6	.	.	PUNCT
ma-386	250	1	by	by	ADP
ma-386	250	2	this	this	DET
ma-386	250	3	definition	definition	NOUN
ma-386	250	4	,	,	PUNCT
ma-386	250	5	the	the	DET
ma-386	250	6	condition	condition	NOUN
ma-386	250	7	(	(	PUNCT
ma-386	250	8	h7	h7	PROPN
ma-386	250	9	)	)	PUNCT
ma-386	250	10	and	and	CCONJ
ma-386	250	11	(	(	PUNCT
ma-386	250	12	29	29	NUM
ma-386	250	13	)	)	PUNCT
ma-386	250	14	we	we	PRON
ma-386	250	15	get	get	VERB
ma-386	250	16	in	in	ADP
ma-386	250	17	turn	turn	NOUN
ma-386	250	18	‖e−11	‖e−11	PUNCT
ma-386	250	19	(	(	PUNCT
ma-386	250	20	e1	e1	NOUN
ma-386	250	21	−	−	NOUN
ma-386	250	22	e)‖	e)‖	ADJ
ma-386	250	23	≤	≤	NOUN
ma-386	251	1	1∫	1∫	NUM
ma-386	251	2	0	0	NUM
ma-386	251	3	φ0(η‖z∗	φ0(η‖z∗	PROPN
ma-386	252	1	−	−	PROPN
ma-386	252	2	x∗‖)dη	x∗‖)dη	PROPN
ma-386	252	3	≤	≤	NUM
ma-386	253	1	1∫	1∫	NUM
ma-386	253	2	0	0	PUNCT
ma-386	253	3	φ0(ηr2)dη	φ0(ηr2)dη	NOUN
ma-386	253	4	<	<	NOUN
ma-386	253	5	1	1	NUM
ma-386	253	6	.	.	PUNCT
ma-386	254	1	thus	thus	ADV
ma-386	254	2	,	,	PUNCT
ma-386	254	3	the	the	DET
ma-386	254	4	linear	linear	ADJ
ma-386	254	5	operator	operator	NOUN
ma-386	254	6	e1	e1	NOUN
ma-386	254	7	is	be	AUX
ma-386	254	8	invertible	invertible	ADJ
ma-386	254	9	.	.	PUNCT
ma-386	255	1	it	it	PRON
ma-386	255	2	follows	follow	VERB
ma-386	255	3	by	by	ADP
ma-386	255	4	the	the	DET
ma-386	255	5	identity	identity	NOUN
ma-386	255	6	z∗	z∗	NOUN
ma-386	255	7	−	−	NOUN
ma-386	255	8	x∗	x∗	PROPN
ma-386	255	9	=	=	SYM
ma-386	255	10	e−11	e−11	X
ma-386	255	11	(	(	PUNCT
ma-386	255	12	g(z∗)−	g(z∗)−	PROPN
ma-386	255	13	g(x∗	g(x∗	NOUN
ma-386	255	14	)	)	PUNCT
ma-386	255	15	)	)	PUNCT
ma-386	256	1	=	=	SYM
ma-386	256	2	e−11	e−11	X
ma-386	256	3	(	(	PUNCT
ma-386	256	4	0	0	NUM
ma-386	256	5	)	)	PUNCT
ma-386	256	6	=	=	SYM
ma-386	256	7	0	0	NUM
ma-386	256	8	,	,	PUNCT
ma-386	256	9	and	and	CCONJ
ma-386	256	10	we	we	PRON
ma-386	256	11	conclude	conclude	VERB
ma-386	256	12	z∗	z∗	NOUN
ma-386	256	13	=	=	SYM
ma-386	256	14	x∗.	x∗.	PROPN
ma-386	256	15	�	�	PROPN
ma-386	256	16	remark	remark	NOUN
ma-386	256	17	2	2	NUM
ma-386	256	18	.	.	PUNCT
ma-386	257	1	under	under	ADP
ma-386	257	2	all	all	DET
ma-386	257	3	the	the	DET
ma-386	257	4	conditions	condition	NOUN
ma-386	257	5	(	(	PUNCT
ma-386	257	6	h4)–(h9	h4)–(h9	NOUN
ma-386	257	7	)	)	PUNCT
ma-386	257	8	,	,	PUNCT
ma-386	257	9	one	one	PRON
ma-386	257	10	can	can	AUX
ma-386	257	11	set	set	VERB
ma-386	257	12	r1	r1	NOUN
ma-386	257	13	=	=	SYM
ma-386	257	14	r∗	r∗	PROPN
ma-386	257	15	in	in	ADP
ma-386	257	16	proposition	proposition	NOUN
ma-386	257	17	1	1	NUM
ma-386	257	18	.	.	X
ma-386	257	19	2.2	2.2	NUM
ma-386	257	20	.	.	PUNCT
ma-386	258	1	semi	semi	ADJ
ma-386	258	2	-	-	ADJ
ma-386	258	3	local	local	ADJ
ma-386	258	4	.	.	PUNCT
ma-386	259	1	the	the	DET
ma-386	259	2	calculations	calculation	NOUN
ma-386	259	3	and	and	CCONJ
ma-386	259	4	formulae	formulae	NOUN
ma-386	259	5	are	be	AUX
ma-386	259	6	as	as	ADP
ma-386	259	7	in	in	ADP
ma-386	259	8	section	section	NOUN
ma-386	259	9	2.1	2.1	NUM
ma-386	259	10	,	,	PUNCT
ma-386	259	11	but	but	CCONJ
ma-386	259	12	x∗	x∗	PROPN
ma-386	259	13	,	,	PUNCT
ma-386	259	14	φ0	φ0	PROPN
ma-386	259	15	,	,	PUNCT
ma-386	259	16	φ	φ	PROPN
ma-386	259	17	are	be	AUX
ma-386	259	18	exchangedby	exchangedby	ADJ
ma-386	259	19	x0	x0	PROPN
ma-386	259	20	,	,	PUNCT
ma-386	259	21	ψ0	ψ0	ADV
ma-386	259	22	,	,	PUNCT
ma-386	259	23	and	and	CCONJ
ma-386	259	24	ψ	ψ	NOUN
ma-386	259	25	,	,	PUNCT
ma-386	259	26	respectively.suppose	respectively.suppose	PROPN
ma-386	259	27	(	(	PUNCT
ma-386	259	28	c1	c1	PROPN
ma-386	259	29	)	)	PUNCT
ma-386	259	30	there	there	PRON
ma-386	259	31	exists	exist	VERB
ma-386	259	32	a	a	DET
ma-386	259	33	nondecreasing	nondecreasing	ADJ
ma-386	259	34	and	and	CCONJ
ma-386	259	35	continuous	continuous	ADJ
ma-386	259	36	function	function	NOUN
ma-386	259	37	ψ0	ψ0	ADV
ma-386	259	38	:	:	PUNCT
ma-386	259	39	a	a	PRON
ma-386	259	40	→	→	X
ma-386	259	41	a	a	DET
ma-386	259	42	such	such	ADJ
ma-386	259	43	that	that	SCONJ
ma-386	259	44	the	the	DET
ma-386	259	45	function	function	NOUN
ma-386	259	46	1−ψ0(t	1−ψ0(t	NUM
ma-386	259	47	)	)	PUNCT
ma-386	259	48	has	have	VERB
ma-386	259	49	a	a	DET
ma-386	259	50	smallest	small	ADJ
ma-386	259	51	positive	positive	ADJ
ma-386	259	52	solution	solution	NOUN
ma-386	259	53	in	in	ADP
ma-386	259	54	the	the	DET
ma-386	259	55	interval	interval	NOUN
ma-386	259	56	a	a	PRON
ma-386	259	57	,	,	PUNCT
ma-386	259	58	which	which	PRON
ma-386	259	59	is	be	AUX
ma-386	259	60	denoted	denote	VERB
ma-386	259	61	by	by	ADP
ma-386	259	62	t0	t0	PROPN
ma-386	259	63	.	.	PUNCT
ma-386	260	1	definethe	definethe	DET
ma-386	260	2	interval	interval	NOUN
ma-386	260	3	s	s	PART
ma-386	260	4	=	=	PUNCT
ma-386	261	1	[	[	X
ma-386	261	2	0	0	NUM
ma-386	261	3	,	,	PUNCT
ma-386	261	4	t0	t0	PROPN
ma-386	261	5	)	)	PUNCT
ma-386	261	6	.	.	PUNCT
ma-386	262	1	(	(	PUNCT
ma-386	262	2	c2	c2	PROPN
ma-386	262	3	)	)	PUNCT
ma-386	262	4	there	there	PRON
ma-386	262	5	exists	exist	VERB
ma-386	262	6	a	a	DET
ma-386	262	7	nondecreasing	nondecreasing	ADJ
ma-386	262	8	and	and	CCONJ
ma-386	262	9	continuous	continuous	ADJ
ma-386	262	10	function	function	NOUN
ma-386	262	11	ψ	ψ	NOUN
ma-386	262	12	:	:	PUNCT
ma-386	262	13	s	s	X
ma-386	262	14	→	→	PUNCT
ma-386	262	15	a.define	a.define	VERB
ma-386	262	16	the	the	DET
ma-386	262	17	sequences	sequence	NOUN
ma-386	262	18	{	{	PUNCT
ma-386	262	19	αin	αin	NOUN
ma-386	262	20	}	}	PUNCT
ma-386	262	21	for	for	ADP
ma-386	262	22	α00	α00	NOUN
ma-386	262	23	=	=	SYM
ma-386	262	24	0	0	NUM
ma-386	262	25	,	,	PUNCT
ma-386	262	26	some	some	PRON
ma-386	262	27	α10	α10	ADJ
ma-386	262	28	≥	≥	NOUN
ma-386	262	29	0	0	NUM
ma-386	262	30	,	,	PUNCT
ma-386	262	31	i	i	PRON
ma-386	262	32	=	=	NOUN
ma-386	262	33	0	0	NUM
ma-386	262	34	,	,	PUNCT
ma-386	262	35	.	.	PUNCT
ma-386	262	36	.	.	PUNCT
ma-386	263	1	.	.	PUNCT
ma-386	264	1	,	,	PUNCT
ma-386	265	1	k	k	NOUN
ma-386	265	2	,	,	PUNCT
ma-386	265	3	and	and	CCONJ
ma-386	265	4	each	each	DET
ma-386	265	5	n	n	NOUN
ma-386	265	6	=	=	SYM
ma-386	265	7	0	0	NUM
ma-386	265	8	,	,	PUNCT
ma-386	265	9	1	1	NUM
ma-386	265	10	,	,	PUNCT
ma-386	265	11	2	2	NUM
ma-386	265	12	,	,	PUNCT
ma-386	265	13	.	.	PUNCT
ma-386	265	14	.	.	PUNCT
ma-386	265	15	.	.	PUNCT
ma-386	266	1	by	by	ADP
ma-386	266	2	ψn	ψn	NOUN
ma-386	266	3	=	=	PUNCT
ma-386	266	4			PROPN
ma-386	266	5	ψ(α1n	ψ(α1n	NOUN
ma-386	266	6	−	−	PROPN
ma-386	266	7	α0n),or	α0n),or	PROPN
ma-386	266	8	ψ0(α	ψ0(α	PROPN
ma-386	266	9	0	0	NUM
ma-386	266	10	n	n	CCONJ
ma-386	266	11	)	)	PUNCT
ma-386	266	12	+	+	CCONJ
ma-386	266	13	ψ0(α	ψ0(α	PROPN
ma-386	266	14	1	1	NUM
ma-386	266	15	n	n	CCONJ
ma-386	266	16	)	)	PUNCT
ma-386	266	17	,	,	PUNCT
ma-386	266	18	pn	pn	PROPN
ma-386	266	19	=	=	SYM
ma-386	266	20	1	1	NUM
ma-386	266	21	2	2	NUM
ma-386	266	22	(	(	PUNCT
ma-386	266	23	ψ0(α	ψ0(α	PROPN
ma-386	266	24	0	0	NUM
ma-386	266	25	n	n	CCONJ
ma-386	266	26	)	)	PUNCT
ma-386	267	1	+	+	CCONJ
ma-386	267	2	ψ0(α	ψ0(α	PROPN
ma-386	267	3	1	1	NUM
ma-386	267	4	n	n	CCONJ
ma-386	267	5	)	)	PUNCT
ma-386	267	6	)	)	PUNCT
ma-386	267	7	,	,	PUNCT
ma-386	267	8	α2n	α2n	PROPN
ma-386	267	9	=	=	SYM
ma-386	267	10	α1n	α1n	PROPN
ma-386	267	11	+	+	NUM
ma-386	267	12	ψn(α1n	ψn(α1n	PROPN
ma-386	267	13	−	−	PROPN
ma-386	267	14	α0n	α0n	PROPN
ma-386	267	15	)	)	PUNCT
ma-386	267	16	2(1−	2(1−	X
ma-386	267	17	pn	pn	NOUN
ma-386	267	18	)	)	PUNCT
ma-386	267	19	,	,	PUNCT
ma-386	267	20	(	(	PUNCT
ma-386	267	21	30	30	NUM
ma-386	267	22	)	)	PUNCT
ma-386	267	23	λj−1n	λj−1n	NOUN
ma-386	268	1	=	=	PUNCT
ma-386	269	1	1∫	1∫	NUM
ma-386	269	2	0	0	NUM
ma-386	269	3	ψ((1−	ψ((1−	PUNCT
ma-386	269	4	η)(αj−1n	η)(αj−1n	ADJ
ma-386	269	5	−	−	NOUN
ma-386	269	6	α0n))dη	α0n))dη	NOUN
ma-386	269	7	·	·	PUNCT
ma-386	269	8	(	(	PUNCT
ma-386	269	9	αj−1n	αj−1n	NOUN
ma-386	269	10	−	−	PROPN
ma-386	269	11	α0n	α0n	PROPN
ma-386	269	12	)	)	PUNCT
ma-386	270	1	+	+	CCONJ
ma-386	270	2	(	(	PUNCT
ma-386	270	3	1	1	NUM
ma-386	270	4	+	+	NUM
ma-386	270	5	ψ0(α	ψ0(α	PROPN
ma-386	270	6	0	0	X
ma-386	270	7	n))(αj−1n	n))(αj−1n	PROPN
ma-386	270	8	−	−	PROPN
ma-386	270	9	α1n	α1n	NOUN
ma-386	270	10	)	)	PUNCT
ma-386	270	11	,	,	PUNCT
ma-386	270	12	qn	qn	NOUN
ma-386	270	13	=	=	NOUN
ma-386	270	14	1	1	NUM
ma-386	270	15	2	2	NUM
ma-386	270	16	(	(	PUNCT
ma-386	270	17	3ψ0(α	3ψ0(α	NUM
ma-386	270	18	1	1	NUM
ma-386	270	19	n	n	CCONJ
ma-386	270	20	)	)	PUNCT
ma-386	270	21	+	+	CCONJ
ma-386	270	22	ψ0(α	ψ0(α	PROPN
ma-386	270	23	0	0	NUM
ma-386	270	24	n	n	CCONJ
ma-386	270	25	)	)	PUNCT
ma-386	270	26	)	)	PUNCT
ma-386	270	27	,	,	PUNCT
ma-386	270	28	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	270	29	eur	eur	PROPN
ma-386	270	30	.	.	PUNCT
ma-386	271	1	j.	j.	PROPN
ma-386	271	2	math	math	PROPN
ma-386	271	3	.	.	PUNCT
ma-386	272	1	anal	anal	PROPN
ma-386	272	2	.	.	PUNCT
ma-386	273	1	10.28924	10.28924	NUM
ma-386	273	2	/	/	SYM
ma-386	273	3	ada	ada	PROPN
ma-386	273	4	/	/	SYM
ma-386	273	5	ma.5.18	ma.5.18	PROPN
ma-386	273	6	10	10	NUM
ma-386	273	7	αjn	αjn	NOUN
ma-386	273	8	=	=	SYM
ma-386	273	9	αj−1n	αj−1n	NOUN
ma-386	273	10	+	+	CCONJ
ma-386	273	11	(	(	PUNCT
ma-386	273	12	ψ0(α	ψ0(α	PROPN
ma-386	273	13	0	0	NUM
ma-386	273	14	n	n	CCONJ
ma-386	273	15	)	)	PUNCT
ma-386	274	1	+	+	CCONJ
ma-386	274	2	ψ0(α	ψ0(α	PROPN
ma-386	274	3	1	1	NUM
ma-386	274	4	n	n	CCONJ
ma-386	274	5	)	)	PUNCT
ma-386	274	6	+	+	CCONJ
ma-386	274	7	2)λj−1n	2)λj−1n	ADJ
ma-386	274	8	2(1−	2(1−	X
ma-386	274	9	ψ0(α0n))(1−	ψ0(α0n))(1−	X
ma-386	274	10	qn	qn	NOUN
ma-386	274	11	)	)	PUNCT
ma-386	274	12	,	,	PUNCT
ma-386	274	13	µn+1	µn+1	X
ma-386	274	14	=	=	SYM
ma-386	274	15	1∫	1∫	NUM
ma-386	274	16	0	0	NUM
ma-386	274	17	ψ((1−	ψ((1−	PRON
ma-386	274	18	η)(α0n+1	η)(α0n+1	ADJ
ma-386	274	19	−	−	ADP
ma-386	274	20	α0n))dη(α0n+1	α0n))dη(α0n+1	NOUN
ma-386	274	21	−	−	NOUN
ma-386	274	22	α0n	α0n	NOUN
ma-386	274	23	)	)	PUNCT
ma-386	275	1	+	+	CCONJ
ma-386	275	2	(	(	PUNCT
ma-386	275	3	1	1	NUM
ma-386	275	4	+	+	NUM
ma-386	275	5	ψ0(α	ψ0(α	PROPN
ma-386	275	6	0	0	NUM
ma-386	275	7	n))(α0n	n))(α0n	NUM
ma-386	275	8	−	−	PROPN
ma-386	275	9	α0n	α0n	PROPN
ma-386	275	10	)	)	PUNCT
ma-386	275	11	,	,	PUNCT
ma-386	275	12	and	and	CCONJ
ma-386	275	13	α1n+1	α1n+1	PROPN
ma-386	275	14	=	=	SYM
ma-386	276	1	α0n+1	α0n+1	PROPN
ma-386	276	2	+	+	PUNCT
ma-386	276	3	µn+1	µn+1	VERB
ma-386	276	4	1−	1−	NUM
ma-386	276	5	ψ0(α0n+1	ψ0(α0n+1	NOUN
ma-386	276	6	)	)	PUNCT
ma-386	276	7	,	,	PUNCT
ma-386	276	8	where	where	SCONJ
ma-386	276	9	again	again	ADV
ma-386	276	10	α0n+1	α0n+1	PROPN
ma-386	276	11	=	=	NOUN
ma-386	276	12	αkn	αkn	NOUN
ma-386	276	13	.the	.the	PROPN
ma-386	276	14	sequence	sequence	NOUN
ma-386	276	15	{	{	PUNCT
ma-386	276	16	αin}n	αin}n	NOUN
ma-386	276	17	is	be	AUX
ma-386	276	18	shown	show	VERB
ma-386	276	19	to	to	PART
ma-386	276	20	be	be	AUX
ma-386	276	21	majorizing	majorize	VERB
ma-386	276	22	for	for	ADP
ma-386	276	23	{	{	PUNCT
ma-386	276	24	y	y	PROPN
ma-386	276	25	(	(	PUNCT
ma-386	276	26	i)n	i)n	X
ma-386	276	27	}	}	PUNCT
ma-386	276	28	n	n	CCONJ
ma-386	276	29	in	in	ADP
ma-386	276	30	theorem	theorem	NOUN
ma-386	277	1	2.but	2.but	CCONJ
ma-386	277	2	let	let	VERB
ma-386	277	3	us	we	PRON
ma-386	277	4	first	first	ADV
ma-386	277	5	provide	provide	VERB
ma-386	277	6	a	a	DET
ma-386	277	7	convergence	convergence	NOUN
ma-386	277	8	condition	condition	NOUN
ma-386	277	9	for	for	ADP
ma-386	277	10	it	it	PRON
ma-386	277	11	.	.	PUNCT
ma-386	278	1	(	(	PUNCT
ma-386	278	2	c3	c3	NOUN
ma-386	278	3	)	)	PUNCT
ma-386	278	4	there	there	PRON
ma-386	278	5	exists	exist	VERB
ma-386	278	6	t	t	PROPN
ma-386	278	7	∈	∈	PROPN
ma-386	279	1	[	[	X
ma-386	279	2	0	0	NUM
ma-386	279	3	,	,	PUNCT
ma-386	279	4	t0	t0	PROPN
ma-386	279	5	)	)	PUNCT
ma-386	280	1	such	such	ADJ
ma-386	280	2	that	that	PRON
ma-386	280	3	for	for	ADP
ma-386	280	4	each	each	DET
ma-386	280	5	i	i	NOUN
ma-386	280	6	=	=	NOUN
ma-386	280	7	0	0	NUM
ma-386	280	8	,	,	PUNCT
ma-386	280	9	1	1	NUM
ma-386	280	10	,	,	PUNCT
ma-386	280	11	2	2	NUM
ma-386	280	12	,	,	PUNCT
ma-386	280	13	.	.	PUNCT
ma-386	280	14	.	.	PUNCT
ma-386	280	15	.	.	PUNCT
ma-386	281	1	,	,	PUNCT
ma-386	281	2	k	k	PROPN
ma-386	281	3	and	and	CCONJ
ma-386	281	4	each	each	DET
ma-386	281	5	n	n	NOUN
ma-386	281	6	=	=	SYM
ma-386	281	7	0	0	NUM
ma-386	281	8	,	,	PUNCT
ma-386	281	9	1	1	NUM
ma-386	281	10	,	,	PUNCT
ma-386	281	11	2	2	NUM
ma-386	281	12	,	,	PUNCT
ma-386	281	13	.	.	PUNCT
ma-386	281	14	.	.	PUNCT
ma-386	281	15	.	.	PUNCT
ma-386	282	1	ψ0(α	ψ0(α	PROPN
ma-386	282	2	0	0	NUM
ma-386	282	3	n	n	CCONJ
ma-386	282	4	)	)	PUNCT
ma-386	282	5	<	<	X
ma-386	282	6	1	1	NUM
ma-386	282	7	,	,	PUNCT
ma-386	282	8	pn	pn	X
ma-386	282	9	<	<	X
ma-386	282	10	1	1	NUM
ma-386	282	11	,	,	PUNCT
ma-386	282	12	qn	qn	NOUN
ma-386	282	13	<	<	X
ma-386	282	14	1	1	NUM
ma-386	282	15	,	,	PUNCT
ma-386	282	16	and	and	CCONJ
ma-386	282	17	αin	αin	ADJ
ma-386	282	18	≤	≤	ADJ
ma-386	282	19	t.	t.	NOUN
ma-386	282	20	it	it	PRON
ma-386	282	21	follows	follow	VERB
ma-386	282	22	by	by	ADP
ma-386	282	23	this	this	DET
ma-386	282	24	condition	condition	NOUN
ma-386	282	25	and	and	CCONJ
ma-386	282	26	(	(	PUNCT
ma-386	282	27	30	30	NUM
ma-386	282	28	)	)	PUNCT
ma-386	282	29	that	that	SCONJ
ma-386	282	30	the	the	DET
ma-386	282	31	sequence	sequence	NOUN
ma-386	282	32	{	{	PUNCT
ma-386	282	33	αin	αin	NOUN
ma-386	282	34	}	}	PUNCT
ma-386	282	35	is	be	AUX
ma-386	282	36	nondecreasing	nondecreasing	AUX
ma-386	282	37	andbounded	andbounde	VERB
ma-386	282	38	from	from	ADP
ma-386	282	39	above	above	ADV
ma-386	282	40	by	by	ADP
ma-386	282	41	t	t	PROPN
ma-386	282	42	and	and	CCONJ
ma-386	282	43	as	as	ADV
ma-386	282	44	such	such	ADJ
ma-386	282	45	it	it	PRON
ma-386	282	46	converges	converge	VERB
ma-386	282	47	to	to	ADP
ma-386	282	48	some	some	DET
ma-386	282	49	α∗	α∗	NOUN
ma-386	282	50	∈	∈	PROPN
ma-386	283	1	[	[	X
ma-386	283	2	0	0	NUM
ma-386	283	3	,	,	PUNCT
ma-386	283	4	t	t	PROPN
ma-386	283	5	]	]	PUNCT
ma-386	283	6	.	.	PUNCT
ma-386	284	1	the	the	DET
ma-386	284	2	limit	limit	NOUN
ma-386	284	3	point	point	NOUN
ma-386	284	4	α∗is	α∗i	NOUN
ma-386	284	5	the	the	DET
ma-386	284	6	unique	unique	ADJ
ma-386	284	7	least	least	ADV
ma-386	284	8	upper	upper	ADJ
ma-386	284	9	bound	bind	VERB
ma-386	284	10	of	of	ADP
ma-386	284	11	the	the	DET
ma-386	284	12	sequence	sequence	NOUN
ma-386	284	13	{	{	PUNCT
ma-386	284	14	αin}.as	αin}.as	NOUN
ma-386	284	15	in	in	ADP
ma-386	284	16	the	the	DET
ma-386	284	17	local	local	ADJ
ma-386	284	18	analysis	analysis	NOUN
ma-386	284	19	,	,	PUNCT
ma-386	284	20	the	the	DET
ma-386	284	21	operators	operator	NOUN
ma-386	284	22	on	on	ADP
ma-386	284	23	the	the	DET
ma-386	284	24	method	method	NOUN
ma-386	284	25	(	(	PUNCT
ma-386	284	26	2	2	X
ma-386	284	27	)	)	PUNCT
ma-386	284	28	connect	connect	VERB
ma-386	284	29	to	to	ADP
ma-386	284	30	the	the	DET
ma-386	284	31	functions	function	NOUN
ma-386	284	32	ψ0	ψ0	ADJ
ma-386	284	33	and	and	CCONJ
ma-386	284	34	ψ	ψ	ADJ
ma-386	284	35	.	.	PUNCT
ma-386	285	1	(	(	PUNCT
ma-386	285	2	c4	c4	NOUN
ma-386	285	3	)	)	PUNCT
ma-386	285	4	there	there	PRON
ma-386	285	5	exist	exist	VERB
ma-386	286	1	x0	x0	PROPN
ma-386	286	2	∈	∈	PROPN
ma-386	286	3	d	d	NOUN
ma-386	286	4	and	and	CCONJ
ma-386	286	5	a	a	DET
ma-386	286	6	linear	linear	ADJ
ma-386	286	7	operator	operator	NOUN
ma-386	286	8	e	e	NOUN
ma-386	286	9	such	such	ADJ
ma-386	286	10	that	that	PRON
ma-386	286	11	for	for	ADP
ma-386	286	12	each	each	DET
ma-386	286	13	u	u	NOUN
ma-386	286	14	∈	∈	PROPN
ma-386	286	15	d	d	PROPN
ma-386	286	16	‖e−1(g′(u)−	‖e−1(g′(u)−	PROPN
ma-386	286	17	e)‖	e)‖	ADJ
ma-386	286	18	≤	≤	X
ma-386	286	19	ψ0(‖u	ψ0(‖u	NOUN
ma-386	286	20	−	−	PROPN
ma-386	286	21	x0‖	x0‖	PROPN
ma-386	286	22	)	)	PUNCT
ma-386	286	23	.	.	PUNCT
ma-386	287	1	it	it	PRON
ma-386	287	2	follows	follow	VERB
ma-386	287	3	by	by	ADP
ma-386	287	4	the	the	DET
ma-386	287	5	conditions	condition	NOUN
ma-386	287	6	(	(	PUNCT
ma-386	287	7	c1	c1	PROPN
ma-386	287	8	)	)	PUNCT
ma-386	287	9	,	,	PUNCT
ma-386	287	10	(	(	PUNCT
ma-386	287	11	c4	c4	NOUN
ma-386	287	12	)	)	PUNCT
ma-386	287	13	,	,	PUNCT
ma-386	287	14	and	and	CCONJ
ma-386	287	15	(	(	PUNCT
ma-386	287	16	30	30	NUM
ma-386	287	17	)	)	PUNCT
ma-386	287	18	that	that	SCONJ
ma-386	287	19	if	if	SCONJ
ma-386	287	20	u	u	PROPN
ma-386	287	21	=	=	PROPN
ma-386	287	22	x0	x0	PROPN
ma-386	287	23	,	,	PUNCT
ma-386	287	24	we	we	PRON
ma-386	287	25	get	get	VERB
ma-386	287	26	‖e−1(g′(x0)−	‖e−1(g′(x0)−	PROPN
ma-386	287	27	e)‖	e)‖	ADP
ma-386	287	28	≤	≤	NUM
ma-386	287	29	ψ0(0	ψ0(0	PROPN
ma-386	287	30	)	)	PUNCT
ma-386	287	31	<	<	X
ma-386	288	1	1	1	X
ma-386	288	2	.	.	PUNCT
ma-386	289	1	so	so	ADV
ma-386	289	2	,	,	PUNCT
ma-386	289	3	the	the	DET
ma-386	289	4	linear	linear	ADJ
ma-386	289	5	operator	operator	NOUN
ma-386	289	6	g′(x0	g′(x0	NOUN
ma-386	289	7	)	)	PUNCT
ma-386	289	8	is	be	AUX
ma-386	289	9	invertible	invertible	ADJ
ma-386	289	10	,	,	PUNCT
ma-386	289	11	in	in	ADP
ma-386	289	12	which	which	DET
ma-386	289	13	case	case	NOUN
ma-386	289	14	we	we	PRON
ma-386	289	15	can	can	AUX
ma-386	289	16	take	take	VERB
ma-386	289	17	α10	α10	NOUN
ma-386	289	18	≥	≥	VERB
ma-386	289	19	‖g′(x0)−1g(x0)‖.	‖g′(x0)−1g(x0)‖.	AUX
ma-386	289	20	define	define	VERB
ma-386	289	21	the	the	DET
ma-386	289	22	region	region	NOUN
ma-386	289	23	d2	d2	PROPN
ma-386	289	24	=	=	SYM
ma-386	289	25	u[x0	u[x0	NOUN
ma-386	289	26	,	,	PUNCT
ma-386	289	27	α	α	NOUN
ma-386	289	28	∗	∗	NOUN
ma-386	289	29	]	]	PUNCT
ma-386	289	30	∩d	∩d	NOUN
ma-386	289	31	.	.	PUNCT
ma-386	290	1	(	(	PUNCT
ma-386	290	2	c5	c5	PROPN
ma-386	290	3	)	)	PUNCT
ma-386	290	4	‖e−1(g′(u2)−	‖e−1(g′(u2)−	PROPN
ma-386	290	5	g′(u1))‖	g′(u1))‖	PROPN
ma-386	290	6	≤	≤	NOUN
ma-386	290	7	ψ(‖u2	ψ(‖u2	ADP
ma-386	290	8	−	−	PROPN
ma-386	290	9	u1‖	u1‖	PROPN
ma-386	290	10	)	)	PUNCT
ma-386	290	11	,	,	PUNCT
ma-386	290	12	for	for	ADP
ma-386	290	13	each	each	DET
ma-386	290	14	u2	u2	NOUN
ma-386	290	15	,	,	PUNCT
ma-386	290	16	u1	u1	NOUN
ma-386	290	17	∈	∈	PROPN
ma-386	290	18	d2	d2	PROPN
ma-386	290	19	.	.	PUNCT
ma-386	291	1	(	(	PUNCT
ma-386	291	2	c6	c6	PROPN
ma-386	291	3	)	)	PUNCT
ma-386	291	4	u[x0	u[x0	PROPN
ma-386	291	5	,	,	PUNCT
ma-386	291	6	α	α	PROPN
ma-386	291	7	∗	∗	NOUN
ma-386	291	8	]	]	PUNCT
ma-386	292	1	⊂	⊂	PROPN
ma-386	292	2	d.	d.	PROPN
ma-386	292	3	remark	remark	VERB
ma-386	292	4	3	3	NUM
ma-386	292	5	.	.	PUNCT
ma-386	293	1	as	as	ADP
ma-386	293	2	in	in	ADP
ma-386	293	3	the	the	DET
ma-386	293	4	local	local	ADJ
ma-386	293	5	analysis	analysis	NOUN
ma-386	293	6	,	,	PUNCT
ma-386	293	7	possible	possible	ADJ
ma-386	293	8	selections	selection	NOUN
ma-386	293	9	for	for	ADP
ma-386	293	10	e	e	NOUN
ma-386	293	11	can	can	AUX
ma-386	293	12	be	be	AUX
ma-386	293	13	e	e	NOUN
ma-386	293	14	=	=	PUNCT
ma-386	293	15	i	i	PRON
ma-386	293	16	or	or	CCONJ
ma-386	293	17	e	e	NOUN
ma-386	293	18	=	=	SYM
ma-386	293	19	g′(z̄	g′(z̄	PROPN
ma-386	293	20	)	)	PUNCT
ma-386	293	21	for	for	ADP
ma-386	293	22	someauxiliary	someauxiliary	ADJ
ma-386	293	23	point	point	NOUN
ma-386	293	24	x̄	x̄	X
ma-386	294	1	∈	∈	PROPN
ma-386	295	1	d	d	X
ma-386	295	2	such	such	ADJ
ma-386	295	3	that	that	DET
ma-386	295	4	x̄	x̄	NOUN
ma-386	295	5	6=	6=	NUM
ma-386	295	6	x0	x0	PROPN
ma-386	295	7	,	,	PUNCT
ma-386	295	8	or	or	CCONJ
ma-386	295	9	e	e	NOUN
ma-386	295	10	=	=	PROPN
ma-386	295	11	g′(x0	g′(x0	PROPN
ma-386	295	12	)	)	PUNCT
ma-386	295	13	,	,	PUNCT
ma-386	295	14	or	or	CCONJ
ma-386	295	15	some	some	DET
ma-386	295	16	other	other	ADJ
ma-386	295	17	selection	selection	NOUN
ma-386	295	18	.	.	PUNCT
ma-386	296	1	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	296	2	eur	eur	PROPN
ma-386	296	3	.	.	PUNCT
ma-386	297	1	j.	j.	PROPN
ma-386	297	2	math	math	PROPN
ma-386	297	3	.	.	PUNCT
ma-386	298	1	anal	anal	PROPN
ma-386	298	2	.	.	PUNCT
ma-386	299	1	10.28924	10.28924	NUM
ma-386	299	2	/	/	SYM
ma-386	299	3	ada	ada	PROPN
ma-386	299	4	/	/	SYM
ma-386	299	5	ma.5.18	ma.5.18	PROPN
ma-386	299	6	11the	11the	PROPN
ma-386	299	7	semi	semi	ADJ
ma-386	299	8	-	-	ADJ
ma-386	299	9	local	local	ADJ
ma-386	299	10	analysis	analysis	NOUN
ma-386	299	11	of	of	ADP
ma-386	299	12	the	the	DET
ma-386	299	13	method	method	NOUN
ma-386	299	14	(	(	PUNCT
ma-386	299	15	2	2	X
ma-386	299	16	)	)	PUNCT
ma-386	299	17	follows	follow	VERB
ma-386	299	18	in	in	ADP
ma-386	299	19	the	the	DET
ma-386	299	20	next	next	ADJ
ma-386	299	21	result	result	NOUN
ma-386	299	22	.	.	PUNCT
ma-386	300	1	theorem	theorem	NOUN
ma-386	300	2	2	2	NUM
ma-386	300	3	.	.	PUNCT
ma-386	300	4	suppose	suppose	VERB
ma-386	300	5	the	the	DET
ma-386	300	6	conditions	condition	NOUN
ma-386	300	7	(	(	PUNCT
ma-386	300	8	c1	c1	NOUN
ma-386	300	9	)	)	PUNCT
ma-386	300	10	−	−	PROPN
ma-386	301	1	(	(	PUNCT
ma-386	301	2	c6	c6	PROPN
ma-386	301	3	)	)	PUNCT
ma-386	301	4	hold	hold	VERB
ma-386	301	5	.	.	PUNCT
ma-386	302	1	then	then	ADV
ma-386	302	2	,	,	PUNCT
ma-386	302	3	the	the	DET
ma-386	302	4	sequence	sequence	NOUN
ma-386	302	5	{	{	PUNCT
ma-386	302	6	xn	xn	PROPN
ma-386	302	7	}	}	PUNCT
ma-386	302	8	generated	generate	VERB
ma-386	302	9	by	by	ADP
ma-386	302	10	the	the	DET
ma-386	302	11	method	method	NOUN
ma-386	302	12	(	(	PUNCT
ma-386	302	13	2	2	NUM
ma-386	302	14	)	)	PUNCT
ma-386	302	15	is	be	AUX
ma-386	302	16	well	well	ADV
ma-386	302	17	-	-	PUNCT
ma-386	302	18	defined	define	VERB
ma-386	302	19	in	in	ADP
ma-386	302	20	u(x0	u(x0	NOUN
ma-386	302	21	,	,	PUNCT
ma-386	302	22	α	α	PROPN
ma-386	302	23	∗	∗	NOUN
ma-386	302	24	)	)	PUNCT
ma-386	302	25	,	,	PUNCT
ma-386	302	26	remains	remain	VERB
ma-386	302	27	in	in	ADP
ma-386	302	28	u(x0	u(x0	NOUN
ma-386	302	29	,	,	PUNCT
ma-386	302	30	α	α	PROPN
ma-386	302	31	∗	∗	NOUN
ma-386	302	32	)	)	PUNCT
ma-386	302	33	,	,	PUNCT
ma-386	302	34	and	and	CCONJ
ma-386	302	35	is	be	AUX
ma-386	302	36	convergent	convergent	ADJ
ma-386	302	37	to	to	ADP
ma-386	302	38	a	a	DET
ma-386	302	39	solution	solution	NOUN
ma-386	302	40	x∗	x∗	PROPN
ma-386	302	41	∈	∈	PROPN
ma-386	302	42	u[x0	u[x0	NOUN
ma-386	302	43	,	,	PUNCT
ma-386	302	44	α	α	PROPN
ma-386	302	45	∗	∗	NOUN
ma-386	302	46	]	]	PUNCT
ma-386	302	47	of	of	ADP
ma-386	302	48	the	the	DET
ma-386	302	49	equation	equation	NOUN
ma-386	302	50	g(x	g(x	NOUN
ma-386	302	51	)	)	PUNCT
ma-386	303	1	=	=	SYM
ma-386	303	2	0	0	NUM
ma-386	303	3	such	such	ADJ
ma-386	303	4	that	that	PRON
ma-386	303	5	for	for	ADP
ma-386	303	6	each	each	DET
ma-386	303	7	n	n	NOUN
ma-386	303	8	=	=	SYM
ma-386	303	9	0	0	NUM
ma-386	303	10	,	,	PUNCT
ma-386	303	11	1	1	NUM
ma-386	303	12	,	,	PUNCT
ma-386	303	13	2	2	NUM
ma-386	303	14	,	,	PUNCT
ma-386	303	15	.	.	PUNCT
ma-386	303	16	.	.	PUNCT
ma-386	303	17	.	.	PUNCT
ma-386	303	18	‖x∗	‖x∗	PUNCT
ma-386	304	1	−	−	NOUN
ma-386	304	2	xn‖	xn‖	PROPN
ma-386	304	3	≤	≤	NOUN
ma-386	304	4	α∗αn	α∗αn	NOUN
ma-386	304	5	.	.	PUNCT
ma-386	305	1	proof	proof	NOUN
ma-386	305	2	.	.	PUNCT
ma-386	306	1	as	as	ADP
ma-386	306	2	in	in	ADP
ma-386	306	3	the	the	DET
ma-386	306	4	local	local	ADJ
ma-386	306	5	analysis	analysis	NOUN
ma-386	306	6	,	,	PUNCT
ma-386	306	7	induction	induction	NOUN
ma-386	306	8	is	be	AUX
ma-386	306	9	used	use	VERB
ma-386	306	10	to	to	PART
ma-386	306	11	first	first	ADV
ma-386	306	12	establish	establish	VERB
ma-386	306	13	the	the	DET
ma-386	306	14	assertions	assertion	NOUN
ma-386	306	15	‖y	‖y	PUNCT
ma-386	307	1	(	(	PUNCT
ma-386	307	2	1)n	1)n	NUM
ma-386	307	3	−	−	NOUN
ma-386	307	4	xn‖	xn‖	PROPN
ma-386	307	5	≤	≤	PROPN
ma-386	307	6	α1n	α1n	PROPN
ma-386	307	7	−	−	PROPN
ma-386	307	8	α0n	α0n	PROPN
ma-386	307	9	,	,	PUNCT
ma-386	307	10	(	(	PUNCT
ma-386	307	11	31	31	NUM
ma-386	307	12	)	)	PUNCT
ma-386	307	13	‖y	‖y	PUNCT
ma-386	308	1	(	(	PUNCT
ma-386	308	2	2)n	2)n	NUM
ma-386	308	3	−	−	PROPN
ma-386	308	4	y	y	PROPN
ma-386	308	5	(	(	PUNCT
ma-386	308	6	1)n	1)n	X
ma-386	308	7	‖	‖	PROPN
ma-386	308	8	≤	≤	PROPN
ma-386	308	9	α2n	α2n	PROPN
ma-386	308	10	−	−	PROPN
ma-386	308	11	α1n	α1n	PROPN
ma-386	308	12	,	,	PUNCT
ma-386	308	13	(	(	PUNCT
ma-386	308	14	32	32	NUM
ma-386	308	15	)	)	PUNCT
ma-386	308	16	‖y	‖y	PUNCT
ma-386	309	1	(	(	PUNCT
ma-386	309	2	j)n	j)n	NOUN
ma-386	309	3	−	−	PROPN
ma-386	309	4	y	y	PROPN
ma-386	309	5	(	(	PUNCT
ma-386	309	6	j−1)n	j−1)n	PROPN
ma-386	309	7	‖	‖	PROPN
ma-386	309	8	≤	≤	PROPN
ma-386	309	9	αjn	αjn	NOUN
ma-386	309	10	−	−	PROPN
ma-386	309	11	αj−1n	αj−1n	PROPN
ma-386	309	12	.	.	PUNCT
ma-386	310	1	(	(	PUNCT
ma-386	310	2	33	33	NUM
ma-386	310	3	)	)	PUNCT
ma-386	310	4	by	by	ADP
ma-386	310	5	switching	switch	VERB
ma-386	310	6	the	the	DET
ma-386	310	7	conditions	condition	NOUN
ma-386	310	8	(	(	PUNCT
ma-386	310	9	h1)−	h1)−	PROPN
ma-386	310	10	(	(	PUNCT
ma-386	310	11	h9	h9	NOUN
ma-386	310	12	)	)	PUNCT
ma-386	310	13	by	by	ADP
ma-386	310	14	(	(	PUNCT
ma-386	310	15	c1)−	c1)−	PROPN
ma-386	310	16	(	(	PUNCT
ma-386	310	17	c5	c5	PROPN
ma-386	310	18	)	)	PUNCT
ma-386	310	19	but	but	CCONJ
ma-386	310	20	using	use	VERB
ma-386	310	21	the	the	DET
ma-386	310	22	same	same	ADJ
ma-386	310	23	formulas	formula	NOUN
ma-386	310	24	,	,	PUNCT
ma-386	310	25	we	we	PRON
ma-386	310	26	get	get	VERB
ma-386	310	27	inturn	inturn	ADJ
ma-386	310	28	y	y	PROPN
ma-386	310	29	(	(	PUNCT
ma-386	310	30	2	2	NUM
ma-386	310	31	)	)	PUNCT
ma-386	310	32	n	n	CCONJ
ma-386	310	33	−	−	PROPN
ma-386	310	34	y	y	PROPN
ma-386	310	35	(	(	PUNCT
ma-386	310	36	1)n	1)n	PROPN
ma-386	310	37	=	=	SYM
ma-386	310	38	t	t	PROPN
ma-386	310	39	(	(	PUNCT
ma-386	310	40	g′(y	g′(y	X
ma-386	310	41	(	(	PUNCT
ma-386	310	42	1	1	NUM
ma-386	310	43	)	)	PUNCT
ma-386	310	44	n	n	CCONJ
ma-386	310	45	)	)	PUNCT
ma-386	310	46	−	−	PROPN
ma-386	311	1	g′(xn	g′(xn	NOUN
ma-386	311	2	)	)	PUNCT
ma-386	311	3	)	)	PUNCT
ma-386	312	1	g′(xn)−1g(xn	g′(xn)−1g(xn	X
ma-386	312	2	)	)	PUNCT
ma-386	312	3	=	=	SYM
ma-386	312	4	−	−	PROPN
ma-386	312	5	[	[	PUNCT
ma-386	312	6	te−1	te−1	PROPN
ma-386	312	7	]	]	PUNCT
ma-386	312	8	[	[	PUNCT
ma-386	312	9	e−1(g′(y	e−1(g′(y	X
ma-386	312	10	(	(	PUNCT
ma-386	312	11	1	1	NUM
ma-386	312	12	)	)	PUNCT
ma-386	312	13	n	n	CCONJ
ma-386	312	14	)	)	PUNCT
ma-386	312	15	−	−	PROPN
ma-386	312	16	g′(xn	g′(xn	NOUN
ma-386	312	17	)	)	PUNCT
ma-386	312	18	)	)	PUNCT
ma-386	312	19	]	]	PUNCT
ma-386	313	1	(	(	PUNCT
ma-386	313	2	y	y	NOUN
ma-386	313	3	(	(	PUNCT
ma-386	313	4	1	1	NUM
ma-386	313	5	)	)	PUNCT
ma-386	313	6	n	n	CCONJ
ma-386	313	7	−	−	NOUN
ma-386	313	8	xn	xn	NUM
ma-386	313	9	)	)	PUNCT
ma-386	313	10	,	,	PUNCT
ma-386	313	11	‖y	‖y	PUNCT
ma-386	313	12	(	(	PUNCT
ma-386	313	13	2)n	2)n	NUM
ma-386	313	14	−	−	PROPN
ma-386	313	15	y	y	PROPN
ma-386	313	16	(	(	PUNCT
ma-386	313	17	1)n	1)n	X
ma-386	313	18	‖	‖	PROPN
ma-386	313	19	≤	≤	PROPN
ma-386	313	20	ψn(α1n	ψn(α1n	PROPN
ma-386	313	21	−	−	PROPN
ma-386	313	22	α0n	α0n	PROPN
ma-386	313	23	)	)	PUNCT
ma-386	313	24	2(1−	2(1−	X
ma-386	313	25	pn	pn	NOUN
ma-386	313	26	)	)	PUNCT
ma-386	313	27	≤	≤	NUM
ma-386	313	28	α2n	α2n	PROPN
ma-386	313	29	−	−	PROPN
ma-386	313	30	α1n	α1n	PROPN
ma-386	313	31	,	,	PUNCT
ma-386	313	32	‖y	‖y	PUNCT
ma-386	313	33	(	(	PUNCT
ma-386	313	34	2)n	2)n	NUM
ma-386	313	35	−	−	NOUN
ma-386	313	36	x0‖	x0‖	PROPN
ma-386	313	37	≤	≤	PROPN
ma-386	313	38	‖y	‖y	PUNCT
ma-386	313	39	(	(	PUNCT
ma-386	313	40	2)n	2)n	NUM
ma-386	313	41	−	−	PROPN
ma-386	313	42	y	y	PROPN
ma-386	313	43	(	(	PUNCT
ma-386	313	44	1)n	1)n	X
ma-386	313	45	‖+	‖+	NUM
ma-386	313	46	‖y	‖y	PUNCT
ma-386	313	47	(	(	PUNCT
ma-386	313	48	1)n	1)n	NUM
ma-386	313	49	−	−	PROPN
ma-386	313	50	x0‖	x0‖	PROPN
ma-386	313	51	≤	≤	PROPN
ma-386	314	1	α2n	α2n	PROPN
ma-386	314	2	−	−	PROPN
ma-386	315	1	α1n	α1n	PROPN
ma-386	315	2	+	+	NUM
ma-386	315	3	α1n	α1n	PROPN
ma-386	315	4	−	−	PROPN
ma-386	315	5	α0n	α0n	PROPN
ma-386	315	6	=	=	SYM
ma-386	315	7	α2n	α2n	PROPN
ma-386	315	8	<	<	X
ma-386	315	9	α∗.	α∗.	NOUN
ma-386	316	1	so	so	ADV
ma-386	316	2	,	,	PUNCT
ma-386	316	3	the	the	DET
ma-386	316	4	estimate	estimate	NOUN
ma-386	316	5	(	(	PUNCT
ma-386	316	6	32	32	NUM
ma-386	316	7	)	)	PUNCT
ma-386	316	8	holds	hold	VERB
ma-386	316	9	and	and	CCONJ
ma-386	316	10	the	the	DET
ma-386	316	11	iterate	iterate	NOUN
ma-386	316	12	y	y	PROPN
ma-386	316	13	(	(	PUNCT
ma-386	316	14	2)n	2)n	NUM
ma-386	316	15	∈	∈	NOUN
ma-386	316	16	u[x0	u[x0	NOUN
ma-386	316	17	,	,	PUNCT
ma-386	316	18	α	α	PROPN
ma-386	316	19	∗].then	∗].then	ADV
ma-386	316	20	,	,	PUNCT
ma-386	316	21	by	by	ADP
ma-386	316	22	the	the	DET
ma-386	316	23	identity	identity	NOUN
ma-386	316	24	g(y	g(y	PROPN
ma-386	316	25	(	(	PUNCT
ma-386	316	26	j−1	j−1	PROPN
ma-386	316	27	)	)	PUNCT
ma-386	316	28	n	n	NOUN
ma-386	316	29	)	)	PUNCT
ma-386	317	1	=	=	PUNCT
ma-386	317	2	g(y	g(y	PROPN
ma-386	317	3	(	(	PUNCT
ma-386	317	4	j−1	j−1	PROPN
ma-386	317	5	)	)	PUNCT
ma-386	317	6	n	n	NOUN
ma-386	317	7	)	)	PUNCT
ma-386	317	8	−	−	PROPN
ma-386	317	9	g(xn)−	g(xn)−	NOUN
ma-386	317	10	g′(xn)(y	g′(xn)(y	X
ma-386	317	11	(	(	PUNCT
ma-386	317	12	1	1	NUM
ma-386	317	13	)	)	PUNCT
ma-386	317	14	n	n	CCONJ
ma-386	317	15	−	−	NOUN
ma-386	317	16	xn	xn	NUM
ma-386	317	17	)	)	PUNCT
ma-386	317	18	,	,	PUNCT
ma-386	317	19	=	=	PUNCT
ma-386	317	20	g(y	g(y	PROPN
ma-386	317	21	(	(	PUNCT
ma-386	317	22	j−1	j−1	PROPN
ma-386	317	23	)	)	PUNCT
ma-386	317	24	n	n	NOUN
ma-386	317	25	)	)	PUNCT
ma-386	317	26	−	−	PROPN
ma-386	317	27	g(xn)−	g(xn)−	NOUN
ma-386	317	28	g′(xn)(y	g′(xn)(y	X
ma-386	317	29	(	(	PUNCT
ma-386	317	30	j−1	j−1	PROPN
ma-386	317	31	)	)	PUNCT
ma-386	317	32	n	n	CCONJ
ma-386	317	33	−	−	NOUN
ma-386	317	34	xn	xn	X
ma-386	317	35	)	)	PUNCT
ma-386	318	1	+	+	CCONJ
ma-386	318	2	g′(xn)(y	g′(xn)(y	X
ma-386	318	3	(	(	PUNCT
ma-386	318	4	j−1	j−1	PROPN
ma-386	318	5	)	)	PUNCT
ma-386	318	6	n	n	CCONJ
ma-386	318	7	−	−	PROPN
ma-386	318	8	y	y	PROPN
ma-386	318	9	(	(	PUNCT
ma-386	318	10	1)n	1)n	PROPN
ma-386	318	11	)	)	PUNCT
ma-386	318	12	,	,	PUNCT
ma-386	318	13	which	which	PRON
ma-386	318	14	can	can	AUX
ma-386	318	15	imply	imply	VERB
ma-386	318	16	‖e−1g(y	‖e−1g(y	PROPN
ma-386	318	17	(	(	PUNCT
ma-386	318	18	j−1	j−1	PROPN
ma-386	318	19	)	)	PUNCT
ma-386	318	20	n	n	CCONJ
ma-386	318	21	)	)	PUNCT
ma-386	318	22	‖	‖	PROPN
ma-386	318	23	≤	≤	NUM
ma-386	319	1	1∫	1∫	NUM
ma-386	319	2	0	0	NUM
ma-386	319	3	ψ((1−η)(αj−1n	ψ((1−η)(αj−1n	NOUN
ma-386	319	4	−α0n))dη(αj−1n	−α0n))dη(αj−1n	ADV
ma-386	319	5	−α0n)+(1+ψ0(α	−α0n)+(1+ψ0(α	PROPN
ma-386	319	6	0	0	PUNCT
ma-386	319	7	n))(αj−1n	n))(αj−1n	PROPN
ma-386	319	8	−α1n	−α1n	PROPN
ma-386	319	9	)	)	PUNCT
ma-386	320	1	=	=	SYM
ma-386	321	1	λj−1n	λj−1n	NOUN
ma-386	321	2	(	(	PUNCT
ma-386	321	3	34	34	NUM
ma-386	321	4	)	)	PUNCT
ma-386	321	5	‖y	‖y	PUNCT
ma-386	322	1	(	(	PUNCT
ma-386	322	2	j)n	j)n	NOUN
ma-386	322	3	−	−	PROPN
ma-386	322	4	y	y	PROPN
ma-386	322	5	(	(	PUNCT
ma-386	322	6	j−1)n	j−1)n	PROPN
ma-386	322	7	‖	‖	PROPN
ma-386	322	8	≤	≤	PROPN
ma-386	322	9	(	(	PUNCT
ma-386	322	10	ψ0(α	ψ0(α	PROPN
ma-386	322	11	0	0	NUM
ma-386	322	12	n	n	CCONJ
ma-386	322	13	)	)	PUNCT
ma-386	323	1	+	+	CCONJ
ma-386	323	2	ψ0(α	ψ0(α	PROPN
ma-386	323	3	1	1	NUM
ma-386	323	4	n	n	CCONJ
ma-386	323	5	)	)	PUNCT
ma-386	323	6	+	+	CCONJ
ma-386	323	7	2)λj−1n	2)λj−1n	ADJ
ma-386	323	8	2(1−	2(1−	X
ma-386	323	9	ψ0(α0n))(1−	ψ0(α0n))(1−	NOUN
ma-386	323	10	qn	qn	NOUN
ma-386	323	11	)	)	PUNCT
ma-386	323	12	=	=	SYM
ma-386	323	13	αjn	αjn	NOUN
ma-386	323	14	−	−	PROPN
ma-386	323	15	αj−1n	αj−1n	PROPN
ma-386	323	16	.	.	PUNCT
ma-386	324	1	thus	thus	ADV
ma-386	324	2	,	,	PUNCT
ma-386	324	3	‖y	‖y	PUNCT
ma-386	324	4	(	(	PUNCT
ma-386	324	5	j)n	j)n	NOUN
ma-386	324	6	−	−	PROPN
ma-386	324	7	x0‖	x0‖	PROPN
ma-386	324	8	≤	≤	PROPN
ma-386	324	9	‖y	‖y	PUNCT
ma-386	325	1	(	(	PUNCT
ma-386	325	2	j)n	j)n	NOUN
ma-386	325	3	−	−	PROPN
ma-386	325	4	y	y	NOUN
ma-386	325	5	(	(	PUNCT
ma-386	325	6	j−1)n	j−1)n	PROPN
ma-386	325	7	‖+	‖+	PROPN
ma-386	325	8	‖y	‖y	PUNCT
ma-386	325	9	(	(	PUNCT
ma-386	325	10	j−1)n	j−1)n	PROPN
ma-386	325	11	−	−	PROPN
ma-386	325	12	x0‖	x0‖	PROPN
ma-386	325	13	≤	≤	PROPN
ma-386	325	14	αjn	αjn	NOUN
ma-386	325	15	−	−	PROPN
ma-386	325	16	αj−1n	αj−1n	PROPN
ma-386	325	17	+	+	CCONJ
ma-386	325	18	αj−1n	αj−1n	PROPN
ma-386	325	19	−	−	PROPN
ma-386	325	20	α00	α00	NOUN
ma-386	325	21	=	=	SYM
ma-386	325	22	αjn	αjn	NOUN
ma-386	325	23	<	<	X
ma-386	325	24	α∗.	α∗.	NOUN
ma-386	325	25	thus	thus	ADV
ma-386	325	26	,	,	PUNCT
ma-386	325	27	the	the	DET
ma-386	325	28	assertions	assertion	NOUN
ma-386	325	29	(	(	PUNCT
ma-386	325	30	33	33	NUM
ma-386	325	31	)	)	PUNCT
ma-386	325	32	hold	hold	VERB
ma-386	325	33	and	and	CCONJ
ma-386	325	34	all	all	DET
ma-386	325	35	the	the	DET
ma-386	325	36	iterates	iterate	NOUN
ma-386	325	37	{	{	PUNCT
ma-386	325	38	y	y	PROPN
ma-386	325	39	(	(	PUNCT
ma-386	325	40	j)n	j)n	PROPN
ma-386	325	41	}	}	PUNCT
ma-386	325	42	⊂	⊂	PROPN
ma-386	325	43	u(x0	u(x0	NOUN
ma-386	325	44	,	,	PUNCT
ma-386	325	45	α	α	PROPN
ma-386	325	46	∗).it	∗).it	PROPN
ma-386	325	47	is	be	AUX
ma-386	325	48	left	leave	VERB
ma-386	325	49	to	to	PART
ma-386	325	50	show	show	VERB
ma-386	325	51	that	that	DET
ma-386	325	52	assertion	assertion	NOUN
ma-386	325	53	(	(	PUNCT
ma-386	325	54	31	31	NUM
ma-386	325	55	)	)	PUNCT
ma-386	325	56	holds	hold	VERB
ma-386	325	57	if	if	SCONJ
ma-386	325	58	n	n	PRON
ma-386	325	59	+	+	CCONJ
ma-386	325	60	1	1	NUM
ma-386	325	61	replaces	replace	VERB
ma-386	325	62	n.	n.	NOUN
ma-386	325	63	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	325	64	eur	eur	PROPN
ma-386	325	65	.	.	PUNCT
ma-386	326	1	j.	j.	PROPN
ma-386	326	2	math	math	PROPN
ma-386	326	3	.	.	PUNCT
ma-386	327	1	anal	anal	PROPN
ma-386	327	2	.	.	PUNCT
ma-386	328	1	10.28924	10.28924	NUM
ma-386	328	2	/	/	SYM
ma-386	328	3	ada	ada	PROPN
ma-386	328	4	/	/	SYM
ma-386	328	5	ma.5.18	ma.5.18	PROPN
ma-386	328	6	12but	12but	NOUN
ma-386	328	7	we	we	PRON
ma-386	328	8	can	can	AUX
ma-386	328	9	write	write	VERB
ma-386	328	10	in	in	ADP
ma-386	328	11	turn	turn	NOUN
ma-386	328	12	g(xn+1	g(xn+1	NOUN
ma-386	328	13	)	)	PUNCT
ma-386	329	1	=	=	SYM
ma-386	329	2	g(xn+1)−	g(xn+1)−	PROPN
ma-386	329	3	g(xn)−	g(xn)−	NOUN
ma-386	329	4	g′(xn)(y1	g′(xn)(y1	VERB
ma-386	329	5	−	−	PROPN
ma-386	329	6	xn	xn	NOUN
ma-386	329	7	)	)	PUNCT
ma-386	330	1	=	=	SYM
ma-386	330	2	g(xn+1)−	g(xn+1)−	PROPN
ma-386	330	3	g(xn)−	g(xn)−	NOUN
ma-386	330	4	g′(xn)(xn+1	g′(xn)(xn+1	VERB
ma-386	330	5	−	−	PROPN
ma-386	330	6	xn	xn	PUNCT
ma-386	330	7	)	)	PUNCT
ma-386	331	1	+	+	CCONJ
ma-386	331	2	g′(xn)(xn+1	g′(xn)(xn+1	VERB
ma-386	331	3	−	−	PROPN
ma-386	331	4	y	y	PROPN
ma-386	331	5	(	(	PUNCT
ma-386	331	6	1)n	1)n	PROPN
ma-386	331	7	)	)	PUNCT
ma-386	331	8	,	,	PUNCT
ma-386	331	9	which	which	PRON
ma-386	331	10	can	can	AUX
ma-386	331	11	give	give	VERB
ma-386	331	12	,	,	PUNCT
ma-386	331	13	as	as	ADP
ma-386	331	14	in	in	ADP
ma-386	331	15	(	(	PUNCT
ma-386	331	16	34	34	NUM
ma-386	331	17	)	)	PUNCT
ma-386	331	18	,	,	PUNCT
ma-386	331	19	‖e−1g(xn+1)‖	‖e−1g(xn+1)‖	VERB
ma-386	331	20	≤	≤	NOUN
ma-386	331	21	1∫	1∫	NUM
ma-386	331	22	0	0	NUM
ma-386	331	23	ψ((1−η)(α0n+1−α0n))dη(α0n+1−α0n)+(1+ψ0(α	ψ((1−η)(α0n+1−α0n))dη(α0n+1−α0n)+(1+ψ0(α	PROPN
ma-386	331	24	0	0	NUM
ma-386	331	25	n))(α0n+1−α1n	n))(α0n+1−α1n	PROPN
ma-386	331	26	)	)	PUNCT
ma-386	331	27	=	=	SYM
ma-386	331	28	µn+1	µn+1	PROPN
ma-386	331	29	.	.	PUNCT
ma-386	331	30	(	(	PUNCT
ma-386	331	31	35	35	NUM
ma-386	331	32	)	)	PUNCT
ma-386	331	33	consequently	consequently	ADV
ma-386	331	34	,	,	PUNCT
ma-386	331	35	we	we	PRON
ma-386	331	36	obtain	obtain	VERB
ma-386	331	37	‖y	‖y	PUNCT
ma-386	332	1	(	(	PUNCT
ma-386	332	2	1)n+1	1)n+1	NUM
ma-386	332	3	−	−	NOUN
ma-386	332	4	xn+1‖	xn+1‖	PROPN
ma-386	332	5	≤	≤	PROPN
ma-386	332	6	‖g	‖g	PROPN
ma-386	332	7	′(xn+1	′(xn+1	PROPN
ma-386	332	8	)	)	PUNCT
ma-386	332	9	−1e‖‖e−1g(xn+1)‖	−1e‖‖e−1g(xn+1)‖	PROPN
ma-386	332	10	,	,	PUNCT
ma-386	332	11	≤	≤	NUM
ma-386	332	12	µn+1	µn+1	NUM
ma-386	332	13	1−	1−	NUM
ma-386	332	14	ψ0(α0n+1	ψ0(α0n+1	PROPN
ma-386	332	15	)	)	PUNCT
ma-386	332	16	=	=	SYM
ma-386	332	17	α1n+1	α1n+1	PROPN
ma-386	332	18	−	−	PROPN
ma-386	333	1	α0n+1	α0n+1	PROPN
ma-386	333	2	and	and	CCONJ
ma-386	333	3	‖y	‖y	PUNCT
ma-386	333	4	(	(	PUNCT
ma-386	333	5	1)n+1	1)n+1	NUM
ma-386	333	6	−	−	NOUN
ma-386	333	7	x0‖	x0‖	PROPN
ma-386	333	8	≤	≤	PROPN
ma-386	333	9	‖y	‖y	PUNCT
ma-386	334	1	(	(	PUNCT
ma-386	334	2	1	1	NUM
ma-386	334	3	)	)	PUNCT
ma-386	334	4	n+1	n+1	NUM
ma-386	334	5	−	−	NOUN
ma-386	334	6	xn+1‖+	xn+1‖+	PUNCT
ma-386	334	7	‖xn+1	‖xn+1	NUM
ma-386	335	1	−	−	PROPN
ma-386	335	2	x0‖	x0‖	PROPN
ma-386	335	3	≤	≤	PROPN
ma-386	335	4	(	(	PUNCT
ma-386	335	5	α1n+1	α1n+1	NOUN
ma-386	335	6	−	−	PROPN
ma-386	335	7	α0n+1	α0n+1	PROPN
ma-386	335	8	)	)	PUNCT
ma-386	336	1	+	+	CCONJ
ma-386	336	2	(	(	PUNCT
ma-386	336	3	α0n+1	α0n+1	INTJ
ma-386	336	4	−	−	PROPN
ma-386	336	5	α00	α00	NOUN
ma-386	336	6	)	)	PUNCT
ma-386	336	7	=	=	SYM
ma-386	336	8	α1n+1	α1n+1	PROPN
ma-386	336	9	<	<	X
ma-386	336	10	α∗.	α∗.	NOUN
ma-386	336	11	thus	thus	ADV
ma-386	336	12	,	,	PUNCT
ma-386	336	13	the	the	DET
ma-386	336	14	induction	induction	NOUN
ma-386	336	15	for	for	ADP
ma-386	336	16	assertions	assertion	NOUN
ma-386	336	17	(	(	PUNCT
ma-386	336	18	31)–(33	31)–(33	NUM
ma-386	336	19	)	)	PUNCT
ma-386	336	20	is	be	AUX
ma-386	336	21	completed	complete	VERB
ma-386	336	22	,	,	PUNCT
ma-386	336	23	and	and	CCONJ
ma-386	336	24	all	all	DET
ma-386	336	25	the	the	DET
ma-386	336	26	iterates	iterate	NOUN
ma-386	336	27	{	{	PUNCT
ma-386	336	28	y	y	PROPN
ma-386	336	29	(	(	PUNCT
ma-386	336	30	i)n	i)n	ADJ
ma-386	336	31	}	}	PUNCT
ma-386	336	32	∈	∈	PROPN
ma-386	336	33	u(x0	u(x0	NOUN
ma-386	336	34	,	,	PUNCT
ma-386	336	35	α	α	X
ma-386	336	36	∗).it	∗).it	PROPN
ma-386	336	37	also	also	ADV
ma-386	336	38	follows	follow	VERB
ma-386	336	39	that	that	SCONJ
ma-386	336	40	the	the	DET
ma-386	336	41	sequence	sequence	NOUN
ma-386	336	42	{	{	PUNCT
ma-386	336	43	x	x	SYM
ma-386	336	44	jn	jn	PROPN
ma-386	336	45	}	}	PUNCT
ma-386	336	46	is	be	AUX
ma-386	336	47	complete	complete	ADJ
ma-386	336	48	in	in	ADP
ma-386	336	49	banach	banach	NOUN
ma-386	336	50	space	space	NOUN
ma-386	336	51	b0	b0	NOUN
ma-386	336	52	,	,	PUNCT
ma-386	336	53	since	since	SCONJ
ma-386	336	54	{	{	PUNCT
ma-386	336	55	αin	αin	NOUN
ma-386	336	56	}	}	PUNCT
ma-386	336	57	is	be	AUX
ma-386	336	58	alsocomplete	alsocomplete	ADJ
ma-386	336	59	as	as	ADP
ma-386	336	60	convergent	convergent	NOUN
ma-386	336	61	by	by	ADP
ma-386	336	62	the	the	DET
ma-386	336	63	condition	condition	NOUN
ma-386	336	64	(	(	PUNCT
ma-386	336	65	c4	c4	NOUN
ma-386	336	66	)	)	PUNCT
ma-386	336	67	.	.	PUNCT
ma-386	337	1	therefore	therefore	ADV
ma-386	337	2	,	,	PUNCT
ma-386	337	3	there	there	PRON
ma-386	337	4	exists	exist	VERB
ma-386	337	5	x∗	x∗	PROPN
ma-386	337	6	∈	∈	PROPN
ma-386	337	7	u[x0	u[x0	NOUN
ma-386	337	8	,	,	PUNCT
ma-386	337	9	α	α	PROPN
ma-386	337	10	∗	∗	NOUN
ma-386	337	11	]	]	PUNCT
ma-386	337	12	such	such	ADJ
ma-386	337	13	that	that	SCONJ
ma-386	337	14	lim	lim	PROPN
ma-386	337	15	n→+∞	n→+∞	VERB
ma-386	337	16	y	y	PROPN
ma-386	337	17	(	(	PUNCT
ma-386	337	18	k	k	NOUN
ma-386	337	19	)	)	PUNCT
ma-386	337	20	n	n	NOUN
ma-386	337	21	=	=	SYM
ma-386	337	22	x∗	x∗	PROPN
ma-386	337	23	or	or	CCONJ
ma-386	337	24	lim	lim	PROPN
ma-386	337	25	n→+∞	n→+∞	VERB
ma-386	337	26	xn	xn	PUNCT
ma-386	338	1	=	=	PUNCT
ma-386	338	2	x∗.	x∗.	PROPN
ma-386	339	1	moreover	moreover	ADV
ma-386	339	2	,	,	PUNCT
ma-386	339	3	by	by	ADP
ma-386	339	4	letting	let	VERB
ma-386	339	5	n	n	X
ma-386	339	6	→	→	PUNCT
ma-386	339	7	+	+	NUM
ma-386	339	8	∞	∞	PROPN
ma-386	339	9	in	in	ADP
ma-386	339	10	(	(	PUNCT
ma-386	339	11	35	35	NUM
ma-386	339	12	)	)	PUNCT
ma-386	339	13	,	,	PUNCT
ma-386	339	14	we	we	PRON
ma-386	339	15	obtain	obtain	VERB
ma-386	339	16	g(x∗	g(x∗	PRON
ma-386	339	17	)	)	PUNCT
ma-386	340	1	=	=	SYM
ma-386	340	2	0	0	NUM
ma-386	340	3	,	,	PUNCT
ma-386	340	4	where	where	SCONJ
ma-386	340	5	the	the	DET
ma-386	340	6	continuity	continuity	NOUN
ma-386	340	7	of	of	ADP
ma-386	340	8	the	the	DET
ma-386	340	9	operator	operator	NOUN
ma-386	340	10	g	g	NOUN
ma-386	340	11	has	have	AUX
ma-386	340	12	also	also	ADV
ma-386	340	13	been	be	AUX
ma-386	340	14	used	use	VERB
ma-386	340	15	.	.	PUNCT
ma-386	341	1	furthermore	furthermore	ADV
ma-386	341	2	,	,	PUNCT
ma-386	341	3	by	by	ADP
ma-386	341	4	noticing	notice	VERB
ma-386	341	5	that	that	DET
ma-386	341	6	αkn	αkn	NOUN
ma-386	341	7	=	=	SYM
ma-386	341	8	αn+1	αn+1	NUM
ma-386	341	9	and	and	CCONJ
ma-386	341	10	αkn	αkn	NOUN
ma-386	341	11	=	=	SYM
ma-386	341	12	α0n+1	α0n+1	PROPN
ma-386	341	13	,	,	PUNCT
ma-386	341	14	estimate	estimate	INTJ
ma-386	341	15	(	(	PUNCT
ma-386	341	16	33)can	33)can	NUM
ma-386	341	17	be	be	AUX
ma-386	341	18	rewritten	rewrite	VERB
ma-386	341	19	for	for	ADP
ma-386	341	20	j	j	PROPN
ma-386	341	21	=	=	SYM
ma-386	341	22	k	k	PROPN
ma-386	341	23	as	as	ADP
ma-386	341	24	‖xn+1	‖xn+1	PROPN
ma-386	341	25	−	−	NOUN
ma-386	341	26	xn‖	xn‖	PROPN
ma-386	341	27	≤	≤	NUM
ma-386	341	28	αn+1	αn+1	NUM
ma-386	341	29	−	−	NOUN
ma-386	341	30	αn	αn	NOUN
ma-386	341	31	,	,	PUNCT
ma-386	341	32	so	so	ADV
ma-386	341	33	‖xn+h	‖xn+h	PROPN
ma-386	341	34	−	−	PROPN
ma-386	341	35	xn‖	xn‖	PROPN
ma-386	341	36	≤	≤	PROPN
ma-386	341	37	αn+h	αn+h	PROPN
ma-386	341	38	−	−	PROPN
ma-386	341	39	αn	αn	NOUN
ma-386	341	40	,	,	PUNCT
ma-386	341	41	h	h	NOUN
ma-386	341	42	=	=	SYM
ma-386	341	43	0	0	NUM
ma-386	341	44	,	,	PUNCT
ma-386	341	45	1	1	NUM
ma-386	341	46	,	,	PUNCT
ma-386	341	47	2	2	NUM
ma-386	341	48	,	,	PUNCT
ma-386	341	49	.	.	PUNCT
ma-386	341	50	.	.	PUNCT
ma-386	341	51	.	.	PUNCT
ma-386	342	1	(	(	PUNCT
ma-386	342	2	36)finally	36)finally	ADV
ma-386	342	3	,	,	PUNCT
ma-386	342	4	by	by	ADP
ma-386	342	5	letting	let	VERB
ma-386	342	6	h	h	PRON
ma-386	342	7	→	→	PUNCT
ma-386	342	8	+	+	ADJ
ma-386	342	9	∞	∞	PROPN
ma-386	342	10	in	in	ADP
ma-386	342	11	(	(	PUNCT
ma-386	342	12	36	36	NUM
ma-386	342	13	)	)	PUNCT
ma-386	342	14	,	,	PUNCT
ma-386	342	15	we	we	PRON
ma-386	342	16	show	show	VERB
ma-386	342	17	the	the	DET
ma-386	342	18	assertion	assertion	NOUN
ma-386	342	19	(	(	PUNCT
ma-386	342	20	2	2	NUM
ma-386	342	21	)	)	PUNCT
ma-386	342	22	.	.	PUNCT
ma-386	343	1	�	�	PROPN
ma-386	343	2	next	next	ADV
ma-386	343	3	,	,	PUNCT
ma-386	343	4	we	we	PRON
ma-386	343	5	study	study	VERB
ma-386	343	6	the	the	DET
ma-386	343	7	uniqueness	uniqueness	NOUN
ma-386	343	8	of	of	ADP
ma-386	343	9	a	a	DET
ma-386	343	10	solution	solution	NOUN
ma-386	343	11	in	in	ADP
ma-386	343	12	a	a	DET
ma-386	343	13	certain	certain	ADJ
ma-386	343	14	region	region	NOUN
ma-386	343	15	.	.	PUNCT
ma-386	344	1	proposition	proposition	NOUN
ma-386	344	2	2	2	NUM
ma-386	344	3	.	.	PUNCT
ma-386	344	4	suppose	suppose	VERB
ma-386	344	5	there	there	PRON
ma-386	344	6	exists	exist	VERB
ma-386	344	7	a	a	DET
ma-386	344	8	solution	solution	NOUN
ma-386	344	9	y∗	y∗	PROPN
ma-386	344	10	∈	∈	PROPN
ma-386	344	11	u(x0	u(x0	NOUN
ma-386	344	12	,	,	PUNCT
ma-386	344	13	r3	r3	PROPN
ma-386	344	14	)	)	PUNCT
ma-386	344	15	of	of	ADP
ma-386	344	16	the	the	DET
ma-386	344	17	equation	equation	NOUN
ma-386	344	18	g(x	g(x	NOUN
ma-386	344	19	)	)	PUNCT
ma-386	345	1	=	=	SYM
ma-386	345	2	0	0	NUM
ma-386	346	1	for	for	ADP
ma-386	346	2	some	some	DET
ma-386	346	3	r3	r3	PROPN
ma-386	346	4	>	>	X
ma-386	346	5	0	0	NUM
ma-386	346	6	;	;	PUNCT
ma-386	346	7	the	the	DET
ma-386	346	8	condition	condition	NOUN
ma-386	346	9	(	(	PUNCT
ma-386	346	10	c4	c4	NOUN
ma-386	346	11	)	)	PUNCT
ma-386	346	12	holds	hold	VERB
ma-386	346	13	in	in	ADP
ma-386	346	14	the	the	DET
ma-386	346	15	ball	ball	NOUN
ma-386	346	16	u(x0	u(x0	PROPN
ma-386	346	17	,	,	PUNCT
ma-386	346	18	r3	r3	PROPN
ma-386	346	19	)	)	PUNCT
ma-386	346	20	,	,	PUNCT
ma-386	346	21	and	and	CCONJ
ma-386	346	22	there	there	PRON
ma-386	346	23	exists	exist	VERB
ma-386	346	24	r4	r4	PROPN
ma-386	346	25	≥	≥	PUNCT
ma-386	346	26	r3	r3	PROPN
ma-386	346	27	such	such	ADJ
ma-386	346	28	that	that	SCONJ
ma-386	346	29	1∫	1∫	NUM
ma-386	346	30	0	0	NUM
ma-386	346	31	ψ0((1−	ψ0((1−	ADJ
ma-386	346	32	η)r3	η)r3	PROPN
ma-386	346	33	+	+	CCONJ
ma-386	346	34	ηr4)dη	ηr4)dη	X
ma-386	346	35	<	<	X
ma-386	346	36	1	1	NUM
ma-386	346	37	.	.	PUNCT
ma-386	347	1	(	(	PUNCT
ma-386	347	2	37	37	NUM
ma-386	347	3	)	)	PUNCT
ma-386	347	4	define	define	VERB
ma-386	347	5	the	the	DET
ma-386	347	6	region	region	NOUN
ma-386	347	7	d3	d3	PROPN
ma-386	347	8	=	=	SYM
ma-386	347	9	d	d	PROPN
ma-386	347	10	∩	∩	ADJ
ma-386	347	11	u[x0	u[x0	NOUN
ma-386	347	12	,	,	PUNCT
ma-386	347	13	r4	r4	NOUN
ma-386	347	14	]	]	PUNCT
ma-386	347	15	.	.	PUNCT
ma-386	348	1	then	then	ADV
ma-386	348	2	,	,	PUNCT
ma-386	348	3	y∗	y∗	ADV
ma-386	348	4	is	be	AUX
ma-386	348	5	the	the	DET
ma-386	348	6	only	only	ADJ
ma-386	348	7	solution	solution	NOUN
ma-386	348	8	of	of	ADP
ma-386	348	9	the	the	DET
ma-386	348	10	equation	equation	NOUN
ma-386	348	11	g(x	g(x	NOUN
ma-386	348	12	)	)	PUNCT
ma-386	349	1	=	=	SYM
ma-386	349	2	0	0	NUM
ma-386	350	1	in	in	ADP
ma-386	350	2	the	the	DET
ma-386	350	3	region	region	NOUN
ma-386	350	4	d3	d3	PROPN
ma-386	350	5	.	.	PUNCT
ma-386	351	1	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	351	2	eur	eur	PROPN
ma-386	351	3	.	.	PUNCT
ma-386	352	1	j.	j.	PROPN
ma-386	352	2	math	math	PROPN
ma-386	352	3	.	.	PUNCT
ma-386	353	1	anal	anal	PROPN
ma-386	353	2	.	.	PUNCT
ma-386	354	1	10.28924	10.28924	NUM
ma-386	354	2	/	/	SYM
ma-386	354	3	ada	ada	PROPN
ma-386	354	4	/	/	SYM
ma-386	354	5	ma.5.18	ma.5.18	PROPN
ma-386	354	6	13	13	NUM
ma-386	354	7	proof	proof	NOUN
ma-386	354	8	.	.	PUNCT
ma-386	355	1	suppose	suppose	VERB
ma-386	355	2	there	there	PRON
ma-386	355	3	exists	exist	VERB
ma-386	355	4	y∗∗	y∗∗	PROPN
ma-386	355	5	∈	∈	PROPN
ma-386	355	6	d3	d3	PROPN
ma-386	355	7	solving	solve	VERB
ma-386	355	8	the	the	DET
ma-386	355	9	equation	equation	NOUN
ma-386	355	10	g(x	g(x	NOUN
ma-386	355	11	)	)	PUNCT
ma-386	356	1	=	=	SYM
ma-386	356	2	0	0	NUM
ma-386	356	3	such	such	ADJ
ma-386	356	4	that	that	DET
ma-386	356	5	y∗∗	y∗∗	NOUN
ma-386	356	6	6=	6=	NUM
ma-386	356	7	y∗.then	y∗.then	PROPN
ma-386	356	8	define	define	VERB
ma-386	356	9	the	the	DET
ma-386	356	10	linear	linear	ADJ
ma-386	356	11	operator	operator	NOUN
ma-386	356	12	e2	e2	NOUN
ma-386	356	13	=	=	PUNCT
ma-386	357	1	1∫	1∫	NUM
ma-386	357	2	0	0	NUM
ma-386	358	1	g′(y∗	g′(y∗	PROPN
ma-386	358	2	+	+	NUM
ma-386	358	3	η(y∗∗	η(y∗∗	PROPN
ma-386	358	4	−	−	PROPN
ma-386	358	5	y∗))dη	y∗))dη	NOUN
ma-386	358	6	.	.	PUNCT
ma-386	359	1	by	by	ADP
ma-386	359	2	applying	apply	VERB
ma-386	359	3	the	the	DET
ma-386	359	4	condition	condition	NOUN
ma-386	359	5	(	(	PUNCT
ma-386	359	6	c4	c4	NOUN
ma-386	359	7	)	)	PUNCT
ma-386	359	8	and	and	CCONJ
ma-386	359	9	(	(	PUNCT
ma-386	359	10	37	37	NUM
ma-386	359	11	)	)	PUNCT
ma-386	359	12	,	,	PUNCT
ma-386	359	13	we	we	PRON
ma-386	359	14	obtain	obtain	VERB
ma-386	359	15	in	in	ADP
ma-386	359	16	turn	turn	NOUN
ma-386	359	17	‖e−1(e2	‖e−1(e2	PUNCT
ma-386	360	1	−	−	PUNCT
ma-386	360	2	e)‖	e)‖	ADJ
ma-386	360	3	≤	≤	NOUN
ma-386	360	4	1∫	1∫	NUM
ma-386	360	5	0	0	NUM
ma-386	360	6	ψ0((1−	ψ0((1−	NOUN
ma-386	360	7	η)‖y∗∗	η)‖y∗∗	NOUN
ma-386	360	8	−	−	PROPN
ma-386	360	9	x0‖+	x0‖+	NUM
ma-386	360	10	η‖y∗	η‖y∗	PROPN
ma-386	360	11	−	−	PROPN
ma-386	360	12	x0‖)dη	x0‖)dη	PUNCT
ma-386	360	13	≤	≤	NUM
ma-386	361	1	1∫	1∫	NUM
ma-386	361	2	0	0	NUM
ma-386	361	3	ψ0((1−	ψ0((1−	PROPN
ma-386	361	4	η)r3	η)r3	PROPN
ma-386	361	5	+	+	CCONJ
ma-386	361	6	ηr4)dη	ηr4)dη	X
ma-386	361	7	<	<	X
ma-386	361	8	1	1	NUM
ma-386	361	9	.	.	PUNCT
ma-386	362	1	it	it	PRON
ma-386	362	2	follows	follow	VERB
ma-386	362	3	that	that	SCONJ
ma-386	362	4	the	the	DET
ma-386	362	5	linear	linear	ADJ
ma-386	362	6	operator	operator	NOUN
ma-386	362	7	e2	e2	NOUN
ma-386	362	8	is	be	AUX
ma-386	362	9	invertible	invertible	ADJ
ma-386	362	10	.	.	PUNCT
ma-386	363	1	hence	hence	ADV
ma-386	363	2	,	,	PUNCT
ma-386	363	3	again	again	ADV
ma-386	363	4	we	we	PRON
ma-386	363	5	conclude	conclude	VERB
ma-386	363	6	y∗∗	y∗∗	PROPN
ma-386	363	7	=	=	SYM
ma-386	363	8	y∗.	y∗.	NUM
ma-386	363	9	�	�	PROPN
ma-386	363	10	remark	remark	NOUN
ma-386	363	11	4	4	NUM
ma-386	363	12	.	.	NOUN
ma-386	363	13	•	•	NOUN
ma-386	364	1	the	the	DET
ma-386	364	2	limit	limit	NOUN
ma-386	364	3	point	point	NOUN
ma-386	364	4	a∗	a∗	NOUN
ma-386	364	5	given	give	VERB
ma-386	364	6	in	in	ADP
ma-386	364	7	the	the	DET
ma-386	364	8	condition	condition	NOUN
ma-386	364	9	(	(	PUNCT
ma-386	364	10	c1	c1	NOUN
ma-386	364	11	)	)	PUNCT
ma-386	364	12	can	can	AUX
ma-386	364	13	be	be	AUX
ma-386	364	14	replaced	replace	VERB
ma-386	364	15	by	by	ADP
ma-386	364	16	t0	t0	PROPN
ma-386	364	17	in	in	ADP
ma-386	364	18	(	(	PUNCT
ma-386	364	19	c6	c6	PROPN
ma-386	364	20	)	)	PUNCT
ma-386	364	21	.	.	PUNCT
ma-386	365	1	•	•	INTJ
ma-386	365	2	if	if	SCONJ
ma-386	365	3	all	all	DET
ma-386	365	4	conditions	condition	NOUN
ma-386	365	5	(	(	PUNCT
ma-386	365	6	c1)−	c1)−	NOUN
ma-386	365	7	(	(	PUNCT
ma-386	365	8	c6	c6	PROPN
ma-386	365	9	)	)	PUNCT
ma-386	365	10	hold	hold	VERB
ma-386	365	11	,	,	PUNCT
ma-386	365	12	then	then	ADV
ma-386	365	13	we	we	PRON
ma-386	365	14	can	can	AUX
ma-386	365	15	set	set	VERB
ma-386	365	16	r3	r3	NOUN
ma-386	365	17	=	=	SYM
ma-386	365	18	α∗	α∗	NOUN
ma-386	365	19	and	and	CCONJ
ma-386	365	20	y∗	y∗	ADV
ma-386	365	21	=	=	PUNCT
ma-386	365	22	x∗	x∗	PROPN
ma-386	365	23	in	in	ADP
ma-386	365	24	proposition	proposition	NOUN
ma-386	365	25	2	2	NUM
ma-386	365	26	.	.	NOUN
ma-386	366	1	3	3	NUM
ma-386	366	2	.	.	NOUN
ma-386	366	3	numerical	numerical	ADJ
ma-386	366	4	results	result	NOUN
ma-386	366	5	to	to	PART
ma-386	366	6	comprehensively	comprehensively	ADV
ma-386	366	7	evaluate	evaluate	VERB
ma-386	366	8	the	the	DET
ma-386	366	9	performance	performance	NOUN
ma-386	366	10	and	and	CCONJ
ma-386	366	11	robustness	robustness	NOUN
ma-386	366	12	of	of	ADP
ma-386	366	13	the	the	DET
ma-386	366	14	proposed	propose	VERB
ma-386	366	15	high	high	ADJ
ma-386	366	16	-	-	PUNCT
ma-386	366	17	order	order	NOUN
ma-386	366	18	iterativemethods	iterativemethod	NOUN
ma-386	366	19	,	,	PUNCT
ma-386	366	20	we	we	PRON
ma-386	366	21	present	present	VERB
ma-386	366	22	five	five	NUM
ma-386	366	23	numerical	numerical	ADJ
ma-386	366	24	examples	example	NOUN
ma-386	366	25	of	of	ADP
ma-386	366	26	different	different	ADJ
ma-386	366	27	complexity	complexity	NOUN
ma-386	366	28	and	and	CCONJ
ma-386	366	29	dimensionality	dimensionality	NOUN
ma-386	366	30	.	.	PUNCT
ma-386	367	1	thesetest	theset	ADJ
ma-386	367	2	problems	problem	NOUN
ma-386	367	3	have	have	AUX
ma-386	367	4	been	be	AUX
ma-386	367	5	selected	select	VERB
ma-386	367	6	from	from	ADP
ma-386	367	7	the	the	DET
ma-386	367	8	literature	literature	NOUN
ma-386	367	9	and	and	CCONJ
ma-386	367	10	include	include	VERB
ma-386	367	11	systems	system	NOUN
ma-386	367	12	with	with	ADP
ma-386	367	13	diverse	diverse	ADJ
ma-386	367	14	nonlinearcharacteristics	nonlinearcharacteristic	NOUN
ma-386	367	15	,	,	PUNCT
ma-386	367	16	such	such	ADJ
ma-386	367	17	as	as	ADP
ma-386	367	18	trigonometric	trigonometric	ADJ
ma-386	367	19	,	,	PUNCT
ma-386	367	20	exponential	exponential	NOUN
ma-386	367	21	,	,	PUNCT
ma-386	367	22	and	and	CCONJ
ma-386	367	23	polynomial	polynomial	ADJ
ma-386	367	24	structures	structure	NOUN
ma-386	367	25	.	.	PUNCT
ma-386	368	1	the	the	DET
ma-386	368	2	examples	example	NOUN
ma-386	368	3	aredesigned	aredesigne	VERB
ma-386	368	4	to	to	PART
ma-386	368	5	assess	assess	VERB
ma-386	368	6	the	the	DET
ma-386	368	7	methods	method	NOUN
ma-386	368	8	’	'	PUNCT
ma-386	368	9	accuracy	accuracy	NOUN
ma-386	368	10	,	,	PUNCT
ma-386	368	11	convergence	convergence	NOUN
ma-386	368	12	speed	speed	NOUN
ma-386	368	13	,	,	PUNCT
ma-386	368	14	and	and	CCONJ
ma-386	368	15	stability.in	stability.in	PRON
ma-386	368	16	all	all	DET
ma-386	368	17	numerical	numerical	ADJ
ma-386	368	18	experiments	experiment	NOUN
ma-386	368	19	,	,	PUNCT
ma-386	368	20	the	the	DET
ma-386	368	21	stopping	stop	VERB
ma-386	368	22	criterion	criterion	NOUN
ma-386	368	23	was	be	AUX
ma-386	368	24	based	base	VERB
ma-386	368	25	on	on	ADP
ma-386	368	26	achieving	achieve	VERB
ma-386	368	27	a	a	DET
ma-386	368	28	residual	residual	ADJ
ma-386	368	29	norm	norm	NOUN
ma-386	368	30	belowcertain	belowcertain	NOUN
ma-386	368	31	ε	ε	PROPN
ma-386	368	32	,	,	PUNCT
ma-386	368	33	ensuring	ensure	VERB
ma-386	368	34	a	a	DET
ma-386	368	35	high	high	ADJ
ma-386	368	36	level	level	NOUN
ma-386	368	37	of	of	ADP
ma-386	368	38	numerical	numerical	ADJ
ma-386	368	39	precision	precision	NOUN
ma-386	368	40	.	.	PUNCT
ma-386	369	1	a	a	DET
ma-386	369	2	maximum	maximum	NOUN
ma-386	369	3	of	of	ADP
ma-386	369	4	50	50	NUM
ma-386	369	5	iterations	iteration	NOUN
ma-386	369	6	was	be	AUX
ma-386	369	7	imposedto	imposedto	PROPN
ma-386	369	8	prevent	prevent	VERB
ma-386	369	9	excessive	excessive	ADJ
ma-386	369	10	computational	computational	ADJ
ma-386	369	11	effort	effort	NOUN
ma-386	369	12	.	.	PUNCT
ma-386	370	1	this	this	DET
ma-386	370	2	limit	limit	NOUN
ma-386	370	3	is	be	AUX
ma-386	370	4	justified	justify	VERB
ma-386	370	5	by	by	ADP
ma-386	370	6	empirical	empirical	ADJ
ma-386	370	7	evidence	evidence	NOUN
ma-386	370	8	indicatingthat	indicatingthat	X
ma-386	370	9	well	well	ADV
ma-386	370	10	-	-	PUNCT
ma-386	370	11	designed	design	VERB
ma-386	370	12	,	,	PUNCT
ma-386	370	13	high	high	ADJ
ma-386	370	14	-	-	PUNCT
ma-386	370	15	order	order	NOUN
ma-386	370	16	methods	method	NOUN
ma-386	370	17	typically	typically	ADV
ma-386	370	18	achieve	achieve	VERB
ma-386	370	19	convergence	convergence	NOUN
ma-386	370	20	within	within	ADP
ma-386	370	21	this	this	DET
ma-386	370	22	range	range	NOUN
ma-386	370	23	.	.	PUNCT
ma-386	371	1	to	to	ADP
ma-386	371	2	ensurereliable	ensurereliable	ADJ
ma-386	371	3	performance	performance	NOUN
ma-386	371	4	metrics	metric	NOUN
ma-386	371	5	,	,	PUNCT
ma-386	371	6	cpu	cpu	NOUN
ma-386	371	7	execution	execution	NOUN
ma-386	371	8	times	time	NOUN
ma-386	371	9	were	be	AUX
ma-386	371	10	averaged	average	VERB
ma-386	371	11	over	over	ADP
ma-386	371	12	50	50	NUM
ma-386	371	13	independent	independent	ADJ
ma-386	371	14	runs	run	NOUN
ma-386	371	15	,	,	PUNCT
ma-386	371	16	therebymitigating	therebymitigate	VERB
ma-386	371	17	the	the	DET
ma-386	371	18	influence	influence	NOUN
ma-386	371	19	of	of	ADP
ma-386	371	20	background	background	NOUN
ma-386	371	21	system	system	NOUN
ma-386	371	22	noise	noise	NOUN
ma-386	371	23	and	and	CCONJ
ma-386	371	24	transient	transient	ADJ
ma-386	371	25	operational	operational	ADJ
ma-386	371	26	conditionsall	conditionsall	NOUN
ma-386	371	27	simulations	simulation	NOUN
ma-386	371	28	were	be	AUX
ma-386	371	29	conducted	conduct	VERB
ma-386	371	30	within	within	ADP
ma-386	371	31	a	a	DET
ma-386	371	32	google	google	PROPN
ma-386	371	33	colaboratory	colaboratory	PROPN
ma-386	371	34	runtime	runtime	NOUN
ma-386	371	35	environment	environment	PROPN
ma-386	371	36	.	.	PUNCT
ma-386	372	1	this	this	DET
ma-386	372	2	envi	envi	NOUN
ma-386	372	3	-	-	PUNCT
ma-386	372	4	ronment	ronment	NOUN
ma-386	372	5	was	be	AUX
ma-386	372	6	configured	configure	VERB
ma-386	372	7	with	with	ADP
ma-386	372	8	an	an	DET
ma-386	372	9	intel	intel	PROPN
ma-386	372	10	xeon	xeon	PROPN
ma-386	372	11	cpu	cpu	NOUN
ma-386	372	12	operating	operate	VERB
ma-386	372	13	at	at	ADP
ma-386	372	14	2.20	2.20	NUM
ma-386	372	15	ghz	ghz	NOUN
ma-386	372	16	,	,	PUNCT
ma-386	372	17	13	13	NUM
ma-386	372	18	gb	gb	NOUN
ma-386	372	19	of	of	ADP
ma-386	372	20	system	system	NOUN
ma-386	372	21	ram	ram	NOUN
ma-386	372	22	,	,	PUNCT
ma-386	372	23	and	and	CCONJ
ma-386	372	24	an	an	DET
ma-386	372	25	nvidia	nvidia	PROPN
ma-386	372	26	tesla	tesla	PROPN
ma-386	372	27	k80	k80	PROPN
ma-386	372	28	gpu	gpu	PROPN
ma-386	372	29	equipped	equip	VERB
ma-386	372	30	with	with	ADP
ma-386	372	31	12	12	NUM
ma-386	372	32	gb	gb	NOUN
ma-386	372	33	of	of	ADP
ma-386	372	34	vram	vram	NOUN
ma-386	372	35	.	.	PUNCT
ma-386	373	1	numerical	numerical	PROPN
ma-386	373	2	computations	computations	PROPN
ma-386	373	3	wereperformed	wereperforme	VERB
ma-386	373	4	using	use	VERB
ma-386	373	5	the	the	DET
ma-386	373	6	python	python	NOUN
ma-386	373	7	library	library	NOUN
ma-386	373	8	mpmath	mpmath	ADV
ma-386	373	9	,	,	PUNCT
ma-386	373	10	with	with	ADP
ma-386	373	11	the	the	DET
ma-386	373	12	arithmetic	arithmetic	ADJ
ma-386	373	13	precision	precision	NOUN
ma-386	373	14	set	set	VERB
ma-386	373	15	to	to	ADP
ma-386	373	16	100	100	NUM
ma-386	373	17	decimal	decimal	ADJ
ma-386	373	18	dig	dig	NOUN
ma-386	373	19	-	-	PUNCT
ma-386	373	20	its	its	PRON
ma-386	373	21	.	.	PUNCT
ma-386	374	1	this	this	DET
ma-386	374	2	standardized	standardized	ADJ
ma-386	374	3	setup	setup	NOUN
ma-386	374	4	was	be	AUX
ma-386	374	5	maintained	maintain	VERB
ma-386	374	6	across	across	ADP
ma-386	374	7	all	all	DET
ma-386	374	8	test	test	NOUN
ma-386	374	9	cases	case	NOUN
ma-386	374	10	to	to	PART
ma-386	374	11	ensure	ensure	VERB
ma-386	374	12	fair	fair	ADJ
ma-386	374	13	and	and	CCONJ
ma-386	374	14	reproduciblecomparisons.we	reproduciblecomparisons.we	NUM
ma-386	374	15	compare	compare	NOUN
ma-386	374	16	method	method	NOUN
ma-386	374	17	(	(	PUNCT
ma-386	374	18	2	2	NUM
ma-386	374	19	)	)	PUNCT
ma-386	374	20	with	with	ADP
ma-386	374	21	several	several	ADJ
ma-386	374	22	established	establish	VERB
ma-386	374	23	iterative	iterative	NOUN
ma-386	374	24	methods	method	NOUN
ma-386	374	25	,	,	PUNCT
ma-386	374	26	specifically	specifically	ADV
ma-386	374	27	the	the	DET
ma-386	374	28	sixth	sixth	ADJ
ma-386	374	29	-	-	PUNCT
ma-386	374	30	ordermethod	ordermethod	NOUN
ma-386	374	31	(	(	PUNCT
ma-386	374	32	29	29	NUM
ma-386	374	33	)	)	PUNCT
ma-386	374	34	of	of	ADP
ma-386	374	35	wang	wang	PROPN
ma-386	374	36	et	et	PROPN
ma-386	374	37	al	al	PROPN
ma-386	374	38	.	.	PUNCT
ma-386	375	1	[	[	X
ma-386	375	2	18	18	NUM
ma-386	375	3	]	]	PUNCT
ma-386	375	4	,	,	PUNCT
ma-386	375	5	the	the	DET
ma-386	375	6	method	method	NOUN
ma-386	375	7	(	(	PUNCT
ma-386	375	8	14	14	NUM
ma-386	375	9	)	)	PUNCT
ma-386	375	10	by	by	ADP
ma-386	375	11	hueso	hueso	PROPN
ma-386	375	12	et	et	PROPN
ma-386	375	13	al	al	PROPN
ma-386	375	14	.	.	PUNCT
ma-386	376	1	[	[	X
ma-386	376	2	12	12	NUM
ma-386	376	3	]	]	PUNCT
ma-386	376	4	,	,	PUNCT
ma-386	376	5	the	the	DET
ma-386	376	6	scheme	scheme	NOUN
ma-386	376	7	(	(	PUNCT
ma-386	376	8	6	6	NUM
ma-386	376	9	)	)	PUNCT
ma-386	376	10	of	of	ADP
ma-386	376	11	cordero	cordero	PROPN
ma-386	376	12	etal	etal	PROPN
ma-386	376	13	.	.	PUNCT
ma-386	377	1	[	[	X
ma-386	377	2	10	10	NUM
ma-386	377	3	]	]	PUNCT
ma-386	377	4	and	and	CCONJ
ma-386	377	5	the	the	DET
ma-386	377	6	method	method	NOUN
ma-386	377	7	(	(	PUNCT
ma-386	377	8	14	14	NUM
ma-386	377	9	)	)	PUNCT
ma-386	377	10	proposed	propose	VERB
ma-386	377	11	by	by	ADP
ma-386	377	12	abbasbandy	abbasbandy	PROPN
ma-386	377	13	et	et	PROPN
ma-386	377	14	al	al	PROPN
ma-386	377	15	.	.	PUNCT
ma-386	378	1	[	[	X
ma-386	378	2	1	1	NUM
ma-386	378	3	]	]	PUNCT
ma-386	378	4	.	.	PUNCT
ma-386	379	1	these	these	DET
ma-386	379	2	benchmark	benchmark	NOUN
ma-386	379	3	techniques	technique	NOUN
ma-386	379	4	arewell	arewell	VERB
ma-386	379	5	known	know	VERB
ma-386	379	6	in	in	ADP
ma-386	379	7	the	the	DET
ma-386	379	8	literature	literature	NOUN
ma-386	379	9	for	for	ADP
ma-386	379	10	their	their	PRON
ma-386	379	11	high	high	ADJ
ma-386	379	12	-	-	PUNCT
ma-386	379	13	order	order	NOUN
ma-386	379	14	convergence	convergence	NOUN
ma-386	379	15	properties	property	NOUN
ma-386	379	16	and	and	CCONJ
ma-386	379	17	are	be	AUX
ma-386	379	18	frequently	frequently	ADV
ma-386	379	19	used	use	VERB
ma-386	379	20	fortesting	forteste	VERB
ma-386	379	21	nonlinear	nonlinear	ADJ
ma-386	379	22	solvers	solver	NOUN
ma-386	379	23	.	.	PUNCT
ma-386	380	1	our	our	PRON
ma-386	380	2	method	method	NOUN
ma-386	380	3	is	be	AUX
ma-386	380	4	evaluated	evaluate	VERB
ma-386	380	5	against	against	ADP
ma-386	380	6	these	these	PRON
ma-386	380	7	in	in	ADP
ma-386	380	8	terms	term	NOUN
ma-386	380	9	of	of	ADP
ma-386	380	10	number	number	NOUN
ma-386	380	11	of	of	ADP
ma-386	380	12	iterations	iteration	NOUN
ma-386	380	13	,	,	PUNCT
ma-386	380	14	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	380	15	eur	eur	PROPN
ma-386	380	16	.	.	PUNCT
ma-386	381	1	j.	j.	PROPN
ma-386	381	2	math	math	PROPN
ma-386	381	3	.	.	PUNCT
ma-386	382	1	anal	anal	PROPN
ma-386	382	2	.	.	PUNCT
ma-386	383	1	10.28924	10.28924	NUM
ma-386	383	2	/	/	SYM
ma-386	383	3	ada	ada	PROPN
ma-386	383	4	/	/	SYM
ma-386	383	5	ma.5.18	ma.5.18	PROPN
ma-386	383	6	14residual	14residual	NUM
ma-386	383	7	norm	norm	NOUN
ma-386	383	8	‖g(x)‖	‖g(x)‖	VERB
ma-386	383	9	,	,	PUNCT
ma-386	383	10	step	step	NOUN
ma-386	383	11	difference	difference	NOUN
ma-386	383	12	‖xn+1	‖xn+1	PUNCT
ma-386	383	13	−	−	NOUN
ma-386	383	14	xn‖	xn‖	PROPN
ma-386	383	15	,	,	PUNCT
ma-386	383	16	and	and	CCONJ
ma-386	383	17	cpu	cpu	NOUN
ma-386	383	18	time	time	NOUN
ma-386	383	19	.	.	PUNCT
ma-386	384	1	the	the	DET
ma-386	384	2	results	result	NOUN
ma-386	384	3	are	be	AUX
ma-386	384	4	demonstratedin	demonstratedin	VERB
ma-386	384	5	tables	table	NOUN
ma-386	384	6	1–5	1–5	NUM
ma-386	384	7	.	.	NOUN
ma-386	384	8	example	example	NOUN
ma-386	385	1	1	1	NUM
ma-386	385	2	.	.	X
ma-386	386	1	consider	consider	VERB
ma-386	386	2	the	the	DET
ma-386	386	3	nonlinear	nonlinear	ADJ
ma-386	386	4	system	system	NOUN
ma-386	386	5	defined	define	VERB
ma-386	386	6	as	as	ADP
ma-386	386	7	:	:	PUNCT
ma-386	386	8	gi(x	gi(x	X
ma-386	386	9	)	)	PUNCT
ma-386	387	1	=	=	SYM
ma-386	387	2	arctan(xi	arctan(xi	PROPN
ma-386	387	3	)	)	PUNCT
ma-386	388	1	+	+	CCONJ
ma-386	388	2	1−	1−	NUM
ma-386	388	3	2	2	NUM
ma-386	388	4	20∑	20∑	NUM
ma-386	388	5	j=1	j=1	NOUN
ma-386	388	6	j	j	PROPN
ma-386	388	7	6	6	NUM
ma-386	388	8	=	=	NOUN
ma-386	388	9	i	i	X
ma-386	388	10	x2j	x2j	PUNCT
ma-386	389	1	=	=	SYM
ma-386	389	2	0	0	PROPN
ma-386	389	3	,	,	PUNCT
ma-386	389	4	i	i	PRON
ma-386	389	5	=	=	NOUN
ma-386	389	6	1	1	NUM
ma-386	389	7	,	,	PUNCT
ma-386	389	8	2	2	NUM
ma-386	389	9	,	,	PUNCT
ma-386	389	10	.	.	PUNCT
ma-386	389	11	.	.	PUNCT
ma-386	389	12	.	.	PUNCT
ma-386	390	1	,	,	PUNCT
ma-386	390	2	20	20	NUM
ma-386	390	3	.	.	PUNCT
ma-386	391	1	the	the	DET
ma-386	391	2	methods	method	NOUN
ma-386	391	3	converge	converge	VERB
ma-386	391	4	to	to	ADP
ma-386	391	5	the	the	DET
ma-386	391	6	zero	zero	NUM
ma-386	391	7	x∗	x∗	X
ma-386	391	8	=	=	SYM
ma-386	391	9	(	(	PUNCT
ma-386	391	10	0.1757683	0.1757683	NUM
ma-386	391	11	,	,	PUNCT
ma-386	391	12	0.1757683	0.1757683	NUM
ma-386	391	13	,	,	PUNCT
ma-386	391	14	.	.	PUNCT
ma-386	391	15	.	.	PUNCT
ma-386	391	16	.	.	PUNCT
ma-386	392	1	,	,	PUNCT
ma-386	392	2	0.1757683)t	0.1757683)t	NOUN
ma-386	392	3	,	,	PUNCT
ma-386	392	4	starting	start	VERB
ma-386	392	5	fromthe	fromthe	ADJ
ma-386	392	6	initial	initial	ADJ
ma-386	392	7	approximation	approximation	NOUN
ma-386	392	8	x0	x0	PROPN
ma-386	392	9	=	=	PUNCT
ma-386	392	10	(	(	PUNCT
ma-386	392	11	0.15	0.15	NUM
ma-386	392	12	,	,	PUNCT
ma-386	392	13	0.15	0.15	NUM
ma-386	392	14	,	,	PUNCT
ma-386	392	15	.	.	PUNCT
ma-386	392	16	.	.	PUNCT
ma-386	392	17	.	.	PUNCT
ma-386	393	1	,	,	PUNCT
ma-386	393	2	0.15)t	0.15)t	PROPN
ma-386	393	3	.	.	PUNCT
ma-386	394	1	table	table	NOUN
ma-386	394	2	1	1	NUM
ma-386	394	3	.	.	PUNCT
ma-386	394	4	results	result	NOUN
ma-386	394	5	for	for	ADP
ma-386	394	6	example	example	NOUN
ma-386	394	7	1	1	NUM
ma-386	394	8	method	method	NOUN
ma-386	394	9	iterations	iteration	NOUN
ma-386	394	10	‖g(x)‖	‖g(x)‖	NOUN
ma-386	394	11	‖xn+1	‖xn+1	NUM
ma-386	394	12	−	−	NOUN
ma-386	394	13	xn‖	xn‖	PROPN
ma-386	394	14	cpu	cpu	VERB
ma-386	394	15	time	time	NOUN
ma-386	394	16	(	(	PUNCT
ma-386	394	17	s	s	NOUN
ma-386	394	18	)	)	PUNCT
ma-386	394	19	method	method	NOUN
ma-386	394	20	(	(	PUNCT
ma-386	394	21	2	2	NUM
ma-386	394	22	)	)	PUNCT
ma-386	394	23	2	2	NUM
ma-386	394	24	6.7121×	6.7121×	NUM
ma-386	394	25	10−31	10−31	NUM
ma-386	394	26	8.1782×	8.1782×	NUM
ma-386	394	27	10−30	10−30	PROPN
ma-386	394	28	0.342917wang	0.342917wang	PROPN
ma-386	394	29	et	et	PROPN
ma-386	394	30	al	al	PROPN
ma-386	394	31	.	.	PROPN
ma-386	395	1	3	3	NUM
ma-386	395	2	1.8677×	1.8677×	NUM
ma-386	395	3	10−52	10−52	NUM
ma-386	395	4	1.4708×	1.4708×	NUM
ma-386	395	5	10−26	10−26	NUM
ma-386	395	6	0.656792hueso	0.656792hueso	NOUN
ma-386	395	7	et	et	PROPN
ma-386	395	8	al	al	PROPN
ma-386	395	9	.	.	PROPN
ma-386	395	10	4	4	NUM
ma-386	395	11	6.4643×	6.4643×	NUM
ma-386	396	1	10−44	10−44	NUM
ma-386	396	2	8.6687×	8.6687×	NUM
ma-386	396	3	10−46	10−46	PROPN
ma-386	396	4	1.112088cordero	1.112088cordero	NUM
ma-386	396	5	et	et	NOUN
ma-386	396	6	al	al	PROPN
ma-386	396	7	.	.	PROPN
ma-386	396	8	2	2	NUM
ma-386	396	9	1.8677×	1.8677×	NUM
ma-386	396	10	10−52	10−52	NUM
ma-386	396	11	1.0138×	1.0138×	NUM
ma-386	396	12	10−10	10−10	NUM
ma-386	396	13	0.333056abbasbandy	0.333056abbasbandy	NUM
ma-386	396	14	et	et	PROPN
ma-386	396	15	al	al	PROPN
ma-386	396	16	.	.	PROPN
ma-386	397	1	3	3	NUM
ma-386	397	2	1.2046×	1.2046×	NUM
ma-386	397	3	10−23	10−23	NUM
ma-386	397	4	2.0006×	2.0006×	NUM
ma-386	397	5	10−23	10−23	NOUN
ma-386	397	6	0.307392	0.307392	NUM
ma-386	397	7	example	example	NOUN
ma-386	397	8	2	2	NUM
ma-386	397	9	.	.	X
ma-386	397	10	consider	consider	VERB
ma-386	397	11	the	the	DET
ma-386	397	12	nonlinear	nonlinear	ADJ
ma-386	397	13	system	system	NOUN
ma-386	397	14	:	:	PUNCT
ma-386	397	15	gi(x	gi(x	X
ma-386	397	16	)	)	PUNCT
ma-386	398	1	=	=	PRON
ma-386	398	2	xi	xi	X
ma-386	398	3	−	−	PROPN
ma-386	398	4	cos	cos	PROPN
ma-386	398	5	2πxi	2πxi	PROPN
ma-386	398	6	−	−	PROPN
ma-386	398	7	50∑	50∑	NUM
ma-386	399	1	j=1	j=1	PROPN
ma-386	399	2	xj	xj	PROPN
ma-386	399	3			PROPN
ma-386	399	4	=	=	SYM
ma-386	399	5	0	0	NUM
ma-386	399	6	,	,	PUNCT
ma-386	399	7	i	i	PRON
ma-386	399	8	=	=	NOUN
ma-386	399	9	1	1	NUM
ma-386	399	10	,	,	PUNCT
ma-386	399	11	2	2	NUM
ma-386	399	12	,	,	PUNCT
ma-386	399	13	.	.	PUNCT
ma-386	399	14	.	.	PUNCT
ma-386	400	1	.	.	PUNCT
ma-386	401	1	,	,	PUNCT
ma-386	401	2	50	50	NUM
ma-386	401	3	.	.	PUNCT
ma-386	402	1	the	the	DET
ma-386	402	2	solution	solution	NOUN
ma-386	402	3	is	be	AUX
ma-386	402	4	x∗	x∗	PROPN
ma-386	402	5	=	=	SYM
ma-386	402	6	(	(	PUNCT
ma-386	402	7	0.5018261	0.5018261	NUM
ma-386	402	8	,	,	PUNCT
ma-386	402	9	0.5018261	0.5018261	NUM
ma-386	402	10	,	,	PUNCT
ma-386	402	11	.	.	PUNCT
ma-386	402	12	.	.	PUNCT
ma-386	402	13	.	.	PUNCT
ma-386	403	1	,	,	PUNCT
ma-386	403	2	0.5018261)t	0.5018261)t	PROPN
ma-386	403	3	,	,	PUNCT
ma-386	403	4	with	with	ADP
ma-386	403	5	the	the	DET
ma-386	403	6	initial	initial	ADJ
ma-386	403	7	guess	guess	NOUN
ma-386	403	8	x0	x0	PROPN
ma-386	403	9	=	=	PUNCT
ma-386	403	10	(	(	PUNCT
ma-386	403	11	0.51	0.51	NUM
ma-386	403	12	,	,	PUNCT
ma-386	403	13	0.51	0.51	NUM
ma-386	403	14	,	,	PUNCT
ma-386	403	15	.	.	PUNCT
ma-386	403	16	.	.	PUNCT
ma-386	404	1	.	.	PUNCT
ma-386	405	1	,	,	PUNCT
ma-386	405	2	0.51)t	0.51)t	NOUN
ma-386	405	3	.	.	PUNCT
ma-386	406	1	table	table	NOUN
ma-386	407	1	2	2	NUM
ma-386	407	2	.	.	X
ma-386	407	3	results	result	NOUN
ma-386	407	4	for	for	ADP
ma-386	407	5	example	example	NOUN
ma-386	407	6	2	2	NUM
ma-386	407	7	method	method	NOUN
ma-386	407	8	iterations	iteration	NOUN
ma-386	407	9	‖g(x)‖	‖g(x)‖	NOUN
ma-386	407	10	‖xn+1	‖xn+1	NUM
ma-386	407	11	−	−	NOUN
ma-386	407	12	xn‖	xn‖	PROPN
ma-386	407	13	cpu	cpu	VERB
ma-386	407	14	time	time	NOUN
ma-386	407	15	(	(	PUNCT
ma-386	407	16	s	s	NOUN
ma-386	407	17	)	)	PUNCT
ma-386	407	18	method	method	NOUN
ma-386	407	19	(	(	PUNCT
ma-386	407	20	2	2	NUM
ma-386	407	21	)	)	PUNCT
ma-386	408	1	2	2	NUM
ma-386	408	2	2.221×	2.221×	NUM
ma-386	408	3	10−25	10−25	NUM
ma-386	408	4	4.9027×	4.9027×	NUM
ma-386	408	5	10−12	10−12	NOUN
ma-386	408	6	4.127071wang	4.127071wang	NUM
ma-386	408	7	et	et	NOUN
ma-386	408	8	al	al	PROPN
ma-386	408	9	.	.	PROPN
ma-386	408	10	7	7	NUM
ma-386	408	11	6.9532×	6.9532×	NUM
ma-386	408	12	10−22	10−22	NUM
ma-386	408	13	3.6049×	3.6049×	NUM
ma-386	408	14	10−20	10−20	PROPN
ma-386	408	15	17.881168hueso	17.881168hueso	NUM
ma-386	408	16	et	et	PROPN
ma-386	408	17	al	al	PROPN
ma-386	408	18	.	.	PROPN
ma-386	408	19	8	8	NUM
ma-386	408	20	5.4021×	5.4021×	NUM
ma-386	408	21	10−24	10−24	NOUN
ma-386	408	22	2.8007×	2.8007×	NUM
ma-386	408	23	10−22	10−22	NUM
ma-386	408	24	29.956985cordero	29.956985cordero	NUM
ma-386	408	25	et	et	PROPN
ma-386	408	26	al	al	PROPN
ma-386	408	27	.	.	PROPN
ma-386	408	28	7	7	NUM
ma-386	408	29	5.5536×	5.5536×	NUM
ma-386	408	30	10−23	10−23	NUM
ma-386	408	31	2.8792×	2.8792×	NUM
ma-386	408	32	10−21	10−21	NUM
ma-386	408	33	15.002068abbasbandy	15.002068abbasbandy	NUM
ma-386	408	34	et	et	PROPN
ma-386	408	35	al	al	PROPN
ma-386	408	36	.	.	PROPN
ma-386	408	37	9	9	NUM
ma-386	408	38	6.4707×	6.4707×	NUM
ma-386	408	39	10−16	10−16	NUM
ma-386	408	40	7.4808×	7.4808×	NUM
ma-386	408	41	10−16	10−16	PROPN
ma-386	408	42	12.348433	12.348433	NUM
ma-386	408	43	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	408	44	eur	eur	PROPN
ma-386	408	45	.	.	PUNCT
ma-386	409	1	j.	j.	PROPN
ma-386	409	2	math	math	PROPN
ma-386	409	3	.	.	PUNCT
ma-386	410	1	anal	anal	PROPN
ma-386	410	2	.	.	PUNCT
ma-386	411	1	10.28924	10.28924	NUM
ma-386	411	2	/	/	SYM
ma-386	411	3	ada	ada	PROPN
ma-386	411	4	/	/	SYM
ma-386	411	5	ma.5.18	ma.5.18	PROPN
ma-386	411	6	15	15	NUM
ma-386	411	7	example	example	NOUN
ma-386	411	8	3	3	NUM
ma-386	411	9	.	.	PUNCT
ma-386	412	1	let	let	VERB
ma-386	412	2	us	we	PRON
ma-386	412	3	consider	consider	VERB
ma-386	412	4	the	the	DET
ma-386	412	5	following	follow	VERB
ma-386	412	6	system	system	NOUN
ma-386	412	7	of	of	ADP
ma-386	412	8	99	99	NUM
ma-386	412	9	nonlinear	nonlinear	ADJ
ma-386	412	10	equations	equation	NOUN
ma-386	412	11	:	:	PUNCT
ma-386	412	12	gi(x	gi(x	X
ma-386	412	13	)	)	PUNCT
ma-386	413	1	=	=	VERB
ma-386	414	1	xixi+1	xixi+1	ADJ
ma-386	414	2	−	−	NOUN
ma-386	414	3	1	1	NUM
ma-386	414	4	=	=	SYM
ma-386	414	5	0	0	NUM
ma-386	414	6	,	,	PUNCT
ma-386	414	7	1	1	NUM
ma-386	414	8	≤	≤	NUM
ma-386	414	9	i	i	PRON
ma-386	414	10	≤	≤	ADJ
ma-386	414	11	98	98	NUM
ma-386	414	12	,	,	PUNCT
ma-386	414	13	x99x1	x99x1	NOUN
ma-386	414	14	−	−	PROPN
ma-386	414	15	1	1	NUM
ma-386	414	16	=	=	SYM
ma-386	414	17	0	0	NUM
ma-386	414	18	,	,	PUNCT
ma-386	414	19	i	i	PRON
ma-386	414	20	=	=	NOUN
ma-386	414	21	99	99	NUM
ma-386	414	22	.	.	PUNCT
ma-386	415	1	the	the	DET
ma-386	415	2	exact	exact	ADJ
ma-386	415	3	solution	solution	NOUN
ma-386	415	4	is	be	AUX
ma-386	415	5	x∗	x∗	PROPN
ma-386	415	6	=	=	SYM
ma-386	415	7	(	(	PUNCT
ma-386	415	8	1	1	NUM
ma-386	415	9	,	,	PUNCT
ma-386	415	10	1	1	NUM
ma-386	415	11	,	,	PUNCT
ma-386	415	12	.	.	PUNCT
ma-386	415	13	.	.	PUNCT
ma-386	416	1	.	.	PUNCT
ma-386	417	1	,	,	PUNCT
ma-386	417	2	1)t	1)t	PROPN
ma-386	417	3	,	,	PUNCT
ma-386	417	4	with	with	ADP
ma-386	417	5	the	the	DET
ma-386	417	6	starting	start	VERB
ma-386	417	7	vector	vector	NOUN
ma-386	417	8	x0	x0	PROPN
ma-386	417	9	=	=	PUNCT
ma-386	418	1	(	(	PUNCT
ma-386	418	2	2	2	NUM
ma-386	418	3	,	,	PUNCT
ma-386	418	4	2	2	NUM
ma-386	418	5	,	,	PUNCT
ma-386	418	6	.	.	PUNCT
ma-386	418	7	.	.	PUNCT
ma-386	419	1	.	.	PUNCT
ma-386	420	1	,	,	PUNCT
ma-386	420	2	2)t	2)t	NUM
ma-386	420	3	.	.	PUNCT
ma-386	420	4	table	table	NOUN
ma-386	420	5	3	3	NUM
ma-386	420	6	.	.	PUNCT
ma-386	420	7	results	result	NOUN
ma-386	420	8	for	for	ADP
ma-386	420	9	example	example	NOUN
ma-386	420	10	3	3	NUM
ma-386	420	11	method	method	NOUN
ma-386	420	12	iterations	iteration	NOUN
ma-386	420	13	‖g(x)‖	‖g(x)‖	NOUN
ma-386	420	14	‖xn+1	‖xn+1	NUM
ma-386	420	15	−	−	NOUN
ma-386	420	16	xn‖	xn‖	PROPN
ma-386	420	17	cpu	cpu	VERB
ma-386	420	18	time	time	NOUN
ma-386	420	19	(	(	PUNCT
ma-386	420	20	s	s	NOUN
ma-386	420	21	)	)	PUNCT
ma-386	420	22	method	method	NOUN
ma-386	420	23	(	(	PUNCT
ma-386	420	24	2	2	NUM
ma-386	420	25	)	)	PUNCT
ma-386	420	26	2	2	NUM
ma-386	420	27	0.0	0.0	NUM
ma-386	420	28	9.3704×	9.3704×	NUM
ma-386	420	29	10−5	10−5	NUM
ma-386	420	30	21.838247wang	21.838247wang	NUM
ma-386	420	31	et	et	PROPN
ma-386	421	1	al	al	PROPN
ma-386	421	2	.	.	PROPN
ma-386	421	3	4	4	NUM
ma-386	421	4	0.0	0.0	NUM
ma-386	421	5	4.0358×	4.0358×	NOUN
ma-386	422	1	10−25	10−25	ADV
ma-386	422	2	56.250490hueso	56.250490hueso	NUM
ma-386	422	3	et	et	NOUN
ma-386	422	4	al	al	PROPN
ma-386	422	5	.	.	PROPN
ma-386	423	1	5	5	NUM
ma-386	423	2	0.0	0.0	NUM
ma-386	423	3	8.9985×	8.9985×	NUM
ma-386	423	4	10−39	10−39	NUM
ma-386	423	5	99.436670cordero	99.436670cordero	NUM
ma-386	423	6	et	et	NOUN
ma-386	423	7	al	al	PROPN
ma-386	423	8	.	.	PROPN
ma-386	423	9	3	3	NUM
ma-386	423	10	0.0	0.0	NUM
ma-386	423	11	7.0416×	7.0416×	NUM
ma-386	423	12	10−15	10−15	NUM
ma-386	423	13	33.705407abbasbandy	33.705407abbasbandy	NUM
ma-386	423	14	et	et	NOUN
ma-386	423	15	al	al	PROPN
ma-386	423	16	.	.	PROPN
ma-386	423	17	4	4	NUM
ma-386	423	18	0.0	0.0	NUM
ma-386	423	19	1.3554×	1.3554×	NUM
ma-386	423	20	10−17	10−17	NUM
ma-386	423	21	24.382990	24.382990	NUM
ma-386	423	22	example	example	NOUN
ma-386	423	23	4	4	NUM
ma-386	423	24	.	.	PUNCT
ma-386	423	25	consider	consider	VERB
ma-386	423	26	the	the	DET
ma-386	423	27	following	follow	VERB
ma-386	423	28	system	system	NOUN
ma-386	423	29	of	of	ADP
ma-386	423	30	nonlinear	nonlinear	ADJ
ma-386	423	31	equations	equation	NOUN
ma-386	423	32	g(x	g(x	NOUN
ma-386	423	33	)	)	PUNCT
ma-386	424	1	=	=	PUNCT
ma-386	424	2			X
ma-386	425	1	x1	x1	PROPN
ma-386	426	1	+	+	CCONJ
ma-386	426	2	x2	x2	PROPN
ma-386	427	1	−	−	PROPN
ma-386	427	2	1	1	NUM
ma-386	427	3	=	=	SYM
ma-386	427	4	0	0	NUM
ma-386	427	5	,	,	PUNCT
ma-386	427	6	2x1	2x1	NUM
ma-386	428	1	+	+	CCONJ
ma-386	428	2	x2	x2	PROPN
ma-386	428	3	+	+	CCONJ
ma-386	428	4	2x3	2x3	NUM
ma-386	428	5	−	−	NUM
ma-386	428	6	2	2	NUM
ma-386	428	7	=	=	SYM
ma-386	428	8	0	0	NUM
ma-386	428	9	,	,	PUNCT
ma-386	428	10	x1	x1	PROPN
ma-386	429	1	+	+	NUM
ma-386	429	2	x2	x2	PROPN
ma-386	430	1	+	+	CCONJ
ma-386	430	2	x3	x3	ADJ
ma-386	430	3	−	−	PROPN
ma-386	430	4	x4	x4	PROPN
ma-386	430	5	=	=	PROPN
ma-386	431	1	0	0	PROPN
ma-386	431	2	,	,	PUNCT
ma-386	431	3	x22	x22	NOUN
ma-386	432	1	x3	x3	VERB
ma-386	432	2	x21	x21	PROPN
ma-386	433	1	x4	x4	PROPN
ma-386	433	2	−	−	PROPN
ma-386	433	3	(	(	PUNCT
ma-386	433	4	0.647)2	0.647)2	NUM
ma-386	433	5	=	=	NOUN
ma-386	433	6	0	0	X
ma-386	433	7	.	.	PUNCT
ma-386	434	1	the	the	DET
ma-386	434	2	solution	solution	NOUN
ma-386	434	3	vector	vector	NOUN
ma-386	434	4	is	be	AUX
ma-386	434	5	x∗	x∗	PROPN
ma-386	434	6	=	=	SYM
ma-386	434	7	(	(	PUNCT
ma-386	434	8	0.422499	0.422499	NUM
ma-386	434	9	,	,	PUNCT
ma-386	434	10	0.577501	0.577501	NUM
ma-386	434	11	,	,	PUNCT
ma-386	434	12	0.288751	0.288751	NUM
ma-386	434	13	,	,	PUNCT
ma-386	434	14	1.288751)t	1.288751)t	NUM
ma-386	434	15	,	,	PUNCT
ma-386	434	16	obtained	obtain	VERB
ma-386	434	17	from	from	ADP
ma-386	434	18	theinitial	theinitial	ADJ
ma-386	434	19	estimate	estimate	NOUN
ma-386	434	20	x0	x0	PROPN
ma-386	434	21	=	=	PUNCT
ma-386	434	22	(	(	PUNCT
ma-386	434	23	0.8	0.8	NUM
ma-386	434	24	,	,	PUNCT
ma-386	434	25	0.2	0.2	NUM
ma-386	434	26	,	,	PUNCT
ma-386	434	27	0.9	0.9	NUM
ma-386	434	28	,	,	PUNCT
ma-386	434	29	1.8)t	1.8)t	NUM
ma-386	434	30	.	.	PUNCT
ma-386	434	31	table	table	NOUN
ma-386	434	32	4	4	NUM
ma-386	434	33	.	.	PUNCT
ma-386	434	34	results	result	NOUN
ma-386	434	35	for	for	ADP
ma-386	434	36	example	example	NOUN
ma-386	434	37	4	4	NUM
ma-386	434	38	method	method	NOUN
ma-386	434	39	iterations	iteration	NOUN
ma-386	434	40	‖g(x)‖	‖g(x)‖	NOUN
ma-386	434	41	‖xn+1	‖xn+1	NUM
ma-386	434	42	−	−	NOUN
ma-386	434	43	xn‖	xn‖	PROPN
ma-386	434	44	cpu	cpu	VERB
ma-386	434	45	time	time	NOUN
ma-386	434	46	(	(	PUNCT
ma-386	434	47	s	s	NOUN
ma-386	434	48	)	)	PUNCT
ma-386	434	49	method	method	NOUN
ma-386	434	50	(	(	PUNCT
ma-386	434	51	2	2	NUM
ma-386	434	52	)	)	PUNCT
ma-386	434	53	4	4	NUM
ma-386	434	54	1.4315×	1.4315×	NUM
ma-386	434	55	10−51	10−51	NUM
ma-386	434	56	4.334×	4.334×	PROPN
ma-386	434	57	10−16	10−16	INTJ
ma-386	434	58	0.04373wang	0.04373wang	PROPN
ma-386	434	59	et	et	PROPN
ma-386	435	1	al	al	PROPN
ma-386	435	2	.	.	PROPN
ma-386	436	1	n	n	CCONJ
ma-386	436	2	/	/	SYM
ma-386	436	3	a	a	DET
ma-386	436	4	n	n	NOUN
ma-386	436	5	/	/	SYM
ma-386	436	6	a	a	PRON
ma-386	436	7	n	n	NOUN
ma-386	436	8	/	/	SYM
ma-386	436	9	a	a	DET
ma-386	436	10	n	n	CCONJ
ma-386	436	11	/	/	SYM
ma-386	436	12	ahueso	ahueso	NOUN
ma-386	436	13	et	et	PROPN
ma-386	436	14	al	al	PROPN
ma-386	436	15	.	.	PROPN
ma-386	437	1	n	n	CCONJ
ma-386	437	2	/	/	SYM
ma-386	437	3	a	a	DET
ma-386	437	4	n	n	NOUN
ma-386	437	5	/	/	SYM
ma-386	437	6	a	a	PRON
ma-386	437	7	n	n	NOUN
ma-386	437	8	/	/	SYM
ma-386	437	9	a	a	PRON
ma-386	437	10	n	n	CCONJ
ma-386	437	11	/	/	SYM
ma-386	437	12	acordero	acordero	PROPN
ma-386	437	13	et	et	PROPN
ma-386	437	14	al	al	PROPN
ma-386	437	15	.	.	PROPN
ma-386	438	1	4	4	NUM
ma-386	438	2	2.3346×	2.3346×	NUM
ma-386	438	3	10−53	10−53	NUM
ma-386	438	4	1.243×	1.243×	NUM
ma-386	438	5	10−21	10−21	NUM
ma-386	438	6	0.01554abbasbandy	0.01554abbasbandy	PROPN
ma-386	438	7	et	et	PROPN
ma-386	438	8	al	al	PROPN
ma-386	438	9	.	.	PROPN
ma-386	438	10	n	n	CCONJ
ma-386	438	11	/	/	SYM
ma-386	438	12	a	a	DET
ma-386	438	13	n	n	NOUN
ma-386	438	14	/	/	SYM
ma-386	438	15	a	a	DET
ma-386	438	16	n	n	NOUN
ma-386	438	17	/	/	SYM
ma-386	438	18	a	a	DET
ma-386	438	19	n	n	NOUN
ma-386	438	20	/	/	SYM
ma-386	438	21	a	a	PRON
ma-386	438	22	n	n	CCONJ
ma-386	438	23	/	/	SYM
ma-386	438	24	a	a	PRON
ma-386	438	25	indicates	indicate	VERB
ma-386	438	26	that	that	SCONJ
ma-386	438	27	the	the	DET
ma-386	438	28	method	method	NOUN
ma-386	438	29	did	do	AUX
ma-386	438	30	not	not	PART
ma-386	438	31	converge	converge	VERB
ma-386	438	32	to	to	ADP
ma-386	438	33	the	the	DET
ma-386	438	34	required	require	VERB
ma-386	438	35	solution	solution	NOUN
ma-386	438	36	within	within	ADP
ma-386	438	37	theprescribed	theprescribe	VERB
ma-386	438	38	iteration	iteration	NOUN
ma-386	438	39	or	or	CCONJ
ma-386	438	40	tolerance	tolerance	NOUN
ma-386	438	41	limits	limit	NOUN
ma-386	438	42	.	.	PUNCT
ma-386	439	1	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	439	2	eur	eur	PROPN
ma-386	439	3	.	.	PUNCT
ma-386	440	1	j.	j.	PROPN
ma-386	440	2	math	math	PROPN
ma-386	440	3	.	.	PUNCT
ma-386	441	1	anal	anal	PROPN
ma-386	441	2	.	.	PUNCT
ma-386	442	1	10.28924	10.28924	NUM
ma-386	442	2	/	/	SYM
ma-386	442	3	ada	ada	PROPN
ma-386	442	4	/	/	SYM
ma-386	442	5	ma.5.18	ma.5.18	PROPN
ma-386	442	6	16	16	NUM
ma-386	442	7	example	example	NOUN
ma-386	442	8	5	5	NUM
ma-386	442	9	.	.	X
ma-386	442	10	consider	consider	VERB
ma-386	442	11	the	the	DET
ma-386	442	12	nonlinear	nonlinear	ADJ
ma-386	442	13	system	system	NOUN
ma-386	442	14	of	of	ADP
ma-386	442	15	equations	equation	NOUN
ma-386	442	16	of	of	ADP
ma-386	442	17	size	size	NOUN
ma-386	442	18	200	200	NUM
ma-386	442	19	gi(x	gi(x	NUM
ma-386	442	20	)	)	PUNCT
ma-386	443	1	=	=	PUNCT
ma-386	443	2	e−xi	e−xi	PROPN
ma-386	444	1	−	−	PROPN
ma-386	444	2	200∑	200∑	NUM
ma-386	444	3	j=1	j=1	PROPN
ma-386	444	4	j	j	PROPN
ma-386	444	5	6	6	NUM
ma-386	444	6	=	=	NOUN
ma-386	444	7	i	i	NOUN
ma-386	444	8	xj	xj	NOUN
ma-386	444	9	=	=	SYM
ma-386	444	10	0	0	PROPN
ma-386	444	11	,	,	PUNCT
ma-386	444	12	i	i	PRON
ma-386	444	13	=	=	NOUN
ma-386	444	14	1	1	NUM
ma-386	444	15	,	,	PUNCT
ma-386	444	16	2	2	NUM
ma-386	444	17	,	,	PUNCT
ma-386	444	18	.	.	PUNCT
ma-386	444	19	.	.	PUNCT
ma-386	444	20	.	.	PUNCT
ma-386	445	1	,	,	PUNCT
ma-386	446	1	200	200	NUM
ma-386	446	2	.	.	PUNCT
ma-386	447	1	the	the	DET
ma-386	447	2	initial	initial	ADJ
ma-386	447	3	approximation	approximation	NOUN
ma-386	447	4	is	be	AUX
ma-386	447	5	set	set	VERB
ma-386	447	6	as	as	ADP
ma-386	447	7	x0	x0	PROPN
ma-386	447	8	=	=	PRON
ma-386	447	9	(	(	PUNCT
ma-386	447	10	3	3	NUM
ma-386	447	11	2	2	NUM
ma-386	447	12	,	,	PUNCT
ma-386	447	13	3	3	NUM
ma-386	447	14	2	2	NUM
ma-386	447	15	,	,	PUNCT
ma-386	447	16	.	.	PUNCT
ma-386	447	17	.	.	PUNCT
ma-386	448	1	.	.	PUNCT
ma-386	449	1	,	,	PUNCT
ma-386	449	2	3	3	NUM
ma-386	449	3	2	2	NUM
ma-386	449	4	)	)	PUNCT
ma-386	449	5	t	t	NOUN
ma-386	449	6	,	,	PUNCT
ma-386	449	7	with	with	ADP
ma-386	449	8	parameters	parameter	NOUN
ma-386	449	9	a	a	DET
ma-386	449	10	=	=	X
ma-386	449	11	−2.0	−2.0	PROPN
ma-386	449	12	and	and	CCONJ
ma-386	449	13	b	b	X
ma-386	450	1	=	=	SYM
ma-386	450	2	2.0,leading	2.0,leade	VERB
ma-386	450	3	to	to	ADP
ma-386	450	4	the	the	DET
ma-386	450	5	solution	solution	NOUN
ma-386	450	6	:	:	PUNCT
ma-386	450	7	x∗	x∗	PROPN
ma-386	450	8	=	=	SYM
ma-386	450	9	(	(	PUNCT
ma-386	450	10	0.0050	0.0050	NUM
ma-386	450	11	,	,	PUNCT
ma-386	450	12	0.0050	0.0050	NUM
ma-386	450	13	,	,	PUNCT
ma-386	450	14	.	.	PUNCT
ma-386	450	15	.	.	PUNCT
ma-386	451	1	.	.	PUNCT
ma-386	452	1	,	,	PUNCT
ma-386	452	2	0.0050)t	0.0050)t	X
ma-386	452	3	.	.	PUNCT
ma-386	453	1	table	table	NOUN
ma-386	453	2	5	5	NUM
ma-386	453	3	.	.	PUNCT
ma-386	453	4	results	result	NOUN
ma-386	453	5	for	for	ADP
ma-386	453	6	example	example	NOUN
ma-386	453	7	5	5	NUM
ma-386	453	8	method	method	NOUN
ma-386	453	9	iterations	iteration	NOUN
ma-386	453	10	‖g(x)‖	‖g(x)‖	NOUN
ma-386	453	11	‖xn+1	‖xn+1	NUM
ma-386	453	12	−	−	NOUN
ma-386	453	13	xn‖	xn‖	PROPN
ma-386	453	14	cpu	cpu	VERB
ma-386	453	15	time	time	NOUN
ma-386	453	16	(	(	PUNCT
ma-386	453	17	s	s	NOUN
ma-386	453	18	)	)	PUNCT
ma-386	453	19	method	method	NOUN
ma-386	453	20	(	(	PUNCT
ma-386	453	21	2	2	NUM
ma-386	453	22	)	)	PUNCT
ma-386	453	23	2	2	NUM
ma-386	453	24	3.4388×	3.4388×	NUM
ma-386	453	25	10−51	10−51	NUM
ma-386	453	26	4.7064×	4.7064×	NOUN
ma-386	453	27	10−37	10−37	NOUN
ma-386	454	1	50.414524wang	50.414524wang	NUM
ma-386	454	2	et	et	NOUN
ma-386	454	3	al	al	PROPN
ma-386	454	4	.	.	PROPN
ma-386	455	1	3	3	NUM
ma-386	455	2	6.8725×	6.8725×	NUM
ma-386	456	1	10−52	10−52	NUM
ma-386	456	2	7.9328×	7.9328×	NUM
ma-386	456	3	10−26	10−26	NUM
ma-386	456	4	86.904696hueso	86.904696hueso	NOUN
ma-386	456	5	et	et	PROPN
ma-386	456	6	al	al	PROPN
ma-386	456	7	.	.	PROPN
ma-386	457	1	3	3	NUM
ma-386	457	2	1.1438×	1.1438×	NUM
ma-386	457	3	10−51	10−51	NUM
ma-386	457	4	1.4069×	1.4069×	NOUN
ma-386	457	5	10−18	10−18	NUM
ma-386	458	1	129.807516cordero	129.807516cordero	NUM
ma-386	458	2	et	et	NOUN
ma-386	458	3	al	al	PROPN
ma-386	458	4	.	.	PROPN
ma-386	459	1	3	3	NUM
ma-386	459	2	2.5137×	2.5137×	NUM
ma-386	459	3	10−51	10−51	NUM
ma-386	459	4	3.0846×	3.0846×	NUM
ma-386	459	5	10−48	10−48	NUM
ma-386	459	6	71.584528abbasbandy	71.584528abbasbandy	NUM
ma-386	459	7	et	et	NOUN
ma-386	459	8	al	al	PROPN
ma-386	459	9	.	.	PROPN
ma-386	460	1	3	3	NUM
ma-386	460	2	6.5891×	6.5891×	NUM
ma-386	460	3	10−52	10−52	NUM
ma-386	460	4	1.7579×	1.7579×	NUM
ma-386	460	5	10−20	10−20	NOUN
ma-386	460	6	98.961347	98.961347	NUM
ma-386	460	7	4	4	NUM
ma-386	460	8	.	.	PUNCT
ma-386	460	9	conclusions	conclusion	NOUN
ma-386	460	10	this	this	DET
ma-386	460	11	paper	paper	NOUN
ma-386	460	12	presented	present	VERB
ma-386	460	13	a	a	DET
ma-386	460	14	general	general	ADJ
ma-386	460	15	high	high	ADJ
ma-386	460	16	-	-	PUNCT
ma-386	460	17	order	order	NOUN
ma-386	460	18	iterative	iterative	NOUN
ma-386	460	19	method	method	NOUN
ma-386	460	20	for	for	ADP
ma-386	460	21	solving	solve	VERB
ma-386	460	22	nonlinear	nonlinear	ADJ
ma-386	460	23	systems	system	NOUN
ma-386	460	24	withoutrequiring	withoutrequire	VERB
ma-386	460	25	higher	high	ADJ
ma-386	460	26	-	-	PUNCT
ma-386	460	27	order	order	NOUN
ma-386	460	28	derivatives	derivative	NOUN
ma-386	460	29	.	.	PUNCT
ma-386	461	1	we	we	PRON
ma-386	461	2	established	establish	VERB
ma-386	461	3	both	both	CCONJ
ma-386	461	4	local	local	ADJ
ma-386	461	5	and	and	CCONJ
ma-386	461	6	semi	semi	ADJ
ma-386	461	7	-	-	ADJ
ma-386	461	8	local	local	ADJ
ma-386	461	9	convergence	convergence	NOUN
ma-386	461	10	resultsusing	resultsusing	NOUN
ma-386	461	11	majorant	majorant	NOUN
ma-386	461	12	conditions	condition	NOUN
ma-386	461	13	and	and	CCONJ
ma-386	461	14	majorizing	majorize	VERB
ma-386	461	15	sequences	sequence	NOUN
ma-386	461	16	,	,	PUNCT
ma-386	461	17	providing	provide	VERB
ma-386	461	18	rigorous	rigorous	ADJ
ma-386	461	19	guarantees	guarantee	NOUN
ma-386	461	20	even	even	ADV
ma-386	461	21	from	from	ADP
ma-386	461	22	dis	dis	PROPN
ma-386	461	23	-	-	PUNCT
ma-386	461	24	tant	tant	ADJ
ma-386	461	25	initial	initial	ADJ
ma-386	461	26	guesses	guess	NOUN
ma-386	461	27	.	.	PUNCT
ma-386	462	1	numerical	numerical	ADJ
ma-386	462	2	experiments	experiment	NOUN
ma-386	462	3	on	on	ADP
ma-386	462	4	benchmark	benchmark	NOUN
ma-386	462	5	problems	problem	NOUN
ma-386	462	6	confirmed	confirm	VERB
ma-386	462	7	the	the	DET
ma-386	462	8	method	method	NOUN
ma-386	462	9	’s	’s	PART
ma-386	462	10	ac	ac	PROPN
ma-386	462	11	-	-	PROPN
ma-386	462	12	curacy	curacy	NOUN
ma-386	462	13	,	,	PUNCT
ma-386	462	14	fast	fast	ADJ
ma-386	462	15	convergence	convergence	NOUN
ma-386	462	16	,	,	PUNCT
ma-386	462	17	and	and	CCONJ
ma-386	462	18	low	low	ADJ
ma-386	462	19	residual	residual	ADJ
ma-386	462	20	errors	error	NOUN
ma-386	462	21	compared	compare	VERB
ma-386	462	22	to	to	ADP
ma-386	462	23	existing	exist	VERB
ma-386	462	24	high	high	ADJ
ma-386	462	25	-	-	PUNCT
ma-386	462	26	order	order	NOUN
ma-386	462	27	methods	method	NOUN
ma-386	462	28	.	.	PUNCT
ma-386	463	1	theresults	theresult	NOUN
ma-386	463	2	validate	validate	VERB
ma-386	463	3	the	the	DET
ma-386	463	4	theoretical	theoretical	ADJ
ma-386	463	5	findings	finding	NOUN
ma-386	463	6	and	and	CCONJ
ma-386	463	7	highlight	highlight	VERB
ma-386	463	8	the	the	DET
ma-386	463	9	method	method	NOUN
ma-386	463	10	’s	’s	PART
ma-386	463	11	applicability	applicability	NOUN
ma-386	463	12	to	to	ADP
ma-386	463	13	a	a	DET
ma-386	463	14	wide	wide	ADJ
ma-386	463	15	range	range	NOUN
ma-386	463	16	ofnonlinear	ofnonlinear	NOUN
ma-386	463	17	problems	problem	NOUN
ma-386	463	18	,	,	PUNCT
ma-386	463	19	suggesting	suggest	VERB
ma-386	463	20	potential	potential	NOUN
ma-386	463	21	for	for	ADP
ma-386	463	22	further	further	ADJ
ma-386	463	23	extensions	extension	NOUN
ma-386	463	24	and	and	CCONJ
ma-386	463	25	refinements	refinement	NOUN
ma-386	463	26	.	.	PUNCT
ma-386	464	1	author	author	NOUN
ma-386	464	2	contributions	contribution	NOUN
ma-386	464	3	.	.	PUNCT
ma-386	465	1	authors	author	NOUN
ma-386	465	2	contributed	contribute	VERB
ma-386	465	3	equally	equally	ADV
ma-386	465	4	.	.	PUNCT
ma-386	466	1	all	all	DET
ma-386	466	2	authors	author	NOUN
ma-386	466	3	have	have	AUX
ma-386	466	4	read	read	VERB
ma-386	466	5	and	and	CCONJ
ma-386	466	6	agreed	agree	VERB
ma-386	466	7	to	to	PART
ma-386	466	8	thepublished	thepublishe	VERB
ma-386	466	9	version	version	NOUN
ma-386	466	10	of	of	ADP
ma-386	466	11	the	the	DET
ma-386	466	12	manuscript	manuscript	NOUN
ma-386	466	13	.	.	PUNCT
ma-386	467	1	references	reference	NOUN
ma-386	467	2	[	[	X
ma-386	467	3	1	1	X
ma-386	467	4	]	]	PUNCT
ma-386	467	5	s.	s.	PROPN
ma-386	467	6	abbasbandy	abbasbandy	PROPN
ma-386	467	7	,	,	PUNCT
ma-386	467	8	p.	p.	NOUN
ma-386	467	9	bakhtiari	bakhtiari	PROPN
ma-386	467	10	,	,	PUNCT
ma-386	467	11	a.	a.	PROPN
ma-386	467	12	cordero	cordero	PROPN
ma-386	467	13	,	,	PUNCT
ma-386	467	14	j.r	j.r	PROPN
ma-386	467	15	.	.	PROPN
ma-386	467	16	torregrosa	torregrosa	PROPN
ma-386	467	17	,	,	PUNCT
ma-386	467	18	t.	t.	NOUN
ma-386	467	19	lotfi	lotfi	PROPN
ma-386	467	20	,	,	PUNCT
ma-386	467	21	new	new	ADJ
ma-386	467	22	efficient	efficient	ADJ
ma-386	467	23	methods	method	NOUN
ma-386	467	24	for	for	ADP
ma-386	467	25	solving	solve	VERB
ma-386	467	26	nonlinear	nonlinear	ADJ
ma-386	467	27	systemsof	systemsof	NOUN
ma-386	467	28	equations	equation	NOUN
ma-386	467	29	with	with	ADP
ma-386	467	30	arbitrary	arbitrary	ADJ
ma-386	467	31	even	even	ADV
ma-386	467	32	order	order	NOUN
ma-386	467	33	,	,	PUNCT
ma-386	467	34	appl	appl	PROPN
ma-386	467	35	.	.	PROPN
ma-386	467	36	math	math	NOUN
ma-386	467	37	.	.	PUNCT
ma-386	468	1	comput	comput	NOUN
ma-386	468	2	.	.	PUNCT
ma-386	469	1	287	287	NUM
ma-386	469	2	-	-	SYM
ma-386	469	3	288	288	NUM
ma-386	469	4	(	(	PUNCT
ma-386	469	5	2016	2016	NUM
ma-386	469	6	)	)	PUNCT
ma-386	469	7	,	,	PUNCT
ma-386	469	8	94–103	94–103	NUM
ma-386	469	9	.	.	PUNCT
ma-386	470	1	https://doi.org/10.1016/	https://doi.org/10.1016/	PROPN
ma-386	470	2	j.amc.2016.04.038.[2	j.amc.2016.04.038.[2	PROPN
ma-386	470	3	]	]	X
ma-386	470	4	c.	c.	PROPN
ma-386	470	5	amorós	amorós	PROPN
ma-386	470	6	,	,	PUNCT
ma-386	470	7	i.k	i.k	PROPN
ma-386	470	8	.	.	PROPN
ma-386	470	9	argyros	argyros	PROPN
ma-386	470	10	,	,	PUNCT
ma-386	470	11	r.	r.	PROPN
ma-386	470	12	gonzález	gonzález	PROPN
ma-386	470	13	,	,	PUNCT
ma-386	470	14	á.a	á.a	PROPN
ma-386	470	15	.	.	PROPN
ma-386	470	16	magreñán	magreñán	PROPN
ma-386	470	17	,	,	PUNCT
ma-386	470	18	l.	l.	PROPN
ma-386	470	19	orcos	orcos	PROPN
ma-386	470	20	,	,	PUNCT
ma-386	470	21	í	í	PROPN
ma-386	470	22	.	.	PROPN
ma-386	470	23	sarría	sarría	PROPN
ma-386	470	24	,	,	PUNCT
ma-386	470	25	study	study	NOUN
ma-386	470	26	of	of	ADP
ma-386	470	27	a	a	DET
ma-386	470	28	high	high	ADJ
ma-386	470	29	-	-	PUNCT
ma-386	470	30	order	order	NOUN
ma-386	470	31	family	family	NOUN
ma-386	470	32	:	:	PUNCT
ma-386	470	33	localconvergence	localconvergence	NOUN
ma-386	470	34	and	and	CCONJ
ma-386	470	35	dynamics	dynamic	NOUN
ma-386	470	36	,	,	PUNCT
ma-386	470	37	mathematics	mathematics	PROPN
ma-386	470	38	7	7	NUM
ma-386	470	39	(	(	PUNCT
ma-386	470	40	2019	2019	NUM
ma-386	470	41	)	)	PUNCT
ma-386	470	42	,	,	PUNCT
ma-386	470	43	225	225	NUM
ma-386	470	44	.	.	PUNCT
ma-386	471	1	https://doi.org/10.3390/math7030225.[3	https://doi.org/10.3390/math7030225.[3	NOUN
ma-386	471	2	]	]	X
ma-386	471	3	i.k	i.k	PROPN
ma-386	471	4	.	.	PROPN
ma-386	471	5	argyros	argyros	PROPN
ma-386	471	6	,	,	PUNCT
ma-386	471	7	convergence	convergence	NOUN
ma-386	471	8	and	and	CCONJ
ma-386	471	9	application	application	NOUN
ma-386	471	10	of	of	ADP
ma-386	471	11	newton	newton	PROPN
ma-386	471	12	-	-	PUNCT
ma-386	471	13	type	type	NOUN
ma-386	471	14	iterations	iteration	NOUN
ma-386	471	15	,	,	PUNCT
ma-386	471	16	springer	springer	NOUN
ma-386	471	17	,	,	PUNCT
ma-386	471	18	berlin	berlin	PROPN
ma-386	471	19	,	,	PUNCT
ma-386	471	20	2008.[4	2008.[4	NUM
ma-386	471	21	]	]	X
ma-386	471	22	i.k	i.k	PROPN
ma-386	471	23	.	.	PROPN
ma-386	471	24	argyros	argyros	PROPN
ma-386	471	25	,	,	PUNCT
ma-386	471	26	the	the	DET
ma-386	471	27	theory	theory	NOUN
ma-386	471	28	and	and	CCONJ
ma-386	471	29	application	application	NOUN
ma-386	471	30	of	of	ADP
ma-386	471	31	iteration	iteration	NOUN
ma-386	471	32	methods	method	NOUN
ma-386	471	33	,	,	PUNCT
ma-386	471	34	2nd	2nd	ADJ
ma-386	471	35	ed	ed	NOUN
ma-386	471	36	.	.	PUNCT
ma-386	471	37	;	;	PUNCT
ma-386	471	38	engineering	engineering	NOUN
ma-386	471	39	series	series	NOUN
ma-386	471	40	;	;	PUNCT
ma-386	471	41	crc	crc	NOUN
ma-386	471	42	press	press	PROPN
ma-386	471	43	,	,	PUNCT
ma-386	471	44	taylor	taylor	PROPN
ma-386	471	45	&	&	CCONJ
ma-386	471	46	francis	francis	PROPN
ma-386	471	47	,	,	PUNCT
ma-386	471	48	boca	boca	PROPN
ma-386	471	49	raton	raton	PROPN
ma-386	471	50	,	,	PUNCT
ma-386	471	51	fl	fl	PROPN
ma-386	471	52	,	,	PUNCT
ma-386	471	53	usa	usa	PROPN
ma-386	471	54	,	,	PUNCT
ma-386	471	55	2022	2022	NUM
ma-386	471	56	.	.	PUNCT
ma-386	472	1	https://doi.org/10.1201/9781003128915.[5	https://doi.org/10.1201/9781003128915.[5	X
ma-386	472	2	]	]	X
ma-386	472	3	i.k	i.k	PROPN
ma-386	472	4	.	.	PROPN
ma-386	472	5	argyros	argyros	PROPN
ma-386	472	6	,	,	PUNCT
ma-386	472	7	á.a	á.a	PROPN
ma-386	472	8	.	.	PROPN
ma-386	472	9	magreñán	magreñán	PROPN
ma-386	472	10	,	,	PUNCT
ma-386	472	11	on	on	ADP
ma-386	472	12	the	the	DET
ma-386	472	13	convergence	convergence	NOUN
ma-386	472	14	of	of	ADP
ma-386	472	15	an	an	DET
ma-386	472	16	optimal	optimal	ADJ
ma-386	472	17	fourth	fourth	ADJ
ma-386	472	18	-	-	PUNCT
ma-386	472	19	order	order	NOUN
ma-386	472	20	family	family	NOUN
ma-386	472	21	of	of	ADP
ma-386	472	22	methods	method	NOUN
ma-386	472	23	and	and	CCONJ
ma-386	472	24	its	its	PRON
ma-386	472	25	dynamics	dynamic	NOUN
ma-386	472	26	,	,	PUNCT
ma-386	472	27	appl	appl	PROPN
ma-386	472	28	.	.	PROPN
ma-386	472	29	math	math	NOUN
ma-386	472	30	.	.	PUNCT
ma-386	473	1	comput	comput	NOUN
ma-386	473	2	.	.	PUNCT
ma-386	474	1	252	252	NUM
ma-386	474	2	(	(	PUNCT
ma-386	474	3	2015	2015	NUM
ma-386	474	4	)	)	PUNCT
ma-386	474	5	,	,	PUNCT
ma-386	474	6	336–346	336–346	NUM
ma-386	474	7	.	.	PUNCT
ma-386	474	8	https://doi.org/10.1016/j.amc.2014.11.074	https://doi.org/10.1016/j.amc.2014.11.074	PROPN
ma-386	474	9	.	.	PUNCT
ma-386	475	1	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	NOUN
ma-386	475	2	https://doi.org/10.1016/j.amc.2016.04.038	https://doi.org/10.1016/j.amc.2016.04.038	PROPN
ma-386	475	3	https://doi.org/10.1016/j.amc.2016.04.038	https://doi.org/10.1016/j.amc.2016.04.038	PROPN
ma-386	475	4	https://doi.org/10.3390/math7030225	https://doi.org/10.3390/math7030225	PROPN
ma-386	475	5	https://doi.org/10.1201/9781003128915	https://doi.org/10.1201/9781003128915	X
ma-386	475	6	https://doi.org/10.1016/j.amc.2014.11.074	https://doi.org/10.1016/j.amc.2014.11.074	PROPN
ma-386	475	7	eur	eur	PROPN
ma-386	475	8	.	.	PUNCT
ma-386	476	1	j.	j.	PROPN
ma-386	476	2	math	math	PROPN
ma-386	476	3	.	.	PUNCT
ma-386	477	1	anal	anal	PROPN
ma-386	477	2	.	.	PUNCT
ma-386	478	1	10.28924	10.28924	NUM
ma-386	478	2	/	/	SYM
ma-386	478	3	ada	ada	PROPN
ma-386	478	4	/	/	SYM
ma-386	478	5	ma.5.18	ma.5.18	NOUN
ma-386	478	6	17	17	NUM
ma-386	479	1	[	[	X
ma-386	479	2	6	6	NUM
ma-386	479	3	]	]	X
ma-386	479	4	i.k	i.k	PROPN
ma-386	479	5	.	.	PROPN
ma-386	479	6	argyros	argyros	PROPN
ma-386	479	7	,	,	PUNCT
ma-386	479	8	s.	s.	PROPN
ma-386	479	9	shakhno	shakhno	PROPN
ma-386	479	10	,	,	PUNCT
ma-386	479	11	extended	extend	VERB
ma-386	479	12	two	two	NUM
ma-386	479	13	-	-	PUNCT
ma-386	479	14	step	step	NOUN
ma-386	479	15	kurchatov	kurchatov	ADJ
ma-386	479	16	method	method	NOUN
ma-386	479	17	for	for	ADP
ma-386	479	18	solving	solve	VERB
ma-386	479	19	banach	banach	NOUN
ma-386	479	20	-	-	PUNCT
ma-386	479	21	space	space	NOUN
ma-386	479	22	-	-	PUNCT
ma-386	479	23	valued	value	VERB
ma-386	479	24	nondifferentiableequations	nondifferentiableequation	NOUN
ma-386	479	25	,	,	PUNCT
ma-386	479	26	int	int	NOUN
ma-386	479	27	.	.	PUNCT
ma-386	480	1	j.	j.	PROPN
ma-386	480	2	appl	appl	PROPN
ma-386	480	3	.	.	PUNCT
ma-386	481	1	comput	comput	PROPN
ma-386	481	2	.	.	PUNCT
ma-386	482	1	math	math	NOUN
ma-386	482	2	.	.	PUNCT
ma-386	483	1	6	6	NUM
ma-386	483	2	(	(	PUNCT
ma-386	483	3	2020	2020	NUM
ma-386	483	4	)	)	PUNCT
ma-386	483	5	,	,	PUNCT
ma-386	483	6	32	32	NUM
ma-386	483	7	.	.	PUNCT
ma-386	484	1	https://doi.org/10.1007/s40819-020-0784-y.[7	https://doi.org/10.1007/s40819-020-0784-y.[7	PROPN
ma-386	484	2	]	]	X
ma-386	484	3	i.	i.	PROPN
ma-386	484	4	argyros	argyros	PROPN
ma-386	484	5	,	,	PUNCT
ma-386	484	6	s.	s.	PROPN
ma-386	484	7	shakhno	shakhno	PROPN
ma-386	484	8	,	,	PUNCT
ma-386	484	9	y.	y.	PROPN
ma-386	484	10	shunkin	shunkin	PROPN
ma-386	484	11	,	,	PUNCT
ma-386	484	12	improved	improve	VERB
ma-386	484	13	convergence	convergence	NOUN
ma-386	484	14	analysis	analysis	NOUN
ma-386	484	15	of	of	ADP
ma-386	484	16	the	the	DET
ma-386	484	17	gauss	gauss	PROPN
ma-386	484	18	–	–	PUNCT
ma-386	484	19	newton	newton	PROPN
ma-386	484	20	–	–	PUNCT
ma-386	484	21	secant	secant	ADJ
ma-386	484	22	method	method	NOUN
ma-386	484	23	for	for	ADP
ma-386	484	24	solvingnonlinear	solvingnonlinear	ADJ
ma-386	484	25	least	least	ADJ
ma-386	484	26	-	-	PUNCT
ma-386	484	27	squares	square	NOUN
ma-386	484	28	problems	problem	NOUN
ma-386	484	29	,	,	PUNCT
ma-386	484	30	math	math	NOUN
ma-386	484	31	.	.	PUNCT
ma-386	484	32	7	7	NUM
ma-386	484	33	(	(	PUNCT
ma-386	484	34	2019	2019	NUM
ma-386	484	35	)	)	PUNCT
ma-386	484	36	,	,	PUNCT
ma-386	484	37	99	99	NUM
ma-386	484	38	.	.	PUNCT
ma-386	484	39	https://doi.org/10.3390/math7010099.[8	https://doi.org/10.3390/math7010099.[8	PROPN
ma-386	484	40	]	]	PUNCT
ma-386	484	41	i.k	i.k	PROPN
ma-386	484	42	.	.	PROPN
ma-386	484	43	argyros	argyros	PROPN
ma-386	484	44	,	,	PUNCT
ma-386	484	45	s.	s.	PROPN
ma-386	484	46	shakhno	shakhno	PROPN
ma-386	484	47	,	,	PUNCT
ma-386	484	48	h.	h.	PROPN
ma-386	484	49	yarmola	yarmola	PROPN
ma-386	484	50	,	,	PUNCT
ma-386	484	51	two	two	NUM
ma-386	484	52	-	-	PUNCT
ma-386	484	53	step	step	NOUN
ma-386	484	54	solver	solver	NOUN
ma-386	484	55	for	for	ADP
ma-386	484	56	nonlinear	nonlinear	ADJ
ma-386	484	57	equations	equation	NOUN
ma-386	484	58	,	,	PUNCT
ma-386	484	59	symmetry	symmetry	NOUN
ma-386	484	60	11	11	NUM
ma-386	484	61	(	(	PUNCT
ma-386	484	62	2019	2019	NUM
ma-386	484	63	)	)	PUNCT
ma-386	484	64	,	,	PUNCT
ma-386	484	65	128	128	NUM
ma-386	484	66	.	.	PUNCT
ma-386	484	67	https	https	NOUN
ma-386	484	68	:	:	PUNCT
ma-386	484	69	//doi.org/10.3390	//doi.org/10.3390	ADJ
ma-386	484	70	/	/	SYM
ma-386	484	71	sym11020128.[9	sym11020128.[9	NOUN
ma-386	484	72	]	]	X
ma-386	484	73	r.	r.	PROPN
ma-386	484	74	behl	behl	PROPN
ma-386	484	75	,	,	PUNCT
ma-386	484	76	s.	s.	PROPN
ma-386	484	77	bhalla	bhalla	PROPN
ma-386	484	78	,	,	PUNCT
ma-386	484	79	á.a	á.a	PROPN
ma-386	484	80	.	.	PROPN
ma-386	484	81	magreñán	magreñán	PROPN
ma-386	484	82	,	,	PUNCT
ma-386	484	83	s.	s.	PROPN
ma-386	484	84	kumar	kumar	PROPN
ma-386	484	85	,	,	PUNCT
ma-386	484	86	an	an	DET
ma-386	484	87	efficient	efficient	ADJ
ma-386	484	88	high	high	ADJ
ma-386	484	89	-	-	PUNCT
ma-386	484	90	order	order	NOUN
ma-386	484	91	iterative	iterative	NOUN
ma-386	484	92	scheme	scheme	NOUN
ma-386	484	93	for	for	ADP
ma-386	484	94	large	large	ADJ
ma-386	484	95	nonlinear	nonlinear	ADJ
ma-386	484	96	systemswith	systemswith	PROPN
ma-386	484	97	dynamics	dynamic	NOUN
ma-386	484	98	,	,	PUNCT
ma-386	484	99	j.	j.	PROPN
ma-386	484	100	comput	comput	PROPN
ma-386	484	101	.	.	PUNCT
ma-386	485	1	appl	appl	PROPN
ma-386	485	2	.	.	PROPN
ma-386	485	3	math	math	NOUN
ma-386	485	4	.	.	PUNCT
ma-386	486	1	404	404	NUM
ma-386	486	2	(	(	PUNCT
ma-386	486	3	2022	2022	NUM
ma-386	486	4	)	)	PUNCT
ma-386	486	5	,	,	PUNCT
ma-386	486	6	113249	113249	NUM
ma-386	486	7	.	.	PUNCT
ma-386	487	1	https://doi.org/10.1016/j.cam.2020.113249.[10	https://doi.org/10.1016/j.cam.2020.113249.[10	PROPN
ma-386	487	2	]	]	PUNCT
ma-386	487	3	a.	a.	PROPN
ma-386	487	4	cordero	cordero	PROPN
ma-386	487	5	,	,	PUNCT
ma-386	487	6	j.l	j.l	PROPN
ma-386	487	7	.	.	PROPN
ma-386	487	8	hueso	hueso	PROPN
ma-386	487	9	,	,	PUNCT
ma-386	487	10	e.	e.	PROPN
ma-386	487	11	martínez	martínez	PROPN
ma-386	487	12	,	,	PUNCT
ma-386	487	13	j.r	j.r	PROPN
ma-386	487	14	.	.	PROPN
ma-386	487	15	torregrosa	torregrosa	PROPN
ma-386	487	16	,	,	PUNCT
ma-386	487	17	a	a	DET
ma-386	487	18	modified	modify	VERB
ma-386	487	19	newton	newton	PROPN
ma-386	487	20	–	–	PUNCT
ma-386	487	21	jarratt	jarratt	PROPN
ma-386	487	22	composition	composition	NOUN
ma-386	487	23	,	,	PUNCT
ma-386	487	24	numer	numer	NOUN
ma-386	487	25	.	.	PUNCT
ma-386	488	1	algorithms	algorithms	PROPN
ma-386	488	2	55(2010	55(2010	NUM
ma-386	488	3	)	)	PUNCT
ma-386	488	4	,	,	PUNCT
ma-386	488	5	87–99	87–99	NUM
ma-386	488	6	.	.	PUNCT
ma-386	489	1	https://doi.org/10.1007/s11075-009-9359-z.[11	https://doi.org/10.1007/s11075-009-9359-z.[11	PROPN
ma-386	489	2	]	]	X
ma-386	489	3	y.h	y.h	PROPN
ma-386	489	4	.	.	PROPN
ma-386	489	5	geum	geum	PROPN
ma-386	489	6	,	,	PUNCT
ma-386	489	7	y.i	y.i	PROPN
ma-386	489	8	.	.	PROPN
ma-386	489	9	kim	kim	PROPN
ma-386	489	10	,	,	PUNCT
ma-386	489	11	á.a	á.a	PROPN
ma-386	489	12	.	.	PROPN
ma-386	489	13	magreñán	magreñán	PROPN
ma-386	489	14	,	,	PUNCT
ma-386	489	15	a	a	DET
ma-386	489	16	study	study	NOUN
ma-386	489	17	of	of	ADP
ma-386	489	18	dynamics	dynamic	NOUN
ma-386	489	19	via	via	ADP
ma-386	489	20	möbius	möbius	PROPN
ma-386	489	21	conjugacy	conjugacy	PROPN
ma-386	489	22	map	map	NOUN
ma-386	489	23	on	on	ADP
ma-386	489	24	a	a	DET
ma-386	489	25	family	family	NOUN
ma-386	489	26	of	of	ADP
ma-386	489	27	sixth	sixth	ADV
ma-386	489	28	-	-	PUNCT
ma-386	489	29	ordermodified	ordermodifie	VERB
ma-386	489	30	newton	newton	NOUN
ma-386	489	31	-	-	PUNCT
ma-386	489	32	like	like	ADJ
ma-386	489	33	multiple	multiple	ADJ
ma-386	489	34	-	-	PUNCT
ma-386	489	35	zero	zero	NUM
ma-386	489	36	finders	finder	NOUN
ma-386	489	37	with	with	ADP
ma-386	489	38	bivariate	bivariate	ADJ
ma-386	489	39	polynomial	polynomial	ADJ
ma-386	489	40	weight	weight	NOUN
ma-386	489	41	functions	function	NOUN
ma-386	489	42	,	,	PUNCT
ma-386	489	43	j.	j.	PROPN
ma-386	489	44	comput	comput	PROPN
ma-386	489	45	.	.	PUNCT
ma-386	490	1	appl	appl	PROPN
ma-386	490	2	.	.	PROPN
ma-386	490	3	math	math	NOUN
ma-386	490	4	.	.	PUNCT
ma-386	491	1	344(2018	344(2018	NOUN
ma-386	491	2	)	)	PUNCT
ma-386	491	3	,	,	PUNCT
ma-386	491	4	608–623	608–623	NUM
ma-386	491	5	.	.	PUNCT
ma-386	492	1	https://doi.org/10.1016/j.cam.2018.06.006.[12	https://doi.org/10.1016/j.cam.2018.06.006.[12	PROPN
ma-386	492	2	]	]	X
ma-386	492	3	j.l	j.l	PROPN
ma-386	492	4	.	.	PROPN
ma-386	492	5	hueso	hueso	PROPN
ma-386	492	6	,	,	PUNCT
ma-386	492	7	e.	e.	PROPN
ma-386	492	8	martínez	martínez	PROPN
ma-386	492	9	,	,	PUNCT
ma-386	492	10	c.	c.	PROPN
ma-386	492	11	teruel	teruel	PROPN
ma-386	492	12	,	,	PUNCT
ma-386	492	13	convergence	convergence	NOUN
ma-386	492	14	,	,	PUNCT
ma-386	492	15	efficiency	efficiency	NOUN
ma-386	492	16	and	and	CCONJ
ma-386	492	17	dynamics	dynamic	NOUN
ma-386	492	18	of	of	ADP
ma-386	492	19	new	new	ADJ
ma-386	492	20	fourthand	fourthand	NOUN
ma-386	492	21	sixth	sixth	ADJ
ma-386	492	22	-	-	PUNCT
ma-386	492	23	order	order	NOUN
ma-386	492	24	families	family	NOUN
ma-386	492	25	ofiterative	ofiterative	ADJ
ma-386	492	26	methods	method	NOUN
ma-386	492	27	for	for	ADP
ma-386	492	28	nonlinear	nonlinear	ADJ
ma-386	492	29	systems	system	NOUN
ma-386	492	30	,	,	PUNCT
ma-386	492	31	j.	j.	PROPN
ma-386	492	32	comput	comput	PROPN
ma-386	492	33	.	.	PUNCT
ma-386	493	1	appl	appl	PROPN
ma-386	493	2	.	.	PROPN
ma-386	493	3	math	math	NOUN
ma-386	493	4	.	.	PUNCT
ma-386	494	1	275	275	NUM
ma-386	494	2	(	(	PUNCT
ma-386	494	3	2015	2015	NUM
ma-386	494	4	)	)	PUNCT
ma-386	494	5	,	,	PUNCT
ma-386	494	6	412–420	412–420	NUM
ma-386	494	7	.	.	PUNCT
ma-386	495	1	https://doi.org/10.1016/	https://doi.org/10.1016/	PROPN
ma-386	495	2	j.cam.2014.06.010.[13	j.cam.2014.06.010.[13	NOUN
ma-386	495	3	]	]	X
ma-386	495	4	j.m	j.m	PROPN
ma-386	495	5	.	.	PROPN
ma-386	495	6	ortega	ortega	PROPN
ma-386	495	7	,	,	PUNCT
ma-386	495	8	w.c	w.c	PROPN
ma-386	495	9	.	.	PROPN
ma-386	495	10	rheinboldt	rheinboldt	ADJ
ma-386	495	11	,	,	PUNCT
ma-386	495	12	iterative	iterative	ADJ
ma-386	495	13	solution	solution	NOUN
ma-386	495	14	of	of	ADP
ma-386	495	15	nonlinear	nonlinear	ADJ
ma-386	495	16	equations	equation	NOUN
ma-386	495	17	in	in	ADP
ma-386	495	18	several	several	ADJ
ma-386	495	19	variables	variable	NOUN
ma-386	495	20	,	,	PUNCT
ma-386	495	21	academic	academic	ADJ
ma-386	495	22	press	press	NOUN
ma-386	495	23	,	,	PUNCT
ma-386	495	24	newyork	newyork	NOUN
ma-386	495	25	,	,	PUNCT
ma-386	495	26	1970.[14	1970.[14	NUM
ma-386	495	27	]	]	X
ma-386	495	28	s.k	s.k	PROPN
ma-386	495	29	.	.	PROPN
ma-386	495	30	parhi	parhi	PROPN
ma-386	495	31	,	,	PUNCT
ma-386	495	32	d.k	d.k	PROPN
ma-386	495	33	.	.	PROPN
ma-386	495	34	gupta	gupta	PROPN
ma-386	495	35	,	,	PUNCT
ma-386	495	36	a	a	DET
ma-386	495	37	sixth	sixth	ADJ
ma-386	495	38	-	-	PUNCT
ma-386	495	39	order	order	NOUN
ma-386	495	40	method	method	NOUN
ma-386	495	41	for	for	ADP
ma-386	495	42	nonlinear	nonlinear	ADJ
ma-386	495	43	equations	equation	NOUN
ma-386	495	44	,	,	PUNCT
ma-386	495	45	appl	appl	PROPN
ma-386	495	46	.	.	PROPN
ma-386	495	47	math	math	PROPN
ma-386	495	48	.	.	PUNCT
ma-386	496	1	comput	comput	NOUN
ma-386	496	2	.	.	PUNCT
ma-386	497	1	203	203	NUM
ma-386	497	2	(	(	PUNCT
ma-386	497	3	2008	2008	NUM
ma-386	497	4	)	)	PUNCT
ma-386	497	5	,	,	PUNCT
ma-386	497	6	50–55	50–55	NUM
ma-386	497	7	.	.	PUNCT
ma-386	498	1	https://doi.org/10.1016/j.amc.2008.03.037.[15	https://doi.org/10.1016/j.amc.2008.03.037.[15	PROPN
ma-386	498	2	]	]	X
ma-386	498	3	m.s	m.s	PROPN
ma-386	498	4	.	.	PROPN
ma-386	498	5	petković	petković	PROPN
ma-386	498	6	,	,	PUNCT
ma-386	498	7	b.	b.	PROPN
ma-386	498	8	neta	neta	PROPN
ma-386	498	9	,	,	PUNCT
ma-386	498	10	l.d	l.d	PROPN
ma-386	498	11	.	.	PROPN
ma-386	498	12	petković	petković	PROPN
ma-386	498	13	,	,	PUNCT
ma-386	498	14	j.	j.	PROPN
ma-386	498	15	džunić	džunić	PROPN
ma-386	498	16	,	,	PUNCT
ma-386	498	17	multipoint	multipoint	NOUN
ma-386	498	18	methods	method	NOUN
ma-386	498	19	for	for	ADP
ma-386	498	20	solving	solve	VERB
ma-386	498	21	nonlinear	nonlinear	ADJ
ma-386	498	22	equations	equation	NOUN
ma-386	498	23	,	,	PUNCT
ma-386	498	24	academicpress	academicpress	ADJ
ma-386	498	25	,	,	PUNCT
ma-386	498	26	london	london	PROPN
ma-386	498	27	,	,	PUNCT
ma-386	498	28	2012.[16	2012.[16	NUM
ma-386	498	29	]	]	X
ma-386	498	30	h.	h.	PROPN
ma-386	498	31	ramos	ramos	PROPN
ma-386	498	32	,	,	PUNCT
ma-386	498	33	m.t.t	m.t.t	PROPN
ma-386	498	34	.	.	PUNCT
ma-386	498	35	monteiro	monteiro	PROPN
ma-386	498	36	,	,	PUNCT
ma-386	498	37	a	a	DET
ma-386	498	38	new	new	ADJ
ma-386	498	39	approach	approach	NOUN
ma-386	498	40	based	base	VERB
ma-386	498	41	on	on	ADP
ma-386	498	42	newton	newton	PROPN
ma-386	498	43	’s	’s	PART
ma-386	498	44	method	method	NOUN
ma-386	498	45	to	to	PART
ma-386	498	46	solve	solve	VERB
ma-386	498	47	systems	system	NOUN
ma-386	498	48	of	of	ADP
ma-386	498	49	nonlinear	nonlinear	ADJ
ma-386	498	50	equations	equation	NOUN
ma-386	498	51	,	,	PUNCT
ma-386	498	52	j.comput	j.comput	NOUN
ma-386	498	53	.	.	PUNCT
ma-386	499	1	appl	appl	PROPN
ma-386	499	2	.	.	PROPN
ma-386	499	3	math	math	NOUN
ma-386	499	4	.	.	PUNCT
ma-386	500	1	318	318	NUM
ma-386	500	2	(	(	PUNCT
ma-386	500	3	2017	2017	NUM
ma-386	500	4	)	)	PUNCT
ma-386	500	5	,	,	PUNCT
ma-386	500	6	3–13	3–13	NUM
ma-386	500	7	.	.	PUNCT
ma-386	501	1	https://doi.org/10.1016/j.cam.2016.12.019.[17	https://doi.org/10.1016/j.cam.2016.12.019.[17	PROPN
ma-386	501	2	]	]	PUNCT
ma-386	501	3	j.f	j.f	PROPN
ma-386	501	4	.	.	PROPN
ma-386	501	5	traub	traub	PROPN
ma-386	501	6	,	,	PUNCT
ma-386	501	7	iterative	iterative	NOUN
ma-386	501	8	methods	method	NOUN
ma-386	501	9	for	for	ADP
ma-386	501	10	the	the	DET
ma-386	501	11	solution	solution	NOUN
ma-386	501	12	of	of	ADP
ma-386	501	13	equations	equation	NOUN
ma-386	501	14	,	,	PUNCT
ma-386	501	15	prentice	prentice	NOUN
ma-386	501	16	-	-	PUNCT
ma-386	501	17	hall	hall	NOUN
ma-386	501	18	,	,	PUNCT
ma-386	501	19	englewood	englewood	PROPN
ma-386	501	20	cliffs	cliff	NOUN
ma-386	501	21	,	,	PUNCT
ma-386	501	22	1964.[18	1964.[18	NUM
ma-386	501	23	]	]	PUNCT
ma-386	501	24	x.	x.	PROPN
ma-386	501	25	wang	wang	PROPN
ma-386	501	26	,	,	PUNCT
ma-386	501	27	j.	j.	PROPN
ma-386	501	28	kou	kou	PROPN
ma-386	501	29	,	,	PUNCT
ma-386	501	30	y.	y.	PROPN
ma-386	501	31	li	li	PROPN
ma-386	501	32	,	,	PUNCT
ma-386	501	33	modified	modify	VERB
ma-386	501	34	jarratt	jarratt	NOUN
ma-386	501	35	method	method	NOUN
ma-386	501	36	with	with	ADP
ma-386	501	37	sixth	sixth	ADJ
ma-386	501	38	-	-	PUNCT
ma-386	501	39	order	order	NOUN
ma-386	501	40	convergence	convergence	NOUN
ma-386	501	41	,	,	PUNCT
ma-386	501	42	appl	appl	PROPN
ma-386	501	43	.	.	PROPN
ma-386	501	44	math	math	PROPN
ma-386	501	45	.	.	PUNCT
ma-386	502	1	lett	lett	PROPN
ma-386	502	2	.	.	PUNCT
ma-386	503	1	22	22	NUM
ma-386	503	2	(	(	PUNCT
ma-386	503	3	2009	2009	NUM
ma-386	503	4	)	)	PUNCT
ma-386	503	5	,	,	PUNCT
ma-386	503	6	1798–1802	1798–1802	NUM
ma-386	503	7	.	.	PUNCT
ma-386	504	1	https://doi.org/10.1016/j.aml.2009.06.022.[19	https://doi.org/10.1016/j.aml.2009.06.022.[19	NUM
ma-386	504	2	]	]	PUNCT
ma-386	504	3	x.y	x.y	PROPN
ma-386	504	4	.	.	PROPN
ma-386	504	5	xiao	xiao	PROPN
ma-386	504	6	,	,	PUNCT
ma-386	504	7	h.m	h.m	PROPN
ma-386	504	8	.	.	PROPN
ma-386	504	9	yin	yin	PROPN
ma-386	504	10	,	,	PUNCT
ma-386	504	11	increasing	increase	VERB
ma-386	504	12	the	the	DET
ma-386	504	13	order	order	NOUN
ma-386	504	14	of	of	ADP
ma-386	504	15	convergence	convergence	NOUN
ma-386	504	16	for	for	ADP
ma-386	504	17	iterative	iterative	ADJ
ma-386	504	18	methods	method	NOUN
ma-386	504	19	to	to	PART
ma-386	504	20	solve	solve	VERB
ma-386	504	21	nonlinear	nonlinear	ADJ
ma-386	504	22	systems	system	NOUN
ma-386	504	23	,	,	PUNCT
ma-386	504	24	calcolo53	calcolo53	NOUN
ma-386	504	25	(	(	PUNCT
ma-386	504	26	2016	2016	NUM
ma-386	504	27	)	)	PUNCT
ma-386	504	28	,	,	PUNCT
ma-386	504	29	285–300	285–300	NUM
ma-386	504	30	.	.	PUNCT
ma-386	505	1	https://doi.org/10.1007/s10092-015-0149-9	https://doi.org/10.1007/s10092-015-0149-9	NUM
ma-386	505	2	.	.	PUNCT
ma-386	506	1	https://doi.org/10.28924/ada/ma.5.18	https://doi.org/10.28924/ada/ma.5.18	PROPN
ma-386	506	2	https://doi.org/10.1007/s40819-020-0784-y	https://doi.org/10.1007/s40819-020-0784-y	PROPN
ma-386	506	3	https://doi.org/10.3390/math7010099	https://doi.org/10.3390/math7010099	ADJ
ma-386	506	4	https://doi.org/10.3390/sym11020128	https://doi.org/10.3390/sym11020128	PROPN
ma-386	506	5	https://doi.org/10.3390/sym11020128	https://doi.org/10.3390/sym11020128	NOUN
ma-386	506	6	https://doi.org/10.1016/j.cam.2020.113249	https://doi.org/10.1016/j.cam.2020.113249	PUNCT
ma-386	506	7	https://doi.org/10.1007/s11075-009-9359-z	https://doi.org/10.1007/s11075-009-9359-z	PROPN
ma-386	506	8	https://doi.org/10.1016/j.cam.2018.06.006	https://doi.org/10.1016/j.cam.2018.06.006	PROPN
ma-386	506	9	https://doi.org/10.1016/j.cam.2014.06.010	https://doi.org/10.1016/j.cam.2014.06.010	VERB
ma-386	506	10	https://doi.org/10.1016/j.cam.2014.06.010	https://doi.org/10.1016/j.cam.2014.06.010	NOUN
ma-386	506	11	https://doi.org/10.1016/j.amc.2008.03.037	https://doi.org/10.1016/j.amc.2008.03.037	PROPN
ma-386	506	12	https://doi.org/10.1016/j.cam.2016.12.019	https://doi.org/10.1016/j.cam.2016.12.019	VERB
ma-386	506	13	https://doi.org/10.1016/j.aml.2009.06.022	https://doi.org/10.1016/j.aml.2009.06.022	NOUN
ma-386	506	14	https://doi.org/10.1007/s10092-015-0149-9	https://doi.org/10.1007/s10092-015-0149-9	PROPN
ma-386	506	15	1	1	NUM
ma-386	506	16	.	.	PUNCT
ma-386	507	1	introduction	introduction	NOUN
ma-386	507	2	2	2	NUM
ma-386	507	3	.	.	PUNCT
ma-386	507	4	convergence	convergence	NOUN
ma-386	507	5	analysis	analysis	NOUN
ma-386	507	6	2.1	2.1	NUM
ma-386	507	7	.	.	PUNCT
ma-386	508	1	local	local	ADJ
ma-386	508	2	2.2	2.2	NUM
ma-386	508	3	.	.	PUNCT
ma-386	508	4	semi	semi	ADJ
ma-386	508	5	-	-	ADJ
ma-386	508	6	local	local	ADJ
ma-386	508	7	3	3	NUM
ma-386	508	8	.	.	PUNCT
ma-386	508	9	numerical	numerical	PROPN
ma-386	508	10	results	result	NOUN
ma-386	508	11	example	example	VERB
ma-386	508	12	1	1	NUM
ma-386	508	13	example	example	NOUN
ma-386	508	14	2	2	NUM
ma-386	508	15	example	example	NOUN
ma-386	508	16	3	3	NUM
ma-386	508	17	example	example	NOUN
ma-386	508	18	4	4	NUM
ma-386	508	19	example	example	NOUN
ma-386	508	20	5	5	NUM
ma-386	508	21	4	4	NUM
ma-386	508	22	.	.	PUNCT
ma-386	509	1	conclusions	conclusion	NOUN
ma-386	509	2	references	reference	NOUN