id	sid	tid	token	lemma	pos
ma-345	1	1	2025	2025	NUM
ma-345	1	2	ada	ada	PROPN
ma-345	1	3	academica	academica	PROPN
ma-345	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-345	1	5	.	.	PUNCT
ma-345	2	1	j.	j.	PROPN
ma-345	2	2	math	math	PROPN
ma-345	2	3	.	.	PUNCT
ma-345	3	1	anal	anal	ADJ
ma-345	3	2	.	.	PUNCT
ma-345	4	1	5	5	NUM
ma-345	4	2	(	(	PUNCT
ma-345	4	3	2025	2025	NUM
ma-345	4	4	)	)	PUNCT
ma-345	4	5	15doi	15doi	NOUN
ma-345	4	6	:	:	PUNCT
ma-345	4	7	10.28924	10.28924	NUM
ma-345	4	8	/	/	SYM
ma-345	4	9	ada	ada	PROPN
ma-345	4	10	/	/	SYM
ma-345	4	11	ma.5.15	ma.5.15	NOUN
ma-345	4	12	three	three	NUM
ma-345	4	13	step	step	NOUN
ma-345	4	14	inverse	inverse	NOUN
ma-345	4	15	free	free	ADJ
ma-345	4	16	kurchatov	kurchatov	ADJ
ma-345	4	17	-	-	PUNCT
ma-345	4	18	like	like	ADJ
ma-345	4	19	methods	method	NOUN
ma-345	4	20	of	of	ADP
ma-345	4	21	convergence	convergence	NOUN
ma-345	4	22	order	order	NOUN
ma-345	4	23	close	close	ADV
ma-345	4	24	to	to	ADP
ma-345	4	25	four	four	NUM
ma-345	4	26	for	for	ADP
ma-345	4	27	equations	equation	NOUN
ma-345	4	28	ioannis	ioannis	PROPN
ma-345	4	29	k.	k.	PROPN
ma-345	4	30	argyros1,∗	argyros1,∗	PROPN
ma-345	4	31	,	,	PUNCT
ma-345	4	32	stepan	stepan	PROPN
ma-345	4	33	shakhno2	shakhno2	PROPN
ma-345	4	34	,	,	PUNCT
ma-345	4	35	halyna	halyna	NOUN
ma-345	4	36	yarmola3,∗	yarmola3,∗	PROPN
ma-345	4	37	,	,	PUNCT
ma-345	4	38	samundra	samundra	NOUN
ma-345	4	39	regmi4	regmi4	NOUN
ma-345	4	40	,	,	PUNCT
ma-345	4	41	nirjalshrestha5	nirjalshrestha5	PROPN
ma-345	4	42	1department	1department	NUM
ma-345	4	43	of	of	ADP
ma-345	4	44	computing	computing	NOUN
ma-345	4	45	and	and	CCONJ
ma-345	4	46	mathematics	mathematic	NOUN
ma-345	4	47	sciences	sciences	PROPN
ma-345	4	48	,	,	PUNCT
ma-345	4	49	cameron	cameron	PROPN
ma-345	4	50	university	university	PROPN
ma-345	4	51	,	,	PUNCT
ma-345	4	52	lawton	lawton	PROPN
ma-345	4	53	,	,	PUNCT
ma-345	4	54	ok	ok	PROPN
ma-345	4	55	73505	73505	NUM
ma-345	4	56	,	,	PUNCT
ma-345	4	57	usa	usa	PROPN
ma-345	4	58	iargyros@cameron.edu	iargyros@cameron.edu	PROPN
ma-345	5	1	2department	2department	NUM
ma-345	5	2	of	of	ADP
ma-345	5	3	theory	theory	NOUN
ma-345	5	4	of	of	ADP
ma-345	5	5	optimal	optimal	ADJ
ma-345	5	6	processes	process	NOUN
ma-345	5	7	,	,	PUNCT
ma-345	5	8	ivan	ivan	PROPN
ma-345	5	9	franko	franko	PROPN
ma-345	5	10	national	national	PROPN
ma-345	5	11	university	university	PROPN
ma-345	5	12	of	of	ADP
ma-345	5	13	lviv	lviv	PROPN
ma-345	5	14	,	,	PUNCT
ma-345	5	15	lviv	lviv	PROPN
ma-345	5	16	,	,	PUNCT
ma-345	5	17	ukraine	ukraine	PROPN
ma-345	5	18	stepan.shakhno@lnu.edu.ua	stepan.shakhno@lnu.edu.ua	PROPN
ma-345	6	1	3department	3department	NUM
ma-345	6	2	of	of	ADP
ma-345	6	3	computational	computational	ADJ
ma-345	6	4	mathematics	mathematic	NOUN
ma-345	6	5	,	,	PUNCT
ma-345	6	6	ivan	ivan	PROPN
ma-345	6	7	franko	franko	PROPN
ma-345	6	8	national	national	PROPN
ma-345	6	9	university	university	PROPN
ma-345	6	10	of	of	ADP
ma-345	6	11	lviv	lviv	PROPN
ma-345	6	12	,	,	PUNCT
ma-345	6	13	lviv	lviv	PROPN
ma-345	6	14	,	,	PUNCT
ma-345	6	15	ukraine	ukraine	PROPN
ma-345	6	16	halyna.yarmola@lnu.edu.ua	halyna.yarmola@lnu.edu.ua	PROPN
ma-345	6	17	4department	4department	NUM
ma-345	6	18	of	of	ADP
ma-345	6	19	mathematics	mathematic	NOUN
ma-345	6	20	,	,	PUNCT
ma-345	6	21	university	university	PROPN
ma-345	6	22	of	of	ADP
ma-345	6	23	houston	houston	PROPN
ma-345	6	24	,	,	PUNCT
ma-345	6	25	houston	houston	PROPN
ma-345	6	26	,	,	PUNCT
ma-345	6	27	tx	tx	PROPN
ma-345	6	28	77004	77004	NUM
ma-345	6	29	,	,	PUNCT
ma-345	6	30	usa	usa	PROPN
ma-345	6	31	sregmi5@uh.edu	sregmi5@uh.edu	PROPN
ma-345	6	32	5department	5department	NUM
ma-345	6	33	of	of	ADP
ma-345	6	34	mathematics	mathematic	NOUN
ma-345	6	35	,	,	PUNCT
ma-345	6	36	university	university	PROPN
ma-345	6	37	of	of	ADP
ma-345	6	38	florida	florida	PROPN
ma-345	6	39	,	,	PUNCT
ma-345	6	40	gainesville	gainesville	PROPN
ma-345	6	41	,	,	PUNCT
ma-345	6	42	fl	fl	PROPN
ma-345	6	43	32603	32603	NUM
ma-345	6	44	,	,	PUNCT
ma-345	7	1	usa	usa	PROPN
ma-345	7	2	n.shrestha@ufl.edu	n.shrestha@ufl.edu	PROPN
ma-345	7	3	∗correspondence	∗correspondence	NOUN
ma-345	7	4	:	:	PUNCT
ma-345	7	5	iargyros@cameron.edu	iargyros@cameron.edu	PROPN
ma-345	7	6	,	,	PUNCT
ma-345	7	7	halyna.yarmola@lnu.edu.ua	halyna.yarmola@lnu.edu.ua	PROPN
ma-345	7	8	abstract	abstract	NOUN
ma-345	7	9	.	.	PUNCT
ma-345	8	1	an	an	DET
ma-345	8	2	inverse	inverse	NOUN
ma-345	8	3	free	free	ADJ
ma-345	8	4	kurchatov	kurchatov	ADJ
ma-345	8	5	-	-	PUNCT
ma-345	8	6	like	like	ADJ
ma-345	8	7	methods	method	NOUN
ma-345	8	8	with	with	ADP
ma-345	8	9	three	three	NUM
ma-345	8	10	steps	step	NOUN
ma-345	8	11	is	be	AUX
ma-345	8	12	introduced	introduce	VERB
ma-345	8	13	of	of	ADP
ma-345	8	14	convergence	convergence	NOUN
ma-345	8	15	orderclose	orderclose	ADJ
ma-345	8	16	to	to	ADP
ma-345	8	17	four	four	NUM
ma-345	8	18	to	to	PART
ma-345	8	19	generate	generate	VERB
ma-345	8	20	sequences	sequence	NOUN
ma-345	8	21	approximating	approximate	VERB
ma-345	8	22	solutions	solution	NOUN
ma-345	8	23	of	of	ADP
ma-345	8	24	equations	equation	NOUN
ma-345	8	25	defined	define	VERB
ma-345	8	26	on	on	ADP
ma-345	8	27	complete	complete	ADJ
ma-345	8	28	normedspaces	normedspace	NOUN
ma-345	8	29	.	.	PUNCT
ma-345	9	1	the	the	DET
ma-345	9	2	local	local	ADJ
ma-345	9	3	analysis	analysis	NOUN
ma-345	9	4	shows	show	VERB
ma-345	9	5	r	r	NOUN
ma-345	9	6	-	-	PUNCT
ma-345	9	7	convergence	convergence	NOUN
ma-345	9	8	close	close	ADJ
ma-345	9	9	to	to	ADP
ma-345	9	10	four	four	NUM
ma-345	9	11	under	under	ADP
ma-345	9	12	conditions	condition	NOUN
ma-345	9	13	controlling	control	VERB
ma-345	9	14	the	the	DET
ma-345	9	15	divideddifference	divideddifference	NOUN
ma-345	9	16	.	.	PUNCT
ma-345	10	1	numerous	numerous	ADJ
ma-345	10	2	experiments	experiment	NOUN
ma-345	10	3	demonstrate	demonstrate	VERB
ma-345	10	4	the	the	DET
ma-345	10	5	performance	performance	NOUN
ma-345	10	6	of	of	ADP
ma-345	10	7	the	the	DET
ma-345	10	8	method	method	NOUN
ma-345	10	9	.	.	PUNCT
ma-345	11	1	1	1	X
ma-345	11	2	.	.	X
ma-345	11	3	introduction	introduction	NOUN
ma-345	11	4	let	let	VERB
ma-345	11	5	e1	e1	PROPN
ma-345	11	6	,	,	PUNCT
ma-345	11	7	e2	e2	PROPN
ma-345	11	8	represent	represent	VERB
ma-345	11	9	complete	complete	ADJ
ma-345	11	10	normed	norme	VERB
ma-345	11	11	spaces	space	NOUN
ma-345	11	12	[	[	X
ma-345	11	13	1	1	X
ma-345	11	14	]	]	PUNCT
ma-345	11	15	and	and	CCONJ
ma-345	11	16	ω	ω	NUM
ma-345	11	17	⊂	⊂	PROPN
ma-345	11	18	e1	e1	PROPN
ma-345	11	19	be	be	AUX
ma-345	11	20	open	open	ADJ
ma-345	11	21	and	and	CCONJ
ma-345	11	22	convex	convex	ADJ
ma-345	11	23	.	.	PUNCT
ma-345	12	1	a	a	DET
ma-345	12	2	plethoraof	plethoraof	NOUN
ma-345	12	3	applications	application	NOUN
ma-345	12	4	from	from	ADP
ma-345	12	5	different	different	ADJ
ma-345	12	6	fields	field	NOUN
ma-345	12	7	can	can	AUX
ma-345	12	8	be	be	AUX
ma-345	12	9	formulated	formulate	VERB
ma-345	12	10	as	as	ADP
ma-345	12	11	f	f	PROPN
ma-345	12	12	(	(	PUNCT
ma-345	12	13	x	x	NOUN
ma-345	12	14	)	)	PUNCT
ma-345	12	15	=	=	SYM
ma-345	13	1	0	0	X
ma-345	13	2	.	.	PUNCT
ma-345	14	1	(	(	PUNCT
ma-345	14	2	1.1	1.1	NUM
ma-345	14	3	)	)	PUNCT
ma-345	14	4	here	here	ADV
ma-345	14	5	f	f	X
ma-345	14	6	:	:	PUNCT
ma-345	14	7	ω→	ω→	PROPN
ma-345	14	8	e2	e2	PROPN
ma-345	14	9	is	be	AUX
ma-345	14	10	a	a	DET
ma-345	14	11	continuos	continuos	ADJ
ma-345	14	12	operator	operator	NOUN
ma-345	14	13	.	.	PUNCT
ma-345	15	1	a	a	DET
ma-345	15	2	solution	solution	NOUN
ma-345	15	3	of	of	ADP
ma-345	15	4	equation	equation	NOUN
ma-345	15	5	(	(	PUNCT
ma-345	15	6	1.1	1.1	NUM
ma-345	15	7	)	)	PUNCT
ma-345	15	8	,	,	PUNCT
ma-345	15	9	which	which	PRON
ma-345	15	10	is	be	AUX
ma-345	15	11	denoted	denote	VERB
ma-345	15	12	by	by	ADP
ma-345	15	13	x∗	x∗	PROPN
ma-345	15	14	∈	∈	PROPN
ma-345	15	15	ωis	ωis	NOUN
ma-345	15	16	given	give	VERB
ma-345	15	17	in	in	ADP
ma-345	15	18	analytical	analytical	ADJ
ma-345	15	19	form	form	NOUN
ma-345	15	20	only	only	ADV
ma-345	15	21	in	in	ADP
ma-345	15	22	rare	rare	ADJ
ma-345	15	23	cases	case	NOUN
ma-345	15	24	.	.	PUNCT
ma-345	16	1	that	that	PRON
ma-345	16	2	leads	lead	VERB
ma-345	16	3	to	to	ADP
ma-345	16	4	the	the	DET
ma-345	16	5	development	development	NOUN
ma-345	16	6	of	of	ADP
ma-345	16	7	iterative	iterative	NOUN
ma-345	16	8	methodsgenerating	methodsgenerate	VERB
ma-345	16	9	sequence	sequence	NOUN
ma-345	16	10	converging	converge	VERB
ma-345	16	11	to	to	ADP
ma-345	16	12	x∗	x∗	PROPN
ma-345	16	13	provided	provide	VERB
ma-345	16	14	some	some	DET
ma-345	16	15	conditions	condition	NOUN
ma-345	16	16	are	be	AUX
ma-345	16	17	satisfied	satisfied	ADJ
ma-345	16	18	involving	involve	VERB
ma-345	16	19	the	the	DET
ma-345	16	20	initialinformation.one	initialinformation.one	NOUN
ma-345	16	21	of	of	ADP
ma-345	16	22	the	the	DET
ma-345	16	23	most	most	ADJ
ma-345	16	24	time	time	NOUN
ma-345	16	25	-	-	PUNCT
ma-345	16	26	consuming	consume	VERB
ma-345	16	27	part	part	NOUN
ma-345	16	28	of	of	ADP
ma-345	16	29	iterative	iterative	ADJ
ma-345	16	30	methods	method	NOUN
ma-345	16	31	for	for	ADP
ma-345	16	32	solving	solve	VERB
ma-345	16	33	nonlinear	nonlinear	ADJ
ma-345	16	34	problems	problem	NOUN
ma-345	16	35	isfinding	isfinde	VERB
ma-345	16	36	the	the	DET
ma-345	16	37	inverse	inverse	NOUN
ma-345	16	38	operator	operator	NOUN
ma-345	16	39	or	or	CCONJ
ma-345	16	40	solving	solve	VERB
ma-345	16	41	the	the	DET
ma-345	16	42	corresponding	corresponding	ADJ
ma-345	16	43	linear	linear	PROPN
ma-345	16	44	problem	problem	NOUN
ma-345	16	45	.	.	PUNCT
ma-345	17	1	to	to	PART
ma-345	17	2	avoid	avoid	VERB
ma-345	17	3	this	this	PRON
ma-345	17	4	,	,	PUNCT
ma-345	17	5	methods	method	NOUN
ma-345	17	6	received	receive	VERB
ma-345	17	7	:	:	PUNCT
ma-345	17	8	9	9	NUM
ma-345	17	9	mar	mar	PROPN
ma-345	17	10	2025	2025	NUM
ma-345	17	11	.	.	PUNCT
ma-345	18	1	key	key	ADJ
ma-345	18	2	words	word	NOUN
ma-345	18	3	and	and	CCONJ
ma-345	18	4	phrases	phrase	NOUN
ma-345	18	5	.	.	PUNCT
ma-345	19	1	complete	complete	VERB
ma-345	19	2	normed	normed	ADJ
ma-345	19	3	space	space	NOUN
ma-345	19	4	;	;	PUNCT
ma-345	19	5	divided	divide	VERB
ma-345	19	6	difference	difference	NOUN
ma-345	19	7	;	;	PUNCT
ma-345	20	1	kurchatov	kurchatov	ADJ
ma-345	20	2	method	method	NOUN
ma-345	20	3	;	;	PUNCT
ma-345	20	4	local	local	ADJ
ma-345	20	5	convergence	convergence	NOUN
ma-345	20	6	;	;	PUNCT
ma-345	20	7	order	order	NOUN
ma-345	20	8	four.1	four.1	PUNCT
ma-345	20	9	https://adac.ee	https://adac.ee	PROPN
ma-345	20	10	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
ma-345	20	11	https://orcid.org/0000-0002-9189-9298	https://orcid.org/0000-0002-9189-9298	PROPN
ma-345	20	12	https://orcid.org/0000-0002-3845-6260	https://orcid.org/0000-0002-3845-6260	PROPN
ma-345	20	13	https://orcid.org/0000-0002-8986-2509	https://orcid.org/0000-0002-8986-2509	VERB
ma-345	20	14	https://orcid.org/0000-0003-0035-1022	https://orcid.org/0000-0003-0035-1022	VERB
ma-345	20	15	https://orcid.org/0000-0003-4070-091x	https://orcid.org/0000-0003-4070-091x	PROPN
ma-345	20	16	eur	eur	NOUN
ma-345	20	17	.	.	PUNCT
ma-345	21	1	j.	j.	PROPN
ma-345	21	2	math	math	PROPN
ma-345	21	3	.	.	PUNCT
ma-345	22	1	anal	anal	PROPN
ma-345	22	2	.	.	PUNCT
ma-345	23	1	10.28924	10.28924	NUM
ma-345	23	2	/	/	SYM
ma-345	23	3	ada	ada	PROPN
ma-345	23	4	/	/	SYM
ma-345	23	5	ma.5.15	ma.5.15	NOUN
ma-345	23	6	2with	2with	NUM
ma-345	23	7	approximation	approximation	NOUN
ma-345	23	8	of	of	ADP
ma-345	23	9	the	the	DET
ma-345	23	10	inverse	inverse	NOUN
ma-345	23	11	operator	operator	NOUN
ma-345	23	12	were	be	AUX
ma-345	23	13	developed	develop	VERB
ma-345	23	14	.	.	PUNCT
ma-345	24	1	one	one	NUM
ma-345	24	2	of	of	ADP
ma-345	24	3	the	the	DET
ma-345	24	4	first	first	ADJ
ma-345	24	5	such	such	ADJ
ma-345	24	6	methods	method	NOUN
ma-345	24	7	wasproposed	waspropose	VERB
ma-345	24	8	by	by	ADP
ma-345	24	9	ulm	ulm	NOUN
ma-345	24	10	in	in	ADP
ma-345	24	11	[	[	X
ma-345	24	12	17	17	NUM
ma-345	24	13	]	]	SYM
ma-345	24	14	xn+1	xn+1	PROPN
ma-345	25	1	=	=	SYM
ma-345	25	2	xn	xn	PROPN
ma-345	26	1	−	−	PROPN
ma-345	26	2	tnf	tnf	PROPN
ma-345	26	3	(	(	PUNCT
ma-345	26	4	xn	xn	PROPN
ma-345	26	5	)	)	PUNCT
ma-345	26	6	,	,	PUNCT
ma-345	26	7	tn+1	tn+1	NOUN
ma-345	26	8	=	=	SYM
ma-345	27	1	2tn	2tn	NOUN
ma-345	27	2	−	−	PROPN
ma-345	27	3	tnf	tnf	PROPN
ma-345	27	4	′(xn+1)tn	′(xn+1)tn	PROPN
ma-345	27	5	,	,	PUNCT
ma-345	27	6	n	n	NOUN
ma-345	27	7	=	=	SYM
ma-345	27	8	0	0	NUM
ma-345	27	9	,	,	PUNCT
ma-345	27	10	1	1	NUM
ma-345	27	11	,	,	PUNCT
ma-345	27	12	2	2	NUM
ma-345	27	13	,	,	PUNCT
ma-345	27	14	.	.	PUNCT
ma-345	27	15	.	.	PUNCT
ma-345	27	16	.	.	PUNCT
ma-345	27	17	.	.	PUNCT
ma-345	28	1	(	(	PUNCT
ma-345	28	2	1.2	1.2	NUM
ma-345	28	3	)	)	PUNCT
ma-345	28	4	here	here	ADV
ma-345	28	5	x0	x0	PROPN
ma-345	28	6	∈	∈	PROPN
ma-345	28	7	ω	ω	PROPN
ma-345	28	8	and	and	CCONJ
ma-345	28	9	t0	t0	PROPN
ma-345	28	10	∈	∈	PROPN
ma-345	28	11	l(e2	l(e2	PROPN
ma-345	28	12	,	,	PUNCT
ma-345	28	13	e1	e1	PROPN
ma-345	28	14	)	)	PUNCT
ma-345	28	15	are	be	AUX
ma-345	28	16	given	give	VERB
ma-345	28	17	initial	initial	ADJ
ma-345	28	18	approximations	approximation	NOUN
ma-345	28	19	for	for	ADP
ma-345	28	20	the	the	DET
ma-345	28	21	solution	solution	NOUN
ma-345	28	22	x∗	x∗	PROPN
ma-345	28	23	and	and	CCONJ
ma-345	28	24	the	the	DET
ma-345	28	25	inverseoperator	inverseoperator	NOUN
ma-345	28	26	f	f	PROPN
ma-345	28	27	′(x∗)−1	′(x∗)−1	PROPN
ma-345	28	28	,	,	PUNCT
ma-345	28	29	respectively	respectively	ADV
ma-345	28	30	.	.	PUNCT
ma-345	29	1	the	the	DET
ma-345	29	2	ulm	ulm	PROPN
ma-345	29	3	method	method	NOUN
ma-345	29	4	(	(	PUNCT
ma-345	29	5	1.2	1.2	NUM
ma-345	29	6	)	)	PUNCT
ma-345	29	7	was	be	AUX
ma-345	29	8	studied	study	VERB
ma-345	29	9	under	under	ADP
ma-345	29	10	conditions	condition	NOUN
ma-345	29	11	of	of	ADP
ma-345	29	12	differenttypes	differenttype	NOUN
ma-345	29	13	and	and	CCONJ
ma-345	29	14	it	it	PRON
ma-345	29	15	was	be	AUX
ma-345	29	16	shown	show	VERB
ma-345	29	17	that	that	SCONJ
ma-345	29	18	it	it	PRON
ma-345	29	19	converges	converge	VERB
ma-345	29	20	with	with	ADP
ma-345	29	21	second	second	ADJ
ma-345	29	22	order	order	NOUN
ma-345	30	1	[	[	X
ma-345	30	2	2	2	NUM
ma-345	30	3	,	,	PUNCT
ma-345	30	4	3	3	NUM
ma-345	30	5	,	,	PUNCT
ma-345	30	6	10	10	NUM
ma-345	30	7	,	,	PUNCT
ma-345	30	8	12	12	NUM
ma-345	30	9	,	,	PUNCT
ma-345	30	10	13	13	NUM
ma-345	30	11	,	,	PUNCT
ma-345	30	12	15	15	NUM
ma-345	30	13	,	,	PUNCT
ma-345	30	14	17	17	NUM
ma-345	30	15	]	]	PUNCT
ma-345	30	16	.	.	PUNCT
ma-345	31	1	similar	similar	ADJ
ma-345	31	2	methodwas	methodwas	NOUN
ma-345	31	3	prosed	prose	VERB
ma-345	31	4	by	by	ADP
ma-345	31	5	moser	moser	PROPN
ma-345	32	1	[	[	X
ma-345	32	2	13,14	13,14	NUM
ma-345	32	3	]	]	X
ma-345	32	4	xn+1	xn+1	PROPN
ma-345	33	1	=	=	SYM
ma-345	33	2	xn	xn	PROPN
ma-345	34	1	−	−	PROPN
ma-345	34	2	tnf	tnf	PROPN
ma-345	34	3	(	(	PUNCT
ma-345	34	4	xn	xn	PROPN
ma-345	34	5	)	)	PUNCT
ma-345	34	6	,	,	PUNCT
ma-345	34	7	tn+1	tn+1	NOUN
ma-345	34	8	=	=	SYM
ma-345	34	9	2tn	2tn	NOUN
ma-345	34	10	−	−	PROPN
ma-345	34	11	tnf	tnf	PROPN
ma-345	34	12	′(xn)tn	′(xn)tn	PROPN
ma-345	34	13	,	,	PUNCT
ma-345	34	14	n	n	NOUN
ma-345	34	15	=	=	SYM
ma-345	34	16	0	0	NUM
ma-345	34	17	,	,	PUNCT
ma-345	34	18	1	1	NUM
ma-345	34	19	,	,	PUNCT
ma-345	34	20	2	2	NUM
ma-345	34	21	,	,	PUNCT
ma-345	34	22	.	.	PUNCT
ma-345	34	23	.	.	PUNCT
ma-345	34	24	.	.	PUNCT
ma-345	34	25	.	.	PUNCT
ma-345	35	1	(	(	PUNCT
ma-345	35	2	1.3	1.3	NUM
ma-345	35	3	)	)	PUNCT
ma-345	35	4	in	in	ADP
ma-345	35	5	(	(	PUNCT
ma-345	35	6	1.3	1.3	NUM
ma-345	35	7	)	)	PUNCT
ma-345	35	8	f	f	PROPN
ma-345	35	9	′(xn	′(xn	PROPN
ma-345	35	10	)	)	PUNCT
ma-345	35	11	appears	appear	VERB
ma-345	35	12	instead	instead	ADV
ma-345	35	13	of	of	ADP
ma-345	35	14	f	f	PROPN
ma-345	35	15	′(xn+1	′(xn+1	PROPN
ma-345	35	16	)	)	PUNCT
ma-345	35	17	in	in	ADP
ma-345	35	18	(	(	PUNCT
ma-345	35	19	1.2	1.2	NUM
ma-345	35	20	)	)	PUNCT
ma-345	35	21	.	.	PUNCT
ma-345	36	1	the	the	DET
ma-345	36	2	convergence	convergence	NOUN
ma-345	36	3	order	order	NOUN
ma-345	36	4	for	for	ADP
ma-345	36	5	(	(	PUNCT
ma-345	36	6	1.3	1.3	NUM
ma-345	36	7	)	)	PUNCT
ma-345	36	8	is	be	AUX
ma-345	36	9	equal	equal	ADJ
ma-345	36	10	to	to	ADP
ma-345	36	11	1	1	NUM
ma-345	36	12	+	+	CCONJ
ma-345	36	13	√	√	NUM
ma-345	36	14	5	5	NUM
ma-345	36	15	2	2	NUM
ma-345	36	16	.	.	PUNCT
ma-345	37	1	the	the	DET
ma-345	37	2	methods	method	NOUN
ma-345	37	3	with	with	ADP
ma-345	37	4	approximation	approximation	NOUN
ma-345	37	5	of	of	ADP
ma-345	37	6	the	the	DET
ma-345	37	7	inverse	inverse	NOUN
ma-345	37	8	operator	operator	NOUN
ma-345	37	9	with	with	ADP
ma-345	37	10	higher	high	ADJ
ma-345	37	11	convergence	convergence	NOUN
ma-345	37	12	order	order	NOUN
ma-345	37	13	werestudied	werestudie	VERB
ma-345	37	14	in	in	ADP
ma-345	37	15	[	[	X
ma-345	37	16	6	6	NUM
ma-345	37	17	,	,	PUNCT
ma-345	37	18	9].in	9].in	NUM
ma-345	37	19	this	this	DET
ma-345	37	20	paper	paper	NOUN
ma-345	37	21	we	we	PRON
ma-345	37	22	propose	propose	VERB
ma-345	37	23	the	the	DET
ma-345	37	24	three	three	NUM
ma-345	37	25	step	step	NOUN
ma-345	37	26	kurchatov	kurchatov	ADJ
ma-345	37	27	-	-	PUNCT
ma-345	37	28	like	like	ADJ
ma-345	37	29	method	method	NOUN
ma-345	37	30	(	(	PUNCT
ma-345	37	31	tsklm	tsklm	PROPN
ma-345	37	32	)	)	PUNCT
ma-345	37	33	.	.	PUNCT
ma-345	38	1	this	this	DET
ma-345	38	2	method	method	NOUN
ma-345	38	3	is	be	AUX
ma-345	38	4	definedfor	definedfor	ADP
ma-345	38	5	t0	t0	PROPN
ma-345	38	6	∈	∈	PROPN
ma-345	38	7	l(e2	l(e2	PROPN
ma-345	38	8	,	,	PUNCT
ma-345	38	9	e1	e1	PROPN
ma-345	38	10	)	)	PUNCT
ma-345	38	11	and	and	CCONJ
ma-345	38	12	each	each	DET
ma-345	38	13	n	n	NOUN
ma-345	38	14	=	=	SYM
ma-345	38	15	0	0	NUM
ma-345	38	16	,	,	PUNCT
ma-345	38	17	1	1	NUM
ma-345	38	18	,	,	PUNCT
ma-345	38	19	2	2	NUM
ma-345	38	20	,	,	PUNCT
ma-345	38	21	.	.	PUNCT
ma-345	38	22	.	.	PUNCT
ma-345	38	23	.	.	PUNCT
ma-345	39	1	by	by	ADP
ma-345	39	2	yn	yn	PROPN
ma-345	39	3	=	=	PUNCT
ma-345	39	4	xn	xn	PROPN
ma-345	40	1	−	−	PROPN
ma-345	40	2	tnf	tnf	PROPN
ma-345	40	3	(	(	PUNCT
ma-345	40	4	xn	xn	PROPN
ma-345	40	5	)	)	PUNCT
ma-345	40	6	,	,	PUNCT
ma-345	40	7	zn	zn	PROPN
ma-345	40	8	=	=	SYM
ma-345	40	9	yn	yn	PROPN
ma-345	40	10	−	−	PROPN
ma-345	40	11	tnf	tnf	PROPN
ma-345	40	12	(	(	PUNCT
ma-345	40	13	yn	yn	PROPN
ma-345	40	14	)	)	PUNCT
ma-345	40	15	,	,	PUNCT
ma-345	40	16	xn+1	xn+1	PROPN
ma-345	40	17	=	=	SYM
ma-345	40	18	zn	zn	PROPN
ma-345	40	19	−	−	PROPN
ma-345	41	1	tnf	tnf	PROPN
ma-345	42	1	(	(	PUNCT
ma-345	43	1	zn	zn	PROPN
ma-345	43	2	)	)	PUNCT
ma-345	43	3	,	,	PUNCT
ma-345	44	1	kn+1	kn+1	PROPN
ma-345	44	2	=	=	PUNCT
ma-345	45	1	[	[	X
ma-345	45	2	2yn	2yn	ADJ
ma-345	45	3	−	−	PROPN
ma-345	45	4	xn	xn	PROPN
ma-345	45	5	,	,	PUNCT
ma-345	45	6	xn;f	xn;f	PUNCT
ma-345	46	1	]	]	PUNCT
ma-345	46	2	,	,	PUNCT
ma-345	46	3	mn	mn	PROPN
ma-345	46	4	=	=	PUNCT
ma-345	46	5	2tn	2tn	NOUN
ma-345	46	6	−	−	PROPN
ma-345	47	1	tnkn+1tn	tnkn+1tn	PROPN
ma-345	47	2	,	,	PUNCT
ma-345	47	3	tn+1	tn+1	PROPN
ma-345	47	4	=	=	SYM
ma-345	47	5	mn	mn	PROPN
ma-345	47	6	+	+	NOUN
ma-345	47	7	mn(2i	mn(2i	NUM
ma-345	47	8	−kn+1mn)(i	−kn+1mn)(i	PROPN
ma-345	47	9	−kn+1mn	−kn+1mn	PROPN
ma-345	47	10	)	)	PUNCT
ma-345	47	11	,	,	PUNCT
ma-345	47	12	(	(	PUNCT
ma-345	47	13	1.4	1.4	NUM
ma-345	47	14	)	)	PUNCT
ma-345	48	1	where	where	SCONJ
ma-345	48	2	[	[	X
ma-345	48	3	·	·	PUNCT
ma-345	48	4	,	,	PUNCT
ma-345	48	5	·	·	PUNCT
ma-345	48	6	;	;	PUNCT
ma-345	48	7	f	f	X
ma-345	48	8	]	]	X
ma-345	48	9	:	:	PUNCT
ma-345	48	10	ω	ω	NUM
ma-345	48	11	×	×	PROPN
ma-345	48	12	ω	ω	PROPN
ma-345	48	13	→	→	SYM
ma-345	48	14	e2	e2	PROPN
ma-345	48	15	is	be	AUX
ma-345	48	16	a	a	DET
ma-345	48	17	divided	divided	ADJ
ma-345	48	18	difference	difference	NOUN
ma-345	48	19	of	of	ADP
ma-345	48	20	order	order	NOUN
ma-345	48	21	one	one	NUM
ma-345	48	22	[	[	X
ma-345	48	23	1	1	NUM
ma-345	48	24	,	,	PUNCT
ma-345	48	25	7	7	NUM
ma-345	48	26	]	]	PUNCT
ma-345	48	27	and	and	CCONJ
ma-345	48	28	l(e2	l(e2	NOUN
ma-345	48	29	,	,	PUNCT
ma-345	48	30	e1	e1	PROPN
ma-345	48	31	)	)	PUNCT
ma-345	48	32	is	be	AUX
ma-345	48	33	the	the	DET
ma-345	48	34	spaceof	spaceof	PROPN
ma-345	48	35	linear	linear	PROPN
ma-345	48	36	operators	operator	NOUN
ma-345	48	37	mapping	mapping	PROPN
ma-345	48	38	e2	e2	PROPN
ma-345	48	39	into	into	ADP
ma-345	48	40	e1	e1	PROPN
ma-345	48	41	,	,	PUNCT
ma-345	48	42	x0	x0	PROPN
ma-345	48	43	∈	∈	PROPN
ma-345	48	44	ω	ω	PROPN
ma-345	48	45	.	.	PUNCT
ma-345	49	1	definition	definition	NOUN
ma-345	49	2	1.1	1.1	NUM
ma-345	49	3	.	.	PUNCT
ma-345	50	1	[	[	X
ma-345	50	2	1	1	NUM
ma-345	50	3	,	,	PUNCT
ma-345	50	4	7	7	NUM
ma-345	50	5	]	]	PUNCT
ma-345	50	6	let	let	VERB
ma-345	50	7	f	f	PRON
ma-345	50	8	be	be	AUX
ma-345	50	9	a	a	DET
ma-345	50	10	nonlinear	nonlinear	ADJ
ma-345	50	11	operator	operator	NOUN
ma-345	50	12	defined	define	VERB
ma-345	50	13	on	on	ADP
ma-345	50	14	a	a	DET
ma-345	50	15	subset	subset	NOUN
ma-345	50	16	ω	ω	NOUN
ma-345	50	17	of	of	ADP
ma-345	50	18	a	a	DET
ma-345	50	19	banach	banach	NOUN
ma-345	50	20	space	space	NOUN
ma-345	50	21	e1	e1	NOUN
ma-345	50	22	with	with	ADP
ma-345	50	23	values	value	NOUN
ma-345	50	24	in	in	ADP
ma-345	50	25	a	a	DET
ma-345	50	26	banach	banach	NOUN
ma-345	50	27	space	space	NOUN
ma-345	50	28	e2	e2	NOUN
ma-345	50	29	,	,	PUNCT
ma-345	50	30	and	and	CCONJ
ma-345	50	31	let	let	VERB
ma-345	50	32	x	x	PRON
ma-345	50	33	,	,	PUNCT
ma-345	50	34	y	y	PROPN
ma-345	50	35	,	,	PUNCT
ma-345	50	36	be	be	AUX
ma-345	50	37	two	two	NUM
ma-345	50	38	different	different	ADJ
ma-345	50	39	points	point	NOUN
ma-345	50	40	of	of	ADP
ma-345	50	41	ω	ω	PROPN
ma-345	50	42	.	.	PUNCT
ma-345	51	1	a	a	DET
ma-345	51	2	linear	linear	ADJ
ma-345	51	3	operator	operator	NOUN
ma-345	51	4	from	from	ADP
ma-345	51	5	e1	e1	PROPN
ma-345	51	6	to	to	ADP
ma-345	51	7	e2	e2	PROPN
ma-345	51	8	which	which	PRON
ma-345	51	9	is	be	AUX
ma-345	51	10	denoted	denote	VERB
ma-345	51	11	by	by	ADP
ma-345	51	12	[	[	X
ma-345	51	13	x	x	X
ma-345	51	14	,	,	PUNCT
ma-345	51	15	y	y	PROPN
ma-345	51	16	;	;	PUNCT
ma-345	51	17	f	f	X
ma-345	51	18	]	]	PUNCT
ma-345	51	19	and	and	CCONJ
ma-345	51	20	satisfies	satisfy	VERB
ma-345	51	21	the	the	DET
ma-345	51	22	following	follow	VERB
ma-345	51	23	conditions	condition	NOUN
ma-345	51	24	[	[	X
ma-345	51	25	x	x	X
ma-345	51	26	,	,	PUNCT
ma-345	51	27	y	y	PROPN
ma-345	51	28	;	;	PUNCT
ma-345	51	29	f	f	X
ma-345	51	30	]	]	X
ma-345	51	31	(	(	PUNCT
ma-345	51	32	x	x	SYM
ma-345	51	33	−	−	PROPN
ma-345	51	34	y	y	NOUN
ma-345	51	35	)	)	PUNCT
ma-345	52	1	=	=	SYM
ma-345	52	2	f	f	PROPN
ma-345	52	3	(	(	PUNCT
ma-345	52	4	x)−	x)−	PROPN
ma-345	52	5	f	f	PROPN
ma-345	52	6	(	(	PUNCT
ma-345	52	7	y	y	NOUN
ma-345	52	8	)	)	PUNCT
ma-345	52	9	is	be	AUX
ma-345	52	10	called	call	VERB
ma-345	52	11	a	a	DET
ma-345	52	12	first	first	ADJ
ma-345	52	13	-	-	PUNCT
ma-345	52	14	order	order	NOUN
ma-345	52	15	divided	divide	VERB
ma-345	52	16	difference	difference	NOUN
ma-345	52	17	of	of	ADP
ma-345	52	18	f	f	PROPN
ma-345	52	19	at	at	ADP
ma-345	52	20	the	the	DET
ma-345	52	21	points	point	NOUN
ma-345	52	22	x	x	PUNCT
ma-345	52	23	and	and	CCONJ
ma-345	52	24	y	y	PROPN
ma-345	52	25	.	.	PUNCT
ma-345	53	1	if	if	SCONJ
ma-345	53	2	there	there	PRON
ma-345	53	3	exists	exist	VERB
ma-345	53	4	a	a	DET
ma-345	53	5	fréchet	fréchet	ADJ
ma-345	53	6	derivative	derivative	ADJ
ma-345	53	7	f	f	PROPN
ma-345	53	8	′(x	′(x	PROPN
ma-345	53	9	)	)	PUNCT
ma-345	53	10	,	,	PUNCT
ma-345	53	11	then	then	ADV
ma-345	53	12	[	[	X
ma-345	53	13	x	x	X
ma-345	53	14	,	,	PUNCT
ma-345	53	15	x	x	X
ma-345	53	16	;	;	PUNCT
ma-345	53	17	f	f	X
ma-345	53	18	]	]	PUNCT
ma-345	54	1	=	=	PUNCT
ma-345	54	2	f	f	PROPN
ma-345	54	3	′(x	′(x	NOUN
ma-345	54	4	)	)	PUNCT
ma-345	54	5	.	.	PUNCT
ma-345	55	1	notice	notice	VERB
ma-345	55	2	that	that	SCONJ
ma-345	55	3	there	there	PRON
ma-345	55	4	are	be	VERB
ma-345	55	5	other	other	ADJ
ma-345	55	6	selection	selection	NOUN
ma-345	55	7	for	for	ADP
ma-345	55	8	the	the	DET
ma-345	55	9	kurchatov	kurchatov	ADJ
ma-345	55	10	operator	operator	NOUN
ma-345	55	11	kn+1	kn+1	PROPN
ma-345	55	12	such	such	ADJ
ma-345	55	13	as	as	ADP
ma-345	55	14	kn+1	kn+1	PROPN
ma-345	55	15	=	=	PROPN
ma-345	56	1	[	[	X
ma-345	56	2	2xn+1−	2xn+1−	PROPN
ma-345	56	3	zn	zn	NUM
ma-345	56	4	,	,	PUNCT
ma-345	56	5	zn;f	zn;f	PUNCT
ma-345	56	6	]	]	PUNCT
ma-345	56	7	or	or	CCONJ
ma-345	56	8	kn+1	kn+1	PROPN
ma-345	56	9	=	=	PUNCT
ma-345	57	1	[	[	X
ma-345	57	2	2xn+1	2xn+1	NUM
ma-345	57	3	−	−	NOUN
ma-345	57	4	xn	xn	PROPN
ma-345	57	5	,	,	PUNCT
ma-345	57	6	xn;f	xn;f	PUNCT
ma-345	57	7	]	]	PUNCT
ma-345	57	8	or	or	CCONJ
ma-345	57	9	kn+1	kn+1	PROPN
ma-345	57	10	=	=	SYM
ma-345	57	11	f	f	PROPN
ma-345	57	12	′(xn+1	′(xn+1	PROPN
ma-345	57	13	)	)	PUNCT
ma-345	57	14	or	or	CCONJ
ma-345	57	15	kn+1	kn+1	PROPN
ma-345	57	16	=	=	PROPN
ma-345	57	17	l(xn+1	l(xn+1	PROPN
ma-345	57	18	)	)	PUNCT
ma-345	57	19	,	,	PUNCT
ma-345	57	20	where	where	SCONJ
ma-345	57	21	l(xn+1	l(xn+1	X
ma-345	57	22	)	)	PUNCT
ma-345	57	23	is	be	AUX
ma-345	57	24	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
ma-345	57	25	eur	eur	PROPN
ma-345	57	26	.	.	PUNCT
ma-345	58	1	j.	j.	PROPN
ma-345	58	2	math	math	PROPN
ma-345	58	3	.	.	PUNCT
ma-345	59	1	anal	anal	PROPN
ma-345	59	2	.	.	PUNCT
ma-345	60	1	10.28924	10.28924	NUM
ma-345	60	2	/	/	SYM
ma-345	60	3	ada	ada	PROPN
ma-345	60	4	/	/	SYM
ma-345	60	5	ma.5.15	ma.5.15	PROPN
ma-345	60	6	3an	3an	ADJ
ma-345	60	7	approximation	approximation	NOUN
ma-345	60	8	to	to	ADP
ma-345	60	9	f	f	PROPN
ma-345	60	10	′(xn+1	′(xn+1	PROPN
ma-345	60	11	)	)	PUNCT
ma-345	60	12	,	,	PUNCT
ma-345	60	13	or	or	CCONJ
ma-345	60	14	other	other	ADJ
ma-345	60	15	options	option	NOUN
ma-345	61	1	[	[	X
ma-345	61	2	1,4,5,8,16	1,4,5,8,16	NUM
ma-345	61	3	]	]	PUNCT
ma-345	61	4	.	.	PUNCT
ma-345	62	1	denote	denote	VERB
ma-345	62	2	the	the	DET
ma-345	62	3	corresponding	corresponding	ADJ
ma-345	62	4	methods	method	NOUN
ma-345	62	5	by	by	ADP
ma-345	62	6	yn	yn	PROPN
ma-345	63	1	=	=	PUNCT
ma-345	63	2	xn	xn	PROPN
ma-345	63	3	−	−	PROPN
ma-345	63	4	tnf	tnf	PROPN
ma-345	63	5	(	(	PUNCT
ma-345	63	6	xn	xn	PROPN
ma-345	63	7	)	)	PUNCT
ma-345	63	8	,	,	PUNCT
ma-345	63	9	zn	zn	PROPN
ma-345	63	10	=	=	SYM
ma-345	63	11	yn	yn	PROPN
ma-345	63	12	−	−	PROPN
ma-345	63	13	tnf	tnf	PROPN
ma-345	63	14	(	(	PUNCT
ma-345	63	15	yn	yn	PROPN
ma-345	63	16	)	)	PUNCT
ma-345	63	17	,	,	PUNCT
ma-345	63	18	xn+1	xn+1	PROPN
ma-345	63	19	=	=	SYM
ma-345	63	20	zn	zn	PROPN
ma-345	63	21	−	−	PROPN
ma-345	64	1	tnf	tnf	PROPN
ma-345	65	1	(	(	PUNCT
ma-345	66	1	zn	zn	PROPN
ma-345	66	2	)	)	PUNCT
ma-345	66	3	,	,	PUNCT
ma-345	66	4	kn+1	kn+1	PROPN
ma-345	66	5	=	=	PUNCT
ma-345	67	1	[	[	X
ma-345	67	2	2xn+1	2xn+1	NUM
ma-345	67	3	−	−	NOUN
ma-345	67	4	zn	zn	NOUN
ma-345	67	5	,	,	PUNCT
ma-345	67	6	zn;f	zn;f	NUM
ma-345	67	7	]	]	X
ma-345	67	8	,	,	PUNCT
ma-345	67	9	mn	mn	PROPN
ma-345	67	10	=	=	PUNCT
ma-345	67	11	2tn	2tn	NOUN
ma-345	67	12	−	−	PROPN
ma-345	68	1	tnkn+1tn	tnkn+1tn	PROPN
ma-345	68	2	,	,	PUNCT
ma-345	68	3	tn+1	tn+1	PROPN
ma-345	68	4	=	=	SYM
ma-345	68	5	mn	mn	PROPN
ma-345	68	6	+	+	NOUN
ma-345	68	7	mn(2i	mn(2i	NUM
ma-345	68	8	−kn+1mn)(i	−kn+1mn)(i	PROPN
ma-345	68	9	−kn+1mn	−kn+1mn	PROPN
ma-345	68	10	)	)	PUNCT
ma-345	68	11	,	,	PUNCT
ma-345	68	12	(	(	PUNCT
ma-345	68	13	1.5	1.5	NUM
ma-345	68	14	)	)	PUNCT
ma-345	68	15	yn	yn	PROPN
ma-345	68	16	=	=	PUNCT
ma-345	68	17	xn	xn	PROPN
ma-345	69	1	−	−	PROPN
ma-345	69	2	tnf	tnf	PROPN
ma-345	69	3	(	(	PUNCT
ma-345	69	4	xn	xn	PROPN
ma-345	69	5	)	)	PUNCT
ma-345	69	6	,	,	PUNCT
ma-345	69	7	zn	zn	PROPN
ma-345	69	8	=	=	SYM
ma-345	69	9	yn	yn	PROPN
ma-345	69	10	−	−	PROPN
ma-345	69	11	tnf	tnf	PROPN
ma-345	69	12	(	(	PUNCT
ma-345	69	13	yn	yn	PROPN
ma-345	69	14	)	)	PUNCT
ma-345	69	15	,	,	PUNCT
ma-345	69	16	xn+1	xn+1	PROPN
ma-345	69	17	=	=	SYM
ma-345	69	18	zn	zn	PROPN
ma-345	69	19	−	−	PROPN
ma-345	70	1	tnf	tnf	PROPN
ma-345	71	1	(	(	PUNCT
ma-345	72	1	zn	zn	PROPN
ma-345	72	2	)	)	PUNCT
ma-345	72	3	,	,	PUNCT
ma-345	72	4	kn+1	kn+1	PROPN
ma-345	72	5	=	=	PUNCT
ma-345	73	1	[	[	X
ma-345	73	2	2xn+1	2xn+1	NUM
ma-345	73	3	−	−	NOUN
ma-345	73	4	xn	xn	PROPN
ma-345	73	5	,	,	PUNCT
ma-345	73	6	xn;f	xn;f	PUNCT
ma-345	74	1	]	]	PUNCT
ma-345	74	2	,	,	PUNCT
ma-345	74	3	mn	mn	PROPN
ma-345	74	4	=	=	PUNCT
ma-345	74	5	2tn	2tn	NOUN
ma-345	74	6	−	−	PROPN
ma-345	75	1	tnkn+1tn	tnkn+1tn	PROPN
ma-345	75	2	,	,	PUNCT
ma-345	75	3	tn+1	tn+1	PROPN
ma-345	75	4	=	=	SYM
ma-345	75	5	mn	mn	PROPN
ma-345	75	6	+	+	NOUN
ma-345	75	7	mn(2i	mn(2i	NUM
ma-345	75	8	−kn+1mn)(i	−kn+1mn)(i	PROPN
ma-345	75	9	−kn+1mn	−kn+1mn	PROPN
ma-345	75	10	)	)	PUNCT
ma-345	75	11	,	,	PUNCT
ma-345	75	12	(	(	PUNCT
ma-345	75	13	1.6	1.6	NUM
ma-345	75	14	)	)	PUNCT
ma-345	75	15	yn	yn	NOUN
ma-345	76	1	=	=	PUNCT
ma-345	76	2	xn	xn	PROPN
ma-345	77	1	−	−	PROPN
ma-345	77	2	tnf	tnf	PROPN
ma-345	77	3	(	(	PUNCT
ma-345	77	4	xn	xn	PROPN
ma-345	77	5	)	)	PUNCT
ma-345	77	6	,	,	PUNCT
ma-345	77	7	zn	zn	PROPN
ma-345	77	8	=	=	SYM
ma-345	77	9	yn	yn	PROPN
ma-345	77	10	−	−	PROPN
ma-345	77	11	tnf	tnf	PROPN
ma-345	77	12	(	(	PUNCT
ma-345	77	13	yn	yn	PROPN
ma-345	77	14	)	)	PUNCT
ma-345	77	15	,	,	PUNCT
ma-345	77	16	xn+1	xn+1	PROPN
ma-345	77	17	=	=	SYM
ma-345	77	18	zn	zn	PROPN
ma-345	77	19	−	−	PROPN
ma-345	78	1	tnf	tnf	PROPN
ma-345	79	1	(	(	PUNCT
ma-345	80	1	zn	zn	PROPN
ma-345	80	2	)	)	PUNCT
ma-345	80	3	,	,	PUNCT
ma-345	80	4	kn+1	kn+1	PROPN
ma-345	80	5	=	=	PROPN
ma-345	80	6	f	f	PROPN
ma-345	80	7	′(xn+1	′(xn+1	PROPN
ma-345	80	8	)	)	PUNCT
ma-345	80	9	,	,	PUNCT
ma-345	80	10	mn	mn	PROPN
ma-345	81	1	=	=	PUNCT
ma-345	81	2	2tn	2tn	NOUN
ma-345	81	3	−	−	PROPN
ma-345	82	1	tnkn+1tn	tnkn+1tn	PROPN
ma-345	82	2	,	,	PUNCT
ma-345	82	3	tn+1	tn+1	PROPN
ma-345	82	4	=	=	SYM
ma-345	82	5	mn	mn	PROPN
ma-345	82	6	+	+	NOUN
ma-345	82	7	mn(2i	mn(2i	NUM
ma-345	82	8	−kn+1mn)(i	−kn+1mn)(i	PROPN
ma-345	82	9	−kn+1mn	−kn+1mn	PROPN
ma-345	82	10	)	)	PUNCT
ma-345	82	11	,	,	PUNCT
ma-345	82	12	(	(	PUNCT
ma-345	82	13	1.7	1.7	NUM
ma-345	82	14	)	)	PUNCT
ma-345	82	15	yn	yn	PROPN
ma-345	83	1	=	=	PUNCT
ma-345	83	2	xn	xn	PROPN
ma-345	84	1	−	−	PROPN
ma-345	84	2	tnf	tnf	PROPN
ma-345	84	3	(	(	PUNCT
ma-345	84	4	xn	xn	PROPN
ma-345	84	5	)	)	PUNCT
ma-345	84	6	,	,	PUNCT
ma-345	84	7	zn	zn	PROPN
ma-345	84	8	=	=	SYM
ma-345	84	9	yn	yn	PROPN
ma-345	84	10	−	−	PROPN
ma-345	84	11	tnf	tnf	PROPN
ma-345	84	12	(	(	PUNCT
ma-345	84	13	yn	yn	PROPN
ma-345	84	14	)	)	PUNCT
ma-345	84	15	,	,	PUNCT
ma-345	84	16	xn+1	xn+1	PROPN
ma-345	84	17	=	=	SYM
ma-345	84	18	zn	zn	PROPN
ma-345	84	19	−	−	PROPN
ma-345	85	1	tnf	tnf	PROPN
ma-345	86	1	(	(	PUNCT
ma-345	87	1	zn	zn	PROPN
ma-345	87	2	)	)	PUNCT
ma-345	87	3	,	,	PUNCT
ma-345	87	4	kn+1	kn+1	PROPN
ma-345	87	5	=	=	PROPN
ma-345	87	6	l(xn+1	l(xn+1	PROPN
ma-345	87	7	)	)	PUNCT
ma-345	87	8	,	,	PUNCT
ma-345	87	9	mn	mn	PROPN
ma-345	88	1	=	=	PUNCT
ma-345	88	2	2tn	2tn	NOUN
ma-345	88	3	−	−	PROPN
ma-345	89	1	tnkn+1tn	tnkn+1tn	PROPN
ma-345	89	2	,	,	PUNCT
ma-345	89	3	tn+1	tn+1	PROPN
ma-345	89	4	=	=	SYM
ma-345	89	5	mn	mn	PROPN
ma-345	89	6	+	+	NOUN
ma-345	89	7	mn(2i	mn(2i	NUM
ma-345	89	8	−kn+1mn)(i	−kn+1mn)(i	PROPN
ma-345	89	9	−kn+1mn	−kn+1mn	PROPN
ma-345	89	10	)	)	PUNCT
ma-345	89	11	,	,	PUNCT
ma-345	89	12	(	(	PUNCT
ma-345	89	13	1.8	1.8	NUM
ma-345	89	14	)	)	PUNCT
ma-345	89	15	respectively	respectively	ADV
ma-345	89	16	.	.	PUNCT
ma-345	90	1	notice	notice	VERB
ma-345	90	2	that	that	DET
ma-345	90	3	method	method	NOUN
ma-345	90	4	(	(	PUNCT
ma-345	90	5	1.8	1.8	NUM
ma-345	90	6	)	)	PUNCT
ma-345	90	7	specializes	specialize	VERB
ma-345	90	8	to	to	ADP
ma-345	90	9	(	(	PUNCT
ma-345	90	10	1.7	1.7	NUM
ma-345	90	11	)	)	PUNCT
ma-345	90	12	if	if	SCONJ
ma-345	90	13	l	l	NOUN
ma-345	90	14	=	=	PUNCT
ma-345	90	15	f	f	PROPN
ma-345	90	16	′.	′.	NOUN
ma-345	90	17	a	a	DET
ma-345	90	18	possible	possible	ADJ
ma-345	90	19	choice	choice	NOUN
ma-345	90	20	for	for	ADP
ma-345	90	21	l	l	NOUN
ma-345	90	22	ispresented	ispresente	VERB
ma-345	90	23	in	in	ADP
ma-345	90	24	the	the	DET
ma-345	90	25	numerical	numerical	ADJ
ma-345	90	26	section.to	section.to	PROPN
ma-345	90	27	test	test	NOUN
ma-345	90	28	numerically	numerically	ADV
ma-345	90	29	the	the	DET
ma-345	90	30	order	order	NOUN
ma-345	90	31	of	of	ADP
ma-345	90	32	convergence	convergence	NOUN
ma-345	90	33	of	of	ADP
ma-345	90	34	the	the	DET
ma-345	90	35	iterative	iterative	NOUN
ma-345	90	36	methods	method	NOUN
ma-345	90	37	very	very	ADV
ma-345	90	38	often	often	ADV
ma-345	90	39	use	use	VERB
ma-345	90	40	computationalorder	computationalorder	NOUN
ma-345	90	41	of	of	ADP
ma-345	90	42	convergence	convergence	NOUN
ma-345	90	43	(	(	PUNCT
ma-345	90	44	coc	coc	PROPN
ma-345	90	45	)	)	PUNCT
ma-345	90	46	and	and	CCONJ
ma-345	90	47	approximated	approximate	VERB
ma-345	90	48	computational	computational	ADJ
ma-345	90	49	order	order	NOUN
ma-345	90	50	of	of	ADP
ma-345	90	51	convergence	convergence	NOUN
ma-345	90	52	(	(	PUNCT
ma-345	90	53	acoc	acoc	ADJ
ma-345	90	54	)	)	PUNCT
ma-345	91	1	[	[	X
ma-345	91	2	11].coc	11].coc	PROPN
ma-345	91	3	is	be	AUX
ma-345	91	4	denoted	denote	VERB
ma-345	91	5	by	by	ADP
ma-345	91	6	δ2	δ2	PROPN
ma-345	91	7	,	,	PUNCT
ma-345	91	8	acoc	acoc	PROPN
ma-345	91	9	can	can	AUX
ma-345	91	10	be	be	AUX
ma-345	91	11	computed	compute	VERB
ma-345	91	12	by	by	ADP
ma-345	91	13	formulas	formula	NOUN
ma-345	91	14	denoted	denote	VERB
ma-345	91	15	by	by	ADP
ma-345	91	16	δ1	δ1	NOUN
ma-345	91	17	and	and	CCONJ
ma-345	91	18	δ3	δ3	PROPN
ma-345	91	19	:	:	PUNCT
ma-345	91	20	δ1	δ1	NOUN
ma-345	91	21	≈	≈	PROPN
ma-345	91	22	ln	ln	INTJ
ma-345	92	1	(	(	PUNCT
ma-345	92	2	‖xn+1−xn‖	‖xn+1−xn‖	NUM
ma-345	92	3	‖xn−xn−1‖	‖xn−xn−1‖	NOUN
ma-345	92	4	)	)	PUNCT
ma-345	92	5	ln	ln	NOUN
ma-345	92	6	(	(	PUNCT
ma-345	92	7	‖xn−xn−1‖	‖xn−xn−1‖	X
ma-345	92	8	‖xn−1−xn−2‖	‖xn−1−xn−2‖	ADV
ma-345	92	9	)	)	PUNCT
ma-345	92	10	,	,	PUNCT
ma-345	92	11	δ2	δ2	PROPN
ma-345	93	1	≈	≈	PROPN
ma-345	93	2	ln	ln	NOUN
ma-345	93	3	(	(	PUNCT
ma-345	93	4	‖xn+1−x∗‖	‖xn+1−x∗‖	NOUN
ma-345	93	5	‖xn−x∗‖	‖xn−x∗‖	NOUN
ma-345	93	6	)	)	PUNCT
ma-345	93	7	ln	ln	CCONJ
ma-345	93	8	(	(	PUNCT
ma-345	93	9	‖xn−x∗‖	‖xn−x∗‖	ADJ
ma-345	93	10	‖xn−1−x∗‖	‖xn−1−x∗‖	PROPN
ma-345	93	11	)	)	PUNCT
ma-345	93	12	,	,	PUNCT
ma-345	93	13	δ3	δ3	PROPN
ma-345	93	14	≈	≈	PROPN
ma-345	93	15	ln	ln	PROPN
ma-345	93	16	(	(	PUNCT
ma-345	93	17	‖f	‖f	ADJ
ma-345	93	18	(	(	PUNCT
ma-345	93	19	xn+1)‖	xn+1)‖	PROPN
ma-345	93	20	‖f	‖f	PROPN
ma-345	93	21	(	(	PUNCT
ma-345	93	22	xn)‖	xn)‖	PROPN
ma-345	93	23	)	)	PUNCT
ma-345	94	1	ln	ln	INTJ
ma-345	94	2	(	(	PUNCT
ma-345	94	3	‖f	‖f	X
ma-345	94	4	(	(	PUNCT
ma-345	94	5	xn)‖	xn)‖	PROPN
ma-345	94	6	‖f	‖f	PRON
ma-345	94	7	(	(	PUNCT
ma-345	94	8	xn−1)‖	xn−1)‖	PROPN
ma-345	94	9	)	)	PUNCT
ma-345	94	10	.	.	PUNCT
ma-345	95	1	in	in	ADP
ma-345	95	2	this	this	DET
ma-345	95	3	article	article	NOUN
ma-345	95	4	,	,	PUNCT
ma-345	95	5	we	we	PRON
ma-345	95	6	provide	provide	VERB
ma-345	95	7	the	the	DET
ma-345	95	8	local	local	ADJ
ma-345	95	9	convergence	convergence	NOUN
ma-345	95	10	analysis	analysis	NOUN
ma-345	95	11	of	of	ADP
ma-345	95	12	the	the	DET
ma-345	95	13	method	method	NOUN
ma-345	95	14	(	(	PUNCT
ma-345	95	15	1.4	1.4	NUM
ma-345	95	16	)	)	PUNCT
ma-345	95	17	under	under	ADP
ma-345	95	18	assumptionsthat	assumptionsthat	NOUN
ma-345	95	19	fréchet	fréchet	VERB
ma-345	95	20	derivative	derivative	ADJ
ma-345	95	21	and	and	CCONJ
ma-345	95	22	first	first	ADJ
ma-345	95	23	-	-	PUNCT
ma-345	95	24	order	order	NOUN
ma-345	95	25	divided	divide	VERB
ma-345	95	26	differences	difference	NOUN
ma-345	95	27	satisfy	satisfy	VERB
ma-345	95	28	classical	classical	ADJ
ma-345	95	29	lipschitz	lipschitz	NOUN
ma-345	95	30	conditions	condition	NOUN
ma-345	95	31	(	(	PUNCT
ma-345	95	32	seesection	seesection	NOUN
ma-345	95	33	2	2	NUM
ma-345	95	34	)	)	PUNCT
ma-345	95	35	.	.	PUNCT
ma-345	96	1	sections	section	NOUN
ma-345	96	2	3	3	NUM
ma-345	96	3	and	and	CCONJ
ma-345	96	4	4	4	NUM
ma-345	96	5	present	present	ADJ
ma-345	96	6	results	result	NOUN
ma-345	96	7	of	of	ADP
ma-345	96	8	numerical	numerical	ADJ
ma-345	96	9	experiments	experiment	NOUN
ma-345	96	10	and	and	CCONJ
ma-345	96	11	conclusions	conclusion	NOUN
ma-345	96	12	,	,	PUNCT
ma-345	96	13	respectively	respectively	ADV
ma-345	96	14	.	.	PUNCT
ma-345	97	1	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
ma-345	97	2	eur	eur	PROPN
ma-345	97	3	.	.	PUNCT
ma-345	98	1	j.	j.	PROPN
ma-345	98	2	math	math	PROPN
ma-345	98	3	.	.	PUNCT
ma-345	99	1	anal	anal	PROPN
ma-345	99	2	.	.	PUNCT
ma-345	100	1	10.28924	10.28924	NUM
ma-345	100	2	/	/	SYM
ma-345	100	3	ada	ada	PROPN
ma-345	100	4	/	/	SYM
ma-345	100	5	ma.5.15	ma.5.15	PROPN
ma-345	100	6	42	42	NUM
ma-345	100	7	.	.	PUNCT
ma-345	101	1	convergence	convergence	VERB
ma-345	101	2	the	the	DET
ma-345	101	3	local	local	ADJ
ma-345	101	4	analysis	analysis	NOUN
ma-345	101	5	of	of	ADP
ma-345	101	6	convergence	convergence	NOUN
ma-345	101	7	is	be	AUX
ma-345	101	8	very	very	ADV
ma-345	101	9	important	important	ADJ
ma-345	101	10	since	since	SCONJ
ma-345	101	11	it	it	PRON
ma-345	101	12	provides	provide	VERB
ma-345	101	13	the	the	DET
ma-345	101	14	degree	degree	NOUN
ma-345	101	15	of	of	ADP
ma-345	101	16	difficulty	difficulty	NOUN
ma-345	101	17	inselecting	inselecte	VERB
ma-345	101	18	the	the	DET
ma-345	101	19	initial	initial	ADJ
ma-345	101	20	points	point	NOUN
ma-345	101	21	x0	x0	PROPN
ma-345	101	22	from	from	ADP
ma-345	101	23	a	a	DET
ma-345	101	24	ball	ball	NOUN
ma-345	101	25	centered	center	VERB
ma-345	101	26	at	at	ADP
ma-345	101	27	the	the	DET
ma-345	101	28	solution	solution	NOUN
ma-345	101	29	x∗	x∗	PROPN
ma-345	101	30	and	and	CCONJ
ma-345	101	31	of	of	ADP
ma-345	101	32	a	a	DET
ma-345	101	33	certain	certain	ADJ
ma-345	101	34	specifiedradius.the	specifiedradius.the	PRON
ma-345	101	35	symbol	symbol	NOUN
ma-345	101	36	s(x	s(x	PROPN
ma-345	101	37	,	,	PUNCT
ma-345	101	38	r	r	NOUN
ma-345	101	39	)	)	PUNCT
ma-345	101	40	is	be	AUX
ma-345	101	41	denoting	denote	VERB
ma-345	101	42	an	an	DET
ma-345	101	43	open	open	ADJ
ma-345	101	44	ball	ball	NOUN
ma-345	101	45	centered	center	VERB
ma-345	101	46	at	at	ADP
ma-345	101	47	x	x	PROPN
ma-345	101	48	∈	∈	PROPN
ma-345	101	49	e1	e1	PROPN
ma-345	101	50	and	and	CCONJ
ma-345	101	51	of	of	ADP
ma-345	101	52	a	a	DET
ma-345	101	53	radius	radius	NOUN
ma-345	101	54	r	r	NOUN
ma-345	101	55	>	>	X
ma-345	101	56	0.define	0.define	NUM
ma-345	101	57	the	the	DET
ma-345	101	58	parameter	parameter	PROPN
ma-345	101	59	ρ	ρ	PROPN
ma-345	101	60	by	by	ADP
ma-345	101	61	ρ	ρ	PROPN
ma-345	101	62	=	=	SYM
ma-345	101	63	sup{t	sup{t	PROPN
ma-345	101	64	>	>	X
ma-345	101	65	0	0	NUM
ma-345	101	66	:	:	PUNCT
ma-345	101	67	s(x∗	s(x∗	ADV
ma-345	101	68	,	,	PUNCT
ma-345	101	69	t	t	PROPN
ma-345	101	70	)	)	PUNCT
ma-345	101	71	⊂	⊂	PROPN
ma-345	101	72	ω	ω	PROPN
ma-345	101	73	}	}	PUNCT
ma-345	101	74	.	.	PUNCT
ma-345	102	1	let	let	VERB
ma-345	102	2	a	a	DET
ma-345	102	3	>	>	X
ma-345	102	4	0	0	NUM
ma-345	102	5	,	,	PUNCT
ma-345	102	6	b0	b0	VERB
ma-345	102	7	≥	≥	NOUN
ma-345	102	8	0	0	NUM
ma-345	102	9	,	,	PUNCT
ma-345	102	10	b	b	X
ma-345	102	11	>	>	X
ma-345	102	12	0	0	PROPN
ma-345	102	13	,	,	PUNCT
ma-345	102	14	d1	d1	PROPN
ma-345	102	15	>	>	X
ma-345	102	16	0	0	NUM
ma-345	102	17	,	,	PUNCT
ma-345	102	18	d2	d2	PROPN
ma-345	102	19	>	>	X
ma-345	102	20	0	0	PROPN
ma-345	102	21	,	,	PUNCT
ma-345	102	22	λ	λ	X
ma-345	102	23	≥	≥	NOUN
ma-345	102	24	0	0	NUM
ma-345	102	25	and	and	CCONJ
ma-345	102	26	l	l	NOUN
ma-345	102	27	≥	≥	X
ma-345	102	28	0	0	NUM
ma-345	102	29	be	be	AUX
ma-345	102	30	given	give	VERB
ma-345	102	31	parameters	parameter	NOUN
ma-345	102	32	.	.	PUNCT
ma-345	103	1	it	it	PRON
ma-345	103	2	is	be	AUX
ma-345	103	3	convenient	convenient	ADJ
ma-345	103	4	todefine	todefine	NOUN
ma-345	103	5	the	the	DET
ma-345	103	6	parameters	parameter	NOUN
ma-345	103	7	q	q	NOUN
ma-345	103	8	=	=	SYM
ma-345	103	9	b	b	PROPN
ma-345	103	10	a	a	PRON
ma-345	103	11	,	,	PUNCT
ma-345	103	12	ρ0	ρ0	PROPN
ma-345	103	13	=	=	SYM
ma-345	103	14	min	min	PROPN
ma-345	103	15	{	{	PUNCT
ma-345	103	16	1	1	NUM
ma-345	103	17	,	,	PUNCT
ma-345	103	18	ρ	ρ	PROPN
ma-345	103	19	,	,	PUNCT
ma-345	103	20	1	1	NUM
ma-345	103	21	4lb(l	4lb(l	PROPN
ma-345	103	22	+	+	NUM
ma-345	103	23	d1)d2	d1)d2	NOUN
ma-345	103	24	}	}	PUNCT
ma-345	103	25	,	,	PUNCT
ma-345	103	26	ρ̄	ρ̄	NOUN
ma-345	103	27	∈	∈	PROPN
ma-345	103	28	(	(	PUNCT
ma-345	103	29	0	0	NUM
ma-345	103	30	,	,	PUNCT
ma-345	103	31	ρ0	ρ0	PROPN
ma-345	103	32	)	)	PUNCT
ma-345	103	33	,	,	PUNCT
ma-345	103	34	c1	c1	PROPN
ma-345	103	35	=	=	PROPN
ma-345	103	36	4lb(l	4lb(l	PROPN
ma-345	104	1	+	+	CCONJ
ma-345	104	2	d1	d1	PROPN
ma-345	104	3	)	)	PUNCT
ma-345	104	4	,	,	PUNCT
ma-345	104	5	c2	c2	PROPN
ma-345	104	6	=	=	PUNCT
ma-345	104	7	1	1	NUM
ma-345	104	8	+	+	CCONJ
ma-345	104	9	2bc1	2bc1	NUM
ma-345	104	10	,	,	PUNCT
ma-345	104	11	c3	c3	PROPN
ma-345	104	12	=	=	PROPN
ma-345	104	13	c2	c2	PROPN
ma-345	104	14	+	+	CCONJ
ma-345	104	15	2	2	NUM
ma-345	104	16	lb	lb	NOUN
ma-345	104	17	,	,	PUNCT
ma-345	104	18	(	(	PUNCT
ma-345	104	19	2.1	2.1	NUM
ma-345	104	20	)	)	PUNCT
ma-345	104	21	c4	c4	NOUN
ma-345	104	22	=	=	SYM
ma-345	104	23	c2	c2	PROPN
ma-345	104	24	+	+	CCONJ
ma-345	104	25	4lb(1	4lb(1	PROPN
ma-345	104	26	+	+	PROPN
ma-345	104	27	c3	c3	PROPN
ma-345	104	28	)	)	PUNCT
ma-345	104	29	,	,	PUNCT
ma-345	104	30	c5	c5	PROPN
ma-345	104	31	=	=	PROPN
ma-345	104	32	c4	c4	PROPN
ma-345	104	33	+	+	CCONJ
ma-345	104	34	4lb(1	4lb(1	PROPN
ma-345	104	35	+	+	CCONJ
ma-345	104	36	c3	c3	PROPN
ma-345	104	37	)	)	PUNCT
ma-345	104	38	,	,	PUNCT
ma-345	104	39	c6	c6	PROPN
ma-345	104	40	=	=	PUNCT
ma-345	105	1	1	1	NUM
ma-345	105	2	+	+	NUM
ma-345	105	3	4bc1	4bc1	NUM
ma-345	105	4	+	+	CCONJ
ma-345	105	5	8	8	NUM
ma-345	105	6	lb	lb	NOUN
ma-345	105	7	,	,	PUNCT
ma-345	105	8	b0	b0	NOUN
ma-345	105	9	=	=	SYM
ma-345	105	10	d2	d2	PROPN
ma-345	105	11	1−	1−	PROPN
ma-345	105	12	c1d2ρ̄	c1d2ρ̄	PROPN
ma-345	105	13	f	f	PROPN
ma-345	105	14	or	or	CCONJ
ma-345	105	15	ρ̄	ρ̄	NOUN
ma-345	105	16	∈	∈	PROPN
ma-345	105	17	(	(	PUNCT
ma-345	105	18	0	0	NUM
ma-345	105	19	,	,	PUNCT
ma-345	105	20	ρ0	ρ0	PROPN
ma-345	105	21	)	)	PUNCT
ma-345	105	22	,	,	PUNCT
ma-345	105	23	a	a	DET
ma-345	105	24	=	=	NOUN
ma-345	105	25	min	min	NOUN
ma-345	105	26	{	{	PUNCT
ma-345	105	27	1	1	NUM
ma-345	105	28	,	,	PUNCT
ma-345	105	29	1	1	NUM
ma-345	105	30	c3c4	c3c4	PROPN
ma-345	105	31	+	+	PROPN
ma-345	105	32	2lbc23	2lbc23	PROPN
ma-345	105	33	,	,	PUNCT
ma-345	105	34	1	1	NUM
ma-345	105	35	c5	c5	PROPN
ma-345	105	36	+	+	CCONJ
ma-345	105	37	2	2	NUM
ma-345	105	38	lb	lb	NOUN
ma-345	105	39	,	,	PUNCT
ma-345	105	40	1	1	NUM
ma-345	105	41	c66	c66	NOUN
ma-345	105	42	}	}	PUNCT
ma-345	105	43	,	,	PUNCT
ma-345	105	44	and	and	CCONJ
ma-345	105	45	b	b	X
ma-345	105	46	=	=	SYM
ma-345	105	47	min{ρ̄	min{ρ̄	NOUN
ma-345	105	48	,	,	PUNCT
ma-345	105	49	a	a	PRON
ma-345	105	50	}	}	PUNCT
ma-345	105	51	.	.	PUNCT
ma-345	106	1	let	let	VERB
ma-345	106	2	x∗	x∗	PROPN
ma-345	106	3	∈	∈	PROPN
ma-345	106	4	ω	ω	NOUN
ma-345	106	5	be	be	AUX
ma-345	106	6	a	a	DET
ma-345	106	7	solution	solution	NOUN
ma-345	106	8	of	of	ADP
ma-345	106	9	the	the	DET
ma-345	106	10	equation	equation	NOUN
ma-345	107	1	f	f	X
ma-345	107	2	(	(	PUNCT
ma-345	107	3	x	x	X
ma-345	107	4	)	)	PUNCT
ma-345	107	5	=	=	SYM
ma-345	108	1	0	0	X
ma-345	108	2	.	.	PUNCT
ma-345	109	1	we	we	PRON
ma-345	109	2	assume	assume	VERB
ma-345	109	3	from	from	ADP
ma-345	109	4	now	now	ADV
ma-345	109	5	on	on	ADP
ma-345	109	6	that	that	PRON
ma-345	109	7	for	for	ADP
ma-345	109	8	each	each	DET
ma-345	109	9	u1	u1	NOUN
ma-345	109	10	,	,	PUNCT
ma-345	109	11	u2	u2	NOUN
ma-345	109	12	,	,	PUNCT
ma-345	109	13	v1	v1	NOUN
ma-345	109	14	,	,	PUNCT
ma-345	109	15	v2	v2	PROPN
ma-345	109	16	∈	∈	PROPN
ma-345	109	17	s(x∗	s(x∗	ADV
ma-345	109	18	,	,	PUNCT
ma-345	109	19	ρ	ρ	PROPN
ma-345	109	20	)	)	PUNCT
ma-345	109	21	there	there	PRON
ma-345	109	22	exists	exist	VERB
ma-345	109	23	l	l	NOUN
ma-345	109	24	>	>	X
ma-345	109	25	0	0	NUM
ma-345	110	1	such	such	ADJ
ma-345	110	2	that	that	DET
ma-345	110	3	‖[u2	‖[u2	NOUN
ma-345	110	4	,	,	PUNCT
ma-345	110	5	u1;f	u1;f	PROPN
ma-345	110	6	]	]	X
ma-345	110	7	−	−	PROPN
ma-345	111	1	[	[	X
ma-345	111	2	v2	v2	PROPN
ma-345	111	3	,	,	PUNCT
ma-345	111	4	v1;f	v1;f	PROPN
ma-345	111	5	]	]	PUNCT
ma-345	111	6	‖	‖	PROPN
ma-345	111	7	≤	≤	X
ma-345	111	8	l(‖u2	l(‖u2	ADJ
ma-345	111	9	−	−	PROPN
ma-345	111	10	v2‖+	v2‖+	NOUN
ma-345	111	11	‖u1	‖u1	ADV
ma-345	111	12	−	−	PROPN
ma-345	111	13	v1‖	v1‖	PROPN
ma-345	111	14	)	)	PUNCT
ma-345	111	15	.	.	PUNCT
ma-345	112	1	(	(	PUNCT
ma-345	112	2	2.2	2.2	NUM
ma-345	112	3	)	)	PUNCT
ma-345	112	4	it	it	PRON
ma-345	112	5	follows	follow	VERB
ma-345	112	6	by	by	ADP
ma-345	112	7	(	(	PUNCT
ma-345	112	8	2.2	2.2	NUM
ma-345	112	9	)	)	PUNCT
ma-345	112	10	that	that	PRON
ma-345	112	11	f	f	PROPN
ma-345	112	12	′	′	NUM
ma-345	112	13	exists	exist	VERB
ma-345	112	14	,	,	PUNCT
ma-345	112	15	[	[	X
ma-345	112	16	x	x	X
ma-345	112	17	,	,	PUNCT
ma-345	112	18	x	x	X
ma-345	112	19	;	;	PUNCT
ma-345	112	20	f	f	X
ma-345	112	21	]	]	PUNCT
ma-345	113	1	=	=	PUNCT
ma-345	113	2	f	f	PROPN
ma-345	113	3	′(x	′(x	NOUN
ma-345	113	4	)	)	PUNCT
ma-345	113	5	and	and	CCONJ
ma-345	113	6	for	for	ADP
ma-345	113	7	each	each	DET
ma-345	113	8	u	u	NOUN
ma-345	113	9	,	,	PUNCT
ma-345	113	10	v	v	PROPN
ma-345	113	11	∈	∈	PROPN
ma-345	113	12	s(x∗	s(x∗	ADV
ma-345	113	13	,	,	PUNCT
ma-345	113	14	ρ̄	ρ̄	NOUN
ma-345	113	15	)	)	PUNCT
ma-345	113	16	‖f	‖f	PUNCT
ma-345	114	1	′(u)−	′(u)−	PROPN
ma-345	114	2	f	f	PROPN
ma-345	115	1	′(v)‖	′(v)‖	PROPN
ma-345	115	2	≤	≤	ADJ
ma-345	115	3	2l‖u	2l‖u	PROPN
ma-345	115	4	−	−	NOUN
ma-345	115	5	v‖.	v‖.	NOUN
ma-345	115	6	(	(	PUNCT
ma-345	115	7	2.3	2.3	NUM
ma-345	115	8	)	)	PUNCT
ma-345	115	9	moreover	moreover	ADV
ma-345	115	10	,	,	PUNCT
ma-345	115	11	assume	assume	VERB
ma-345	115	12	f	f	PROPN
ma-345	115	13	′(x∗	′(x∗	PROPN
ma-345	115	14	)	)	PUNCT
ma-345	115	15	is	be	AUX
ma-345	115	16	invertible	invertible	ADJ
ma-345	115	17	and	and	CCONJ
ma-345	115	18	set	set	VERB
ma-345	115	19	‖f	‖f	PRON
ma-345	115	20	′(x∗)‖	′(x∗)‖	VERB
ma-345	115	21	≤	≤	ADJ
ma-345	115	22	d1	d1	NOUN
ma-345	115	23	,	,	PUNCT
ma-345	115	24	‖f	‖f	ADP
ma-345	115	25	′(x∗)−1‖	′(x∗)−1‖	PROPN
ma-345	115	26	≤	≤	NUM
ma-345	115	27	d2	d2	PROPN
ma-345	115	28	.	.	PUNCT
ma-345	116	1	(	(	PUNCT
ma-345	116	2	2.4	2.4	NUM
ma-345	116	3	)	)	PUNCT
ma-345	116	4	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
ma-345	116	5	eur	eur	PROPN
ma-345	116	6	.	.	PUNCT
ma-345	117	1	j.	j.	PROPN
ma-345	117	2	math	math	PROPN
ma-345	117	3	.	.	PUNCT
ma-345	118	1	anal	anal	PROPN
ma-345	118	2	.	.	PUNCT
ma-345	119	1	10.28924	10.28924	NUM
ma-345	119	2	/	/	SYM
ma-345	119	3	ada	ada	PROPN
ma-345	119	4	/	/	SYM
ma-345	119	5	ma.5.15	ma.5.15	PROPN
ma-345	119	6	5furthermore	5furthermore	NUM
ma-345	119	7	,	,	PUNCT
ma-345	119	8	assume	assume	VERB
ma-345	119	9	t0	t0	PROPN
ma-345	119	10	,	,	PUNCT
ma-345	119	11	k0	k0	PROPN
ma-345	119	12	satisfy	satisfy	PROPN
ma-345	119	13	‖t0‖	‖t0‖	PROPN
ma-345	119	14	≤	≤	PROPN
ma-345	119	15	b0	b0	VERB
ma-345	119	16	≤	≤	ADJ
ma-345	119	17	b	b	NOUN
ma-345	119	18	,	,	PUNCT
ma-345	119	19	‖i	‖i	ADJ
ma-345	119	20	−	−	NOUN
ma-345	119	21	t0k0‖	t0k0‖	ADP
ma-345	119	22	≤	≤	PROPN
ma-345	119	23	λ	λ	PROPN
ma-345	119	24	,	,	PUNCT
ma-345	119	25	b	b	PROPN
ma-345	119	26	≥	≥	NOUN
ma-345	119	27	b0	b0	NOUN
ma-345	119	28	and	and	CCONJ
ma-345	119	29	λ	λ	X
ma-345	119	30	∈	∈	PROPN
ma-345	120	1	[	[	X
ma-345	120	2	0	0	NUM
ma-345	120	3	,	,	PUNCT
ma-345	120	4	b	b	NOUN
ma-345	120	5	]	]	X
ma-345	120	6	.	.	PUNCT
ma-345	121	1	(	(	PUNCT
ma-345	121	2	2.5	2.5	NUM
ma-345	121	3	)	)	PUNCT
ma-345	121	4	finally	finally	ADV
ma-345	121	5	,	,	PUNCT
ma-345	121	6	assume	assume	VERB
ma-345	121	7	s(x∗	s(x∗	ADV
ma-345	121	8	,	,	PUNCT
ma-345	121	9	ρ∗	ρ∗	PROPN
ma-345	121	10	)	)	PUNCT
ma-345	122	1	⊂	⊂	PROPN
ma-345	122	2	ω	ω	PROPN
ma-345	122	3	,	,	PUNCT
ma-345	122	4	ρ∗	ρ∗	NOUN
ma-345	122	5	=	=	SYM
ma-345	122	6	max{ρ̄	max{ρ̄	NOUN
ma-345	122	7	,	,	PUNCT
ma-345	122	8	3b	3b	NUM
ma-345	122	9	}	}	PUNCT
ma-345	122	10	.	.	PUNCT
ma-345	123	1	(	(	PUNCT
ma-345	123	2	2.6)the	2.6)the	DET
ma-345	123	3	conditions	condition	NOUN
ma-345	123	4	(	(	PUNCT
ma-345	123	5	2.2	2.2	NUM
ma-345	123	6	)	)	PUNCT
ma-345	123	7	,	,	PUNCT
ma-345	123	8	(	(	PUNCT
ma-345	123	9	2.4)-(2.6	2.4)-(2.6	NUM
ma-345	123	10	)	)	PUNCT
ma-345	123	11	are	be	AUX
ma-345	123	12	called	call	VERB
ma-345	123	13	(	(	PUNCT
ma-345	123	14	a	a	NOUN
ma-345	123	15	)	)	PUNCT
ma-345	123	16	from	from	ADP
ma-345	123	17	now	now	ADV
ma-345	123	18	on.next	on.next	ADV
ma-345	123	19	,	,	PUNCT
ma-345	123	20	the	the	DET
ma-345	123	21	main	main	ADJ
ma-345	123	22	local	local	ADJ
ma-345	123	23	analysis	analysis	NOUN
ma-345	123	24	of	of	ADP
ma-345	123	25	convergence	convergence	NOUN
ma-345	123	26	is	be	AUX
ma-345	123	27	presented	present	VERB
ma-345	123	28	under	under	ADP
ma-345	123	29	the	the	DET
ma-345	123	30	conditions	condition	NOUN
ma-345	123	31	(	(	PUNCT
ma-345	123	32	a	a	X
ma-345	123	33	)	)	PUNCT
ma-345	123	34	and	and	CCONJ
ma-345	123	35	thepreceding	theprecede	VERB
ma-345	123	36	notation	notation	NOUN
ma-345	123	37	.	.	PUNCT
ma-345	124	1	theorem	theorem	VERB
ma-345	124	2	2.1	2.1	NUM
ma-345	124	3	.	.	PUNCT
ma-345	125	1	assume	assume	VERB
ma-345	125	2	that	that	SCONJ
ma-345	125	3	the	the	DET
ma-345	125	4	conditions	condition	NOUN
ma-345	125	5	(	(	PUNCT
ma-345	125	6	a	a	X
ma-345	125	7	)	)	PUNCT
ma-345	125	8	hold	hold	NOUN
ma-345	125	9	and	and	CCONJ
ma-345	125	10	b	b	NOUN
ma-345	125	11	<	<	X
ma-345	125	12	a.	a.	NOUN
ma-345	125	13	then	then	ADV
ma-345	125	14	,	,	PUNCT
ma-345	125	15	the	the	DET
ma-345	125	16	sequence	sequence	NOUN
ma-345	125	17	{	{	PUNCT
ma-345	125	18	xn	xn	PROPN
ma-345	125	19	}	}	PUNCT
ma-345	125	20	generated	generate	VERB
ma-345	125	21	by	by	ADP
ma-345	125	22	(	(	PUNCT
ma-345	125	23	tsklm	tsklm	PROPN
ma-345	125	24	)	)	PUNCT
ma-345	125	25	converges	converge	VERB
ma-345	125	26	to	to	ADP
ma-345	125	27	the	the	DET
ma-345	125	28	solution	solution	NOUN
ma-345	125	29	of	of	ADP
ma-345	125	30	the	the	DET
ma-345	125	31	equation	equation	NOUN
ma-345	125	32	f	f	X
ma-345	125	33	(	(	PUNCT
ma-345	125	34	x	x	X
ma-345	125	35	)	)	PUNCT
ma-345	125	36	=	=	SYM
ma-345	125	37	0	0	NUM
ma-345	125	38	provided	provide	VERB
ma-345	125	39	that	that	SCONJ
ma-345	125	40	x0	x0	PROPN
ma-345	125	41	∈	∈	PROPN
ma-345	125	42	s(x∗	s(x∗	ADV
ma-345	125	43	,	,	PUNCT
ma-345	125	44	b	b	NOUN
ma-345	125	45	)	)	PUNCT
ma-345	125	46	.	.	PUNCT
ma-345	126	1	moreover	moreover	ADV
ma-345	126	2	,	,	PUNCT
ma-345	126	3	the	the	DET
ma-345	126	4	following	follow	VERB
ma-345	126	5	assertions	assertion	NOUN
ma-345	126	6	hold	hold	VERB
ma-345	126	7	for	for	ADP
ma-345	126	8	en	en	X
ma-345	126	9	=	=	SYM
ma-345	126	10	‖xn	‖xn	PROPN
ma-345	126	11	−	−	PROPN
ma-345	126	12	x∗‖	x∗‖	PROPN
ma-345	126	13	,	,	PUNCT
ma-345	126	14	hn	hn	PROPN
ma-345	126	15	=	=	PUNCT
ma-345	126	16	‖i	‖i	NOUN
ma-345	126	17	−	−	NOUN
ma-345	126	18	tnkn‖	tnkn‖	NUM
ma-345	126	19	,	,	PUNCT
ma-345	126	20	en	en	X
ma-345	126	21	≤	≤	NUM
ma-345	126	22	aq4	aq4	ADV
ma-345	126	23	n	n	PROPN
ma-345	126	24	(	(	PUNCT
ma-345	126	25	2.7	2.7	NUM
ma-345	126	26	)	)	PUNCT
ma-345	126	27	and	and	CCONJ
ma-345	126	28	hn	hn	PROPN
ma-345	126	29	≤	≤	PROPN
ma-345	126	30	aq4	aq4	ADV
ma-345	126	31	n−1	n−1	PROPN
ma-345	126	32	,	,	PUNCT
ma-345	126	33	h0	h0	VERB
ma-345	126	34	≤	≤	PROPN
ma-345	126	35	b	b	PROPN
ma-345	126	36	,	,	PUNCT
ma-345	126	37	(	(	PUNCT
ma-345	126	38	2.8	2.8	NUM
ma-345	126	39	)	)	PUNCT
ma-345	126	40	n	n	NOUN
ma-345	126	41	=	=	SYM
ma-345	126	42	0	0	NUM
ma-345	126	43	,	,	PUNCT
ma-345	126	44	1	1	NUM
ma-345	126	45	,	,	PUNCT
ma-345	126	46	2	2	NUM
ma-345	126	47	,	,	PUNCT
ma-345	126	48	.	.	PUNCT
ma-345	126	49	.	.	PUNCT
ma-345	127	1	.	.	PUNCT
ma-345	128	1	,	,	PUNCT
ma-345	128	2	where	where	SCONJ
ma-345	128	3	ρ	ρ	PROPN
ma-345	128	4	,	,	PUNCT
ma-345	128	5	a	a	DET
ma-345	128	6	,	,	PUNCT
ma-345	128	7	b	b	NOUN
ma-345	128	8	,	,	PUNCT
ma-345	128	9	q	q	X
ma-345	128	10	are	be	AUX
ma-345	128	11	given	give	VERB
ma-345	128	12	by	by	ADP
ma-345	128	13	(	(	PUNCT
ma-345	128	14	2.1	2.1	NUM
ma-345	128	15	)	)	PUNCT
ma-345	128	16	.	.	PUNCT
ma-345	129	1	proof	proof	NOUN
ma-345	129	2	.	.	PUNCT
ma-345	130	1	the	the	DET
ma-345	130	2	assertions	assertion	NOUN
ma-345	130	3	(	(	PUNCT
ma-345	130	4	2.7	2.7	NUM
ma-345	130	5	)	)	PUNCT
ma-345	130	6	and	and	CCONJ
ma-345	130	7	(	(	PUNCT
ma-345	130	8	2.8	2.8	NUM
ma-345	130	9	)	)	PUNCT
ma-345	130	10	are	be	AUX
ma-345	130	11	shown	show	VERB
ma-345	130	12	by	by	ADP
ma-345	130	13	induction	induction	NOUN
ma-345	130	14	.	.	PUNCT
ma-345	131	1	if	if	SCONJ
ma-345	131	2	n	n	NOUN
ma-345	131	3	=	=	SYM
ma-345	131	4	0	0	NUM
ma-345	131	5	,	,	PUNCT
ma-345	131	6	assertion	assertion	NOUN
ma-345	131	7	(	(	PUNCT
ma-345	131	8	2.7	2.7	NUM
ma-345	131	9	)	)	PUNCT
ma-345	131	10	for	for	ADP
ma-345	131	11	n	n	NOUN
ma-345	131	12	=	=	SYM
ma-345	131	13	0holds	0hold	NOUN
ma-345	131	14	,	,	PUNCT
ma-345	131	15	since	since	SCONJ
ma-345	131	16	e0	e0	PROPN
ma-345	131	17	≤	≤	PROPN
ma-345	131	18	b.	b.	PROPN
ma-345	131	19	then	then	ADV
ma-345	131	20	,	,	PUNCT
ma-345	131	21	by	by	ADP
ma-345	131	22	(	(	PUNCT
ma-345	131	23	2.5	2.5	NUM
ma-345	131	24	)	)	PUNCT
ma-345	131	25	,	,	PUNCT
ma-345	131	26	we	we	PRON
ma-345	131	27	get	get	VERB
ma-345	131	28	a	a	DET
ma-345	131	29	∈	∈	NOUN
ma-345	132	1	[	[	X
ma-345	132	2	0	0	NUM
ma-345	132	3	,	,	PUNCT
ma-345	132	4	1	1	NUM
ma-345	132	5	]	]	PUNCT
ma-345	132	6	and	and	CCONJ
ma-345	132	7	h0	h0	PROPN
ma-345	132	8	≤	≤	PROPN
ma-345	132	9	λ	λ	PROPN
ma-345	132	10	≤	≤	NUM
ma-345	132	11	b	b	NUM
ma-345	132	12	,	,	PUNCT
ma-345	132	13	so	so	CCONJ
ma-345	132	14	(	(	PUNCT
ma-345	132	15	2.8	2.8	NUM
ma-345	132	16	)	)	PUNCT
ma-345	132	17	holds	hold	VERB
ma-345	132	18	if	if	SCONJ
ma-345	132	19	n	n	X
ma-345	132	20	=	=	SYM
ma-345	132	21	0.assume	0.assume	NUM
ma-345	132	22	(	(	PUNCT
ma-345	132	23	2.7	2.7	NUM
ma-345	132	24	)	)	PUNCT
ma-345	132	25	and	and	CCONJ
ma-345	132	26	(	(	PUNCT
ma-345	132	27	2.8	2.8	NUM
ma-345	132	28	)	)	PUNCT
ma-345	132	29	hold	hold	VERB
ma-345	132	30	if	if	SCONJ
ma-345	132	31	n	n	NOUN
ma-345	132	32	=	=	NOUN
ma-345	132	33	i	i	PROPN
ma-345	132	34	.	.	PUNCT
ma-345	133	1	that	that	PRON
ma-345	133	2	is	be	AUX
ma-345	133	3	ei	ei	ADP
ma-345	133	4	≤	≤	NUM
ma-345	133	5	aq4	aq4	ADV
ma-345	133	6	i	i	PRON
ma-345	133	7	<	<	X
ma-345	133	8	b	b	X
ma-345	133	9	<	<	X
ma-345	133	10	ρ̄	ρ̄	X
ma-345	133	11	(	(	PUNCT
ma-345	133	12	2.9	2.9	NUM
ma-345	133	13	)	)	PUNCT
ma-345	133	14	and	and	CCONJ
ma-345	133	15	hi	hi	INTJ
ma-345	133	16	≤	≤	NUM
ma-345	133	17	aq4	aq4	ADV
ma-345	133	18	i−1	i−1	PROPN
ma-345	133	19	.	.	PUNCT
ma-345	134	1	(	(	PUNCT
ma-345	134	2	2.10)we	2.10)we	NOUN
ma-345	134	3	need	need	VERB
ma-345	134	4	the	the	DET
ma-345	134	5	estimate	estimate	NOUN
ma-345	134	6	‖ki+1	‖ki+1	NOUN
ma-345	135	1	−	−	NOUN
ma-345	136	1	f	f	PROPN
ma-345	136	2	′(xi)‖	′(xi)‖	NOUN
ma-345	136	3	=	=	PUNCT
ma-345	136	4	‖[2yi	‖[2yi	PROPN
ma-345	137	1	−	−	PROPN
ma-345	137	2	xi	xi	INTJ
ma-345	137	3	,	,	PUNCT
ma-345	137	4	xi	xi	PROPN
ma-345	137	5	;	;	PUNCT
ma-345	137	6	f	f	X
ma-345	137	7	]	]	X
ma-345	137	8	−	−	PROPN
ma-345	138	1	[	[	X
ma-345	138	2	xi	xi	X
ma-345	138	3	,	,	PUNCT
ma-345	138	4	xi	xi	PROPN
ma-345	138	5	;	;	PUNCT
ma-345	138	6	f	f	X
ma-345	138	7	]	]	PUNCT
ma-345	138	8	‖	‖	PROPN
ma-345	138	9	≤	≤	PROPN
ma-345	138	10	l(‖2yi	l(‖2yi	PRON
ma-345	138	11	−	−	PROPN
ma-345	138	12	xi	xi	ADP
ma-345	138	13	−	−	PROPN
ma-345	138	14	xi‖+	xi‖+	PROPN
ma-345	139	1	‖xi	‖xi	NUM
ma-345	139	2	−	−	PROPN
ma-345	139	3	xi‖	xi‖	NOUN
ma-345	139	4	)	)	PUNCT
ma-345	139	5	=	=	SYM
ma-345	140	1	2l‖yi	2l‖yi	NUM
ma-345	140	2	−	−	NOUN
ma-345	140	3	xi‖	xi‖	PROPN
ma-345	140	4	(	(	PUNCT
ma-345	140	5	2.11	2.11	NUM
ma-345	140	6	)	)	PUNCT
ma-345	140	7	≤	≤	NOUN
ma-345	140	8	2l‖tif	2l‖tif	NUM
ma-345	140	9	(	(	PUNCT
ma-345	140	10	xi)‖	xi)‖	PROPN
ma-345	140	11	≤	≤	PROPN
ma-345	140	12	2l‖ti‖(l	2l‖ti‖(l	NUM
ma-345	140	13	+	+	CCONJ
ma-345	140	14	d1)‖xi	d1)‖xi	PROPN
ma-345	140	15	−	−	PROPN
ma-345	140	16	x∗‖	x∗‖	PROPN
ma-345	140	17	≤	≤	PROPN
ma-345	140	18	c1ei	c1ei	PUNCT
ma-345	140	19	≤	≤	NUM
ma-345	141	1	c1aq4	c1aq4	NOUN
ma-345	142	1	i	i	PRON
ma-345	142	2	,	,	PUNCT
ma-345	142	3	where	where	SCONJ
ma-345	142	4	we	we	PRON
ma-345	142	5	used	use	VERB
ma-345	142	6	(	(	PUNCT
ma-345	142	7	2.1	2.1	NUM
ma-345	142	8	)	)	PUNCT
ma-345	142	9	,	,	PUNCT
ma-345	142	10	(	(	PUNCT
ma-345	142	11	2.2	2.2	NUM
ma-345	142	12	)	)	PUNCT
ma-345	142	13	(	(	PUNCT
ma-345	142	14	i.e	i.e	X
ma-345	142	15	(	(	PUNCT
ma-345	142	16	2.3	2.3	NUM
ma-345	142	17	)	)	PUNCT
ma-345	142	18	)	)	PUNCT
ma-345	142	19	,	,	PUNCT
ma-345	142	20	(	(	PUNCT
ma-345	142	21	2.5	2.5	NUM
ma-345	142	22	)	)	PUNCT
ma-345	142	23	,	,	PUNCT
ma-345	142	24	the	the	DET
ma-345	142	25	induction	induction	NOUN
ma-345	142	26	hypotheses	hypothesis	NOUN
ma-345	142	27	(	(	PUNCT
ma-345	142	28	2.9	2.9	NUM
ma-345	142	29	)	)	PUNCT
ma-345	142	30	,	,	PUNCT
ma-345	142	31	(	(	PUNCT
ma-345	142	32	2.10	2.10	NUM
ma-345	142	33	)	)	PUNCT
ma-345	142	34	and	and	CCONJ
ma-345	142	35	f	f	PROPN
ma-345	142	36	(	(	PUNCT
ma-345	142	37	xi	xi	PROPN
ma-345	142	38	)	)	PUNCT
ma-345	142	39	=	=	SYM
ma-345	142	40	f	f	PROPN
ma-345	142	41	(	(	PUNCT
ma-345	142	42	xi)−	xi)−	PROPN
ma-345	142	43	f	f	X
ma-345	142	44	(	(	PUNCT
ma-345	142	45	x∗	x∗	PROPN
ma-345	142	46	)	)	PUNCT
ma-345	142	47	=	=	PUNCT
ma-345	143	1	1∫	1∫	NUM
ma-345	143	2	0	0	NUM
ma-345	143	3	f	f	PROPN
ma-345	143	4	′(x∗	′(x∗	NOUN
ma-345	143	5	+	+	CCONJ
ma-345	143	6	θ(xi	θ(xi	PROPN
ma-345	143	7	−	−	PROPN
ma-345	143	8	x∗))dθ(xi	x∗))dθ(xi	PROPN
ma-345	143	9	−	−	NOUN
ma-345	143	10	x∗	x∗	PROPN
ma-345	143	11	)	)	PUNCT
ma-345	143	12	=	=	PUNCT
ma-345	144	1	1∫	1∫	NUM
ma-345	144	2	0	0	NUM
ma-345	145	1	[	[	PUNCT
ma-345	145	2	f	f	X
ma-345	145	3	′(x∗	′(x∗	NOUN
ma-345	145	4	+	+	CCONJ
ma-345	145	5	θ(xi	θ(xi	PROPN
ma-345	145	6	−	−	PROPN
ma-345	146	1	x∗))−	x∗))−	NOUN
ma-345	146	2	f	f	PROPN
ma-345	146	3	′(x∗	′(x∗	PROPN
ma-345	146	4	)	)	PUNCT
ma-345	147	1	+	+	CCONJ
ma-345	147	2	f	f	PROPN
ma-345	147	3	′(x∗	′(x∗	NOUN
ma-345	147	4	)	)	PUNCT
ma-345	147	5	]	]	PUNCT
ma-345	148	1	dθ(xi	dθ(xi	PROPN
ma-345	148	2	−	−	PROPN
ma-345	148	3	x∗	x∗	PROPN
ma-345	148	4	)	)	PUNCT
ma-345	148	5	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
ma-345	148	6	eur	eur	PROPN
ma-345	148	7	.	.	PUNCT
ma-345	149	1	j.	j.	PROPN
ma-345	149	2	math	math	PROPN
ma-345	149	3	.	.	PUNCT
ma-345	150	1	anal	anal	PROPN
ma-345	150	2	.	.	PUNCT
ma-345	151	1	10.28924	10.28924	NUM
ma-345	151	2	/	/	SYM
ma-345	151	3	ada	ada	PROPN
ma-345	151	4	/	/	SYM
ma-345	151	5	ma.5.15	ma.5.15	NOUN
ma-345	151	6	6leading	6leading	NUM
ma-345	151	7	to	to	ADP
ma-345	151	8	‖f	‖f	PRON
ma-345	151	9	(	(	PUNCT
ma-345	151	10	xi)‖	xi)‖	PROPN
ma-345	151	11	≤	≤	PROPN
ma-345	151	12	(	(	PUNCT
ma-345	152	1	l	l	NOUN
ma-345	152	2	+	+	CCONJ
ma-345	153	1	d1)‖xi	d1)‖xi	PROPN
ma-345	153	2	−	−	PROPN
ma-345	153	3	x∗‖.	x∗‖.	PROPN
ma-345	153	4	(	(	PUNCT
ma-345	153	5	2.12	2.12	NUM
ma-345	153	6	)	)	PUNCT
ma-345	153	7	it	it	PRON
ma-345	153	8	follows	follow	VERB
ma-345	153	9	by	by	ADP
ma-345	153	10	the	the	DET
ma-345	153	11	banach	banach	ADV
ma-345	153	12	lemma	lemma	PROPN
ma-345	153	13	on	on	ADP
ma-345	153	14	invertible	invertible	ADJ
ma-345	153	15	operators	operator	NOUN
ma-345	154	1	[	[	X
ma-345	154	2	1	1	NUM
ma-345	154	3	]	]	PUNCT
ma-345	154	4	,	,	PUNCT
ma-345	154	5	(	(	PUNCT
ma-345	154	6	2.1	2.1	NUM
ma-345	154	7	)	)	PUNCT
ma-345	154	8	and	and	CCONJ
ma-345	154	9	(	(	PUNCT
ma-345	154	10	2.11	2.11	NUM
ma-345	154	11	)	)	PUNCT
ma-345	154	12	that	that	SCONJ
ma-345	154	13	the	the	DET
ma-345	154	14	operator	operator	NOUN
ma-345	154	15	ki+1is	ki+1i	VERB
ma-345	154	16	invertible	invertible	ADJ
ma-345	154	17	and	and	CCONJ
ma-345	154	18	‖k−1i+1‖	‖k−1i+1‖	ADJ
ma-345	154	19	≤	≤	NOUN
ma-345	154	20	‖f	‖f	ADP
ma-345	155	1	′(x∗)−1‖	′(x∗)−1‖	PROPN
ma-345	155	2	1−	1−	NUM
ma-345	155	3	‖f	‖f	X
ma-345	155	4	′(x∗)−1‖‖ki+1	′(x∗)−1‖‖ki+1	NOUN
ma-345	155	5	−	−	PROPN
ma-345	155	6	f	f	PROPN
ma-345	155	7	′(xi)‖	′(xi)‖	PROPN
ma-345	155	8	≤	≤	PROPN
ma-345	155	9	d2	d2	PROPN
ma-345	155	10	1−	1−	PROPN
ma-345	155	11	d2c1ei	d2c1ei	PROPN
ma-345	155	12	≤	≤	PROPN
ma-345	155	13	d2	d2	PROPN
ma-345	155	14	1−	1−	NUM
ma-345	155	15	d2c1ρ̄	d2c1ρ̄	PROPN
ma-345	155	16	=	=	SYM
ma-345	155	17	b0	b0	VERB
ma-345	155	18	≤	≤	NUM
ma-345	155	19	b	b	NOUN
ma-345	155	20	,	,	PUNCT
ma-345	155	21	(	(	PUNCT
ma-345	155	22	2.13	2.13	NUM
ma-345	155	23	)	)	PUNCT
ma-345	156	1	so	so	SCONJ
ma-345	156	2	‖ti‖	‖ti‖	PROPN
ma-345	156	3	=	=	PROPN
ma-345	156	4	‖tikik−1i	‖tikik−1i	PROPN
ma-345	156	5	‖	‖	PROPN
ma-345	156	6	=	=	AUX
ma-345	156	7	‖(−i	‖(−i	VERB
ma-345	157	1	+	+	CCONJ
ma-345	157	2	(	(	PUNCT
ma-345	157	3	i	i	PRON
ma-345	157	4	−	−	PROPN
ma-345	157	5	tiki))k−1i	tiki))k−1i	PROPN
ma-345	157	6	‖	‖	PROPN
ma-345	157	7	≤	≤	NOUN
ma-345	157	8	(	(	PUNCT
ma-345	157	9	1	1	NUM
ma-345	157	10	+	+	CCONJ
ma-345	157	11	‖i	‖i	NOUN
ma-345	157	12	−	−	NOUN
ma-345	157	13	tiki‖)‖k−1i	tiki‖)‖k−1i	SYM
ma-345	157	14	‖	‖	PROPN
ma-345	157	15	≤	≤	NOUN
ma-345	157	16	(	(	PUNCT
ma-345	157	17	1	1	NUM
ma-345	157	18	+	+	CCONJ
ma-345	157	19	aq4	aq4	ADV
ma-345	157	20	i	i	PRON
ma-345	157	21	)	)	PUNCT
ma-345	157	22	b	b	PROPN
ma-345	157	23	≤	≤	NUM
ma-345	157	24	(	(	PUNCT
ma-345	157	25	1	1	NUM
ma-345	157	26	+	+	NUM
ma-345	157	27	1)b	1)b	X
ma-345	157	28	=	=	SYM
ma-345	157	29	2b	2b	NOUN
ma-345	157	30	,	,	PUNCT
ma-345	157	31	(	(	PUNCT
ma-345	157	32	2.14	2.14	NUM
ma-345	157	33	)	)	PUNCT
ma-345	157	34	and	and	CCONJ
ma-345	157	35	ξi	ξi	NOUN
ma-345	157	36	=	=	SYM
ma-345	157	37	‖i	‖i	NOUN
ma-345	157	38	−	−	NOUN
ma-345	157	39	tif	tif	PROPN
ma-345	157	40	′(xi)‖	′(xi)‖	NOUN
ma-345	157	41	=	=	PUNCT
ma-345	157	42	‖(i	‖(i	NOUN
ma-345	157	43	−	−	NOUN
ma-345	157	44	tiki	tiki	NOUN
ma-345	157	45	)	)	PUNCT
ma-345	158	1	+	+	CCONJ
ma-345	158	2	(	(	PUNCT
ma-345	158	3	tiki	tiki	NOUN
ma-345	158	4	−	−	PROPN
ma-345	158	5	tif	tif	PROPN
ma-345	158	6	′(xi))‖	′(xi))‖	VERB
ma-345	158	7	≤	≤	ADJ
ma-345	158	8	‖i	‖i	NOUN
ma-345	158	9	−	−	NOUN
ma-345	158	10	tiki‖+	tiki‖+	NOUN
ma-345	158	11	‖ti‖‖ki	‖ti‖‖ki	NOUN
ma-345	158	12	−	−	NOUN
ma-345	158	13	f	f	NOUN
ma-345	158	14	′(xi)‖	′(xi)‖	NOUN
ma-345	158	15	≤	≤	PROPN
ma-345	159	1	aq4	aq4	ADV
ma-345	159	2	i	i	PRON
ma-345	159	3	+	+	CCONJ
ma-345	159	4	2bc1aq	2bc1aq	NUM
ma-345	159	5	4i	4i	NOUN
ma-345	159	6	=	=	SYM
ma-345	159	7	c2aq	c2aq	PUNCT
ma-345	159	8	4i	4i	NOUN
ma-345	159	9	.	.	PUNCT
ma-345	160	1	(	(	PUNCT
ma-345	160	2	2.15	2.15	NUM
ma-345	160	3	)	)	PUNCT
ma-345	160	4	then	then	ADV
ma-345	160	5	,	,	PUNCT
ma-345	160	6	by	by	ADP
ma-345	160	7	the	the	DET
ma-345	160	8	first	first	ADJ
ma-345	160	9	substep	substep	NOUN
ma-345	160	10	of	of	ADP
ma-345	160	11	(	(	PUNCT
ma-345	160	12	tsklm	tsklm	PROPN
ma-345	160	13	)	)	PUNCT
ma-345	160	14	we	we	PRON
ma-345	160	15	can	can	AUX
ma-345	160	16	write	write	VERB
ma-345	160	17	in	in	ADP
ma-345	160	18	turn	turn	NOUN
ma-345	160	19	yi	yi	PROPN
ma-345	161	1	−	−	NOUN
ma-345	161	2	x∗	x∗	PROPN
ma-345	161	3	=	=	SYM
ma-345	161	4	xi	xi	ADP
ma-345	161	5	−	−	PROPN
ma-345	161	6	x∗	x∗	PROPN
ma-345	161	7	−	−	PROPN
ma-345	161	8	ti(f	ti(f	PUNCT
ma-345	161	9	(	(	PUNCT
ma-345	161	10	xi)−	xi)−	PROPN
ma-345	161	11	f	f	X
ma-345	161	12	(	(	PUNCT
ma-345	161	13	x∗	x∗	PROPN
ma-345	161	14	)	)	PUNCT
ma-345	161	15	)	)	PUNCT
ma-345	161	16	=	=	PUNCT
ma-345	162	1	1∫	1∫	NUM
ma-345	162	2	0	0	NUM
ma-345	163	1	[	[	PUNCT
ma-345	163	2	(	(	PUNCT
ma-345	163	3	i	i	PRON
ma-345	163	4	−	−	PROPN
ma-345	163	5	tif	tif	PROPN
ma-345	163	6	′(xi	′(xi	PROPN
ma-345	163	7	)	)	PUNCT
ma-345	163	8	)	)	PUNCT
ma-345	164	1	+	+	CCONJ
ma-345	164	2	ti(f	ti(f	PUNCT
ma-345	164	3	′(xi)−	′(xi)−	PROPN
ma-345	164	4	f	f	PROPN
ma-345	164	5	′(x∗	′(x∗	PROPN
ma-345	164	6	+	+	CCONJ
ma-345	164	7	θ(xi	θ(xi	PROPN
ma-345	164	8	−	−	NOUN
ma-345	164	9	x∗	x∗	NOUN
ma-345	164	10	)	)	PUNCT
ma-345	164	11	)	)	PUNCT
ma-345	164	12	)	)	PUNCT
ma-345	164	13	]	]	PUNCT
ma-345	165	1	(	(	PUNCT
ma-345	165	2	xi	xi	X
ma-345	165	3	−	−	PROPN
ma-345	165	4	x∗)dθ	x∗)dθ	PROPN
ma-345	165	5	.	.	PUNCT
ma-345	166	1	(	(	PUNCT
ma-345	166	2	2.16	2.16	NUM
ma-345	166	3	)	)	PUNCT
ma-345	166	4	it	it	PRON
ma-345	166	5	follows	follow	VERB
ma-345	166	6	by	by	ADP
ma-345	166	7	the	the	DET
ma-345	166	8	induction	induction	NOUN
ma-345	166	9	hypotheses	hypothesis	NOUN
ma-345	166	10	(	(	PUNCT
ma-345	166	11	2.9	2.9	NUM
ma-345	166	12	)	)	PUNCT
ma-345	166	13	,	,	PUNCT
ma-345	166	14	(	(	PUNCT
ma-345	166	15	2.10	2.10	NUM
ma-345	166	16	)	)	PUNCT
ma-345	166	17	,	,	PUNCT
ma-345	166	18	the	the	DET
ma-345	166	19	(	(	PUNCT
ma-345	166	20	2.16	2.16	NUM
ma-345	166	21	)	)	PUNCT
ma-345	166	22	triangle	triangle	NOUN
ma-345	166	23	inequality	inequality	NOUN
ma-345	166	24	,	,	PUNCT
ma-345	166	25	(	(	PUNCT
ma-345	166	26	2.3	2.3	NUM
ma-345	166	27	)	)	PUNCT
ma-345	166	28	,	,	PUNCT
ma-345	166	29	and	and	CCONJ
ma-345	166	30	(	(	PUNCT
ma-345	166	31	2.13)-(2.16	2.13)-(2.16	NUM
ma-345	166	32	)	)	PUNCT
ma-345	166	33	,	,	PUNCT
ma-345	166	34	we	we	PRON
ma-345	166	35	have	have	VERB
ma-345	166	36	in	in	ADP
ma-345	166	37	turn	turn	NOUN
ma-345	166	38	that	that	SCONJ
ma-345	166	39	‖yi	‖yi	PROPN
ma-345	166	40	−	−	PROPN
ma-345	166	41	x∗‖	x∗‖	PROPN
ma-345	166	42	=	=	SYM
ma-345	166	43	ξiei	ξiei	PROPN
ma-345	167	1	+	+	CCONJ
ma-345	167	2	l‖ti‖e2i	l‖ti‖e2i	ADV
ma-345	167	3	≤	≤	NUM
ma-345	167	4	c2aq	c2aq	PUNCT
ma-345	168	1	4iaq4	4iaq4	NUM
ma-345	168	2	i	i	PRON
ma-345	168	3	+	+	NOUN
ma-345	168	4	2	2	NUM
ma-345	168	5	lb	lb	ADP
ma-345	168	6	(	(	PUNCT
ma-345	168	7	aq4	aq4	VERB
ma-345	168	8	i	i	PRON
ma-345	168	9	)	)	PUNCT
ma-345	168	10	2	2	NUM
ma-345	168	11	≤	≤	NOUN
ma-345	168	12	c3a2q2×4	c3a2q2×4	PROPN
ma-345	168	13	i	i	PRON
ma-345	168	14	.	.	PUNCT
ma-345	169	1	(	(	PUNCT
ma-345	169	2	2.17	2.17	NUM
ma-345	169	3	)	)	PUNCT
ma-345	169	4	and	and	CCONJ
ma-345	169	5	since	since	SCONJ
ma-345	169	6	a	a	DET
ma-345	169	7	∈	∈	PROPN
ma-345	170	1	[	[	X
ma-345	170	2	0	0	NUM
ma-345	170	3	,	,	PUNCT
ma-345	170	4	1	1	NUM
ma-345	170	5	]	]	PUNCT
ma-345	170	6	‖xi	‖xi	NUM
ma-345	170	7	−	−	NOUN
ma-345	170	8	yi‖	yi‖	PROPN
ma-345	170	9	≤	≤	PROPN
ma-345	170	10	ei	ei	ADP
ma-345	171	1	+	+	CCONJ
ma-345	171	2	‖yi	‖yi	PROPN
ma-345	171	3	−	−	PROPN
ma-345	171	4	x∗‖	x∗‖	PROPN
ma-345	171	5	≤	≤	NOUN
ma-345	172	1	aq4	aq4	ADV
ma-345	172	2	i	i	PRON
ma-345	172	3	+	+	CCONJ
ma-345	172	4	c3a	c3a	X
ma-345	173	1	2q2×4	2q2×4	NUM
ma-345	173	2	i	i	NOUN
ma-345	173	3	≤	≤	X
ma-345	173	4	(	(	PUNCT
ma-345	173	5	1	1	NUM
ma-345	173	6	+	+	CCONJ
ma-345	173	7	c3)aq	c3)aq	ADJ
ma-345	173	8	4i	4i	NOUN
ma-345	173	9	(	(	PUNCT
ma-345	173	10	2.18	2.18	NUM
ma-345	173	11	)	)	PUNCT
ma-345	173	12	and	and	CCONJ
ma-345	173	13	‖i	‖i	NOUN
ma-345	173	14	−	−	NOUN
ma-345	173	15	tif	tif	PROPN
ma-345	173	16	′(yi)‖	′(yi)‖	NOUN
ma-345	174	1	=	=	SYM
ma-345	175	1	‖(i	‖(i	NOUN
ma-345	175	2	−	−	PROPN
ma-345	175	3	tif	tif	PROPN
ma-345	175	4	′(xi	′(xi	PROPN
ma-345	175	5	)	)	PUNCT
ma-345	175	6	)	)	PUNCT
ma-345	176	1	+	+	CCONJ
ma-345	176	2	(	(	PUNCT
ma-345	176	3	tif	tif	PROPN
ma-345	176	4	′(xi)−	′(xi)−	PROPN
ma-345	176	5	tif	tif	PROPN
ma-345	176	6	′(yi))‖	′(yi))‖	PROPN
ma-345	176	7	≤	≤	PUNCT
ma-345	176	8	c2aq	c2aq	PUNCT
ma-345	176	9	4i	4i	PROPN
ma-345	176	10	+	+	CCONJ
ma-345	176	11	4lb(1	4lb(1	PROPN
ma-345	176	12	+	+	CCONJ
ma-345	176	13	c3)aq	c3)aq	ADJ
ma-345	176	14	4i	4i	NOUN
ma-345	176	15	=	=	SYM
ma-345	176	16	c4aq	c4aq	PUNCT
ma-345	176	17	4i	4i	NOUN
ma-345	176	18	.	.	PUNCT
ma-345	177	1	(	(	PUNCT
ma-345	177	2	2.19	2.19	NUM
ma-345	177	3	)	)	PUNCT
ma-345	177	4	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
ma-345	177	5	eur	eur	PROPN
ma-345	177	6	.	.	PUNCT
ma-345	178	1	j.	j.	PROPN
ma-345	178	2	math	math	PROPN
ma-345	178	3	.	.	PUNCT
ma-345	179	1	anal	anal	PROPN
ma-345	179	2	.	.	PUNCT
ma-345	180	1	10.28924	10.28924	NUM
ma-345	180	2	/	/	SYM
ma-345	180	3	ada	ada	PROPN
ma-345	180	4	/	/	SYM
ma-345	180	5	ma.5.15	ma.5.15	NOUN
ma-345	180	6	7	7	NUM
ma-345	180	7	in	in	ADP
ma-345	180	8	an	an	DET
ma-345	180	9	analogous	analogous	ADJ
ma-345	180	10	way	way	NOUN
ma-345	180	11	,	,	PUNCT
ma-345	180	12	we	we	PRON
ma-345	180	13	get	get	VERB
ma-345	180	14	in	in	ADP
ma-345	180	15	turn	turn	NOUN
ma-345	180	16	‖zi	‖zi	PROPN
ma-345	180	17	−	−	PROPN
ma-345	180	18	x∗‖	x∗‖	SYM
ma-345	180	19	≤	≤	NUM
ma-345	180	20	‖(i	‖(i	NOUN
ma-345	180	21	−	−	PROPN
ma-345	180	22	tif	tif	NOUN
ma-345	180	23	′(yi))(yi	′(yi))(yi	PROPN
ma-345	180	24	−	−	PROPN
ma-345	180	25	x∗)‖+	x∗)‖+	PROPN
ma-345	181	1	l‖ti‖‖yi	l‖ti‖‖yi	PROPN
ma-345	181	2	−	−	PROPN
ma-345	182	1	x∗‖2	x∗‖2	PROPN
ma-345	182	2	≤	≤	PROPN
ma-345	182	3	c4aq	c4aq	NUM
ma-345	182	4	4i	4i	NUM
ma-345	182	5	c3a	c3a	X
ma-345	183	1	2q2×4	2q2×4	NUM
ma-345	184	1	i	i	PRON
ma-345	184	2	+	+	CCONJ
ma-345	184	3	l(2bc23a	l(2bc23a	VERB
ma-345	184	4	4q4×4	4q4×4	NUM
ma-345	184	5	i	i	NOUN
ma-345	184	6	)	)	PUNCT
ma-345	184	7	≤	≤	NOUN
ma-345	184	8	(	(	PUNCT
ma-345	184	9	c3c4	c3c4	PROPN
ma-345	184	10	+	+	PROPN
ma-345	184	11	2lbc23	2lbc23	NUM
ma-345	184	12	)	)	PUNCT
ma-345	184	13	a2q3×4	a2q3×4	PROPN
ma-345	185	1	i	i	NOUN
ma-345	185	2	=	=	SYM
ma-345	186	1	a2q3×4	a2q3×4	PROPN
ma-345	186	2	i	i	PRON
ma-345	186	3	,	,	PUNCT
ma-345	186	4	(	(	PUNCT
ma-345	186	5	2.20	2.20	NUM
ma-345	186	6	)	)	PUNCT
ma-345	186	7	‖yi	‖yi	PROPN
ma-345	186	8	−	−	PROPN
ma-345	186	9	zi‖	zi‖	PROPN
ma-345	186	10	≤	≤	PROPN
ma-345	187	1	‖yi	‖yi	NUM
ma-345	187	2	−	−	PROPN
ma-345	187	3	x∗‖+	x∗‖+	PUNCT
ma-345	188	1	‖zi	‖zi	NUM
ma-345	188	2	−	−	PROPN
ma-345	188	3	x∗‖	x∗‖	PROPN
ma-345	188	4	≤	≤	NUM
ma-345	188	5	c3a	c3a	X
ma-345	188	6	2q2×4	2q2×4	NUM
ma-345	188	7	i	i	NOUN
ma-345	188	8	+	+	CCONJ
ma-345	188	9	a2q3×4	a2q3×4	NOUN
ma-345	188	10	i	i	NOUN
ma-345	188	11	=	=	PUNCT
ma-345	188	12	(	(	PUNCT
ma-345	188	13	1	1	NUM
ma-345	188	14	+	+	NUM
ma-345	188	15	c3)a	c3)a	NOUN
ma-345	188	16	2q2×4	2q2×4	NUM
ma-345	188	17	i	i	PRON
ma-345	188	18	(	(	PUNCT
ma-345	188	19	2.21	2.21	NUM
ma-345	188	20	)	)	PUNCT
ma-345	188	21	and	and	CCONJ
ma-345	188	22	‖i	‖i	NOUN
ma-345	188	23	−	−	NOUN
ma-345	188	24	tif	tif	PROPN
ma-345	188	25	′(zi)‖	′(zi)‖	NOUN
ma-345	188	26	≤	≤	NOUN
ma-345	188	27	‖i	‖i	NOUN
ma-345	188	28	−	−	PROPN
ma-345	188	29	tif	tif	PROPN
ma-345	188	30	′(yi)‖+	′(yi)‖+	PROPN
ma-345	188	31	‖ti‖‖f	‖ti‖‖f	PROPN
ma-345	188	32	′(yi)−	′(yi)−	PROPN
ma-345	188	33	f	f	PROPN
ma-345	188	34	′(zi))‖	′(zi))‖	NOUN
ma-345	188	35	≤	≤	NUM
ma-345	188	36	c4aq	c4aq	PUNCT
ma-345	188	37	4i	4i	NOUN
ma-345	188	38	+	+	CCONJ
ma-345	188	39	4lb(1	4lb(1	PROPN
ma-345	188	40	+	+	NUM
ma-345	188	41	c3)a	c3)a	NOUN
ma-345	188	42	2q2×4	2q2×4	NUM
ma-345	189	1	i	i	NOUN
ma-345	189	2	=	=	SYM
ma-345	189	3	c5aq	c5aq	PROPN
ma-345	189	4	4i	4i	NUM
ma-345	189	5	(	(	PUNCT
ma-345	189	6	2.22	2.22	NUM
ma-345	189	7	)	)	PUNCT
ma-345	189	8	leading	lead	VERB
ma-345	189	9	to	to	ADP
ma-345	189	10	ei+1	ei+1	PRON
ma-345	189	11	≤	≤	NUM
ma-345	189	12	‖i	‖i	NOUN
ma-345	189	13	−	−	PROPN
ma-345	189	14	tif	tif	NOUN
ma-345	189	15	′(zi)‖‖zi	′(zi)‖‖zi	NOUN
ma-345	189	16	−	−	PROPN
ma-345	189	17	x∗‖+	x∗‖+	PUNCT
ma-345	190	1	l‖ti‖‖zi	l‖ti‖‖zi	PROPN
ma-345	190	2	−	−	NOUN
ma-345	191	1	x∗‖2	x∗‖2	PROPN
ma-345	191	2	≤	≤	NOUN
ma-345	191	3	c5aq	c5aq	PUNCT
ma-345	191	4	4ia2q3×4	4ia2q3×4	VERB
ma-345	191	5	i	i	PRON
ma-345	191	6	+	+	CCONJ
ma-345	191	7	l(2ba4q6×4	l(2ba4q6×4	PROPN
ma-345	191	8	i	i	NOUN
ma-345	191	9	)	)	PUNCT
ma-345	191	10	≤	≤	NOUN
ma-345	191	11	(	(	PUNCT
ma-345	191	12	c5	c5	PROPN
ma-345	191	13	+	+	PROPN
ma-345	192	1	2lb)q4	2lb)q4	NUM
ma-345	192	2	i+1	i+1	NUM
ma-345	192	3	≤	≤	NUM
ma-345	192	4	aq4i+1	aq4i+1	NOUN
ma-345	192	5	(	(	PUNCT
ma-345	192	6	2.23	2.23	NUM
ma-345	192	7	)	)	PUNCT
ma-345	192	8	showing	show	VERB
ma-345	192	9	(	(	PUNCT
ma-345	192	10	2.7	2.7	NUM
ma-345	192	11	)	)	PUNCT
ma-345	192	12	for	for	ADP
ma-345	192	13	n	n	NOUN
ma-345	192	14	=	=	SYM
ma-345	192	15	i	i	PRON
ma-345	192	16	+	+	NOUN
ma-345	192	17	1	1	X
ma-345	192	18	.	.	PUNCT
ma-345	193	1	moreover	moreover	ADV
ma-345	193	2	,	,	PUNCT
ma-345	193	3	we	we	PRON
ma-345	193	4	have	have	VERB
ma-345	193	5	‖xi+1	‖xi+1	ADV
ma-345	193	6	−	−	PROPN
ma-345	194	1	xi‖	xi‖	PROPN
ma-345	194	2	≤	≤	NUM
ma-345	194	3	‖xi+1	‖xi+1	ADP
ma-345	194	4	−	−	PROPN
ma-345	194	5	x∗‖+	x∗‖+	PUNCT
ma-345	195	1	‖xi	‖xi	X
ma-345	195	2	−	−	X
ma-345	195	3	x∗‖	x∗‖	PROPN
ma-345	195	4	≤	≤	NOUN
ma-345	195	5	aq4	aq4	ADV
ma-345	195	6	i+1	i+1	PRON
ma-345	195	7	+	+	CCONJ
ma-345	195	8	aq4	aq4	ADV
ma-345	195	9	i	i	PRON
ma-345	195	10	≤	≤	NOUN
ma-345	195	11	2aq4	2aq4	NUM
ma-345	195	12	i	i	PRON
ma-345	195	13	(	(	PUNCT
ma-345	195	14	2.24	2.24	NUM
ma-345	195	15	)	)	PUNCT
ma-345	195	16	notice	notice	VERB
ma-345	195	17	that	that	SCONJ
ma-345	195	18	2yi	2yi	ADJ
ma-345	195	19	−	−	PROPN
ma-345	195	20	xi	xi	PROPN
ma-345	195	21	∈	∈	PROPN
ma-345	195	22	s(x∗	s(x∗	ADV
ma-345	195	23	,	,	PUNCT
ma-345	195	24	3b	3b	NUM
ma-345	195	25	)	)	PUNCT
ma-345	195	26	by	by	ADP
ma-345	195	27	(	(	PUNCT
ma-345	195	28	2.6	2.6	NUM
ma-345	195	29	)	)	PUNCT
ma-345	195	30	and	and	CCONJ
ma-345	195	31	ei+1	ei+1	X
ma-345	196	1	≤	≤	NUM
ma-345	196	2	q4i+1	q4i+1	X
ma-345	196	3	<	<	X
ma-345	196	4	b	b	X
ma-345	196	5	<	<	X
ma-345	196	6	ρ̄.hence	ρ̄.hence	PROPN
ma-345	196	7	,	,	PUNCT
ma-345	196	8	we	we	PRON
ma-345	196	9	can	can	AUX
ma-345	196	10	have	have	VERB
ma-345	196	11	‖ki+1	‖ki+1	PROPN
ma-345	196	12	−ki‖	−ki‖	NUM
ma-345	196	13	≤	≤	NUM
ma-345	197	1	‖(ki+1	‖(ki+1	ADP
ma-345	197	2	−	−	PROPN
ma-345	198	1	f	f	PROPN
ma-345	198	2	′(xi	′(xi	PROPN
ma-345	198	3	)	)	PUNCT
ma-345	198	4	)	)	PUNCT
ma-345	199	1	+	+	CCONJ
ma-345	199	2	(	(	PUNCT
ma-345	199	3	f	f	PROPN
ma-345	199	4	′(xi)−	′(xi)−	PROPN
ma-345	199	5	f	f	PROPN
ma-345	199	6	′(xi−1	′(xi−1	PROPN
ma-345	199	7	)	)	PUNCT
ma-345	199	8	)	)	PUNCT
ma-345	200	1	+	+	CCONJ
ma-345	200	2	(	(	PUNCT
ma-345	200	3	f	f	PROPN
ma-345	200	4	′(xi−1)−ki)‖	′(xi−1)−ki)‖	NUM
ma-345	200	5	≤	≤	NUM
ma-345	200	6	c1aq	c1aq	PUNCT
ma-345	200	7	4i	4i	NOUN
ma-345	200	8	+	+	CCONJ
ma-345	200	9	4laq4	4laq4	NOUN
ma-345	200	10	i−1	i−1	PROPN
ma-345	200	11	+	+	CCONJ
ma-345	200	12	c1aq	c1aq	X
ma-345	200	13	4i−1	4i−1	PROPN
ma-345	200	14	≤	≤	NOUN
ma-345	200	15	(	(	PUNCT
ma-345	200	16	2c1	2c1	NUM
ma-345	201	1	+	+	NUM
ma-345	201	2	4l)aq4	4l)aq4	NUM
ma-345	201	3	i−1	i−1	PROPN
ma-345	201	4	(	(	PUNCT
ma-345	201	5	2.25	2.25	NUM
ma-345	201	6	)	)	PUNCT
ma-345	201	7	‖i	‖i	NOUN
ma-345	201	8	−	−	NUM
ma-345	201	9	tiki+1‖	tiki+1‖	NOUN
ma-345	201	10	=	=	SYM
ma-345	201	11	‖(i	‖(i	NOUN
ma-345	201	12	−	−	NOUN
ma-345	201	13	tiki	tiki	NOUN
ma-345	201	14	)	)	PUNCT
ma-345	201	15	+	+	CCONJ
ma-345	201	16	(	(	PUNCT
ma-345	201	17	tiki+1	tiki+1	INTJ
ma-345	201	18	−	−	PROPN
ma-345	201	19	tiki)‖	tiki)‖	NOUN
ma-345	201	20	≤	≤	NUM
ma-345	201	21	aq4	aq4	ADV
ma-345	201	22	i	i	PRON
ma-345	201	23	+	+	CCONJ
ma-345	201	24	2b(2c1	2b(2c1	NUM
ma-345	202	1	+	+	CCONJ
ma-345	202	2	4l)aq4	4l)aq4	NUM
ma-345	202	3	i−1	i−1	PROPN
ma-345	202	4	=	=	SYM
ma-345	202	5	c6aq	c6aq	X
ma-345	202	6	4i−1	4i−1	NUM
ma-345	202	7	.	.	PUNCT
ma-345	203	1	(	(	PUNCT
ma-345	203	2	2.26	2.26	NUM
ma-345	203	3	)	)	PUNCT
ma-345	203	4	next	next	ADV
ma-345	203	5	,	,	PUNCT
ma-345	203	6	by	by	ADP
ma-345	203	7	the	the	DET
ma-345	203	8	fourth	fourth	ADJ
ma-345	203	9	equation	equation	NOUN
ma-345	203	10	of	of	ADP
ma-345	203	11	(	(	PUNCT
ma-345	203	12	tsklm	tsklm	PROPN
ma-345	203	13	)	)	PUNCT
ma-345	203	14	,	,	PUNCT
ma-345	203	15	we	we	PRON
ma-345	203	16	can	can	AUX
ma-345	203	17	write	write	VERB
ma-345	203	18	i	i	PRON
ma-345	203	19	−miki+1	−miki+1	PUNCT
ma-345	204	1	=	=	PUNCT
ma-345	204	2	(	(	PUNCT
ma-345	204	3	i	i	PRON
ma-345	204	4	−	−	PROPN
ma-345	204	5	tiki+1)2	tiki+1)2	PROPN
ma-345	204	6	,	,	PUNCT
ma-345	204	7	so	so	SCONJ
ma-345	204	8	‖i	‖i	NOUN
ma-345	204	9	−miki+1‖	−miki+1‖	PRON
ma-345	204	10	≤	≤	ADJ
ma-345	204	11	‖i	‖i	NOUN
ma-345	204	12	−	−	PROPN
ma-345	204	13	tiki+1‖2	tiki+1‖2	PROPN
ma-345	204	14	≤	≤	NUM
ma-345	204	15	c26a2q2×4	c26a2q2×4	VERB
ma-345	204	16	i−1	i−1	PROPN
ma-345	204	17	.	.	PUNCT
ma-345	205	1	(	(	PUNCT
ma-345	205	2	2.27	2.27	NUM
ma-345	205	3	)	)	PUNCT
ma-345	206	1	but	but	CCONJ
ma-345	206	2	,	,	PUNCT
ma-345	206	3	we	we	PRON
ma-345	206	4	can	can	AUX
ma-345	206	5	also	also	ADV
ma-345	206	6	write	write	VERB
ma-345	206	7	ti+1	ti+1	PRON
ma-345	206	8	=	=	SYM
ma-345	206	9	mi	mi	PROPN
ma-345	207	1	+	+	PROPN
ma-345	207	2	mi(2i	mi(2i	PROPN
ma-345	207	3	−ki+1mi)(i	−ki+1mi)(i	PROPN
ma-345	207	4	−ki+1mi	−ki+1mi	PROPN
ma-345	207	5	)	)	PUNCT
ma-345	207	6	.	.	PUNCT
ma-345	208	1	(	(	PUNCT
ma-345	208	2	2.28	2.28	NUM
ma-345	208	3	)	)	PUNCT
ma-345	208	4	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
ma-345	208	5	eur	eur	PROPN
ma-345	208	6	.	.	PUNCT
ma-345	209	1	j.	j.	PROPN
ma-345	209	2	math	math	PROPN
ma-345	209	3	.	.	PUNCT
ma-345	210	1	anal	anal	PROPN
ma-345	210	2	.	.	PUNCT
ma-345	211	1	10.28924	10.28924	NUM
ma-345	211	2	/	/	SYM
ma-345	211	3	ada	ada	PROPN
ma-345	211	4	/	/	SYM
ma-345	211	5	ma.5.15	ma.5.15	NOUN
ma-345	211	6	8thus	8thus	NUM
ma-345	211	7	,	,	PUNCT
ma-345	211	8	we	we	PRON
ma-345	211	9	get	get	VERB
ma-345	211	10	i	i	PRON
ma-345	211	11	−	−	NOUN
ma-345	212	1	ti+1ki+1	ti+1ki+1	NOUN
ma-345	213	1	=	=	NOUN
ma-345	213	2	i	i	PRON
ma-345	213	3	−	−	PROPN
ma-345	213	4	(	(	PUNCT
ma-345	213	5	mi	mi	PROPN
ma-345	213	6	+	+	PROPN
ma-345	213	7	mi(2i	mi(2i	PROPN
ma-345	213	8	−ki+1mi)(i	−ki+1mi)(i	PROPN
ma-345	213	9	−ki+1mi))ki+1	−ki+1mi))ki+1	NOUN
ma-345	214	1	=	=	SYM
ma-345	215	1	(	(	PUNCT
ma-345	215	2	i	i	NOUN
ma-345	215	3	−miki+1	−miki+1	PROPN
ma-345	215	4	)	)	PUNCT
ma-345	215	5	3	3	NUM
ma-345	215	6	.	.	PUNCT
ma-345	215	7	(	(	PUNCT
ma-345	215	8	2.29	2.29	NUM
ma-345	215	9	)	)	PUNCT
ma-345	215	10	therefore	therefore	ADV
ma-345	215	11	,	,	PUNCT
ma-345	215	12	since	since	SCONJ
ma-345	215	13	a	a	DET
ma-345	215	14	∈	∈	PROPN
ma-345	216	1	[	[	X
ma-345	216	2	0	0	NUM
ma-345	216	3	,	,	PUNCT
ma-345	216	4	1	1	NUM
ma-345	216	5	]	]	PUNCT
ma-345	216	6	,	,	PUNCT
ma-345	216	7	we	we	PRON
ma-345	216	8	get	get	VERB
ma-345	216	9	by	by	ADP
ma-345	216	10	the	the	DET
ma-345	216	11	inductions	induction	NOUN
ma-345	216	12	hypotheses	hypothesis	NOUN
ma-345	216	13	and	and	CCONJ
ma-345	216	14	(	(	PUNCT
ma-345	216	15	2.29	2.29	NUM
ma-345	216	16	)	)	PUNCT
ma-345	216	17	that	that	SCONJ
ma-345	216	18	‖i	‖i	NOUN
ma-345	216	19	−	−	PROPN
ma-345	216	20	ti+1ki+1‖	ti+1ki+1‖	PROPN
ma-345	216	21	≤	≤	NOUN
ma-345	216	22	‖i	‖i	NOUN
ma-345	216	23	−miki+1‖3	−miki+1‖3	NOUN
ma-345	216	24	≤	≤	NUM
ma-345	216	25	c66a6q6×4	c66a6q6×4	NOUN
ma-345	216	26	i−1	i−1	PROPN
ma-345	216	27	≤	≤	NOUN
ma-345	217	1	aq4i	aq4i	NOUN
ma-345	217	2	showing	show	VERB
ma-345	217	3	(	(	PUNCT
ma-345	217	4	2.8	2.8	NUM
ma-345	217	5	)	)	PUNCT
ma-345	217	6	for	for	ADP
ma-345	217	7	n	n	NOUN
ma-345	217	8	=	=	SYM
ma-345	217	9	i	i	PRON
ma-345	218	1	+	+	CCONJ
ma-345	218	2	1.consequently	1.consequently	ADV
ma-345	218	3	the	the	DET
ma-345	218	4	induction	induction	NOUN
ma-345	218	5	for	for	ADP
ma-345	218	6	(	(	PUNCT
ma-345	218	7	2.7	2.7	NUM
ma-345	218	8	)	)	PUNCT
ma-345	218	9	and	and	CCONJ
ma-345	218	10	(	(	PUNCT
ma-345	218	11	2.8	2.8	NUM
ma-345	218	12	)	)	PUNCT
ma-345	218	13	is	be	AUX
ma-345	218	14	completed.finally	completed.finally	ADV
ma-345	218	15	,	,	PUNCT
ma-345	218	16	by	by	ADP
ma-345	218	17	letting	let	VERB
ma-345	218	18	n	n	PRON
ma-345	218	19	→∞	→∞	NOUN
ma-345	218	20	in	in	ADP
ma-345	218	21	(	(	PUNCT
ma-345	218	22	2.7	2.7	NUM
ma-345	218	23	)	)	PUNCT
ma-345	218	24	,	,	PUNCT
ma-345	218	25	we	we	PRON
ma-345	218	26	deduce	deduce	VERB
ma-345	218	27	that	that	SCONJ
ma-345	218	28	lim	lim	PROPN
ma-345	218	29	n→∞	n→∞	X
ma-345	218	30	xn	xn	PROPN
ma-345	218	31	=	=	SYM
ma-345	218	32	x∗	x∗	PROPN
ma-345	218	33	,	,	PUNCT
ma-345	218	34	since	since	SCONJ
ma-345	218	35	q	q	PROPN
ma-345	218	36	∈	∈	PROPN
ma-345	219	1	[	[	X
ma-345	219	2	0	0	NUM
ma-345	219	3	,	,	PUNCT
ma-345	219	4	1	1	NUM
ma-345	219	5	)	)	PUNCT
ma-345	219	6	.	.	PUNCT
ma-345	220	1	remark	remark	PROPN
ma-345	220	2	2.2	2.2	NUM
ma-345	220	3	.	.	PUNCT
ma-345	221	1	it	it	PRON
ma-345	221	2	turns	turn	VERB
ma-345	221	3	out	out	ADP
ma-345	221	4	that	that	SCONJ
ma-345	221	5	the	the	DET
ma-345	221	6	proof	proof	NOUN
ma-345	221	7	of	of	ADP
ma-345	221	8	theorem	theorem	ADJ
ma-345	221	9	2.1	2.1	NUM
ma-345	221	10	can	can	AUX
ma-345	221	11	be	be	AUX
ma-345	221	12	repeated	repeat	VERB
ma-345	221	13	in	in	ADP
ma-345	221	14	the	the	DET
ma-345	221	15	case	case	NOUN
ma-345	221	16	of	of	ADP
ma-345	221	17	the	the	DET
ma-345	221	18	method	method	NOUN
ma-345	221	19	(	(	PUNCT
ma-345	221	20	1.8	1.8	NUM
ma-345	221	21	)	)	PUNCT
ma-345	221	22	as	as	ADV
ma-345	221	23	long	long	ADV
ma-345	221	24	as	as	SCONJ
ma-345	221	25	we	we	PRON
ma-345	221	26	add	add	VERB
ma-345	221	27	an	an	DET
ma-345	221	28	additional	additional	ADJ
ma-345	221	29	condition	condition	NOUN
ma-345	221	30	of	of	ADP
ma-345	221	31	the	the	DET
ma-345	221	32	form	form	NOUN
ma-345	221	33	for	for	ADP
ma-345	221	34	each	each	DET
ma-345	221	35	n	n	NOUN
ma-345	221	36	=	=	SYM
ma-345	221	37	0	0	NUM
ma-345	221	38	,	,	PUNCT
ma-345	221	39	1	1	NUM
ma-345	221	40	,	,	PUNCT
ma-345	221	41	2	2	NUM
ma-345	221	42	,	,	PUNCT
ma-345	221	43	.	.	PUNCT
ma-345	221	44	.	.	PUNCT
ma-345	222	1	.	.	PUNCT
ma-345	223	1	‖ln	‖ln	NUM
ma-345	223	2	−	−	PROPN
ma-345	223	3	f	f	PROPN
ma-345	223	4	′(xn)‖	′(xn)‖	NOUN
ma-345	223	5	≤	≤	PUNCT
ma-345	223	6	σn‖f	σn‖f	PROPN
ma-345	223	7	(	(	PUNCT
ma-345	223	8	xn)‖	xn)‖	PROPN
ma-345	223	9	,	,	PUNCT
ma-345	223	10	(	(	PUNCT
ma-345	223	11	2.30	2.30	NUM
ma-345	223	12	)	)	PUNCT
ma-345	223	13	where	where	SCONJ
ma-345	223	14	{	{	PUNCT
ma-345	223	15	σn	σn	NOUN
ma-345	223	16	}	}	PUNCT
ma-345	223	17	is	be	AUX
ma-345	223	18	a	a	DET
ma-345	223	19	nonnegative	nonnegative	ADJ
ma-345	223	20	sequence	sequence	NOUN
ma-345	223	21	such	such	ADJ
ma-345	223	22	that	that	DET
ma-345	223	23	sup	sup	NOUN
ma-345	223	24	n≥0	n≥0	ADJ
ma-345	223	25	σn	σn	PRON
ma-345	223	26	≤	≤	NUM
ma-345	223	27	σ	σ	PROPN
ma-345	223	28	,	,	PUNCT
ma-345	223	29	where	where	SCONJ
ma-345	223	30	σ	σ	PROPN
ma-345	223	31	≥	≥	X
ma-345	223	32	0	0	NUM
ma-345	223	33	3	3	X
ma-345	223	34	.	.	PUNCT
ma-345	223	35	numerical	numerical	ADJ
ma-345	223	36	examples	example	NOUN
ma-345	223	37	in	in	ADP
ma-345	223	38	this	this	DET
ma-345	223	39	section	section	NOUN
ma-345	223	40	,	,	PUNCT
ma-345	223	41	we	we	PRON
ma-345	223	42	present	present	VERB
ma-345	223	43	the	the	DET
ma-345	223	44	results	result	NOUN
ma-345	223	45	of	of	ADP
ma-345	223	46	numerical	numerical	ADJ
ma-345	223	47	investigation	investigation	NOUN
ma-345	223	48	of	of	ADP
ma-345	223	49	the	the	DET
ma-345	223	50	three	three	NUM
ma-345	223	51	-	-	PUNCT
ma-345	223	52	step	step	NOUN
ma-345	223	53	kurchatov	kurchatov	ADJ
ma-345	223	54	-	-	PUNCT
ma-345	223	55	like	like	ADJ
ma-345	223	56	method	method	NOUN
ma-345	223	57	for	for	ADP
ma-345	223	58	solving	solve	VERB
ma-345	223	59	the	the	DET
ma-345	223	60	nonlinear	nonlinear	ADJ
ma-345	223	61	equation	equation	NOUN
ma-345	223	62	(	(	PUNCT
ma-345	223	63	1.1	1.1	NUM
ma-345	223	64	)	)	PUNCT
ma-345	223	65	.	.	PUNCT
ma-345	224	1	we	we	PRON
ma-345	224	2	give	give	VERB
ma-345	224	3	errors	error	NOUN
ma-345	224	4	at	at	ADP
ma-345	224	5	each	each	DET
ma-345	224	6	iteration	iteration	NOUN
ma-345	224	7	andacoc	andacoc	NOUN
ma-345	224	8	and	and	CCONJ
ma-345	224	9	coc	coc	NOUN
ma-345	224	10	for	for	ADP
ma-345	224	11	considered	consider	VERB
ma-345	224	12	methods	method	NOUN
ma-345	224	13	(	(	PUNCT
ma-345	224	14	1.4	1.4	NUM
ma-345	224	15	)	)	PUNCT
ma-345	224	16	,	,	PUNCT
ma-345	224	17	(	(	PUNCT
ma-345	224	18	1.5	1.5	NUM
ma-345	224	19	)	)	PUNCT
ma-345	224	20	,	,	PUNCT
ma-345	224	21	(	(	PUNCT
ma-345	224	22	1.6	1.6	NUM
ma-345	224	23	)	)	PUNCT
ma-345	224	24	,	,	PUNCT
ma-345	224	25	(	(	PUNCT
ma-345	224	26	1.7	1.7	NUM
ma-345	224	27	)	)	PUNCT
ma-345	224	28	,	,	PUNCT
ma-345	224	29	(	(	PUNCT
ma-345	224	30	1.8	1.8	NUM
ma-345	224	31	)	)	PUNCT
ma-345	224	32	.	.	PUNCT
ma-345	225	1	the	the	DET
ma-345	225	2	computations	computation	NOUN
ma-345	225	3	werecarried	werecarrie	VERB
ma-345	225	4	out	out	ADP
ma-345	225	5	on	on	ADP
ma-345	225	6	a	a	DET
ma-345	225	7	pc	pc	NOUN
ma-345	225	8	with	with	ADP
ma-345	225	9	1.00	1.00	NUM
ma-345	225	10	ghz	ghz	NOUN
ma-345	225	11	processor	processor	NOUN
ma-345	225	12	and	and	CCONJ
ma-345	225	13	8	8	NUM
ma-345	225	14	gb	gb	NOUN
ma-345	225	15	of	of	ADP
ma-345	225	16	memory	memory	NOUN
ma-345	225	17	with	with	ADP
ma-345	225	18	use	use	NOUN
ma-345	225	19	of	of	ADP
ma-345	225	20	softwaregnu	softwaregnu	NOUN
ma-345	225	21	octave	octave	VERB
ma-345	225	22	7.3.0	7.3.0	NUM
ma-345	225	23	.	.	PUNCT
ma-345	226	1	the	the	DET
ma-345	226	2	euclidean	euclidean	ADJ
ma-345	226	3	norm	norm	NOUN
ma-345	226	4	was	be	AUX
ma-345	226	5	used	use	VERB
ma-345	226	6	.	.	PUNCT
ma-345	227	1	the	the	DET
ma-345	227	2	initial	initial	ADJ
ma-345	227	3	approximation	approximation	NOUN
ma-345	227	4	t0	t0	PROPN
ma-345	227	5	was	be	AUX
ma-345	227	6	com	com	NOUN
ma-345	227	7	-	-	PUNCT
ma-345	227	8	puted	put	VERB
ma-345	227	9	by	by	ADP
ma-345	227	10	formulas	formula	NOUN
ma-345	227	11	t0	t0	PROPN
ma-345	227	12	=	=	PUNCT
ma-345	228	1	[	[	X
ma-345	228	2	2x0	2x0	NUM
ma-345	228	3	−	−	PROPN
ma-345	228	4	x−1	x−1	PROPN
ma-345	228	5	,	,	PUNCT
ma-345	228	6	x−1;f	x−1;f	PROPN
ma-345	228	7	]	]	X
ma-345	228	8	−1	−1	NOUN
ma-345	228	9	for	for	ADP
ma-345	228	10	methods	method	NOUN
ma-345	228	11	(	(	PUNCT
ma-345	228	12	1.4	1.4	NUM
ma-345	228	13	)	)	PUNCT
ma-345	228	14	,	,	PUNCT
ma-345	228	15	(	(	PUNCT
ma-345	228	16	1.5	1.5	NUM
ma-345	228	17	)	)	PUNCT
ma-345	228	18	,	,	PUNCT
ma-345	228	19	(	(	PUNCT
ma-345	228	20	1.6	1.6	NUM
ma-345	228	21	)	)	PUNCT
ma-345	228	22	,	,	PUNCT
ma-345	228	23	t0	t0	X
ma-345	228	24	=	=	SYM
ma-345	228	25	f	f	PROPN
ma-345	228	26	′(x0	′(x0	NOUN
ma-345	228	27	)	)	PUNCT
ma-345	228	28	−1	−1	NOUN
ma-345	228	29	–	–	PUNCT
ma-345	228	30	for	for	ADP
ma-345	228	31	method	method	NOUN
ma-345	228	32	(	(	PUNCT
ma-345	228	33	1.7	1.7	NUM
ma-345	228	34	)	)	PUNCT
ma-345	228	35	and	and	CCONJ
ma-345	228	36	t0	t0	PROPN
ma-345	228	37	=	=	SYM
ma-345	228	38	l(x0	l(x0	PROPN
ma-345	228	39	)	)	PUNCT
ma-345	228	40	−1	−1	NOUN
ma-345	228	41	–	–	PUNCT
ma-345	228	42	for	for	ADP
ma-345	228	43	method	method	NOUN
ma-345	228	44	(	(	PUNCT
ma-345	228	45	1.8	1.8	NUM
ma-345	228	46	)	)	PUNCT
ma-345	228	47	,	,	PUNCT
ma-345	228	48	where	where	SCONJ
ma-345	228	49	(	(	PUNCT
ma-345	228	50	a	a	X
ma-345	228	51	)	)	PUNCT
ma-345	228	52	l(x	l(x	PROPN
ma-345	228	53	)	)	PUNCT
ma-345	228	54	=	=	PUNCT
ma-345	229	1	[	[	X
ma-345	229	2	x	x	X
ma-345	229	3	,	,	PUNCT
ma-345	229	4	x	x	PROPN
ma-345	229	5	+	+	NUM
ma-345	229	6	α;f	α;f	NUM
ma-345	229	7	]	]	PUNCT
ma-345	229	8	and(b	and(b	PROPN
ma-345	229	9	)	)	PUNCT
ma-345	229	10	l(x	l(x	PROPN
ma-345	229	11	)	)	PUNCT
ma-345	229	12	=	=	PUNCT
ma-345	230	1	[	[	X
ma-345	230	2	x	x	X
ma-345	230	3	+	+	PUNCT
ma-345	230	4	α1f	α1f	NOUN
ma-345	230	5	(	(	PUNCT
ma-345	230	6	x	x	NOUN
ma-345	230	7	)	)	PUNCT
ma-345	230	8	,	,	PUNCT
ma-345	230	9	x	x	X
ma-345	230	10	+	+	NUM
ma-345	230	11	α2f	α2f	PROPN
ma-345	230	12	(	(	PUNCT
ma-345	230	13	x);f	x);f	PUNCT
ma-345	230	14	]	]	X
ma-345	230	15	with	with	ADP
ma-345	230	16	α	α	PROPN
ma-345	230	17	∈	∈	PROPN
ma-345	230	18	r.	r.	PROPN
ma-345	230	19	example	example	NOUN
ma-345	230	20	3.1	3.1	NUM
ma-345	230	21	.	.	PUNCT
ma-345	231	1	let	let	VERB
ma-345	231	2	f	f	NOUN
ma-345	231	3	:	:	PUNCT
ma-345	231	4	r→	r→	PROPN
ma-345	231	5	r	r	NOUN
ma-345	231	6	and	and	CCONJ
ma-345	231	7	consider	consider	VERB
ma-345	231	8	the	the	DET
ma-345	231	9	nonlinear	nonlinear	ADJ
ma-345	231	10	equation	equation	NOUN
ma-345	231	11	f	f	X
ma-345	231	12	(	(	PUNCT
ma-345	231	13	x	x	X
ma-345	231	14	)	)	PUNCT
ma-345	231	15	=	=	SYM
ma-345	231	16	ex−0.1	ex−0.1	PROPN
ma-345	231	17	−	−	PROPN
ma-345	231	18	10x	10x	PROPN
ma-345	231	19	|x	|x	NOUN
ma-345	231	20	−	−	PROPN
ma-345	231	21	1|	1|	NUM
ma-345	231	22	−	−	NOUN
ma-345	231	23	0.1	0.1	NUM
ma-345	231	24	=	=	SYM
ma-345	231	25	0	0	NUM
ma-345	231	26	with	with	ADP
ma-345	231	27	the	the	DET
ma-345	231	28	exact	exact	ADJ
ma-345	231	29	solution	solution	NOUN
ma-345	231	30	x∗	x∗	PROPN
ma-345	231	31	=	=	PUNCT
ma-345	231	32	0.1	0.1	NUM
ma-345	231	33	.	.	PUNCT
ma-345	231	34	example	example	NOUN
ma-345	231	35	3.2	3.2	NUM
ma-345	231	36	.	.	PUNCT
ma-345	232	1	let	let	VERB
ma-345	232	2	f	f	NOUN
ma-345	232	3	:	:	PUNCT
ma-345	232	4	r2	r2	PROPN
ma-345	232	5	→	→	SYM
ma-345	232	6	r2	r2	PROPN
ma-345	232	7	and	and	CCONJ
ma-345	232	8	consider	consider	VERB
ma-345	232	9	the	the	DET
ma-345	232	10	system	system	NOUN
ma-345	232	11	of	of	ADP
ma-345	232	12	two	two	NUM
ma-345	232	13	equations	equation	NOUN
ma-345	232	14	with	with	ADP
ma-345	232	15	x	x	X
ma-345	232	16	=	=	SYM
ma-345	232	17	(	(	PUNCT
ma-345	232	18	ξ	ξ	PROPN
ma-345	232	19	;	;	PUNCT
ma-345	232	20	η	η	NOUN
ma-345	232	21	)	)	PUNCT
ma-345	232	22	{	{	PUNCT
ma-345	232	23	f1(x	f1(x	NOUN
ma-345	232	24	)	)	PUNCT
ma-345	232	25	=	=	SYM
ma-345	233	1	3ξ2η	3ξ2η	NUM
ma-345	233	2	+	+	CCONJ
ma-345	233	3	η2	η2	ADJ
ma-345	233	4	+	+	CCONJ
ma-345	233	5	|ξ	|ξ	VERB
ma-345	233	6	−	−	PROPN
ma-345	233	7	1|	1|	NUM
ma-345	233	8	−	−	NOUN
ma-345	233	9	0.75	0.75	NUM
ma-345	233	10	=	=	SYM
ma-345	233	11	0	0	NUM
ma-345	233	12	,	,	PUNCT
ma-345	233	13	f2(x	f2(x	NUM
ma-345	233	14	)	)	PUNCT
ma-345	233	15	=	=	VERB
ma-345	233	16	ξ4	ξ4	NOUN
ma-345	233	17	+	+	NUM
ma-345	233	18	ξη3	ξη3	NOUN
ma-345	233	19	+	+	CCONJ
ma-345	234	1	|η|	|η|	PROPN
ma-345	234	2	−	−	PROPN
ma-345	234	3	0.5625	0.5625	NUM
ma-345	234	4	=	=	SYM
ma-345	234	5	0	0	NUM
ma-345	234	6	,	,	PUNCT
ma-345	234	7	and	and	CCONJ
ma-345	234	8	the	the	DET
ma-345	234	9	exact	exact	ADJ
ma-345	234	10	solution	solution	NOUN
ma-345	234	11	x∗	x∗	PROPN
ma-345	234	12	=	=	SYM
ma-345	234	13	(	(	PUNCT
ma-345	234	14	0.5	0.5	NUM
ma-345	234	15	;	;	PUNCT
ma-345	234	16	−1	−1	NUM
ma-345	234	17	)	)	PUNCT
ma-345	234	18	.	.	PUNCT
ma-345	235	1	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
ma-345	235	2	eur	eur	PROPN
ma-345	235	3	.	.	PUNCT
ma-345	236	1	j.	j.	PROPN
ma-345	236	2	math	math	PROPN
ma-345	236	3	.	.	PUNCT
ma-345	237	1	anal	anal	PROPN
ma-345	237	2	.	.	PUNCT
ma-345	238	1	10.28924	10.28924	NUM
ma-345	238	2	/	/	SYM
ma-345	238	3	ada	ada	PROPN
ma-345	238	4	/	/	SYM
ma-345	238	5	ma.5.15	ma.5.15	NOUN
ma-345	238	6	9table	9table	NUM
ma-345	238	7	1	1	NUM
ma-345	238	8	.	.	PUNCT
ma-345	238	9	error	error	NOUN
ma-345	238	10	’s	’s	PART
ma-345	238	11	value	value	NOUN
ma-345	238	12	at	at	ADP
ma-345	238	13	each	each	DET
ma-345	238	14	iteration	iteration	NOUN
ma-345	238	15	for	for	ADP
ma-345	238	16	example	example	NOUN
ma-345	238	17	3.1	3.1	NUM
ma-345	238	18	.	.	PUNCT
ma-345	239	1	n	n	PRON
ma-345	239	2	method	method	NOUN
ma-345	239	3	(	(	PUNCT
ma-345	239	4	1.4	1.4	NUM
ma-345	239	5	)	)	PUNCT
ma-345	239	6	method	method	NOUN
ma-345	239	7	(	(	PUNCT
ma-345	239	8	1.5	1.5	NUM
ma-345	239	9	)	)	PUNCT
ma-345	239	10	method	method	NOUN
ma-345	239	11	(	(	PUNCT
ma-345	239	12	1.6	1.6	NUM
ma-345	239	13	)	)	PUNCT
ma-345	240	1	‖xn	‖xn	PROPN
ma-345	240	2	−	−	NUM
ma-345	240	3	x∗‖	x∗‖	PROPN
ma-345	240	4	‖f	‖f	ADJ
ma-345	240	5	(	(	PUNCT
ma-345	240	6	xn)‖	xn)‖	PROPN
ma-345	240	7	‖xn	‖xn	PROPN
ma-345	240	8	−	−	PROPN
ma-345	240	9	x∗‖	x∗‖	PROPN
ma-345	240	10	‖f	‖f	ADJ
ma-345	240	11	(	(	PUNCT
ma-345	240	12	xn)‖	xn)‖	PROPN
ma-345	240	13	‖xn	‖xn	PROPN
ma-345	240	14	−	−	PROPN
ma-345	240	15	x∗‖	x∗‖	PROPN
ma-345	240	16	‖f	‖f	PROPN
ma-345	240	17	(	(	PUNCT
ma-345	240	18	xn)‖0	xn)‖0	PROPN
ma-345	240	19	6.0000e-01	6.0000e-01	NUM
ma-345	240	20	7.9488e+00	7.9488e+00	NUM
ma-345	240	21	6.0000e-01	6.0000e-01	NUM
ma-345	240	22	7.9488e+00	7.9488e+00	NUM
ma-345	240	23	6.0000e-01	6.0000e-01	NUM
ma-345	240	24	7.9488e+001	7.9488e+001	NUM
ma-345	240	25	6.0089e-02	6.0089e-02	NUM
ma-345	240	26	4.5850e-01	4.5850e-01	NUM
ma-345	240	27	6.0089e-02	6.0089e-02	NUM
ma-345	240	28	4.5850e-01	4.5850e-01	NUM
ma-345	240	29	6.0089e-02	6.0089e-02	NUM
ma-345	240	30	4.5850e-012	4.5850e-012	PROPN
ma-345	240	31	2.3413e-03	2.3413e-03	NUM
ma-345	240	32	1.6447e-02	1.6447e-02	NUM
ma-345	240	33	2.1002e-04	2.1002e-04	NUM
ma-345	240	34	1.4706e-03	1.4706e-03	NUM
ma-345	240	35	1.9390e-04	1.9390e-04	NUM
ma-345	240	36	1.3577e-033	1.3577e-033	PROPN
ma-345	240	37	3.4615e-07	3.4615e-07	NUM
ma-345	240	38	2.4231e-06	2.4231e-06	NUM
ma-345	240	39	3.2876e-14	3.2876e-14	NUM
ma-345	240	40	2.3012e-13	2.3012e-13	NUM
ma-345	240	41	1.2934e-14	1.2934e-14	NUM
ma-345	240	42	9.0566e-144	9.0566e-144	PROPN
ma-345	240	43	1.3878e-17	1.3878e-17	NUM
ma-345	240	44	8.3267e-17	8.3267e-17	NUM
ma-345	240	45	table	table	NOUN
ma-345	240	46	2	2	NUM
ma-345	240	47	.	.	PUNCT
ma-345	240	48	error	error	NOUN
ma-345	240	49	’s	’s	PART
ma-345	240	50	value	value	NOUN
ma-345	240	51	at	at	ADP
ma-345	240	52	each	each	DET
ma-345	240	53	iteration	iteration	NOUN
ma-345	240	54	for	for	ADP
ma-345	240	55	example	example	NOUN
ma-345	240	56	3.1	3.1	NUM
ma-345	240	57	(	(	PUNCT
ma-345	240	58	method	method	NOUN
ma-345	240	59	(	(	PUNCT
ma-345	240	60	1.8	1.8	NUM
ma-345	240	61	)	)	PUNCT
ma-345	240	62	)	)	PUNCT
ma-345	240	63	.	.	PUNCT
ma-345	241	1	n	n	X
ma-345	241	2	(	(	PUNCT
ma-345	241	3	a	a	X
ma-345	241	4	)	)	PUNCT
ma-345	241	5	,	,	PUNCT
ma-345	241	6	α	α	X
ma-345	241	7	=	=	SYM
ma-345	241	8	10−6	10−6	NUM
ma-345	241	9	(	(	PUNCT
ma-345	241	10	b	b	NOUN
ma-345	241	11	)	)	PUNCT
ma-345	241	12	,	,	PUNCT
ma-345	241	13	α1	α1	PROPN
ma-345	241	14	=	=	SYM
ma-345	241	15	0	0	NUM
ma-345	241	16	,	,	PUNCT
ma-345	241	17	α2	α2	NOUN
ma-345	241	18	=	=	SYM
ma-345	241	19	0.01	0.01	NUM
ma-345	241	20	‖xn	‖xn	PROPN
ma-345	241	21	−	−	PROPN
ma-345	241	22	x∗‖	x∗‖	PROPN
ma-345	241	23	‖f	‖f	ADJ
ma-345	241	24	(	(	PUNCT
ma-345	241	25	xn)‖	xn)‖	PROPN
ma-345	241	26	‖xn	‖xn	PROPN
ma-345	241	27	−	−	PROPN
ma-345	241	28	x∗‖	x∗‖	PROPN
ma-345	241	29	‖f	‖f	PROPN
ma-345	241	30	(	(	PUNCT
ma-345	241	31	xn)‖0	xn)‖0	PROPN
ma-345	241	32	6.0000e-01	6.0000e-01	NUM
ma-345	242	1	7.9488e+00	7.9488e+00	NUM
ma-345	242	2	6.0000e-01	6.0000e-01	NUM
ma-345	242	3	7.9488e+001	7.9488e+001	NUM
ma-345	242	4	6.0098e-02	6.0098e-02	NUM
ma-345	242	5	4.5857e-01	4.5857e-01	NUM
ma-345	242	6	5.2350e-02	5.2350e-02	NUM
ma-345	242	7	3.9520e-012	3.9520e-012	PROPN
ma-345	242	8	2.1022e-04	2.1022e-04	NUM
ma-345	242	9	1.4720e-03	1.4720e-03	NUM
ma-345	242	10	1.2109e-04	1.2109e-04	NUM
ma-345	242	11	8.4780e-043	8.4780e-043	NOUN
ma-345	242	12	3.2724e-14	3.2724e-14	NUM
ma-345	242	13	2.2890e-13	2.2890e-13	NUM
ma-345	242	14	3.0254e-15	3.0254e-15	NUM
ma-345	242	15	2.1178e-14	2.1178e-14	NUM
ma-345	242	16	table	table	NOUN
ma-345	242	17	3	3	NUM
ma-345	242	18	.	.	PUNCT
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ma-345	242	20	’s	’s	PART
ma-345	242	21	value	value	NOUN
ma-345	242	22	at	at	ADP
ma-345	242	23	each	each	DET
ma-345	242	24	iteration	iteration	NOUN
ma-345	242	25	for	for	ADP
ma-345	242	26	example	example	NOUN
ma-345	242	27	3.1	3.1	NUM
ma-345	242	28	(	(	PUNCT
ma-345	242	29	method	method	NOUN
ma-345	242	30	(	(	PUNCT
ma-345	242	31	1.8	1.8	NUM
ma-345	242	32	)	)	PUNCT
ma-345	242	33	)	)	PUNCT
ma-345	242	34	.	.	PUNCT
ma-345	243	1	n	n	PROPN
ma-345	243	2	(	(	PUNCT
ma-345	243	3	b	b	NOUN
ma-345	243	4	)	)	PUNCT
ma-345	243	5	,	,	PUNCT
ma-345	243	6	α1	α1	PROPN
ma-345	243	7	=	=	SYM
ma-345	243	8	−1	−1	NOUN
ma-345	243	9	,	,	PUNCT
ma-345	243	10	α2	α2	PROPN
ma-345	243	11	=	=	SYM
ma-345	243	12	1	1	NUM
ma-345	243	13	(	(	PUNCT
ma-345	243	14	b	b	NOUN
ma-345	243	15	)	)	PUNCT
ma-345	243	16	,	,	PUNCT
ma-345	243	17	α1	α1	PROPN
ma-345	243	18	=	=	SYM
ma-345	243	19	0	0	NUM
ma-345	243	20	,	,	PUNCT
ma-345	243	21	α2	α2	NOUN
ma-345	243	22	=	=	SYM
ma-345	243	23	1	1	NUM
ma-345	243	24	(	(	PUNCT
ma-345	243	25	b	b	NOUN
ma-345	243	26	)	)	PUNCT
ma-345	243	27	,	,	PUNCT
ma-345	243	28	α1	α1	PROPN
ma-345	243	29	=	=	SYM
ma-345	243	30	−1	−1	NOUN
ma-345	243	31	,	,	PUNCT
ma-345	243	32	α2	α2	PROPN
ma-345	243	33	=	=	SYM
ma-345	243	34	0	0	PROPN
ma-345	243	35	‖xn	‖xn	PROPN
ma-345	243	36	−	−	PROPN
ma-345	243	37	x∗‖	x∗‖	PROPN
ma-345	243	38	‖f	‖f	ADJ
ma-345	243	39	(	(	PUNCT
ma-345	243	40	xn)‖	xn)‖	PROPN
ma-345	243	41	‖xn	‖xn	PROPN
ma-345	243	42	−	−	PROPN
ma-345	243	43	x∗‖	x∗‖	PROPN
ma-345	243	44	‖f	‖f	ADJ
ma-345	243	45	(	(	PUNCT
ma-345	243	46	xn)‖	xn)‖	PROPN
ma-345	243	47	‖xn	‖xn	PROPN
ma-345	243	48	−	−	PROPN
ma-345	243	49	x∗‖	x∗‖	PROPN
ma-345	243	50	‖f	‖f	PROPN
ma-345	243	51	(	(	PUNCT
ma-345	243	52	xn)‖0	xn)‖0	PROPN
ma-345	243	53	2.2500e-01	2.2500e-01	NUM
ma-345	243	54	2.1048e+00	2.1048e+00	NUM
ma-345	243	55	2.2500e-01	2.2500e-01	NUM
ma-345	243	56	2.1048e+00	2.1048e+00	NUM
ma-345	243	57	2.2500e-01	2.2500e-01	NUM
ma-345	243	58	2.1048e+001	2.1048e+001	NUM
ma-345	243	59	4.3916e-02	4.3916e-02	NUM
ma-345	243	60	3.2765e-01	3.2765e-01	NUM
ma-345	243	61	2.8627e-04	2.8627e-04	NUM
ma-345	243	62	2.0031e-03	2.0031e-03	NUM
ma-345	243	63	8.9687e-02	8.9687e-02	NUM
ma-345	244	1	7.1215e-012	7.1215e-012	NUM
ma-345	244	2	1.1100e-04	1.1100e-04	NUM
ma-345	244	3	7.7714e-04	7.7714e-04	NUM
ma-345	244	4	3.3741e-12	3.3741e-12	NUM
ma-345	244	5	2.3618e-11	2.3618e-11	NUM
ma-345	244	6	1.4334e-02	1.4334e-02	NUM
ma-345	244	7	1.0249e-013	1.0249e-013	PROPN
ma-345	244	8	2.4702e-15	2.4702e-15	NUM
ma-345	244	9	1.7292e-14	1.7292e-14	NUM
ma-345	244	10	6.9350e-05	6.9350e-05	NUM
ma-345	245	1	4.8550e-044	4.8550e-044	NUM
ma-345	245	2	5.5539e-14	5.5539e-14	NUM
ma-345	245	3	3.8877e-13	3.8877e-13	NUM
ma-345	245	4	table	table	NOUN
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ma-345	245	8	,	,	PUNCT
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ma-345	245	10	for	for	ADP
ma-345	245	11	example	example	NOUN
ma-345	245	12	3.1	3.1	NUM
ma-345	245	13	.	.	PUNCT
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ma-345	245	15	δ1	δ1	NOUN
ma-345	245	16	δ2	δ2	VERB
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ma-345	245	18	(	(	PUNCT
ma-345	245	19	1.4	1.4	NUM
ma-345	245	20	)	)	PUNCT
ma-345	245	21	2.7545	2.7545	NUM
ma-345	245	22	2.7145	2.7145	NUM
ma-345	245	23	2.7309method	2.7309method	NOUN
ma-345	245	24	(	(	PUNCT
ma-345	245	25	1.5	1.5	NUM
ma-345	245	26	)	)	PUNCT
ma-345	245	27	3.1543	3.1543	NUM
ma-345	245	28	3.9915	3.9915	NUM
ma-345	245	29	3.9319method	3.9319method	NUM
ma-345	245	30	(	(	PUNCT
ma-345	245	31	1.6	1.6	NUM
ma-345	245	32	)	)	PUNCT
ma-345	245	33	4.0870	4.0870	NUM
ma-345	245	34	4.0870	4.0870	NUM
ma-345	245	35	4.0244method	4.0244method	PROPN
ma-345	245	36	(	(	PUNCT
ma-345	245	37	1.8	1.8	NUM
ma-345	245	38	)	)	PUNCT
ma-345	245	39	(	(	PUNCT
ma-345	245	40	a	a	X
ma-345	245	41	)	)	PUNCT
ma-345	245	42	,	,	PUNCT
ma-345	245	43	α	α	X
ma-345	245	44	=	=	PUNCT
ma-345	246	1	10−6	10−6	NUM
ma-345	246	2	3.9956	3.9956	NUM
ma-345	246	3	3.9931	3.9931	NUM
ma-345	246	4	3.9935method	3.9935method	NUM
ma-345	246	5	(	(	PUNCT
ma-345	246	6	1.8	1.8	NUM
ma-345	246	7	)	)	PUNCT
ma-345	246	8	(	(	PUNCT
ma-345	246	9	b	b	NOUN
ma-345	246	10	)	)	PUNCT
ma-345	246	11	,	,	PUNCT
ma-345	246	12	α1	α1	PROPN
ma-345	246	13	=	=	SYM
ma-345	246	14	0	0	NUM
ma-345	246	15	,	,	PUNCT
ma-345	246	16	α2	α2	NOUN
ma-345	246	17	=	=	NOUN
ma-345	246	18	0.01	0.01	NUM
ma-345	246	19	3.2266	3.2266	NUM
ma-345	246	20	4.0224	4.0224	NUM
ma-345	246	21	3.9731	3.9731	NUM
ma-345	246	22	tables	table	NOUN
ma-345	246	23	1	1	NUM
ma-345	246	24	,	,	PUNCT
ma-345	246	25	2	2	NUM
ma-345	246	26	,	,	PUNCT
ma-345	246	27	3	3	NUM
ma-345	246	28	,	,	PUNCT
ma-345	246	29	6	6	NUM
ma-345	246	30	and	and	CCONJ
ma-345	246	31	7	7	NUM
ma-345	246	32	contain	contain	VERB
ma-345	246	33	the	the	DET
ma-345	246	34	values	value	NOUN
ma-345	246	35	‖xn−	‖xn−	PROPN
ma-345	246	36	x∗‖	x∗‖	PROPN
ma-345	246	37	and	and	CCONJ
ma-345	246	38	‖f	‖f	ADJ
ma-345	246	39	(	(	PUNCT
ma-345	246	40	xn)‖	xn)‖	VERB
ma-345	246	41	at	at	ADP
ma-345	246	42	each	each	DET
ma-345	246	43	iteration	iteration	NOUN
ma-345	246	44	.	.	PUNCT
ma-345	247	1	the	the	DET
ma-345	247	2	iterativeprocess	iterativeprocess	NOUN
ma-345	247	3	was	be	AUX
ma-345	247	4	stopped	stop	VERB
ma-345	247	5	if	if	SCONJ
ma-345	247	6	‖f	‖f	ADP
ma-345	247	7	(	(	PUNCT
ma-345	247	8	xn)‖	xn)‖	PROPN
ma-345	247	9	≤	≤	PROPN
ma-345	247	10	10−10	10−10	NUM
ma-345	247	11	.	.	PUNCT
ma-345	248	1	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
ma-345	248	2	eur	eur	PROPN
ma-345	248	3	.	.	PUNCT
ma-345	249	1	j.	j.	PROPN
ma-345	249	2	math	math	PROPN
ma-345	249	3	.	.	PUNCT
ma-345	250	1	anal	anal	PROPN
ma-345	250	2	.	.	PUNCT
ma-345	251	1	10.28924	10.28924	NUM
ma-345	251	2	/	/	SYM
ma-345	251	3	ada	ada	PROPN
ma-345	251	4	/	/	SYM
ma-345	251	5	ma.5.15	ma.5.15	PROPN
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ma-345	251	37	(	(	PUNCT
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ma-345	251	39	)	)	PUNCT
ma-345	251	40	(	(	PUNCT
ma-345	251	41	b	b	NOUN
ma-345	251	42	)	)	PUNCT
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ma-345	251	54	(	(	PUNCT
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ma-345	251	56	)	)	PUNCT
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ma-345	252	6	.	.	PUNCT
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ma-345	253	3	(	(	PUNCT
ma-345	253	4	1.4	1.4	NUM
ma-345	253	5	)	)	PUNCT
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ma-345	253	7	(	(	PUNCT
ma-345	253	8	1.5	1.5	NUM
ma-345	253	9	)	)	PUNCT
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ma-345	253	11	(	(	PUNCT
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ma-345	253	13	)	)	PUNCT
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ma-345	254	5	(	(	PUNCT
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ma-345	254	9	x∗‖	x∗‖	PROPN
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ma-345	254	11	(	(	PUNCT
ma-345	254	12	xn)‖	xn)‖	PROPN
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ma-345	254	17	(	(	PUNCT
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ma-345	254	21	2.9069e-01	2.9069e-01	NUM
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ma-345	254	28	8.8111e-03	8.8111e-03	NUM
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ma-345	255	2	(	(	PUNCT
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ma-345	255	4	)	)	PUNCT
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ma-345	255	9	(	(	PUNCT
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ma-345	255	20	(	(	PUNCT
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ma-345	255	22	)	)	PUNCT
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ma-345	255	25	=	=	SYM
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ma-345	256	5	(	(	PUNCT
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ma-345	256	11	(	(	PUNCT
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ma-345	256	23	(	(	PUNCT
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ma-345	256	27	2.9069e-01	2.9069e-01	NUM
ma-345	256	28	4.9986e-01	4.9986e-01	NUM
ma-345	256	29	2.9069e-01	2.9069e-01	NUM
ma-345	256	30	4.9986e-01	4.9986e-01	NUM
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ma-345	257	23	(	(	PUNCT
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ma-345	257	25	)	)	PUNCT
ma-345	257	26	(	(	PUNCT
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ma-345	257	70	(	(	PUNCT
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ma-345	257	72	)	)	PUNCT
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ma-345	257	75	)	)	PUNCT
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ma-345	257	92	8	8	NUM
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ma-345	257	94	coc	coc	NOUN
ma-345	257	95	and	and	CCONJ
ma-345	257	96	acoc	acoc	VERB
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ma-345	257	98	δ1	δ1	NOUN
ma-345	257	99	was	be	AUX
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ma-345	257	101	if	if	SCONJ
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ma-345	257	103	condition	condition	NOUN
ma-345	257	104	‖xn+1−	‖xn+1−	NOUN
ma-345	257	105	xn‖	xn‖	PROPN
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ma-345	257	107	10−10	10−10	NUM
ma-345	257	108	was	be	AUX
ma-345	257	109	fulfilled	fulfil	VERB
ma-345	257	110	δ2	δ2	VERB
ma-345	257	111	and	and	CCONJ
ma-345	257	112	δ3	δ3	PROPN
ma-345	257	113	were	be	AUX
ma-345	257	114	calculated	calculate	VERB
ma-345	257	115	if	if	SCONJ
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ma-345	257	118	‖f	‖f	ADP
ma-345	257	119	(	(	PUNCT
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ma-345	257	122	10−10	10−10	NUM
ma-345	257	123	wasfulfilled	wasfulfille	VERB
ma-345	257	124	.	.	PUNCT
ma-345	258	1	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
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ma-345	258	3	.	.	PUNCT
ma-345	259	1	j.	j.	PROPN
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ma-345	259	3	.	.	PUNCT
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ma-345	260	2	.	.	PUNCT
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ma-345	261	14	3.1	3.1	NUM
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ma-345	261	23	(	(	PUNCT
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ma-345	261	26	,	,	PUNCT
ma-345	261	27	2	2	NUM
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ma-345	261	29	4	4	NUM
ma-345	261	30	)	)	PUNCT
ma-345	261	31	,	,	PUNCT
ma-345	261	32	x0	x0	PROPN
ma-345	261	33	=	=	PUNCT
ma-345	261	34	−0.15	−0.15	PROPN
ma-345	261	35	,	,	PUNCT
ma-345	261	36	x−1	x−1	PUNCT
ma-345	262	1	=	=	PUNCT
ma-345	262	2	−0.25	−0.25	NOUN
ma-345	262	3	(	(	PUNCT
ma-345	262	4	tables	table	NOUN
ma-345	262	5	3	3	NUM
ma-345	262	6	,	,	PUNCT
ma-345	262	7	5	5	NUM
ma-345	262	8	)	)	PUNCT
ma-345	262	9	and	and	CCONJ
ma-345	262	10	for	for	ADP
ma-345	262	11	example	example	NOUN
ma-345	262	12	3.2	3.2	NUM
ma-345	262	13	–	–	PUNCT
ma-345	262	14	x0	x0	PUNCT
ma-345	262	15	=	=	PUNCT
ma-345	262	16	(	(	PUNCT
ma-345	262	17	0.63	0.63	NUM
ma-345	262	18	;	;	PUNCT
ma-345	262	19	−1.26	−1.26	NOUN
ma-345	262	20	)	)	PUNCT
ma-345	262	21	,	,	PUNCT
ma-345	262	22	x−1	x−1	PROPN
ma-345	262	23	=	=	PUNCT
ma-345	262	24	(	(	PUNCT
ma-345	262	25	0.73	0.73	NUM
ma-345	262	26	;	;	PUNCT
ma-345	262	27	−1.16	−1.16	NUM
ma-345	262	28	)	)	PUNCT
ma-345	262	29	.	.	PUNCT
ma-345	263	1	example	example	NOUN
ma-345	263	2	3.3	3.3	NUM
ma-345	263	3	.	.	PUNCT
ma-345	264	1	let	let	VERB
ma-345	264	2	f	f	PROPN
ma-345	264	3	:	:	PUNCT
ma-345	264	4	rm	rm	PROPN
ma-345	264	5	→	→	SYM
ma-345	264	6	rm	rm	PROPN
ma-345	264	7	and	and	CCONJ
ma-345	264	8	consider	consider	VERB
ma-345	264	9	the	the	DET
ma-345	264	10	system	system	NOUN
ma-345	264	11	of	of	ADP
ma-345	264	12	equations	equation	NOUN
ma-345	264	13	with	with	ADP
ma-345	264	14	x	x	X
ma-345	264	15	=	=	SYM
ma-345	264	16	(	(	PUNCT
ma-345	264	17	ξ1	ξ1	NOUN
ma-345	264	18	;	;	PUNCT
ma-345	264	19	.	.	PUNCT
ma-345	264	20	.	.	PUNCT
ma-345	264	21	.	.	PUNCT
ma-345	265	1	;	;	PUNCT
ma-345	265	2	ξm	ξm	X
ma-345	265	3	)	)	PUNCT
ma-345	265	4	fi(x	fi(x	NUM
ma-345	265	5	)	)	PUNCT
ma-345	266	1	=	=	PUNCT
ma-345	266	2	m∑	m∑	ADV
ma-345	266	3	j=1	j=1	PROPN
ma-345	266	4	ξj	ξj	PROPN
ma-345	266	5	+	+	CCONJ
ma-345	266	6	eξi	eξi	PROPN
ma-345	266	7	−	−	PROPN
ma-345	266	8	1	1	NUM
ma-345	266	9	=	=	SYM
ma-345	266	10	0	0	NUM
ma-345	266	11	,	,	PUNCT
ma-345	266	12	i	i	PRON
ma-345	266	13	=	=	NOUN
ma-345	266	14	1	1	NUM
ma-345	266	15	,	,	PUNCT
ma-345	266	16	.	.	PUNCT
ma-345	266	17	.	.	PUNCT
ma-345	266	18	.	.	PUNCT
ma-345	267	1	,	,	PUNCT
ma-345	267	2	m.	m.	NOUN
ma-345	267	3	here	here	ADV
ma-345	267	4	the	the	DET
ma-345	267	5	exact	exact	ADJ
ma-345	267	6	solution	solution	NOUN
ma-345	267	7	x∗	x∗	PROPN
ma-345	267	8	=	=	SYM
ma-345	267	9	(	(	PUNCT
ma-345	267	10	0	0	NUM
ma-345	267	11	;	;	PUNCT
ma-345	267	12	.	.	PUNCT
ma-345	267	13	.	.	PUNCT
ma-345	267	14	.	.	PUNCT
ma-345	268	1	;	;	PUNCT
ma-345	268	2	0	0	X
ma-345	268	3	)	)	PUNCT
ma-345	268	4	.	.	PUNCT
ma-345	269	1	table	table	NOUN
ma-345	269	2	9	9	NUM
ma-345	269	3	.	.	X
ma-345	269	4	coc	coc	PROPN
ma-345	269	5	,	,	PUNCT
ma-345	269	6	acoc	acoc	VERB
ma-345	269	7	for	for	ADP
ma-345	269	8	example	example	NOUN
ma-345	269	9	3.3	3.3	NUM
ma-345	269	10	.	.	PUNCT
ma-345	270	1	method	method	PROPN
ma-345	270	2	δ1	δ1	NOUN
ma-345	270	3	δ2	δ2	VERB
ma-345	270	4	δ3method	δ3method	NOUN
ma-345	270	5	(	(	PUNCT
ma-345	270	6	1.4	1.4	NUM
ma-345	270	7	)	)	PUNCT
ma-345	270	8	2.6007	2.6007	NUM
ma-345	270	9	2.5860	2.5860	NUM
ma-345	270	10	2.6621method	2.6621method	NUM
ma-345	270	11	(	(	PUNCT
ma-345	270	12	1.5	1.5	NUM
ma-345	270	13	)	)	PUNCT
ma-345	270	14	3.9096	3.9096	NUM
ma-345	270	15	3.9035	3.9035	NUM
ma-345	270	16	3.7967method	3.7967method	NUM
ma-345	270	17	(	(	PUNCT
ma-345	270	18	1.6	1.6	NUM
ma-345	270	19	)	)	PUNCT
ma-345	270	20	2.0176	2.0176	NUM
ma-345	270	21	2.0059	2.0059	NUM
ma-345	270	22	2.0663method	2.0663method	NUM
ma-345	270	23	(	(	PUNCT
ma-345	270	24	1.7	1.7	NUM
ma-345	270	25	)	)	PUNCT
ma-345	270	26	3.9118	3.9118	NUM
ma-345	270	27	3.9059	3.9059	NUM
ma-345	270	28	3.7993method	3.7993method	NUM
ma-345	270	29	(	(	PUNCT
ma-345	270	30	1.8	1.8	NUM
ma-345	270	31	)	)	PUNCT
ma-345	270	32	(	(	PUNCT
ma-345	270	33	a	a	X
ma-345	270	34	)	)	PUNCT
ma-345	270	35	,	,	PUNCT
ma-345	270	36	α	α	X
ma-345	270	37	=	=	PUNCT
ma-345	271	1	10−6	10−6	NUM
ma-345	271	2	3.9117	3.9117	NUM
ma-345	271	3	3.9058	3.9058	NUM
ma-345	271	4	3.7992method	3.7992method	NUM
ma-345	271	5	(	(	PUNCT
ma-345	271	6	1.8	1.8	NUM
ma-345	271	7	)	)	PUNCT
ma-345	271	8	(	(	PUNCT
ma-345	271	9	b	b	NOUN
ma-345	271	10	)	)	PUNCT
ma-345	271	11	,	,	PUNCT
ma-345	271	12	α1	α1	PROPN
ma-345	271	13	=	=	SYM
ma-345	271	14	0	0	NUM
ma-345	271	15	,	,	PUNCT
ma-345	271	16	α2	α2	NOUN
ma-345	271	17	=	=	SYM
ma-345	271	18	−0.1	−0.1	PROPN
ma-345	272	1	3.9097	3.9097	NUM
ma-345	272	2	3.9064	3.9064	NUM
ma-345	272	3	3.9064method	3.9064method	NUM
ma-345	272	4	(	(	PUNCT
ma-345	272	5	1.8	1.8	NUM
ma-345	272	6	)	)	PUNCT
ma-345	272	7	(	(	PUNCT
ma-345	272	8	c	c	X
ma-345	272	9	)	)	PUNCT
ma-345	272	10	2.8165	2.8165	NUM
ma-345	272	11	2.8012	2.8012	NUM
ma-345	272	12	2.8803	2.8803	NUM
ma-345	272	13	table	table	NOUN
ma-345	272	14	10	10	NUM
ma-345	272	15	.	.	PUNCT
ma-345	273	1	coc	coc	PROPN
ma-345	273	2	,	,	PUNCT
ma-345	273	3	acoc	acoc	VERB
ma-345	273	4	for	for	ADP
ma-345	273	5	example	example	NOUN
ma-345	273	6	3.3	3.3	NUM
ma-345	273	7	.	.	PUNCT
ma-345	274	1	method	method	PROPN
ma-345	274	2	δ1	δ1	NOUN
ma-345	274	3	δ2	δ2	VERB
ma-345	274	4	δ3method	δ3method	NOUN
ma-345	274	5	(	(	PUNCT
ma-345	274	6	1.8	1.8	NUM
ma-345	274	7	)	)	PUNCT
ma-345	274	8	(	(	PUNCT
ma-345	274	9	b	b	NOUN
ma-345	274	10	)	)	PUNCT
ma-345	274	11	,	,	PUNCT
ma-345	274	12	α1	α1	PROPN
ma-345	274	13	=	=	SYM
ma-345	274	14	−1	−1	NOUN
ma-345	274	15	,	,	PUNCT
ma-345	274	16	α2	α2	NOUN
ma-345	274	17	=	=	SYM
ma-345	274	18	1	1	NUM
ma-345	274	19	4.3139	4.3139	NUM
ma-345	274	20	4.3096	4.3096	NUM
ma-345	274	21	4.2617method	4.2617method	NOUN
ma-345	274	22	(	(	PUNCT
ma-345	274	23	1.8	1.8	NUM
ma-345	274	24	)	)	PUNCT
ma-345	274	25	(	(	PUNCT
ma-345	274	26	b	b	NOUN
ma-345	274	27	)	)	PUNCT
ma-345	274	28	,	,	PUNCT
ma-345	274	29	α1	α1	PROPN
ma-345	274	30	=	=	SYM
ma-345	274	31	0	0	NUM
ma-345	274	32	,	,	PUNCT
ma-345	274	33	α2	α2	NOUN
ma-345	274	34	=	=	SYM
ma-345	274	35	1	1	NUM
ma-345	274	36	2.7472	2.7472	NUM
ma-345	274	37	2.7326	2.7326	NUM
ma-345	274	38	2.8050method	2.8050method	NUM
ma-345	274	39	(	(	PUNCT
ma-345	274	40	1.8	1.8	NUM
ma-345	274	41	)	)	PUNCT
ma-345	274	42	(	(	PUNCT
ma-345	274	43	b	b	NOUN
ma-345	274	44	)	)	PUNCT
ma-345	274	45	,	,	PUNCT
ma-345	274	46	α1	α1	PROPN
ma-345	274	47	=	=	SYM
ma-345	274	48	−1	−1	NOUN
ma-345	274	49	,	,	PUNCT
ma-345	274	50	α2	α2	PROPN
ma-345	274	51	=	=	SYM
ma-345	274	52	0	0	NUM
ma-345	275	1	3.9118	3.9118	NUM
ma-345	275	2	3.8946	3.8946	NUM
ma-345	275	3	3.8502	3.8502	NUM
ma-345	275	4	for	for	ADP
ma-345	275	5	solving	solve	VERB
ma-345	275	6	nonlinear	nonlinear	ADJ
ma-345	275	7	equations	equation	NOUN
ma-345	275	8	with	with	ADP
ma-345	275	9	differentiable	differentiable	ADJ
ma-345	275	10	operator	operator	NOUN
ma-345	275	11	can	can	AUX
ma-345	275	12	be	be	AUX
ma-345	275	13	also	also	ADV
ma-345	275	14	used	use	VERB
ma-345	275	15	method	method	NOUN
ma-345	275	16	(	(	PUNCT
ma-345	275	17	1.8	1.8	NUM
ma-345	275	18	)	)	PUNCT
ma-345	275	19	with(c	with(c	PROPN
ma-345	275	20	)	)	PUNCT
ma-345	275	21	l(xn+1	l(xn+1	PROPN
ma-345	275	22	)	)	PUNCT
ma-345	275	23	=	=	SYM
ma-345	276	1	1	1	NUM
ma-345	276	2	2(f	2(f	NUM
ma-345	276	3	′(xn+1	′(xn+1	NOUN
ma-345	276	4	)	)	PUNCT
ma-345	277	1	+	+	CCONJ
ma-345	278	1	[	[	X
ma-345	278	2	2xn+1−	2xn+1−	NUM
ma-345	278	3	xn	xn	PROPN
ma-345	278	4	,	,	PUNCT
ma-345	278	5	xn+1;f	xn+1;f	PROPN
ma-345	278	6	]	]	X
ma-345	278	7	)	)	PUNCT
ma-345	278	8	.	.	PUNCT
ma-345	279	1	for	for	ADP
ma-345	279	2	this	this	DET
ma-345	279	3	method	method	NOUN
ma-345	279	4	,	,	PUNCT
ma-345	279	5	the	the	DET
ma-345	279	6	errors	error	NOUN
ma-345	279	7	decrease	decrease	VERB
ma-345	279	8	faster	fast	ADV
ma-345	279	9	thanfor	thanfor	ADV
ma-345	279	10	(	(	PUNCT
ma-345	279	11	1.4	1.4	NUM
ma-345	279	12	)	)	PUNCT
ma-345	279	13	and	and	CCONJ
ma-345	279	14	(	(	PUNCT
ma-345	279	15	1.6).tables	1.6).tables	NUM
ma-345	279	16	9	9	NUM
ma-345	279	17	and	and	CCONJ
ma-345	279	18	10	10	NUM
ma-345	279	19	show	show	NOUN
ma-345	279	20	coc	coc	NOUN
ma-345	279	21	and	and	CCONJ
ma-345	279	22	acoc	acoc	PROPN
ma-345	279	23	for	for	ADP
ma-345	279	24	example	example	NOUN
ma-345	279	25	3.3	3.3	NUM
ma-345	279	26	with	with	ADP
ma-345	279	27	m	m	PROPN
ma-345	279	28	=	=	SYM
ma-345	279	29	1	1	NUM
ma-345	279	30	,	,	PUNCT
ma-345	279	31	the	the	DET
ma-345	279	32	initial	initial	ADJ
ma-345	279	33	approximation	approximation	NOUN
ma-345	279	34	x0	x0	PROPN
ma-345	279	35	=	=	PUNCT
ma-345	279	36	0.5	0.5	NUM
ma-345	279	37	and	and	CCONJ
ma-345	279	38	x0	x0	PROPN
ma-345	279	39	=	=	SYM
ma-345	279	40	0.9	0.9	NUM
ma-345	279	41	,	,	PUNCT
ma-345	279	42	respectively.figures	respectively.figure	VERB
ma-345	279	43	1	1	NUM
ma-345	279	44	and	and	CCONJ
ma-345	279	45	2	2	NUM
ma-345	279	46	show	show	NOUN
ma-345	279	47	changing	change	VERB
ma-345	279	48	of	of	ADP
ma-345	279	49	‖xn−xn−1‖	‖xn−xn−1‖	NOUN
ma-345	279	50	,	,	PUNCT
ma-345	279	51	‖xn−x∗‖	‖xn−x∗‖	ADJ
ma-345	279	52	and	and	CCONJ
ma-345	279	53	‖f	‖f	ADJ
ma-345	279	54	(	(	PUNCT
ma-345	279	55	xn)‖	xn)‖	ADJ
ma-345	279	56	form	form	NOUN
ma-345	279	57	=	=	SYM
ma-345	279	58	20	20	NUM
ma-345	279	59	,	,	PUNCT
ma-345	279	60	x0	x0	PROPN
ma-345	279	61	=	=	PUNCT
ma-345	279	62	(	(	PUNCT
ma-345	279	63	5	5	NUM
ma-345	279	64	;	;	PUNCT
ma-345	279	65	.	.	PUNCT
ma-345	279	66	.	.	PUNCT
ma-345	279	67	.	.	PUNCT
ma-345	280	1	;	;	PUNCT
ma-345	280	2	5	5	X
ma-345	280	3	)	)	PUNCT
ma-345	280	4	,	,	PUNCT
ma-345	280	5	x−1	x−1	PROPN
ma-345	281	1	=	=	PUNCT
ma-345	281	2	(	(	PUNCT
ma-345	281	3	5.1	5.1	NUM
ma-345	281	4	;	;	PUNCT
ma-345	281	5	.	.	PUNCT
ma-345	281	6	.	.	PUNCT
ma-345	281	7	.	.	PUNCT
ma-345	282	1	;	;	PUNCT
ma-345	282	2	5.1	5.1	NUM
ma-345	282	3	)	)	PUNCT
ma-345	282	4	,	,	PUNCT
ma-345	282	5	figure	figure	VERB
ma-345	282	6	3	3	NUM
ma-345	282	7	–	–	PUNCT
ma-345	282	8	for	for	ADP
ma-345	282	9	x0	x0	PROPN
ma-345	282	10	=	=	SYM
ma-345	282	11	(	(	PUNCT
ma-345	282	12	0.05	0.05	NUM
ma-345	282	13	;	;	PUNCT
ma-345	282	14	.	.	PUNCT
ma-345	282	15	.	.	PUNCT
ma-345	283	1	.	.	PUNCT
ma-345	284	1	;	;	PUNCT
ma-345	284	2	0.05	0.05	NUM
ma-345	284	3	)	)	PUNCT
ma-345	284	4	.	.	PUNCT
ma-345	285	1	the	the	DET
ma-345	285	2	iterative	iterative	NOUN
ma-345	285	3	process	process	NOUN
ma-345	285	4	was	be	AUX
ma-345	285	5	stopped	stop	VERB
ma-345	285	6	underthe	underthe	DET
ma-345	285	7	condition	condition	NOUN
ma-345	285	8	‖xn+1	‖xn+1	NUM
ma-345	285	9	−	−	NOUN
ma-345	285	10	xn‖	xn‖	PROPN
ma-345	285	11	≤	≤	NOUN
ma-345	285	12	10−10.from	10−10.from	NUM
ma-345	285	13	the	the	DET
ma-345	285	14	obtained	obtain	VERB
ma-345	285	15	results	result	NOUN
ma-345	285	16	,	,	PUNCT
ma-345	285	17	we	we	PRON
ma-345	285	18	see	see	VERB
ma-345	285	19	that	that	SCONJ
ma-345	285	20	among	among	ADP
ma-345	285	21	methods	method	NOUN
ma-345	285	22	(	(	PUNCT
ma-345	285	23	1.4)-(1.6	1.4)-(1.6	NUM
ma-345	285	24	)	)	PUNCT
ma-345	285	25	,	,	PUNCT
ma-345	285	26	for	for	ADP
ma-345	285	27	method	method	NOUN
ma-345	285	28	(	(	PUNCT
ma-345	285	29	1.5	1.5	NUM
ma-345	285	30	)	)	PUNCT
ma-345	285	31	the	the	DET
ma-345	285	32	errordecreases	errordecrease	NOUN
ma-345	285	33	faster	fast	ADV
ma-345	285	34	and	and	CCONJ
ma-345	285	35	it	it	PRON
ma-345	285	36	has	have	VERB
ma-345	285	37	highest	high	ADJ
ma-345	285	38	computational	computational	ADJ
ma-345	285	39	order	order	NOUN
ma-345	285	40	of	of	ADP
ma-345	285	41	convergence	convergence	NOUN
ma-345	285	42	.	.	PUNCT
ma-345	286	1	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
ma-345	286	2	eur	eur	PROPN
ma-345	286	3	.	.	PUNCT
ma-345	287	1	j.	j.	PROPN
ma-345	287	2	math	math	PROPN
ma-345	287	3	.	.	PUNCT
ma-345	288	1	anal	anal	PROPN
ma-345	288	2	.	.	PUNCT
ma-345	289	1	10.28924	10.28924	NUM
ma-345	289	2	/	/	SYM
ma-345	289	3	ada	ada	PROPN
ma-345	289	4	/	/	SYM
ma-345	289	5	ma.5.15	ma.5.15	NOUN
ma-345	289	6	12	12	NUM
ma-345	289	7	0	0	NUM
ma-345	289	8	1	1	NUM
ma-345	289	9	2	2	NUM
ma-345	289	10	3	3	NUM
ma-345	289	11	4	4	NUM
ma-345	289	12	5	5	NUM
ma-345	289	13	6	6	NUM
ma-345	289	14	1x10	1x10	NUM
ma-345	289	15	-	-	SYM
ma-345	289	16	21	21	NUM
ma-345	289	17	10	10	NUM
ma-345	289	18	-	-	SYM
ma-345	289	19	20	20	NUM
ma-345	289	20	10	10	NUM
ma-345	289	21	-	-	SYM
ma-345	289	22	19	19	NUM
ma-345	289	23	10	10	NUM
ma-345	289	24	-	-	SYM
ma-345	289	25	18	18	NUM
ma-345	289	26	10	10	NUM
ma-345	289	27	-	-	SYM
ma-345	289	28	17	17	NUM
ma-345	289	29	10	10	NUM
ma-345	289	30	-	-	SYM
ma-345	289	31	16	16	NUM
ma-345	289	32	10	10	NUM
ma-345	289	33	-	-	SYM
ma-345	289	34	15	15	NUM
ma-345	289	35	10	10	NUM
ma-345	289	36	-	-	SYM
ma-345	289	37	14	14	NUM
ma-345	289	38	10	10	NUM
ma-345	289	39	-	-	SYM
ma-345	289	40	13	13	NUM
ma-345	289	41	10	10	NUM
ma-345	289	42	-	-	SYM
ma-345	289	43	12	12	NUM
ma-345	289	44	10	10	NUM
ma-345	289	45	-	-	SYM
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ma-345	292	7	-	-	SYM
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ma-345	292	10	-	-	SYM
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ma-345	292	13	-	-	SYM
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ma-345	292	16	-	-	SYM
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ma-345	292	19	-	-	SYM
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ma-345	292	22	-	-	SYM
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ma-345	292	25	-	-	SYM
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ma-345	292	28	-	-	SYM
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ma-345	292	31	-	-	SYM
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ma-345	292	34	-	-	SYM
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ma-345	292	37	-	-	SYM
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ma-345	292	40	-	-	SYM
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ma-345	292	43	-	-	SYM
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ma-345	292	46	-	-	NUM
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ma-345	292	49	-	-	SYM
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ma-345	292	52	-	-	SYM
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ma-345	292	55	-	-	SYM
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ma-345	292	71	:	:	PUNCT
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ma-345	294	7	-	-	SYM
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ma-345	294	10	-	-	SYM
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ma-345	294	13	-	-	SYM
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ma-345	294	16	-	-	SYM
ma-345	294	17	15	15	NUM
ma-345	294	18	10	10	NUM
ma-345	294	19	-	-	SYM
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ma-345	294	22	-	-	SYM
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ma-345	294	25	-	-	SYM
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ma-345	294	28	-	-	SYM
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ma-345	294	31	-	-	SYM
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ma-345	294	34	-	-	SYM
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ma-345	294	37	-	-	SYM
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ma-345	294	40	-	-	SYM
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ma-345	294	43	-	-	SYM
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ma-345	294	46	-	-	SYM
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ma-345	294	52	-	-	SYM
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ma-345	294	88	-	-	SYM
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ma-345	296	9	-	-	SYM
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ma-345	296	18	-	-	SYM
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ma-345	296	21	-	-	SYM
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ma-345	296	24	-	-	SYM
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ma-345	296	27	-	-	SYM
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ma-345	296	45	-	-	SYM
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ma-345	296	117	-	-	SYM
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ma-345	296	142	1002	1002	NUM
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ma-345	296	167	)	)	PUNCT
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ma-345	296	169	α1	α1	PROPN
ma-345	296	170	=	=	SYM
ma-345	296	171	0	0	NUM
ma-345	296	172	,	,	PUNCT
ma-345	296	173	α2	α2	NOUN
ma-345	296	174	=	=	SYM
ma-345	296	175	−0.1	−0.1	PROPN
ma-345	296	176	.	.	PUNCT
ma-345	297	1	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
ma-345	297	2	eur	eur	PROPN
ma-345	297	3	.	.	PUNCT
ma-345	298	1	j.	j.	PROPN
ma-345	298	2	math	math	PROPN
ma-345	298	3	.	.	PUNCT
ma-345	299	1	anal	anal	PROPN
ma-345	299	2	.	.	PUNCT
ma-345	300	1	10.28924	10.28924	NUM
ma-345	300	2	/	/	SYM
ma-345	300	3	ada	ada	PROPN
ma-345	300	4	/	/	SYM
ma-345	300	5	ma.5.15	ma.5.15	PROPN
ma-345	300	6	13	13	NUM
ma-345	300	7	0	0	NUM
ma-345	300	8	0.5	0.5	NUM
ma-345	300	9	1	1	NUM
ma-345	300	10	1.5	1.5	NUM
ma-345	300	11	2	2	NUM
ma-345	300	12	2.5	2.5	NUM
ma-345	300	13	3	3	NUM
ma-345	300	14	10	10	NUM
ma-345	300	15	-	-	SYM
ma-345	300	16	20	20	NUM
ma-345	300	17	10	10	NUM
ma-345	300	18	-	-	SYM
ma-345	300	19	19	19	NUM
ma-345	300	20	10	10	NUM
ma-345	300	21	-	-	SYM
ma-345	300	22	18	18	NUM
ma-345	300	23	10	10	NUM
ma-345	300	24	-	-	SYM
ma-345	300	25	17	17	NUM
ma-345	300	26	10	10	NUM
ma-345	300	27	-	-	SYM
ma-345	300	28	16	16	NUM
ma-345	300	29	10	10	NUM
ma-345	300	30	-	-	SYM
ma-345	300	31	15	15	NUM
ma-345	300	32	10	10	NUM
ma-345	300	33	-	-	SYM
ma-345	300	34	14	14	NUM
ma-345	300	35	10	10	NUM
ma-345	300	36	-	-	SYM
ma-345	300	37	13	13	NUM
ma-345	300	38	10	10	NUM
ma-345	300	39	-	-	SYM
ma-345	300	40	12	12	NUM
ma-345	300	41	10	10	NUM
ma-345	300	42	-	-	SYM
ma-345	300	43	11	11	NUM
ma-345	300	44	10	10	NUM
ma-345	300	45	-	-	SYM
ma-345	300	46	10	10	NUM
ma-345	300	47	10	10	NUM
ma-345	300	48	-	-	SYM
ma-345	300	49	09	09	NUM
ma-345	300	50	10	10	NUM
ma-345	300	51	-	-	SYM
ma-345	300	52	08	08	NUM
ma-345	300	53	10	10	NUM
ma-345	300	54	-	-	SYM
ma-345	300	55	07	07	NUM
ma-345	300	56	10	10	NUM
ma-345	300	57	-	-	SYM
ma-345	300	58	06	06	NUM
ma-345	300	59	10	10	NUM
ma-345	300	60	-	-	SYM
ma-345	300	61	05	05	NUM
ma-345	300	62	10	10	NUM
ma-345	300	63	-	-	NUM
ma-345	300	64	04	04	NUM
ma-345	300	65	10	10	NUM
ma-345	300	66	-	-	SYM
ma-345	300	67	03	03	NUM
ma-345	300	68	10	10	NUM
ma-345	300	69	-	-	SYM
ma-345	300	70	02	02	NUM
ma-345	300	71	10	10	NUM
ma-345	300	72	-	-	SYM
ma-345	300	73	01	01	NUM
ma-345	300	74	1000	1000	NUM
ma-345	300	75	1001	1001	NUM
ma-345	300	76	method	method	NOUN
ma-345	300	77	(	(	PUNCT
ma-345	300	78	1.8	1.8	NUM
ma-345	300	79	)	)	PUNCT
ma-345	300	80	(	(	PUNCT
ma-345	300	81	b)-1	b)-1	SYM
ma-345	300	82	0	0	NUM
ma-345	300	83	0.5	0.5	NUM
ma-345	300	84	1	1	NUM
ma-345	300	85	1.5	1.5	NUM
ma-345	300	86	2	2	NUM
ma-345	300	87	2.5	2.5	NUM
ma-345	300	88	3	3	NUM
ma-345	300	89	10	10	NUM
ma-345	300	90	-	-	SYM
ma-345	300	91	18	18	NUM
ma-345	300	92	10	10	NUM
ma-345	300	93	-	-	SYM
ma-345	300	94	17	17	NUM
ma-345	300	95	10	10	NUM
ma-345	300	96	-	-	SYM
ma-345	300	97	16	16	NUM
ma-345	300	98	10	10	NUM
ma-345	300	99	-	-	SYM
ma-345	300	100	15	15	NUM
ma-345	300	101	10	10	NUM
ma-345	300	102	-	-	SYM
ma-345	300	103	14	14	NUM
ma-345	300	104	10	10	NUM
ma-345	300	105	-	-	SYM
ma-345	300	106	13	13	NUM
ma-345	300	107	10	10	NUM
ma-345	300	108	-	-	SYM
ma-345	300	109	12	12	NUM
ma-345	300	110	10	10	NUM
ma-345	300	111	-	-	SYM
ma-345	300	112	11	11	NUM
ma-345	300	113	10	10	NUM
ma-345	300	114	-	-	SYM
ma-345	300	115	10	10	NUM
ma-345	300	116	10	10	NUM
ma-345	300	117	-	-	SYM
ma-345	300	118	09	09	NUM
ma-345	300	119	10	10	NUM
ma-345	300	120	-	-	SYM
ma-345	300	121	08	08	NUM
ma-345	300	122	10	10	NUM
ma-345	300	123	-	-	SYM
ma-345	300	124	07	07	NUM
ma-345	300	125	10	10	NUM
ma-345	300	126	-	-	SYM
ma-345	300	127	06	06	NUM
ma-345	300	128	10	10	NUM
ma-345	300	129	-	-	SYM
ma-345	300	130	05	05	NUM
ma-345	300	131	10	10	NUM
ma-345	300	132	-	-	NUM
ma-345	300	133	04	04	NUM
ma-345	300	134	10	10	NUM
ma-345	300	135	-	-	SYM
ma-345	300	136	03	03	NUM
ma-345	300	137	10	10	NUM
ma-345	300	138	-	-	SYM
ma-345	300	139	02	02	NUM
ma-345	300	140	10	10	NUM
ma-345	300	141	-	-	SYM
ma-345	300	142	01	01	NUM
ma-345	300	143	1000	1000	NUM
ma-345	300	144	1001	1001	NUM
ma-345	300	145	method	method	NOUN
ma-345	300	146	(	(	PUNCT
ma-345	300	147	1.8	1.8	NUM
ma-345	300	148	)	)	PUNCT
ma-345	300	149	(	(	PUNCT
ma-345	300	150	b)-2	b)-2	NOUN
ma-345	300	151	||xn	||xn	NUM
ma-345	300	152	-	-	PUNCT
ma-345	300	153	xn-1||	xn-1||	NOUN
ma-345	300	154	||xn	||xn	NOUN
ma-345	300	155	-	-	PUNCT
ma-345	300	156	x	x	SYM
ma-345	300	157	*	*	PUNCT
ma-345	300	158	||	||	NOUN
ma-345	301	1	||f(xn)||	||f(xn)||	NOUN
ma-345	301	2	0	0	NUM
ma-345	301	3	0.5	0.5	NUM
ma-345	301	4	1	1	NUM
ma-345	301	5	1.5	1.5	NUM
ma-345	301	6	2	2	NUM
ma-345	301	7	2.5	2.5	NUM
ma-345	301	8	3	3	NUM
ma-345	301	9	1x10	1x10	NUM
ma-345	301	10	-	-	SYM
ma-345	301	11	21	21	NUM
ma-345	301	12	10	10	NUM
ma-345	301	13	-	-	SYM
ma-345	301	14	20	20	NUM
ma-345	301	15	10	10	NUM
ma-345	301	16	-	-	SYM
ma-345	301	17	19	19	NUM
ma-345	301	18	10	10	NUM
ma-345	301	19	-	-	SYM
ma-345	301	20	18	18	NUM
ma-345	301	21	10	10	NUM
ma-345	301	22	-	-	SYM
ma-345	301	23	17	17	NUM
ma-345	301	24	10	10	NUM
ma-345	301	25	-	-	SYM
ma-345	301	26	16	16	NUM
ma-345	301	27	10	10	NUM
ma-345	301	28	-	-	SYM
ma-345	301	29	15	15	NUM
ma-345	301	30	10	10	NUM
ma-345	301	31	-	-	SYM
ma-345	301	32	14	14	NUM
ma-345	301	33	10	10	NUM
ma-345	301	34	-	-	SYM
ma-345	301	35	13	13	NUM
ma-345	301	36	10	10	NUM
ma-345	301	37	-	-	SYM
ma-345	301	38	12	12	NUM
ma-345	301	39	10	10	NUM
ma-345	301	40	-	-	SYM
ma-345	301	41	11	11	NUM
ma-345	301	42	10	10	NUM
ma-345	301	43	-	-	SYM
ma-345	301	44	10	10	NUM
ma-345	301	45	10	10	NUM
ma-345	301	46	-	-	SYM
ma-345	301	47	09	09	NUM
ma-345	301	48	10	10	NUM
ma-345	301	49	-	-	SYM
ma-345	301	50	08	08	NUM
ma-345	301	51	10	10	NUM
ma-345	301	52	-	-	SYM
ma-345	301	53	07	07	NUM
ma-345	301	54	10	10	NUM
ma-345	301	55	-	-	SYM
ma-345	301	56	06	06	NUM
ma-345	301	57	10	10	NUM
ma-345	301	58	-	-	SYM
ma-345	301	59	05	05	NUM
ma-345	301	60	10	10	NUM
ma-345	301	61	-	-	NUM
ma-345	301	62	04	04	NUM
ma-345	301	63	10	10	NUM
ma-345	301	64	-	-	SYM
ma-345	301	65	03	03	NUM
ma-345	301	66	10	10	NUM
ma-345	301	67	-	-	SYM
ma-345	301	68	02	02	NUM
ma-345	301	69	10	10	NUM
ma-345	301	70	-	-	SYM
ma-345	301	71	01	01	NUM
ma-345	301	72	1000	1000	NUM
ma-345	301	73	1001	1001	NUM
ma-345	301	74	method	method	NOUN
ma-345	301	75	(	(	PUNCT
ma-345	301	76	1.8	1.8	NUM
ma-345	301	77	)	)	PUNCT
ma-345	301	78	(	(	PUNCT
ma-345	301	79	b)-3	b)-3	PRON
ma-345	301	80	figure	figure	VERB
ma-345	301	81	3	3	NUM
ma-345	301	82	.	.	PUNCT
ma-345	301	83	example	example	NOUN
ma-345	301	84	3.3	3.3	NUM
ma-345	301	85	:	:	PUNCT
ma-345	301	86	error	error	NOUN
ma-345	301	87	’s	’s	PART
ma-345	301	88	value	value	NOUN
ma-345	301	89	at	at	ADP
ma-345	301	90	each	each	DET
ma-345	301	91	iteration	iteration	NOUN
ma-345	301	92	(	(	PUNCT
ma-345	301	93	(	(	PUNCT
ma-345	301	94	b)-1	b)-1	NOUN
ma-345	301	95	,	,	PUNCT
ma-345	301	96	α1	α1	PROPN
ma-345	301	97	=	=	SYM
ma-345	301	98	−1	−1	NOUN
ma-345	301	99	,	,	PUNCT
ma-345	301	100	α2	α2	PROPN
ma-345	301	101	=	=	SYM
ma-345	301	102	1;(b)-2	1;(b)-2	PROPN
ma-345	301	103	,	,	PUNCT
ma-345	301	104	α1	α1	PROPN
ma-345	301	105	=	=	SYM
ma-345	301	106	0	0	NUM
ma-345	301	107	,	,	PUNCT
ma-345	301	108	α2	α2	NOUN
ma-345	301	109	=	=	SYM
ma-345	301	110	1	1	NUM
ma-345	301	111	;	;	PUNCT
ma-345	301	112	(	(	PUNCT
ma-345	301	113	b)-3	b)-3	NOUN
ma-345	301	114	,	,	PUNCT
ma-345	301	115	α1	α1	PROPN
ma-345	301	116	=	=	SYM
ma-345	301	117	−1	−1	NOUN
ma-345	301	118	,	,	PUNCT
ma-345	301	119	α2	α2	PROPN
ma-345	301	120	=	=	SYM
ma-345	301	121	0	0	NUM
ma-345	301	122	)	)	PUNCT
ma-345	301	123	.	.	PUNCT
ma-345	302	1	4	4	X
ma-345	302	2	.	.	X
ma-345	302	3	conclusion	conclusion	NOUN
ma-345	302	4	in	in	ADP
ma-345	302	5	this	this	DET
ma-345	302	6	article	article	NOUN
ma-345	302	7	a	a	DET
ma-345	302	8	three	three	NUM
ma-345	302	9	-	-	PUNCT
ma-345	302	10	step	step	NOUN
ma-345	302	11	kurchatov	kurchatov	ADJ
ma-345	302	12	-	-	PUNCT
ma-345	302	13	like	like	ADJ
ma-345	302	14	method	method	NOUN
ma-345	302	15	with	with	ADP
ma-345	302	16	approximation	approximation	NOUN
ma-345	302	17	of	of	ADP
ma-345	302	18	inverse	inverse	NOUN
ma-345	302	19	operator	operator	NOUN
ma-345	302	20	isintroduced	isintroduce	VERB
ma-345	302	21	and	and	CCONJ
ma-345	302	22	convergence	convergence	NOUN
ma-345	302	23	analysis	analysis	NOUN
ma-345	302	24	is	be	AUX
ma-345	302	25	provided	provide	VERB
ma-345	302	26	.	.	PUNCT
ma-345	303	1	the	the	DET
ma-345	303	2	r	r	NOUN
ma-345	303	3	-	-	PUNCT
ma-345	303	4	convergence	convergence	NOUN
ma-345	303	5	four	four	NUM
ma-345	303	6	is	be	AUX
ma-345	303	7	shown	show	VERB
ma-345	303	8	theoreti	theoreti	NOUN
ma-345	303	9	-	-	PUNCT
ma-345	303	10	cally	cally	ADV
ma-345	303	11	under	under	ADP
ma-345	303	12	lipschitz	lipschitz	NOUN
ma-345	303	13	conditions	condition	NOUN
ma-345	303	14	for	for	ADP
ma-345	303	15	fréchet	fréchet	VERB
ma-345	303	16	derivative	derivative	ADJ
ma-345	303	17	and	and	CCONJ
ma-345	303	18	first	first	ADJ
ma-345	303	19	-	-	PUNCT
ma-345	303	20	order	order	NOUN
ma-345	303	21	divided	divide	VERB
ma-345	303	22	differences	difference	NOUN
ma-345	303	23	.	.	PUNCT
ma-345	304	1	nu	nu	ADJ
ma-345	304	2	-	-	PUNCT
ma-345	304	3	merous	merous	ADJ
ma-345	304	4	experiments	experiment	NOUN
ma-345	304	5	demonstrate	demonstrate	VERB
ma-345	304	6	the	the	DET
ma-345	304	7	performance	performance	NOUN
ma-345	304	8	of	of	ADP
ma-345	304	9	the	the	DET
ma-345	304	10	method	method	NOUN
ma-345	304	11	for	for	ADP
ma-345	304	12	different	different	ADJ
ma-345	304	13	cases	case	NOUN
ma-345	304	14	of	of	ADP
ma-345	304	15	kn+1.among	kn+1.among	NOUN
ma-345	304	16	the	the	DET
ma-345	304	17	methods	method	NOUN
ma-345	304	18	with	with	ADP
ma-345	304	19	divided	divide	VERB
ma-345	304	20	differences	difference	NOUN
ma-345	304	21	,	,	PUNCT
ma-345	304	22	the	the	DET
ma-345	304	23	best	good	ADJ
ma-345	304	24	results	result	NOUN
ma-345	304	25	are	be	AUX
ma-345	304	26	demonstrated	demonstrate	VERB
ma-345	304	27	by	by	ADP
ma-345	304	28	the	the	DET
ma-345	304	29	meth	meth	NOUN
ma-345	304	30	-	-	PUNCT
ma-345	304	31	ods	od	NOUN
ma-345	304	32	(	(	PUNCT
ma-345	304	33	1.5	1.5	NUM
ma-345	304	34	)	)	PUNCT
ma-345	304	35	,	,	PUNCT
ma-345	304	36	namely	namely	ADV
ma-345	304	37	the	the	DET
ma-345	304	38	highest	high	ADJ
ma-345	304	39	computational	computational	ADJ
ma-345	304	40	order	order	NOUN
ma-345	304	41	of	of	ADP
ma-345	304	42	convergence	convergence	NOUN
ma-345	304	43	.	.	PUNCT
ma-345	305	1	the	the	DET
ma-345	305	2	operator	operator	NOUN
ma-345	305	3	l	l	NOUN
ma-345	305	4	was	be	AUX
ma-345	305	5	cho	cho	NOUN
ma-345	305	6	-	-	PUNCT
ma-345	305	7	sen	sen	PROPN
ma-345	305	8	in	in	ADP
ma-345	305	9	the	the	DET
ma-345	305	10	form	form	NOUN
ma-345	305	11	l(xn+1	l(xn+1	PROPN
ma-345	305	12	)	)	PUNCT
ma-345	305	13	=	=	PUNCT
ma-345	306	1	[	[	X
ma-345	306	2	xn+1	xn+1	X
ma-345	306	3	,	,	PUNCT
ma-345	306	4	xn+1	xn+1	PROPN
ma-345	306	5	+	+	CCONJ
ma-345	307	1	α;f	α;f	NOUN
ma-345	307	2	]	]	PUNCT
ma-345	307	3	,	,	PUNCT
ma-345	307	4	where	where	SCONJ
ma-345	307	5	α	α	NOUN
ma-345	307	6	is	be	AUX
ma-345	307	7	a	a	DET
ma-345	307	8	small	small	ADJ
ma-345	307	9	number	number	NOUN
ma-345	307	10	,	,	PUNCT
ma-345	307	11	and	and	CCONJ
ma-345	307	12	l(xn+1	l(xn+1	X
ma-345	307	13	)	)	PUNCT
ma-345	307	14	=	=	PUNCT
ma-345	308	1	[	[	X
ma-345	308	2	xn+1	xn+1	X
ma-345	308	3	+	+	CCONJ
ma-345	308	4	α1f	α1f	NOUN
ma-345	308	5	(	(	PUNCT
ma-345	308	6	xn+1	xn+1	NUM
ma-345	308	7	)	)	PUNCT
ma-345	308	8	,	,	PUNCT
ma-345	308	9	xn+1	xn+1	PROPN
ma-345	308	10	+	+	CCONJ
ma-345	308	11	α2f	α2f	PROPN
ma-345	308	12	(	(	PUNCT
ma-345	308	13	xn+1);f	xn+1);f	PROPN
ma-345	308	14	]	]	PUNCT
ma-345	308	15	with	with	ADP
ma-345	308	16	α1	α1	PROPN
ma-345	308	17	,	,	PUNCT
ma-345	308	18	α2	α2	PROPN
ma-345	308	19	∈	∈	PROPN
ma-345	308	20	r.	r.	NOUN
ma-345	308	21	these	these	DET
ma-345	308	22	approximating	approximate	VERB
ma-345	308	23	of	of	ADP
ma-345	308	24	the	the	DET
ma-345	308	25	deriv	deriv	NOUN
ma-345	308	26	-	-	PUNCT
ma-345	308	27	ative	ative	NOUN
ma-345	308	28	give	give	VERB
ma-345	308	29	quite	quite	ADV
ma-345	308	30	good	good	ADJ
ma-345	308	31	results	result	NOUN
ma-345	308	32	,	,	PUNCT
ma-345	308	33	in	in	ADP
ma-345	308	34	particular	particular	ADJ
ma-345	308	35	if	if	SCONJ
ma-345	308	36	the	the	DET
ma-345	308	37	nonlinear	nonlinear	ADJ
ma-345	308	38	operator	operator	NOUN
ma-345	308	39	is	be	AUX
ma-345	308	40	not	not	PART
ma-345	308	41	differentiable	differentiable	ADJ
ma-345	308	42	.	.	PUNCT
ma-345	309	1	for	for	ADP
ma-345	309	2	somevalues	somevalue	NOUN
ma-345	309	3	α1	α1	PROPN
ma-345	309	4	and	and	CCONJ
ma-345	309	5	α2	α2	ADJ
ma-345	309	6	these	these	DET
ma-345	309	7	methods	method	NOUN
ma-345	309	8	require	require	VERB
ma-345	309	9	a	a	DET
ma-345	309	10	good	good	ADJ
ma-345	309	11	initial	initial	ADJ
ma-345	309	12	approximation	approximation	NOUN
ma-345	309	13	.	.	PUNCT
ma-345	310	1	in	in	ADP
ma-345	310	2	the	the	DET
ma-345	310	3	case	case	NOUN
ma-345	310	4	of	of	ADP
ma-345	310	5	the	the	DET
ma-345	310	6	differen	differen	PROPN
ma-345	310	7	-	-	ADJ
ma-345	310	8	tiable	tiable	ADJ
ma-345	310	9	operator	operator	NOUN
ma-345	310	10	,	,	PUNCT
ma-345	310	11	the	the	DET
ma-345	310	12	following	follow	VERB
ma-345	310	13	choice	choice	NOUN
ma-345	310	14	l(xn+1	l(xn+1	PROPN
ma-345	310	15	)	)	PUNCT
ma-345	310	16	=	=	PUNCT
ma-345	311	1	1	1	NUM
ma-345	311	2	2(f	2(f	NUM
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ma-345	311	7	)	)	PUNCT
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ma-345	311	11	demonstrates	demonstrate	VERB
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ma-345	311	13	over	over	ADP
ma-345	311	14	some	some	DET
ma-345	311	15	methods	method	NOUN
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ma-345	311	19	.	.	PUNCT
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ma-345	312	3	1	1	NUM
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ma-345	313	4	and	and	CCONJ
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ma-345	313	8	-	-	PUNCT
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ma-345	313	11	,	,	PUNCT
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ma-345	313	18	,	,	PUNCT
ma-345	313	19	2008	2008	NUM
ma-345	313	20	.	.	PUNCT
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ma-345	314	2	:	:	PUNCT
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ma-345	314	4	-	-	SYM
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ma-345	314	6	-	-	PUNCT
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ma-345	314	8	-	-	PUNCT
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ma-345	315	14	.	.	PROPN
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ma-345	317	4	)	)	PUNCT
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ma-345	317	6	-	-	SYM
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ma-345	317	8	.	.	PUNCT
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ma-345	318	2	.	.	PUNCT
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ma-345	319	3	https://doi.org/10.1007/978-0-387-72743-1	https://doi.org/10.1007/978-0-387-72743-1	PROPN
ma-345	319	4	https://doi.org/10.1007/s12190-008-0194-5	https://doi.org/10.1007/s12190-008-0194-5	NUM
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ma-345	320	1	j.	j.	PROPN
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ma-345	323	3	]	]	X
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ma-345	323	5	k.	k.	PROPN
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ma-345	324	5	’s	’s	PART
ma-345	324	6	method	method	NOUN
ma-345	324	7	using	use	VERB
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ma-345	324	9	differences	difference	NOUN
ma-345	324	10	of	of	ADP
ma-345	324	11	order	order	NOUN
ma-345	324	12	one	one	NUM
ma-345	324	13	,	,	PUNCT
ma-345	324	14	numer	numer	NOUN
ma-345	324	15	.	.	PUNCT
ma-345	325	1	algorithms	algorithms	PROPN
ma-345	325	2	52	52	NUM
ma-345	325	3	(	(	PUNCT
ma-345	325	4	2009	2009	NUM
ma-345	325	5	)	)	PUNCT
ma-345	325	6	295	295	NUM
ma-345	325	7	-	-	SYM
ma-345	325	8	320	320	NUM
ma-345	325	9	.	.	PUNCT
ma-345	326	1	https://doi.org/10.1007/s11075-009-9274-3.[4	https://doi.org/10.1007/s11075-009-9274-3.[4	PROPN
ma-345	326	2	]	]	X
ma-345	326	3	i.k	i.k	PROPN
ma-345	326	4	.	.	PROPN
ma-345	326	5	argyros	argyros	PROPN
ma-345	326	6	,	,	PUNCT
ma-345	326	7	s.	s.	PROPN
ma-345	326	8	shakhno	shakhno	PROPN
ma-345	326	9	,	,	PUNCT
ma-345	326	10	s.	s.	PROPN
ma-345	326	11	regmi	regmi	PROPN
ma-345	326	12	,	,	PUNCT
ma-345	326	13	h.	h.	PROPN
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ma-345	326	15	,	,	PUNCT
ma-345	326	16	on	on	ADP
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ma-345	326	20	a	a	DET
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ma-345	326	22	convergence	convergence	NOUN
ma-345	326	23	analysis	analysis	NOUN
ma-345	326	24	for	for	ADP
ma-345	326	25	iterativemethods	iterativemethod	NOUN
ma-345	326	26	,	,	PUNCT
ma-345	326	27	j.	j.	PROPN
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ma-345	327	2	(	(	PUNCT
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ma-345	327	4	)	)	PUNCT
ma-345	327	5	101781	101781	NUM
ma-345	327	6	.	.	PUNCT
ma-345	328	1	https://doi.org/10.1016/j.jco.2023.101781.[5	https://doi.org/10.1016/j.jco.2023.101781.[5	PROPN
ma-345	328	2	]	]	PUNCT
ma-345	328	3	i.k	i.k	PROPN
ma-345	328	4	.	.	PROPN
ma-345	328	5	argyros	argyros	PROPN
ma-345	328	6	,	,	PUNCT
ma-345	328	7	s.	s.	PROPN
ma-345	328	8	shakhno	shakhno	PROPN
ma-345	328	9	,	,	PUNCT
ma-345	328	10	h.	h.	PROPN
ma-345	328	11	yarmola	yarmola	PROPN
ma-345	328	12	,	,	PUNCT
ma-345	328	13	improving	improve	VERB
ma-345	328	14	convergence	convergence	NOUN
ma-345	328	15	analysis	analysis	NOUN
ma-345	328	16	of	of	ADP
ma-345	328	17	the	the	DET
ma-345	328	18	newton	newton	PROPN
ma-345	328	19	–	–	PUNCT
ma-345	328	20	kurchatov	kurchatov	PROPN
ma-345	328	21	method	method	NOUN
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ma-345	328	25	-	-	PUNCT
ma-345	328	26	step	step	NOUN
ma-345	328	27	solver	solver	NOUN
ma-345	328	28	for	for	ADP
ma-345	328	29	nonlinear	nonlinear	ADJ
ma-345	328	30	equations	equation	NOUN
ma-345	328	31	,	,	PUNCT
ma-345	328	32	computation	computation	NOUN
ma-345	328	33	8	8	NUM
ma-345	328	34	(	(	PUNCT
ma-345	328	35	2020	2020	NUM
ma-345	328	36	)	)	PUNCT
ma-345	328	37	8	8	NUM
ma-345	328	38	.	.	X
ma-345	329	1	https://doi.org/10.3390/	https://doi.org/10.3390/	PROPN
ma-345	329	2	computation8010008.[6	computation8010008.[6	INTJ
ma-345	329	3	]	]	X
ma-345	329	4	i.k	i.k	PROPN
ma-345	329	5	.	.	PROPN
ma-345	329	6	argyros	argyros	PROPN
ma-345	329	7	,	,	PUNCT
ma-345	329	8	s.m	s.m	PROPN
ma-345	329	9	.	.	PROPN
ma-345	329	10	shakhno	shakhno	PROPN
ma-345	329	11	,	,	PUNCT
ma-345	329	12	h.p	h.p	PROPN
ma-345	329	13	.	.	PROPN
ma-345	329	14	yarmola	yarmola	PROPN
ma-345	329	15	,	,	PUNCT
ma-345	329	16	method	method	NOUN
ma-345	329	17	of	of	ADP
ma-345	329	18	third	third	ADJ
ma-345	329	19	-	-	PUNCT
ma-345	329	20	order	order	NOUN
ma-345	329	21	convergence	convergence	NOUN
ma-345	329	22	with	with	ADP
ma-345	329	23	approximation	approximation	NOUN
ma-345	329	24	of	of	ADP
ma-345	329	25	inverseoperator	inverseoperator	NOUN
ma-345	329	26	for	for	ADP
ma-345	329	27	large	large	ADJ
ma-345	329	28	scale	scale	NOUN
ma-345	329	29	systems	system	NOUN
ma-345	329	30	,	,	PUNCT
ma-345	329	31	symmetry	symmetry	NOUN
ma-345	329	32	12	12	NUM
ma-345	329	33	(	(	PUNCT
ma-345	329	34	2020	2020	NUM
ma-345	329	35	)	)	PUNCT
ma-345	329	36	,	,	PUNCT
ma-345	329	37	978	978	NUM
ma-345	329	38	.	.	PUNCT
ma-345	330	1	https://doi.org/10.3390/sym12060978.[7	https://doi.org/10.3390/sym12060978.[7	PROPN
ma-345	330	2	]	]	PUNCT
ma-345	330	3	m.	m.	NOUN
ma-345	330	4	balázs	balázs	PROPN
ma-345	330	5	,	,	PUNCT
ma-345	330	6	g.	g.	PROPN
ma-345	330	7	goldner	goldner	PROPN
ma-345	330	8	,	,	PUNCT
ma-345	330	9	on	on	ADP
ma-345	330	10	existence	existence	NOUN
ma-345	330	11	of	of	ADP
ma-345	330	12	divided	divide	VERB
ma-345	330	13	differences	difference	NOUN
ma-345	330	14	in	in	ADP
ma-345	330	15	linear	linear	ADJ
ma-345	330	16	spaces	space	NOUN
ma-345	330	17	,	,	PUNCT
ma-345	330	18	rev	rev	PROPN
ma-345	330	19	.	.	PROPN
ma-345	330	20	anal	anal	PROPN
ma-345	330	21	.	.	PUNCT
ma-345	331	1	numér	numér	PROPN
ma-345	331	2	.	.	PUNCT
ma-345	332	1	théorie	théorie	PROPN
ma-345	332	2	approx	approx	PROPN
ma-345	332	3	.	.	PUNCT
ma-345	333	1	2(1973	2(1973	NUM
ma-345	333	2	)	)	PUNCT
ma-345	333	3	5	5	NUM
ma-345	333	4	-	-	SYM
ma-345	333	5	9	9	NUM
ma-345	333	6	.	.	PUNCT
ma-345	334	1	https://doi.org/10.33993/jnaat21-6.[8	https://doi.org/10.33993/jnaat21-6.[8	PROPN
ma-345	334	2	]	]	PUNCT
ma-345	334	3	j.e	j.e	PROPN
ma-345	334	4	.	.	PROPN
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ma-345	334	6	,	,	PUNCT
ma-345	334	7	r.b	r.b	PROPN
ma-345	334	8	.	.	PROPN
ma-345	334	9	schnabel	schnabel	PROPN
ma-345	334	10	,	,	PUNCT
ma-345	334	11	numerical	numerical	ADJ
ma-345	334	12	methods	method	NOUN
ma-345	334	13	for	for	ADP
ma-345	334	14	unconstrained	unconstrained	ADJ
ma-345	334	15	optimization	optimization	NOUN
ma-345	334	16	and	and	CCONJ
ma-345	334	17	nonlinear	nonlinear	ADJ
ma-345	334	18	equations	equation	NOUN
ma-345	334	19	,	,	PUNCT
ma-345	334	20	prentice	prentice	NOUN
ma-345	334	21	-	-	PUNCT
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ma-345	334	23	,	,	PUNCT
ma-345	334	24	englewoods	englewood	VERB
ma-345	334	25	cliffs	cliff	NOUN
ma-345	334	26	,	,	PUNCT
ma-345	334	27	1983.[9	1983.[9	NUM
ma-345	334	28	]	]	PUNCT
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ma-345	334	30	a.	a.	PROPN
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ma-345	334	34	a.	a.	NOUN
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ma-345	334	36	,	,	PUNCT
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ma-345	334	38	ulm	ulm	NOUN
ma-345	334	39	-	-	PUNCT
ma-345	334	40	type	type	NOUN
ma-345	334	41	method	method	NOUN
ma-345	334	42	with	with	ADP
ma-345	334	43	r	r	NOUN
ma-345	334	44	-	-	PUNCT
ma-345	334	45	order	order	NOUN
ma-345	334	46	of	of	ADP
ma-345	334	47	convergence	convergence	NOUN
ma-345	334	48	three	three	NUM
ma-345	334	49	,	,	PUNCT
ma-345	334	50	nonlinear	nonlinear	ADJ
ma-345	334	51	anal	anal	NOUN
ma-345	334	52	.	.	PUNCT
ma-345	334	53	:	:	PUNCT
ma-345	335	1	realworld	realworld	PROPN
ma-345	335	2	appl	appl	PROPN
ma-345	335	3	.	.	PROPN
ma-345	335	4	13	13	NUM
ma-345	335	5	(	(	PUNCT
ma-345	335	6	2012	2012	NUM
ma-345	335	7	)	)	PUNCT
ma-345	335	8	14	14	NUM
ma-345	335	9	-	-	SYM
ma-345	335	10	26	26	NUM
ma-345	335	11	.	.	PUNCT
ma-345	336	1	https://doi.org/10.1016/j.nonrwa.2011.07.039.[10	https://doi.org/10.1016/j.nonrwa.2011.07.039.[10	PROPN
ma-345	336	2	]	]	X
ma-345	336	3	j.	j.	PROPN
ma-345	336	4	a.	a.	PROPN
ma-345	336	5	ezquerro	ezquerro	PROPN
ma-345	336	6	,	,	PUNCT
ma-345	336	7	m.	m.	NOUN
ma-345	336	8	a.	a.	NOUN
ma-345	336	9	hernández	hernández	PROPN
ma-345	336	10	,	,	PUNCT
ma-345	336	11	the	the	DET
ma-345	336	12	ulm	ulm	NOUN
ma-345	336	13	method	method	VERB
ma-345	336	14	under	under	ADP
ma-345	336	15	mild	mild	ADJ
ma-345	336	16	differentiability	differentiability	NOUN
ma-345	336	17	conditions	condition	NOUN
ma-345	336	18	,	,	PUNCT
ma-345	336	19	numer	numer	NOUN
ma-345	336	20	.	.	PROPN
ma-345	336	21	math	math	NOUN
ma-345	336	22	.	.	PUNCT
ma-345	337	1	109	109	NUM
ma-345	337	2	(	(	PUNCT
ma-345	337	3	2008)193	2008)193	NUM
ma-345	337	4	-	-	SYM
ma-345	337	5	207	207	NUM
ma-345	337	6	.	.	PUNCT
ma-345	338	1	https://doi.org/10.1007/s00211-008-0144-z.[11	https://doi.org/10.1007/s00211-008-0144-z.[11	PRON
ma-345	338	2	]	]	PUNCT
ma-345	338	3	m.	m.	NOUN
ma-345	338	4	grau	grau	PROPN
ma-345	338	5	-	-	PUNCT
ma-345	338	6	sánchez	sánchez	PROPN
ma-345	338	7	,	,	PUNCT
ma-345	338	8	m.	m.	NOUN
ma-345	338	9	noguera	noguera	PROPN
ma-345	338	10	,	,	PUNCT
ma-345	338	11	j.m	j.m	PROPN
ma-345	338	12	.	.	PROPN
ma-345	338	13	gutiérrez	gutiérrez	PROPN
ma-345	338	14	,	,	PUNCT
ma-345	338	15	on	on	ADP
ma-345	338	16	some	some	DET
ma-345	338	17	computational	computational	ADJ
ma-345	338	18	orders	order	NOUN
ma-345	338	19	of	of	ADP
ma-345	338	20	convergence	convergence	NOUN
ma-345	338	21	,	,	PUNCT
ma-345	338	22	appl	appl	PROPN
ma-345	338	23	.	.	PROPN
ma-345	338	24	math	math	PROPN
ma-345	338	25	.	.	PUNCT
ma-345	339	1	lett.23	lett.23	PROPN
ma-345	339	2	(	(	PUNCT
ma-345	339	3	2010	2010	NUM
ma-345	339	4	)	)	PUNCT
ma-345	339	5	472	472	NUM
ma-345	339	6	-	-	SYM
ma-345	339	7	478	478	NUM
ma-345	339	8	.	.	PUNCT
ma-345	340	1	https://doi.org/10.1016/j.aml.2009.12.006[12	https://doi.org/10.1016/j.aml.2009.12.006[12	PROPN
ma-345	340	2	]	]	X
ma-345	340	3	j.	j.	PROPN
ma-345	340	4	m.	m.	PROPN
ma-345	340	5	gutiérrez	gutiérrez	PROPN
ma-345	340	6	,	,	PUNCT
ma-345	340	7	m.	m.	NOUN
ma-345	340	8	a.	a.	NOUN
ma-345	340	9	hernández	hernández	PROPN
ma-345	340	10	,	,	PUNCT
ma-345	340	11	n.	n.	PROPN
ma-345	340	12	romero	romero	PROPN
ma-345	340	13	,	,	PUNCT
ma-345	340	14	a	a	DET
ma-345	340	15	note	note	NOUN
ma-345	340	16	on	on	ADP
ma-345	340	17	a	a	DET
ma-345	340	18	modification	modification	NOUN
ma-345	340	19	of	of	ADP
ma-345	340	20	moser	moser	PROPN
ma-345	340	21	’s	’s	PART
ma-345	340	22	method	method	NOUN
ma-345	340	23	,	,	PUNCT
ma-345	340	24	j.	j.	PROPN
ma-345	340	25	complex	complex	PROPN
ma-345	340	26	.	.	PUNCT
ma-345	341	1	24	24	NUM
ma-345	341	2	(	(	PUNCT
ma-345	341	3	2008),185	2008),185	NUM
ma-345	341	4	-	-	SYM
ma-345	341	5	197	197	NUM
ma-345	341	6	.	.	PUNCT
ma-345	342	1	https://doi.org/10.1016/j.jco.2007.04.003.[13	https://doi.org/10.1016/j.jco.2007.04.003.[13	PROPN
ma-345	342	2	]	]	PUNCT
ma-345	342	3	o.	o.	PROPN
ma-345	342	4	h.	h.	PROPN
ma-345	342	5	hald	hald	PROPN
ma-345	342	6	,	,	PUNCT
ma-345	342	7	on	on	ADP
ma-345	342	8	a	a	DET
ma-345	342	9	newton	newton	PROPN
ma-345	342	10	-	-	PUNCT
ma-345	342	11	moser	moser	PROPN
ma-345	342	12	type	type	NOUN
ma-345	342	13	method	method	NOUN
ma-345	342	14	,	,	PUNCT
ma-345	342	15	numer	numer	PROPN
ma-345	342	16	.	.	PUNCT
ma-345	342	17	math	math	NOUN
ma-345	342	18	.	.	PUNCT
ma-345	343	1	23	23	NUM
ma-345	343	2	(	(	PUNCT
ma-345	343	3	1975	1975	NUM
ma-345	343	4	)	)	PUNCT
ma-345	343	5	,	,	PUNCT
ma-345	343	6	411	411	NUM
ma-345	343	7	-	-	SYM
ma-345	343	8	426	426	NUM
ma-345	343	9	.	.	PUNCT
ma-345	344	1	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-345	344	2	bf01437039.[14	bf01437039.[14	PROPN
ma-345	344	3	]	]	PUNCT
ma-345	344	4	j.	j.	PROPN
ma-345	344	5	moser	moser	PROPN
ma-345	344	6	,	,	PUNCT
ma-345	344	7	stable	stable	ADJ
ma-345	344	8	and	and	CCONJ
ma-345	344	9	random	random	ADJ
ma-345	344	10	motions	motion	NOUN
ma-345	344	11	in	in	ADP
ma-345	344	12	dynamical	dynamical	ADJ
ma-345	344	13	systems	system	NOUN
ma-345	344	14	:	:	PUNCT
ma-345	344	15	with	with	ADP
ma-345	344	16	special	special	ADJ
ma-345	344	17	emphasis	emphasis	NOUN
ma-345	344	18	on	on	ADP
ma-345	344	19	celestial	celestial	ADJ
ma-345	344	20	mechanics.herman	mechanics.herman	PROPN
ma-345	344	21	weil	weil	PROPN
ma-345	344	22	lectures	lecture	NOUN
ma-345	344	23	,	,	PUNCT
ma-345	344	24	annals	annal	NOUN
ma-345	344	25	of	of	ADP
ma-345	344	26	mathematics	mathematics	NOUN
ma-345	344	27	studies	study	NOUN
ma-345	344	28	,	,	PUNCT
ma-345	344	29	vol	vol	NOUN
ma-345	344	30	.	.	PROPN
ma-345	344	31	77	77	NUM
ma-345	344	32	,	,	PUNCT
ma-345	344	33	princeton	princeton	PROPN
ma-345	344	34	university	university	PROPN
ma-345	344	35	press	press	PROPN
ma-345	344	36	,	,	PUNCT
ma-345	344	37	princeton	princeton	PROPN
ma-345	344	38	,	,	PUNCT
ma-345	344	39	nj	nj	PROPN
ma-345	344	40	,	,	PUNCT
ma-345	344	41	1973	1973	NUM
ma-345	344	42	.	.	PUNCT
ma-345	345	1	https://www.jstor.org/stable/j.ctt1bd6kg5.[15	https://www.jstor.org/stable/j.ctt1bd6kg5.[15	X
ma-345	345	2	]	]	X
ma-345	345	3	h.	h.	PROPN
ma-345	345	4	petzeltova	petzeltova	PROPN
ma-345	345	5	,	,	PUNCT
ma-345	345	6	remark	remark	NOUN
ma-345	345	7	on	on	ADP
ma-345	345	8	newton	newton	PROPN
ma-345	345	9	-	-	PUNCT
ma-345	345	10	moser	moser	PROPN
ma-345	345	11	type	type	NOUN
ma-345	345	12	method	method	NOUN
ma-345	345	13	,	,	PUNCT
ma-345	345	14	commentat	commentat	NOUN
ma-345	345	15	.	.	PUNCT
ma-345	346	1	math	math	NOUN
ma-345	346	2	.	.	PUNCT
ma-345	347	1	univ	univ	PROPN
ma-345	347	2	.	.	PUNCT
ma-345	347	3	carol	carol	PROPN
ma-345	347	4	.	.	PUNCT
ma-345	348	1	21	21	NUM
ma-345	348	2	(	(	PUNCT
ma-345	348	3	1980	1980	NUM
ma-345	348	4	)	)	PUNCT
ma-345	348	5	,	,	PUNCT
ma-345	348	6	719	719	NUM
ma-345	348	7	-	-	SYM
ma-345	348	8	725	725	NUM
ma-345	348	9	.	.	PUNCT
ma-345	348	10	https	https	NOUN
ma-345	348	11	:	:	PUNCT
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ma-345	348	13	]	]	PUNCT
ma-345	349	1	s.	s.	PROPN
ma-345	349	2	m.	m.	PROPN
ma-345	349	3	shakhno	shakhno	PROPN
ma-345	349	4	,	,	PUNCT
ma-345	349	5	nonlinear	nonlinear	ADJ
ma-345	349	6	majorants	majorant	NOUN
ma-345	349	7	for	for	ADP
ma-345	349	8	investigation	investigation	NOUN
ma-345	349	9	of	of	ADP
ma-345	349	10	methods	method	NOUN
ma-345	349	11	of	of	ADP
ma-345	349	12	linear	linear	ADJ
ma-345	349	13	interpolation	interpolation	NOUN
ma-345	349	14	for	for	ADP
ma-345	349	15	the	the	DET
ma-345	349	16	solution	solution	NOUN
ma-345	349	17	of	of	ADP
ma-345	349	18	non	non	ADJ
ma-345	349	19	-	-	ADJ
ma-345	349	20	linear	linear	ADJ
ma-345	349	21	equations	equation	NOUN
ma-345	349	22	,	,	PUNCT
ma-345	349	23	european	european	PROPN
ma-345	349	24	congress	congress	PROPN
ma-345	349	25	on	on	ADP
ma-345	349	26	computational	computational	ADJ
ma-345	349	27	methods	method	NOUN
ma-345	349	28	in	in	ADP
ma-345	349	29	applied	applied	ADJ
ma-345	349	30	sciences	science	NOUN
ma-345	349	31	and	and	CCONJ
ma-345	349	32	engineering	engineering	NOUN
ma-345	349	33	eccomas2004	eccomas2004	PROPN
ma-345	349	34	–	–	PUNCT
ma-345	349	35	p.	p.	NOUN
ma-345	349	36	neittaanmäki	neittaanmäki	NOUN
ma-345	349	37	,	,	PUNCT
ma-345	349	38	t.	t.	PROPN
ma-345	349	39	rossi	rossi	PROPN
ma-345	349	40	,	,	PUNCT
ma-345	349	41	k.	k.	PROPN
ma-345	349	42	majava	majava	PROPN
ma-345	349	43	and	and	CCONJ
ma-345	349	44	o.	o.	PROPN
ma-345	349	45	pironneau	pironneau	PROPN
ma-345	349	46	(	(	PUNCT
ma-345	349	47	eds	ed	NOUN
ma-345	349	48	.	.	PUNCT
ma-345	349	49	)	)	PUNCT
ma-345	350	1	o.	o.	ADJ
ma-345	350	2	nevanlinna	nevanlinna	NOUN
ma-345	350	3	and	and	CCONJ
ma-345	350	4	r.	r.	PROPN
ma-345	350	5	rannacher	rannacher	PROPN
ma-345	350	6	(	(	PUNCT
ma-345	350	7	assoc	assoc	PROPN
ma-345	350	8	.	.	PUNCT
ma-345	351	1	eds.)yuväskylä	eds.)yuväskylä	PROPN
ma-345	351	2	,	,	PUNCT
ma-345	351	3	24	24	NUM
ma-345	351	4	-	-	SYM
ma-345	351	5	28	28	NUM
ma-345	351	6	july	july	PROPN
ma-345	351	7	2004	2004	NUM
ma-345	351	8	,	,	PUNCT
ma-345	351	9	11	11	NUM
ma-345	351	10	p.	p.	NOUN
ma-345	351	11	https://www.researchgate.net/publication/238701776.[17	https://www.researchgate.net/publication/238701776.[17	PROPN
ma-345	351	12	]	]	PUNCT
ma-345	351	13	s.	s.	PROPN
ma-345	351	14	ulm	ulm	PROPN
ma-345	351	15	,	,	PUNCT
ma-345	351	16	on	on	ADP
ma-345	351	17	iterative	iterative	ADJ
ma-345	351	18	methods	method	NOUN
ma-345	351	19	with	with	ADP
ma-345	351	20	successive	successive	ADJ
ma-345	351	21	approximation	approximation	NOUN
ma-345	351	22	of	of	ADP
ma-345	351	23	the	the	DET
ma-345	351	24	inverse	inverse	NOUN
ma-345	351	25	operator	operator	NOUN
ma-345	351	26	,	,	PUNCT
ma-345	351	27	izv	izv	PROPN
ma-345	351	28	.	.	PROPN
ma-345	351	29	akad	akad	PROPN
ma-345	351	30	.	.	PUNCT
ma-345	352	1	nauk	nauk	PROPN
ma-345	352	2	est	est	PROPN
ma-345	352	3	.	.	PUNCT
ma-345	353	1	ssr	ssr	PROPN
ma-345	353	2	,	,	PUNCT
ma-345	353	3	16(1967	16(1967	NUM
ma-345	353	4	)	)	PUNCT
ma-345	353	5	,	,	PUNCT
ma-345	353	6	403	403	NUM
ma-345	353	7	-	-	SYM
ma-345	353	8	411	411	NUM
ma-345	353	9	.	.	PUNCT
ma-345	354	1	(	(	PUNCT
ma-345	354	2	in	in	ADP
ma-345	354	3	russian	russian	NOUN
ma-345	354	4	)	)	PUNCT
ma-345	354	5	.	.	PUNCT
ma-345	355	1	https://doi.org/10.28924/ada/ma.5.15	https://doi.org/10.28924/ada/ma.5.15	PROPN
ma-345	355	2	https://doi.org/10.1007/s11075-009-9274-3	https://doi.org/10.1007/s11075-009-9274-3	NUM
ma-345	355	3	https://doi.org/10.1016/j.jco.2023.101781	https://doi.org/10.1016/j.jco.2023.101781	PROPN
ma-345	355	4	https://doi.org/10.3390/computation8010008	https://doi.org/10.3390/computation8010008	NOUN
ma-345	355	5	https://doi.org/10.3390/computation8010008	https://doi.org/10.3390/computation8010008	NOUN
ma-345	355	6	https://doi.org/10.3390/sym12060978	https://doi.org/10.3390/sym12060978	ADP
ma-345	355	7	https://doi.org/10.33993/jnaat21-6	https://doi.org/10.33993/jnaat21-6	PROPN
ma-345	355	8	https://doi.org/10.1016/j.nonrwa.2011.07.039	https://doi.org/10.1016/j.nonrwa.2011.07.039	NUM
ma-345	355	9	https://doi.org/10.1007/s00211-008-0144-z	https://doi.org/10.1007/s00211-008-0144-z	PROPN
ma-345	355	10	https://doi.org/10.1016/j.aml.2009.12.006	https://doi.org/10.1016/j.aml.2009.12.006	NOUN
ma-345	355	11	https://doi.org/10.1016/j.jco.2007.04.003	https://doi.org/10.1016/j.jco.2007.04.003	VERB
ma-345	355	12	https://doi.org/10.1007/bf01437039	https://doi.org/10.1007/bf01437039	NOUN
ma-345	355	13	https://doi.org/10.1007/bf01437039	https://doi.org/10.1007/bf01437039	NOUN
ma-345	355	14	https://www.jstor.org/stable/j.ctt1bd6kg5	https://www.jstor.org/stable/j.ctt1bd6kg5	VERB
ma-345	355	15	https://zbmath.org/0455.65042	https://zbmath.org/0455.65042	NOUN
ma-345	355	16	https://zbmath.org/0455.65042	https://zbmath.org/0455.65042	ADP
ma-345	355	17	https://www.researchgate.net/publication/238701776	https://www.researchgate.net/publication/238701776	NOUN
ma-345	355	18	1	1	NUM
ma-345	355	19	.	.	PUNCT
ma-345	356	1	introduction	introduction	NOUN
ma-345	356	2	2	2	NUM
ma-345	356	3	.	.	PUNCT
ma-345	356	4	convergence	convergence	NOUN
ma-345	356	5	3	3	NUM
ma-345	356	6	.	.	PUNCT
ma-345	356	7	numerical	numerical	ADJ
ma-345	356	8	examples	example	NOUN
ma-345	356	9	4	4	NUM
ma-345	356	10	.	.	PUNCT
ma-345	357	1	conclusion	conclusion	NOUN
ma-345	357	2	references	reference	NOUN