id	sid	tid	token	lemma	pos
ma-85	1	1	2022	2022	NUM
ma-85	1	2	ada	ada	PROPN
ma-85	1	3	academica	academica	PROPN
ma-85	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-85	1	5	.	.	PUNCT
ma-85	2	1	j.	j.	PROPN
ma-85	2	2	math	math	PROPN
ma-85	2	3	.	.	PUNCT
ma-85	3	1	anal	anal	ADJ
ma-85	3	2	.	.	PUNCT
ma-85	3	3	2	2	NUM
ma-85	3	4	(	(	PUNCT
ma-85	3	5	2022	2022	NUM
ma-85	3	6	)	)	PUNCT
ma-85	3	7	13doi	13doi	NOUN
ma-85	3	8	:	:	PUNCT
ma-85	3	9	10.28924	10.28924	NUM
ma-85	3	10	/	/	SYM
ma-85	3	11	ada	ada	PROPN
ma-85	3	12	/	/	SYM
ma-85	3	13	ma.2.13	ma.2.13	PROPN
ma-85	3	14	on	on	ADP
ma-85	3	15	the	the	DET
ma-85	3	16	semi	semi	ADJ
ma-85	3	17	-	-	ADJ
ma-85	3	18	local	local	ADJ
ma-85	3	19	convergence	convergence	NOUN
ma-85	3	20	of	of	ADP
ma-85	3	21	a	a	DET
ma-85	3	22	third	third	ADJ
ma-85	3	23	order	order	NOUN
ma-85	3	24	scheme	scheme	NOUN
ma-85	3	25	for	for	ADP
ma-85	3	26	solving	solve	VERB
ma-85	3	27	nonlinear	nonlinear	ADJ
ma-85	3	28	equations	equation	NOUN
ma-85	3	29	samundra	samundra	VERB
ma-85	3	30	regmi1	regmi1	PROPN
ma-85	3	31	,	,	PUNCT
ma-85	3	32	ioannis	ioannis	PROPN
ma-85	3	33	k.	k.	PROPN
ma-85	3	34	argyros2,∗	argyros2,∗	PROPN
ma-85	3	35	,	,	PUNCT
ma-85	3	36	santhosh	santhosh	PROPN
ma-85	3	37	george3	george3	PROPN
ma-85	3	38	,	,	PUNCT
ma-85	3	39	christopher	christopher	PROPN
ma-85	3	40	argyros4	argyros4	PROPN
ma-85	4	1	1learning	1learning	NUM
ma-85	4	2	commons	common	NOUN
ma-85	4	3	,	,	PUNCT
ma-85	4	4	university	university	NOUN
ma-85	4	5	of	of	ADP
ma-85	4	6	north	north	PROPN
ma-85	4	7	texas	texas	PROPN
ma-85	4	8	at	at	ADP
ma-85	4	9	dallas	dallas	PROPN
ma-85	4	10	,	,	PUNCT
ma-85	4	11	dallas	dallas	PROPN
ma-85	4	12	,	,	PUNCT
ma-85	4	13	tx	tx	PROPN
ma-85	4	14	,	,	PUNCT
ma-85	4	15	usa	usa	PROPN
ma-85	4	16	samundra.regmi@untdallas.edu	samundra.regmi@untdallas.edu	PROPN
ma-85	4	17	2department	2department	PROPN
ma-85	4	18	of	of	ADP
ma-85	4	19	mathematical	mathematical	ADJ
ma-85	4	20	sciences	sciences	PROPN
ma-85	4	21	,	,	PUNCT
ma-85	4	22	cameron	cameron	PROPN
ma-85	4	23	university	university	PROPN
ma-85	4	24	,	,	PUNCT
ma-85	4	25	lawton	lawton	PROPN
ma-85	4	26	,	,	PUNCT
ma-85	4	27	ok	ok	PROPN
ma-85	4	28	73505	73505	NUM
ma-85	4	29	,	,	PUNCT
ma-85	4	30	usa	usa	PROPN
ma-85	4	31	iargyros@cameron.edu	iargyros@cameron.edu	PROPN
ma-85	5	1	3department	3department	NUM
ma-85	5	2	of	of	ADP
ma-85	5	3	mathematical	mathematical	ADJ
ma-85	5	4	and	and	CCONJ
ma-85	5	5	computational	computational	ADJ
ma-85	5	6	sciences	science	NOUN
ma-85	5	7	,	,	PUNCT
ma-85	5	8	national	national	PROPN
ma-85	5	9	institute	institute	PROPN
ma-85	5	10	of	of	ADP
ma-85	5	11	technology	technology	PROPN
ma-85	5	12	karnataka	karnataka	PROPN
ma-85	5	13	,	,	PUNCT
ma-85	5	14	india-575	india-575	ADJ
ma-85	5	15	025	025	NUM
ma-85	5	16	sgeorge@nitk.edu.in	sgeorge@nitk.edu.in	NOUN
ma-85	5	17	4department	4department	NUM
ma-85	5	18	of	of	ADP
ma-85	5	19	computing	computing	NOUN
ma-85	5	20	and	and	CCONJ
ma-85	5	21	technology	technology	NOUN
ma-85	5	22	,	,	PUNCT
ma-85	5	23	cameron	cameron	PROPN
ma-85	5	24	university	university	PROPN
ma-85	5	25	,	,	PUNCT
ma-85	5	26	lawton	lawton	PROPN
ma-85	5	27	,	,	PUNCT
ma-85	5	28	ok	ok	PROPN
ma-85	5	29	73505	73505	NUM
ma-85	5	30	,	,	PUNCT
ma-85	5	31	usa	usa	PROPN
ma-85	5	32	christopher.argyros@cameron.edu	christopher.argyros@cameron.edu	PROPN
ma-85	5	33	∗correspondence	∗correspondence	NOUN
ma-85	5	34	:	:	PUNCT
ma-85	5	35	iargyros@cameron.edu	iargyros@cameron.edu	X
ma-85	6	1	abstract	abstract	ADJ
ma-85	6	2	.	.	PUNCT
ma-85	7	1	the	the	DET
ma-85	7	2	semi	semi	ADJ
ma-85	7	3	-	-	ADJ
ma-85	7	4	local	local	ADJ
ma-85	7	5	convergence	convergence	NOUN
ma-85	7	6	analysis	analysis	NOUN
ma-85	7	7	of	of	ADP
ma-85	7	8	a	a	DET
ma-85	7	9	third	third	ADJ
ma-85	7	10	order	order	NOUN
ma-85	7	11	scheme	scheme	NOUN
ma-85	7	12	for	for	ADP
ma-85	7	13	solving	solve	VERB
ma-85	7	14	nonlinear	nonlinear	ADJ
ma-85	7	15	equationin	equationin	NOUN
ma-85	7	16	banach	banach	NOUN
ma-85	7	17	space	space	NOUN
ma-85	7	18	has	have	AUX
ma-85	7	19	not	not	PART
ma-85	7	20	been	be	AUX
ma-85	7	21	given	give	VERB
ma-85	7	22	under	under	ADP
ma-85	7	23	lipschitz	lipschitz	NOUN
ma-85	7	24	continuity	continuity	NOUN
ma-85	7	25	or	or	CCONJ
ma-85	7	26	other	other	ADJ
ma-85	7	27	conditions	condition	NOUN
ma-85	7	28	.	.	PUNCT
ma-85	8	1	our	our	PRON
ma-85	8	2	goal	goal	NOUN
ma-85	8	3	isto	isto	INTJ
ma-85	8	4	extend	extend	VERB
ma-85	8	5	the	the	DET
ma-85	8	6	applicability	applicability	NOUN
ma-85	8	7	of	of	ADP
ma-85	8	8	the	the	DET
ma-85	8	9	cordero	cordero	PROPN
ma-85	8	10	-	-	PUNCT
ma-85	8	11	torregrosa	torregrosa	NOUN
ma-85	8	12	scheme	scheme	NOUN
ma-85	8	13	in	in	ADP
ma-85	8	14	the	the	DET
ma-85	8	15	semi	semi	ADJ
ma-85	8	16	-	-	ADJ
ma-85	8	17	local	local	ADJ
ma-85	8	18	convergence	convergence	NOUN
ma-85	8	19	underconditions	undercondition	NOUN
ma-85	8	20	on	on	ADP
ma-85	8	21	the	the	DET
ma-85	8	22	first	first	ADJ
ma-85	8	23	fréchet	fréchet	NOUN
ma-85	8	24	derivative	derivative	NOUN
ma-85	8	25	of	of	ADP
ma-85	8	26	the	the	DET
ma-85	8	27	operator	operator	NOUN
ma-85	8	28	involved	involve	VERB
ma-85	8	29	.	.	PUNCT
ma-85	9	1	majorizing	majorize	VERB
ma-85	9	2	sequences	sequence	NOUN
ma-85	9	3	are	be	AUX
ma-85	9	4	used	use	VERB
ma-85	9	5	forproving	forprove	VERB
ma-85	9	6	our	our	PRON
ma-85	9	7	results	result	NOUN
ma-85	9	8	.	.	PUNCT
ma-85	10	1	numerical	numerical	ADJ
ma-85	10	2	experiments	experiment	NOUN
ma-85	10	3	testing	test	VERB
ma-85	10	4	the	the	DET
ma-85	10	5	convergence	convergence	NOUN
ma-85	10	6	criteria	criterion	NOUN
ma-85	10	7	are	be	AUX
ma-85	10	8	given	give	VERB
ma-85	10	9	in	in	ADP
ma-85	10	10	this	this	DET
ma-85	10	11	study	study	NOUN
ma-85	10	12	.	.	PUNCT
ma-85	11	1	1	1	X
ma-85	11	2	.	.	X
ma-85	11	3	introduction	introduction	NOUN
ma-85	11	4	cordero	cordero	PROPN
ma-85	11	5	and	and	CCONJ
ma-85	11	6	torregrosa	torregrosa	NOUN
ma-85	11	7	in	in	ADP
ma-85	11	8	[	[	X
ma-85	11	9	10	10	NUM
ma-85	11	10	]	]	PUNCT
ma-85	11	11	considered	consider	VERB
ma-85	11	12	the	the	DET
ma-85	11	13	third	third	ADJ
ma-85	11	14	order	order	NOUN
ma-85	11	15	scheme	scheme	NOUN
ma-85	11	16	,	,	PUNCT
ma-85	11	17	defined	define	VERB
ma-85	11	18	for	for	ADP
ma-85	11	19	n	n	NOUN
ma-85	11	20	=	=	SYM
ma-85	11	21	0	0	NUM
ma-85	11	22	,	,	PUNCT
ma-85	11	23	1	1	NUM
ma-85	11	24	,	,	PUNCT
ma-85	11	25	2	2	NUM
ma-85	11	26	,	,	PUNCT
ma-85	11	27	.	.	PUNCT
ma-85	11	28	.	.	PUNCT
ma-85	11	29	.	.	PUNCT
ma-85	12	1	,	,	PUNCT
ma-85	12	2	by	by	ADP
ma-85	12	3	yn	yn	X
ma-85	12	4	=	=	PUNCT
ma-85	12	5	xn	xn	PROPN
ma-85	13	1	−	−	PROPN
ma-85	13	2	f	f	PROPN
ma-85	13	3	′(xn)−1f	′(xn)−1f	PROPN
ma-85	13	4	(	(	PUNCT
ma-85	13	5	xn	xn	PROPN
ma-85	13	6	)	)	PUNCT
ma-85	13	7	xn+1	xn+1	PUNCT
ma-85	14	1	=	=	SYM
ma-85	14	2	xn	xn	PROPN
ma-85	15	1	−	−	NUM
ma-85	16	1	3m−1n	3m−1n	PRON
ma-85	16	2	f	f	X
ma-85	16	3	(	(	PUNCT
ma-85	16	4	xn	xn	PROPN
ma-85	16	5	)	)	PUNCT
ma-85	16	6	,	,	PUNCT
ma-85	16	7	(	(	PUNCT
ma-85	16	8	1.1	1.1	NUM
ma-85	16	9	)	)	PUNCT
ma-85	16	10	for	for	ADP
ma-85	16	11	solving	solve	VERB
ma-85	16	12	the	the	DET
ma-85	16	13	nonlinear	nonlinear	ADJ
ma-85	16	14	equation	equation	NOUN
ma-85	16	15	f	f	X
ma-85	16	16	(	(	PUNCT
ma-85	16	17	x	x	X
ma-85	16	18	)	)	PUNCT
ma-85	16	19	=	=	SYM
ma-85	16	20	0	0	NUM
ma-85	16	21	,	,	PUNCT
ma-85	16	22	(	(	PUNCT
ma-85	16	23	1.2	1.2	NUM
ma-85	16	24	)	)	PUNCT
ma-85	16	25	where	where	SCONJ
ma-85	16	26	mn	mn	NOUN
ma-85	16	27	=	=	SYM
ma-85	16	28	2f	2f	NUM
ma-85	16	29	′	′	NUM
ma-85	16	30	(	(	PUNCT
ma-85	16	31	3xn+yn	3xn+yn	NUM
ma-85	16	32	4	4	NUM
ma-85	16	33	)	)	PUNCT
ma-85	16	34	−	−	PROPN
ma-85	17	1	f	f	NOUN
ma-85	17	2	′	′	NUM
ma-85	17	3	(	(	PUNCT
ma-85	17	4	xn+yn	xn+yn	PROPN
ma-85	17	5	2	2	X
ma-85	17	6	)	)	PUNCT
ma-85	18	1	+	+	CCONJ
ma-85	18	2	2f	2f	NUM
ma-85	18	3	′	′	NUM
ma-85	18	4	(	(	PUNCT
ma-85	18	5	xn+3yn	xn+3yn	X
ma-85	18	6	4	4	NUM
ma-85	18	7	)	)	PUNCT
ma-85	18	8	.	.	PUNCT
ma-85	19	1	here	here	ADV
ma-85	19	2	f	f	X
ma-85	19	3	:	:	PUNCT
ma-85	20	1	d	d	X
ma-85	20	2	⊂	⊂	PROPN
ma-85	20	3	e	e	PUNCT
ma-85	20	4	−→	−→	NOUN
ma-85	20	5	e1	e1	NOUN
ma-85	20	6	is	be	AUX
ma-85	20	7	an	an	DET
ma-85	20	8	operatoracting	operatoracting	NOUN
ma-85	20	9	between	between	ADP
ma-85	20	10	banach	banach	NOUN
ma-85	20	11	spaces	space	NOUN
ma-85	20	12	e	e	NOUN
ma-85	20	13	and	and	CCONJ
ma-85	20	14	e1	e1	VERB
ma-85	20	15	with	with	ADP
ma-85	20	16	d	d	PROPN
ma-85	20	17	6=	6=	ADP
ma-85	20	18	∅.	∅.	NOUN
ma-85	20	19	in	in	ADP
ma-85	20	20	general	general	ADJ
ma-85	20	21	a	a	DET
ma-85	20	22	closed	closed	ADJ
ma-85	20	23	form	form	NOUN
ma-85	20	24	solution	solution	NOUN
ma-85	20	25	for	for	ADP
ma-85	20	26	(	(	PUNCT
ma-85	20	27	1.2	1.2	NUM
ma-85	20	28	)	)	PUNCT
ma-85	20	29	isnot	isnot	ADV
ma-85	20	30	possible	possible	ADJ
ma-85	20	31	,	,	PUNCT
ma-85	20	32	so	so	SCONJ
ma-85	20	33	iterative	iterative	ADJ
ma-85	20	34	schemes	scheme	NOUN
ma-85	20	35	are	be	AUX
ma-85	20	36	used	use	VERB
ma-85	20	37	for	for	ADP
ma-85	20	38	approximating	approximate	VERB
ma-85	20	39	a	a	DET
ma-85	20	40	solution	solution	NOUN
ma-85	20	41	x∗	x∗	X
ma-85	20	42	of	of	ADP
ma-85	20	43	(	(	PUNCT
ma-85	20	44	1.2	1.2	NUM
ma-85	20	45	)	)	PUNCT
ma-85	20	46	(	(	PUNCT
ma-85	20	47	see	see	VERB
ma-85	20	48	[	[	X
ma-85	20	49	1–27	1–27	NOUN
ma-85	20	50	]	]	PUNCT
ma-85	20	51	)	)	PUNCT
ma-85	20	52	.	.	PUNCT
ma-85	21	1	received	receive	VERB
ma-85	21	2	:	:	PUNCT
ma-85	21	3	14	14	NUM
ma-85	21	4	feb	feb	PROPN
ma-85	21	5	2022	2022	NUM
ma-85	21	6	.	.	PUNCT
ma-85	22	1	key	key	ADJ
ma-85	22	2	words	word	NOUN
ma-85	22	3	and	and	CCONJ
ma-85	22	4	phrases	phrase	NOUN
ma-85	22	5	.	.	PUNCT
ma-85	23	1	semi	semi	ADJ
ma-85	23	2	-	-	ADJ
ma-85	23	3	local	local	ADJ
ma-85	23	4	convergence	convergence	NOUN
ma-85	23	5	;	;	PUNCT
ma-85	23	6	cordero	cordero	NOUN
ma-85	23	7	-	-	PUNCT
ma-85	23	8	torregrosa	torregrosa	NOUN
ma-85	23	9	scheme	scheme	NOUN
ma-85	23	10	;	;	PUNCT
ma-85	23	11	iterative	iterative	NOUN
ma-85	23	12	schemes	scheme	NOUN
ma-85	23	13	;	;	PUNCT
ma-85	23	14	banach	banach	NOUN
ma-85	23	15	space	space	NOUN
ma-85	23	16	;	;	PUNCT
ma-85	23	17	con	con	NOUN
ma-85	23	18	-	-	PUNCT
ma-85	23	19	vergence	vergence	NOUN
ma-85	23	20	criterion	criterion	NOUN
ma-85	23	21	.	.	PUNCT
ma-85	24	1	1	1	NUM
ma-85	24	2	https://adac.ee	https://adac.ee	PROPN
ma-85	24	3	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	X
ma-85	24	4	eur	eur	PROPN
ma-85	24	5	.	.	PUNCT
ma-85	25	1	j.	j.	PROPN
ma-85	25	2	math	math	PROPN
ma-85	25	3	.	.	PUNCT
ma-85	26	1	anal	anal	PROPN
ma-85	26	2	.	.	PUNCT
ma-85	27	1	10.28924	10.28924	NUM
ma-85	27	2	/	/	SYM
ma-85	27	3	ada	ada	PROPN
ma-85	27	4	/	/	SYM
ma-85	27	5	ma.2.13	ma.2.13	PROPN
ma-85	27	6	2the	2the	NUM
ma-85	27	7	local	local	ADJ
ma-85	27	8	convergence	convergence	NOUN
ma-85	27	9	of	of	ADP
ma-85	27	10	the	the	DET
ma-85	27	11	this	this	DET
ma-85	27	12	scheme	scheme	NOUN
ma-85	27	13	in	in	ADP
ma-85	27	14	the	the	DET
ma-85	27	15	special	special	ADJ
ma-85	27	16	case	case	NOUN
ma-85	27	17	when	when	SCONJ
ma-85	27	18	e	e	NOUN
ma-85	27	19	=	=	NOUN
ma-85	27	20	e1	e1	PROPN
ma-85	27	21	=	=	NOUN
ma-85	27	22	r	r	NOUN
ma-85	27	23	was	be	AUX
ma-85	27	24	shown	show	VERB
ma-85	27	25	to	to	PART
ma-85	27	26	beof	beof	VERB
ma-85	27	27	order	order	NOUN
ma-85	27	28	three	three	NUM
ma-85	27	29	using	use	VERB
ma-85	27	30	taylor	taylor	PROPN
ma-85	27	31	expansion	expansion	NOUN
ma-85	27	32	and	and	CCONJ
ma-85	27	33	assumptions	assumption	NOUN
ma-85	27	34	on	on	ADP
ma-85	27	35	the	the	DET
ma-85	27	36	fourth	fourth	ADJ
ma-85	27	37	order	order	NOUN
ma-85	27	38	derivative	derivative	NOUN
ma-85	27	39	of	of	ADP
ma-85	27	40	f	f	PROPN
ma-85	27	41	,	,	PUNCT
ma-85	27	42	whichis	whichi	VERB
ma-85	27	43	not	not	PART
ma-85	27	44	on	on	ADP
ma-85	27	45	these	these	DET
ma-85	27	46	schemes	scheme	NOUN
ma-85	27	47	[	[	X
ma-85	27	48	10	10	NUM
ma-85	27	49	]	]	PUNCT
ma-85	27	50	.	.	PUNCT
ma-85	28	1	so	so	ADV
ma-85	28	2	,	,	PUNCT
ma-85	28	3	the	the	DET
ma-85	28	4	assumptions	assumption	NOUN
ma-85	28	5	on	on	ADP
ma-85	28	6	the	the	DET
ma-85	28	7	fourth	fourth	ADJ
ma-85	28	8	derivative	derivative	NOUN
ma-85	28	9	reduce	reduce	VERB
ma-85	28	10	the	the	DET
ma-85	28	11	applicabilityof	applicabilityof	NOUN
ma-85	28	12	these	these	DET
ma-85	28	13	schemes	scheme	NOUN
ma-85	29	1	[	[	X
ma-85	29	2	1–27].for	1–27].for	NUM
ma-85	29	3	example	example	NOUN
ma-85	29	4	:	:	PUNCT
ma-85	29	5	let	let	VERB
ma-85	29	6	e	e	NOUN
ma-85	29	7	=	=	NOUN
ma-85	29	8	e1	e1	PROPN
ma-85	29	9	=	=	SYM
ma-85	29	10	r	r	NOUN
ma-85	29	11	,	,	PUNCT
ma-85	29	12	d	d	NOUN
ma-85	29	13	=	=	PUNCT
ma-85	30	1	[	[	X
ma-85	30	2	−0.5	−0.5	PROPN
ma-85	30	3	,	,	PUNCT
ma-85	30	4	1.5	1.5	NUM
ma-85	30	5	]	]	PUNCT
ma-85	30	6	.	.	PUNCT
ma-85	31	1	define	define	VERB
ma-85	31	2	λ	λ	PROPN
ma-85	31	3	on	on	ADP
ma-85	31	4	d	d	X
ma-85	31	5	by	by	ADP
ma-85	31	6	λ(t	λ(t	NOUN
ma-85	31	7	)	)	PUNCT
ma-85	31	8	=	=	PRON
ma-85	31	9	{	{	PUNCT
ma-85	31	10	t3	t3	PROPN
ma-85	31	11	log	log	NOUN
ma-85	31	12	t2	t2	PROPN
ma-85	31	13	+	+	CCONJ
ma-85	31	14	t5	t5	PROPN
ma-85	31	15	−	−	PROPN
ma-85	32	1	t4	t4	PROPN
ma-85	33	1	i	i	PRON
ma-85	33	2	f	f	PROPN
ma-85	33	3	t	t	PROPN
ma-85	33	4	6=	6=	PROPN
ma-85	33	5	0	0	NUM
ma-85	33	6	0	0	NUM
ma-85	34	1	i	i	PRON
ma-85	34	2	f	f	NOUN
ma-85	34	3	t	t	NOUN
ma-85	34	4	=	=	SYM
ma-85	34	5	0	0	X
ma-85	34	6	.	.	PUNCT
ma-85	35	1	then	then	ADV
ma-85	35	2	,	,	PUNCT
ma-85	35	3	we	we	PRON
ma-85	35	4	get	get	VERB
ma-85	35	5	f	f	X
ma-85	35	6	(	(	PUNCT
ma-85	35	7	1	1	NUM
ma-85	35	8	)	)	PUNCT
ma-85	35	9	=	=	SYM
ma-85	35	10	0	0	NUM
ma-85	35	11	,	,	PUNCT
ma-85	35	12	and	and	CCONJ
ma-85	35	13	λ′′′(t	λ′′′(t	PROPN
ma-85	35	14	)	)	PUNCT
ma-85	35	15	=	=	SYM
ma-85	35	16	6	6	NUM
ma-85	35	17	log	log	NOUN
ma-85	35	18	t2	t2	NOUN
ma-85	35	19	+	+	CCONJ
ma-85	36	1	60t2	60t2	NUM
ma-85	36	2	−	−	NUM
ma-85	36	3	24	24	NUM
ma-85	36	4	t	t	NOUN
ma-85	36	5	+	+	NOUN
ma-85	36	6	22	22	NUM
ma-85	36	7	.	.	PUNCT
ma-85	37	1	obviously	obviously	ADV
ma-85	37	2	λ′′′(t	λ′′′(t	VERB
ma-85	37	3	)	)	PUNCT
ma-85	37	4	is	be	AUX
ma-85	37	5	not	not	PART
ma-85	37	6	bounded	bound	VERB
ma-85	37	7	on	on	ADP
ma-85	37	8	d.	d.	PROPN
ma-85	38	1	so	so	ADV
ma-85	38	2	,	,	PUNCT
ma-85	38	3	the	the	DET
ma-85	38	4	convergence	convergence	NOUN
ma-85	38	5	of	of	ADP
ma-85	38	6	scheme	scheme	NOUN
ma-85	38	7	(	(	PUNCT
ma-85	38	8	1.1	1.1	NUM
ma-85	38	9	)	)	PUNCT
ma-85	38	10	is	be	AUX
ma-85	38	11	not	not	PART
ma-85	38	12	guaranteed	guarantee	VERB
ma-85	38	13	bythe	bythe	ADP
ma-85	38	14	previous	previous	ADJ
ma-85	38	15	analyses	analysis	NOUN
ma-85	38	16	in	in	ADP
ma-85	38	17	[	[	PUNCT
ma-85	38	18	1–27].in	1–27].in	NUM
ma-85	38	19	this	this	DET
ma-85	38	20	study	study	NOUN
ma-85	38	21	we	we	PRON
ma-85	38	22	introduce	introduce	VERB
ma-85	38	23	a	a	DET
ma-85	38	24	majorant	majorant	NOUN
ma-85	38	25	sequence	sequence	NOUN
ma-85	38	26	and	and	CCONJ
ma-85	38	27	use	use	VERB
ma-85	38	28	general	general	ADJ
ma-85	38	29	continuity	continuity	NOUN
ma-85	38	30	conditions	condition	NOUN
ma-85	38	31	to	to	ADP
ma-85	38	32	extendthe	extendthe	DET
ma-85	38	33	applicability	applicability	NOUN
ma-85	38	34	of	of	ADP
ma-85	38	35	scheme	scheme	NOUN
ma-85	38	36	(	(	PUNCT
ma-85	38	37	1.1	1.1	NUM
ma-85	38	38	)	)	PUNCT
ma-85	38	39	.	.	PUNCT
ma-85	39	1	our	our	PRON
ma-85	39	2	analysis	analysis	NOUN
ma-85	39	3	includes	include	VERB
ma-85	39	4	error	error	NOUN
ma-85	39	5	bounds	bound	NOUN
ma-85	39	6	and	and	CCONJ
ma-85	39	7	results	result	NOUN
ma-85	39	8	on	on	ADP
ma-85	39	9	uniqueness	uniqueness	NOUN
ma-85	39	10	of	of	ADP
ma-85	39	11	x∗	x∗	PROPN
ma-85	39	12	based	base	VERB
ma-85	39	13	on	on	ADP
ma-85	39	14	computable	computable	ADJ
ma-85	39	15	lipschitz	lipschitz	NOUN
ma-85	39	16	constants	constant	NOUN
ma-85	39	17	not	not	PART
ma-85	39	18	given	give	VERB
ma-85	39	19	before	before	ADV
ma-85	39	20	in	in	ADP
ma-85	39	21	[	[	X
ma-85	39	22	1–27	1–27	NOUN
ma-85	39	23	]	]	X
ma-85	39	24	and	and	CCONJ
ma-85	39	25	in	in	ADP
ma-85	39	26	other	other	ADJ
ma-85	39	27	similar	similar	ADJ
ma-85	39	28	studiesusing	studiesuse	VERB
ma-85	39	29	taylor	taylor	PROPN
ma-85	39	30	series	series	PROPN
ma-85	39	31	.	.	PUNCT
ma-85	40	1	our	our	PRON
ma-85	40	2	idea	idea	NOUN
ma-85	40	3	is	be	AUX
ma-85	40	4	very	very	ADV
ma-85	40	5	general	general	ADJ
ma-85	40	6	.	.	PUNCT
ma-85	41	1	so	so	ADV
ma-85	41	2	,	,	PUNCT
ma-85	41	3	it	it	PRON
ma-85	41	4	applies	apply	VERB
ma-85	41	5	on	on	ADP
ma-85	41	6	other	other	ADJ
ma-85	41	7	schemes	scheme	NOUN
ma-85	41	8	too.the	too.the	DET
ma-85	41	9	rest	rest	NOUN
ma-85	41	10	of	of	ADP
ma-85	41	11	the	the	DET
ma-85	41	12	study	study	NOUN
ma-85	41	13	is	be	AUX
ma-85	41	14	set	set	VERB
ma-85	41	15	up	up	ADP
ma-85	41	16	as	as	SCONJ
ma-85	41	17	follows	follow	VERB
ma-85	41	18	:	:	PUNCT
ma-85	41	19	in	in	ADP
ma-85	41	20	section	section	NOUN
ma-85	41	21	2	2	NUM
ma-85	41	22	we	we	PRON
ma-85	41	23	present	present	VERB
ma-85	41	24	results	result	NOUN
ma-85	41	25	on	on	ADP
ma-85	41	26	majorizing	majorize	VERB
ma-85	41	27	sequences.sections	sequences.section	NOUN
ma-85	41	28	3,4	3,4	NUM
ma-85	41	29	contain	contain	VERB
ma-85	41	30	the	the	DET
ma-85	41	31	semi	semi	ADJ
ma-85	41	32	-	-	ADJ
ma-85	41	33	local	local	ADJ
ma-85	41	34	and	and	CCONJ
ma-85	41	35	local	local	ADJ
ma-85	41	36	convergence	convergence	NOUN
ma-85	41	37	,	,	PUNCT
ma-85	41	38	respectively	respectively	ADV
ma-85	41	39	,	,	PUNCT
ma-85	41	40	where	where	SCONJ
ma-85	41	41	in	in	ADP
ma-85	41	42	section	section	NOUN
ma-85	41	43	4	4	NUM
ma-85	41	44	thenumerical	thenumerical	ADJ
ma-85	41	45	experiments	experiment	NOUN
ma-85	41	46	are	be	AUX
ma-85	41	47	presented	present	VERB
ma-85	41	48	.	.	PUNCT
ma-85	42	1	concluding	conclude	VERB
ma-85	42	2	remarks	remark	NOUN
ma-85	42	3	are	be	AUX
ma-85	42	4	given	give	VERB
ma-85	42	5	in	in	ADP
ma-85	42	6	the	the	DET
ma-85	42	7	last	last	ADJ
ma-85	42	8	section	section	NOUN
ma-85	42	9	5	5	NUM
ma-85	42	10	.	.	NOUN
ma-85	42	11	2	2	NUM
ma-85	42	12	.	.	X
ma-85	42	13	majorizing	majorize	VERB
ma-85	42	14	sequences	sequence	NOUN
ma-85	42	15	scalar	scalar	ADJ
ma-85	42	16	sequences	sequence	NOUN
ma-85	42	17	are	be	AUX
ma-85	42	18	developed	develop	VERB
ma-85	42	19	that	that	DET
ma-85	42	20	majorize	majorize	NOUN
ma-85	42	21	scheme	scheme	NOUN
ma-85	42	22	(	(	PUNCT
ma-85	42	23	1.1	1.1	NUM
ma-85	42	24	)	)	PUNCT
ma-85	42	25	.	.	PUNCT
ma-85	43	1	let	let	VERB
ma-85	43	2	k0	k0	PROPN
ma-85	43	3	>	>	X
ma-85	43	4	0	0	PROPN
ma-85	43	5	,	,	PUNCT
ma-85	43	6	k	k	PROPN
ma-85	43	7	>	>	X
ma-85	43	8	0	0	PROPN
ma-85	43	9	and	and	CCONJ
ma-85	43	10	η	η	PROPN
ma-85	43	11	>	>	X
ma-85	43	12	0	0	NUM
ma-85	43	13	begiven	begiven	VERB
ma-85	43	14	constants	constant	NOUN
ma-85	43	15	.	.	PUNCT
ma-85	44	1	define	define	VERB
ma-85	44	2	sequences	sequence	NOUN
ma-85	44	3	{	{	PUNCT
ma-85	44	4	tn	tn	NOUN
ma-85	44	5	}	}	PUNCT
ma-85	44	6	,	,	PUNCT
ma-85	44	7	{	{	PUNCT
ma-85	44	8	sn	sn	X
ma-85	44	9	}	}	PUNCT
ma-85	44	10	by	by	ADP
ma-85	44	11	t0	t0	PROPN
ma-85	44	12	=	=	SYM
ma-85	44	13	0	0	NUM
ma-85	44	14	,	,	PUNCT
ma-85	44	15	s0	s0	PROPN
ma-85	44	16	=	=	SYM
ma-85	44	17	η	η	PROPN
ma-85	44	18	tn+1	tn+1	PROPN
ma-85	44	19	=	=	SYM
ma-85	44	20	sn	sn	PROPN
ma-85	44	21	+	+	CCONJ
ma-85	44	22	2k(sn	2k(sn	NUM
ma-85	44	23	−	−	PROPN
ma-85	44	24	tn)(tn+1	tn)(tn+1	PROPN
ma-85	44	25	−	−	PROPN
ma-85	44	26	tn	tn	PROPN
ma-85	44	27	)	)	PUNCT
ma-85	44	28	9(1−k0tn)(1−	9(1−k0tn)(1−	PROPN
ma-85	44	29	pn	pn	PROPN
ma-85	44	30	)	)	PUNCT
ma-85	44	31	,	,	PUNCT
ma-85	44	32	sn+1	sn+1	X
ma-85	44	33	=	=	SYM
ma-85	44	34	tn+1	tn+1	PROPN
ma-85	44	35	+	+	CCONJ
ma-85	44	36	k(tn+1	k(tn+1	PROPN
ma-85	44	37	−	−	PROPN
ma-85	44	38	tn	tn	PROPN
ma-85	45	1	+	+	CCONJ
ma-85	45	2	sn	sn	PROPN
ma-85	45	3	−	−	PROPN
ma-85	45	4	tn)(tn+1	tn)(tn+1	PROPN
ma-85	45	5	−	−	PROPN
ma-85	45	6	tn	tn	PROPN
ma-85	45	7	)	)	PUNCT
ma-85	45	8	2(1−k0tn+1	2(1−k0tn+1	NUM
ma-85	45	9	)	)	PUNCT
ma-85	45	10	,	,	PUNCT
ma-85	45	11	(	(	PUNCT
ma-85	45	12	2.1	2.1	NUM
ma-85	45	13	)	)	PUNCT
ma-85	45	14	where	where	SCONJ
ma-85	45	15	pn	pn	PROPN
ma-85	45	16	=	=	SYM
ma-85	45	17	5k0	5k0	PROPN
ma-85	45	18	6	6	NUM
ma-85	45	19	(	(	PUNCT
ma-85	45	20	sn	sn	PROPN
ma-85	45	21	+	+	PROPN
ma-85	45	22	tn	tn	NOUN
ma-85	45	23	)	)	PUNCT
ma-85	45	24	.	.	PUNCT
ma-85	46	1	notice	notice	VERB
ma-85	46	2	that	that	SCONJ
ma-85	46	3	tn+1	tn+1	NOUN
ma-85	46	4	is	be	AUX
ma-85	46	5	given	give	VERB
ma-85	46	6	implicitly	implicitly	ADV
ma-85	46	7	in	in	ADP
ma-85	46	8	the	the	DET
ma-85	46	9	first	first	ADJ
ma-85	46	10	substep	substep	NOUN
ma-85	46	11	of	of	ADP
ma-85	46	12	sequence	sequence	NOUN
ma-85	46	13	(	(	PUNCT
ma-85	46	14	2.1).it	2.1).it	NUM
ma-85	46	15	we	we	PRON
ma-85	46	16	solve	solve	VERB
ma-85	46	17	for	for	ADP
ma-85	46	18	tn+1	tn+1	NOUN
ma-85	46	19	,	,	PUNCT
ma-85	46	20	we	we	PRON
ma-85	46	21	get	get	VERB
ma-85	46	22	its	its	PRON
ma-85	46	23	explicit	explicit	ADJ
ma-85	46	24	form	form	NOUN
ma-85	46	25	tn+1	tn+1	NOUN
ma-85	46	26	=	=	SYM
ma-85	46	27	9sn(1−k0tn)(1−	9sn(1−k0tn)(1−	NUM
ma-85	46	28	pn)−	pn)−	NOUN
ma-85	46	29	2tnk(sn	2tnk(sn	NUM
ma-85	46	30	−	−	PROPN
ma-85	46	31	tn	tn	PROPN
ma-85	46	32	)	)	PUNCT
ma-85	46	33	9(1−k0tn)(1−	9(1−k0tn)(1−	PROPN
ma-85	46	34	pn)−	pn)−	NOUN
ma-85	46	35	2k(sn	2k(sn	NUM
ma-85	46	36	−	−	PROPN
ma-85	46	37	tn	tn	NOUN
ma-85	46	38	)	)	PUNCT
ma-85	46	39	.	.	PUNCT
ma-85	47	1	but	but	CCONJ
ma-85	47	2	for	for	ADP
ma-85	47	3	the	the	DET
ma-85	47	4	convergence	convergence	NOUN
ma-85	47	5	analysis	analysis	NOUN
ma-85	47	6	in	in	ADP
ma-85	47	7	theorem	theorem	ADJ
ma-85	47	8	3.1	3.1	NUM
ma-85	47	9	we	we	PRON
ma-85	47	10	prefer	prefer	VERB
ma-85	47	11	tn+1	tn+1	VERB
ma-85	47	12	in	in	ADP
ma-85	47	13	its	its	PRON
ma-85	47	14	implicit	implicit	ADJ
ma-85	47	15	form.next	form.next	NOUN
ma-85	47	16	,	,	PUNCT
ma-85	47	17	we	we	PRON
ma-85	47	18	present	present	VERB
ma-85	47	19	sufficient	sufficient	ADJ
ma-85	47	20	conditions	condition	NOUN
ma-85	47	21	for	for	ADP
ma-85	47	22	the	the	DET
ma-85	47	23	convergence	convergence	NOUN
ma-85	47	24	scheme	scheme	NOUN
ma-85	47	25	(	(	PUNCT
ma-85	47	26	1.1	1.1	NUM
ma-85	47	27	)	)	PUNCT
ma-85	47	28	.	.	PUNCT
ma-85	48	1	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	PROPN
ma-85	48	2	eur	eur	PROPN
ma-85	48	3	.	.	PUNCT
ma-85	49	1	j.	j.	PROPN
ma-85	49	2	math	math	PROPN
ma-85	49	3	.	.	PUNCT
ma-85	50	1	anal	anal	PROPN
ma-85	50	2	.	.	PUNCT
ma-85	51	1	10.28924	10.28924	NUM
ma-85	51	2	/	/	SYM
ma-85	51	3	ada	ada	PROPN
ma-85	51	4	/	/	SYM
ma-85	51	5	ma.2.13	ma.2.13	PROPN
ma-85	51	6	3	3	NUM
ma-85	51	7	lemma	lemma	PROPN
ma-85	51	8	2.1	2.1	NUM
ma-85	51	9	.	.	PUNCT
ma-85	51	10	suppose	suppose	VERB
ma-85	51	11	that	that	SCONJ
ma-85	51	12	5(tn	5(tn	PROPN
ma-85	51	13	+	+	CCONJ
ma-85	51	14	sn	sn	NOUN
ma-85	51	15	)	)	PUNCT
ma-85	51	16	<	<	X
ma-85	51	17	6	6	NUM
ma-85	51	18	k0	k0	PROPN
ma-85	51	19	.	.	PUNCT
ma-85	52	1	(	(	PUNCT
ma-85	52	2	2.2	2.2	NUM
ma-85	52	3	)	)	PUNCT
ma-85	52	4	for	for	ADP
ma-85	52	5	all	all	DET
ma-85	52	6	n	n	NOUN
ma-85	52	7	=	=	SYM
ma-85	52	8	0	0	NUM
ma-85	52	9	,	,	PUNCT
ma-85	52	10	1	1	NUM
ma-85	52	11	,	,	PUNCT
ma-85	52	12	2	2	NUM
ma-85	52	13	,	,	PUNCT
ma-85	52	14	.	.	PUNCT
ma-85	52	15	.	.	PUNCT
ma-85	52	16	.	.	PUNCT
ma-85	52	17	.	.	PUNCT
ma-85	53	1	then	then	ADV
ma-85	53	2	,	,	PUNCT
ma-85	53	3	sequences	sequence	NOUN
ma-85	53	4	{	{	PUNCT
ma-85	53	5	tn	tn	NOUN
ma-85	53	6	}	}	PUNCT
ma-85	53	7	is	be	AUX
ma-85	53	8	nondecreasing	nondecrease	VERB
ma-85	53	9	and	and	CCONJ
ma-85	53	10	bounded	bound	VERB
ma-85	53	11	from	from	ADP
ma-85	53	12	above	above	ADV
ma-85	53	13	by	by	ADP
ma-85	53	14	t	t	PROPN
ma-85	53	15	∗	∗	NOUN
ma-85	53	16	=	=	SYM
ma-85	53	17	3	3	NUM
ma-85	53	18	5k0	5k0	NUM
ma-85	53	19	and	and	CCONJ
ma-85	53	20	as	as	ADV
ma-85	53	21	such	such	ADJ
ma-85	53	22	it	it	PRON
ma-85	53	23	converge	converge	VERB
ma-85	53	24	to	to	ADP
ma-85	53	25	its	its	PRON
ma-85	53	26	unique	unique	ADJ
ma-85	53	27	least	least	ADV
ma-85	53	28	upper	upper	ADJ
ma-85	53	29	t	t	X
ma-85	53	30	∈	∈	PROPN
ma-85	54	1	[	[	X
ma-85	54	2	0	0	NUM
ma-85	54	3	,	,	PUNCT
ma-85	54	4	t	t	PROPN
ma-85	54	5	∗	∗	NOUN
ma-85	54	6	]	]	PUNCT
ma-85	54	7	.	.	PUNCT
ma-85	55	1	proof	proof	NOUN
ma-85	55	2	.	.	PUNCT
ma-85	56	1	it	it	PRON
ma-85	56	2	follows	follow	VERB
ma-85	56	3	from	from	ADP
ma-85	56	4	the	the	DET
ma-85	56	5	definition	definition	NOUN
ma-85	56	6	(	(	PUNCT
ma-85	56	7	2.1	2.1	NUM
ma-85	56	8	)	)	PUNCT
ma-85	56	9	of	of	ADP
ma-85	56	10	sequences	sequence	NOUN
ma-85	56	11	{	{	PUNCT
ma-85	56	12	tn	tn	NOUN
ma-85	56	13	}	}	PUNCT
ma-85	56	14	and	and	CCONJ
ma-85	56	15	(	(	PUNCT
ma-85	56	16	2.2	2.2	NUM
ma-85	56	17	)	)	PUNCT
ma-85	56	18	that	that	SCONJ
ma-85	56	19	this	this	DET
ma-85	56	20	sequence	sequence	NOUN
ma-85	56	21	isnondecreasing	isnondecreasing	NOUN
ma-85	56	22	and	and	CCONJ
ma-85	56	23	bounded	bound	VERB
ma-85	56	24	from	from	ADP
ma-85	56	25	above	above	ADV
ma-85	56	26	by	by	ADP
ma-85	56	27	t	t	PROPN
ma-85	56	28	∗	∗	NOUN
ma-85	56	29	,	,	PUNCT
ma-85	56	30	and	and	CCONJ
ma-85	56	31	as	as	ADP
ma-85	56	32	such	such	ADJ
ma-85	56	33	it	it	PRON
ma-85	56	34	converges	converge	VERB
ma-85	56	35	to	to	ADP
ma-85	56	36	t.	t.	PROPN
ma-85	56	37	�	�	PROPN
ma-85	56	38	the	the	DET
ma-85	56	39	next	next	ADJ
ma-85	56	40	result	result	NOUN
ma-85	56	41	shows	show	VERB
ma-85	56	42	the	the	DET
ma-85	56	43	convergence	convergence	NOUN
ma-85	56	44	of	of	ADP
ma-85	56	45	sequence	sequence	NOUN
ma-85	56	46	{	{	PUNCT
ma-85	56	47	tn	tn	NOUN
ma-85	56	48	}	}	PUNCT
ma-85	56	49	,	,	PUNCT
ma-85	56	50	under	under	ADP
ma-85	56	51	stronger	strong	ADJ
ma-85	56	52	but	but	CCONJ
ma-85	56	53	easier	easy	ADJ
ma-85	56	54	to	to	ADP
ma-85	56	55	verifyconditions	verifycondition	NOUN
ma-85	56	56	than	than	ADP
ma-85	56	57	(	(	PUNCT
ma-85	56	58	2.2	2.2	NUM
ma-85	56	59	)	)	PUNCT
ma-85	56	60	.	.	PUNCT
ma-85	57	1	but	but	CCONJ
ma-85	57	2	first	first	ADV
ma-85	57	3	we	we	PRON
ma-85	57	4	need	need	VERB
ma-85	57	5	to	to	PART
ma-85	57	6	introduce	introduce	VERB
ma-85	57	7	some	some	DET
ma-85	57	8	functions	function	NOUN
ma-85	57	9	and	and	CCONJ
ma-85	57	10	parameters	parameter	NOUN
ma-85	57	11	.	.	PUNCT
ma-85	58	1	definefunctions	definefunction	NOUN
ma-85	58	2	g1	g1	PROPN
ma-85	58	3	and	and	CCONJ
ma-85	58	4	g2	g2	PROPN
ma-85	58	5	on	on	ADP
ma-85	58	6	the	the	DET
ma-85	58	7	interval	interval	NOUN
ma-85	58	8	(	(	PUNCT
ma-85	58	9	0	0	NUM
ma-85	58	10	,	,	PUNCT
ma-85	58	11	1	1	NUM
ma-85	58	12	)	)	PUNCT
ma-85	58	13	by	by	ADP
ma-85	58	14	g1(t	g1(t	NOUN
ma-85	58	15	)	)	PUNCT
ma-85	58	16	=	=	SYM
ma-85	58	17	4k(1	4k(1	NOUN
ma-85	59	1	+	+	CCONJ
ma-85	59	2	t)t	t)t	X
ma-85	59	3	−	−	PROPN
ma-85	59	4	4k(1	4k(1	NUM
ma-85	59	5	+	+	NUM
ma-85	59	6	t	t	PROPN
ma-85	59	7	)	)	PUNCT
ma-85	60	1	+	+	CCONJ
ma-85	60	2	9k0	9k0	NUM
ma-85	60	3	t	t	NOUN
ma-85	60	4	,	,	PUNCT
ma-85	60	5	and	and	CCONJ
ma-85	60	6	g2(t	g2(t	NOUN
ma-85	60	7	)	)	PUNCT
ma-85	61	1	=	=	SYM
ma-85	61	2	k(2	k(2	NOUN
ma-85	61	3	+	+	CCONJ
ma-85	61	4	t)(1	t)(1	X
ma-85	62	1	+	+	CCONJ
ma-85	62	2	t)t	t)t	X
ma-85	62	3	−k(2	−k(2	NOUN
ma-85	62	4	+	+	CCONJ
ma-85	62	5	t)(1	t)(1	X
ma-85	62	6	+	+	X
ma-85	62	7	t	t	NOUN
ma-85	62	8	)	)	PUNCT
ma-85	63	1	+	+	NUM
ma-85	63	2	2k0	2k0	NUM
ma-85	63	3	t	t	NOUN
ma-85	63	4	3.then	3.then	NUM
ma-85	63	5	,	,	PUNCT
ma-85	63	6	we	we	PRON
ma-85	63	7	get	get	VERB
ma-85	63	8	g1(0	g1(0	NOUN
ma-85	63	9	)	)	PUNCT
ma-85	64	1	=	=	PUNCT
ma-85	64	2	−4k	−4k	NOUN
ma-85	64	3	,	,	PUNCT
ma-85	64	4	g1(1	g1(1	NOUN
ma-85	64	5	)	)	PUNCT
ma-85	64	6	=	=	NOUN
ma-85	64	7	9k0	9k0	NUM
ma-85	64	8	,	,	PUNCT
ma-85	64	9	g2(0	g2(0	NOUN
ma-85	64	10	)	)	PUNCT
ma-85	64	11	=	=	SYM
ma-85	64	12	−2k	−2k	PROPN
ma-85	64	13	and	and	CCONJ
ma-85	64	14	g2(1	g2(1	PROPN
ma-85	64	15	)	)	PUNCT
ma-85	64	16	=	=	SYM
ma-85	64	17	2k0.hence	2k0.hence	NUM
ma-85	64	18	,	,	PUNCT
ma-85	64	19	functions	function	NOUN
ma-85	64	20	g1	g1	NOUN
ma-85	64	21	and	and	CCONJ
ma-85	64	22	g2	g2	PROPN
ma-85	64	23	have	have	VERB
ma-85	64	24	roots	root	NOUN
ma-85	64	25	in	in	ADP
ma-85	64	26	(	(	PUNCT
ma-85	64	27	0	0	NUM
ma-85	64	28	,	,	PUNCT
ma-85	64	29	1	1	NUM
ma-85	64	30	)	)	PUNCT
ma-85	64	31	.	.	PUNCT
ma-85	65	1	denote	denote	VERB
ma-85	65	2	the	the	DET
ma-85	65	3	minimal	minimal	ADJ
ma-85	65	4	such	such	ADJ
ma-85	65	5	roots	root	NOUN
ma-85	65	6	by	by	ADP
ma-85	65	7	α1	α1	PROPN
ma-85	65	8	and	and	CCONJ
ma-85	65	9	α2	α2	ADJ
ma-85	65	10	,	,	PUNCT
ma-85	65	11	re	re	VERB
ma-85	65	12	-	-	VERB
ma-85	65	13	spectively	spectively	ADV
ma-85	65	14	.	.	PUNCT
ma-85	66	1	set	set	VERB
ma-85	66	2	a	a	DET
ma-85	66	3	=	=	SYM
ma-85	66	4	2k(t1−t0	2k(t1−t0	NUM
ma-85	66	5	)	)	PUNCT
ma-85	66	6	9(1−k0t)(1−p0	9(1−k0t)(1−p0	NUM
ma-85	66	7	)	)	PUNCT
ma-85	66	8	,	,	PUNCT
ma-85	66	9	b	b	X
ma-85	66	10	=	=	SYM
ma-85	66	11	k(t1−t0+s0−t0)(t1−t0	k(t1−t0+s0−t0)(t1−t0	PROPN
ma-85	66	12	)	)	PUNCT
ma-85	66	13	2η(1−k0t1	2η(1−k0t1	NUM
ma-85	66	14	)	)	PUNCT
ma-85	66	15	,	,	PUNCT
ma-85	66	16	c̄	c̄	PROPN
ma-85	66	17	=	=	SYM
ma-85	66	18	min{a	min{a	NOUN
ma-85	66	19	,	,	PUNCT
ma-85	66	20	b	b	NOUN
ma-85	66	21	}	}	PUNCT
ma-85	66	22	,	,	PUNCT
ma-85	66	23	c	c	NOUN
ma-85	66	24	=	=	SYM
ma-85	66	25	max{a	max{a	PROPN
ma-85	66	26	,	,	PUNCT
ma-85	66	27	b	b	NOUN
ma-85	66	28	}	}	PUNCT
ma-85	66	29	,	,	PUNCT
ma-85	66	30	α3	α3	PROPN
ma-85	66	31	=	=	SYM
ma-85	66	32	min{α1	min{α1	PROPN
ma-85	66	33	,	,	PUNCT
ma-85	66	34	α2	α2	ADJ
ma-85	66	35	}	}	PUNCT
ma-85	66	36	and	and	CCONJ
ma-85	66	37	α	α	NOUN
ma-85	66	38	=	=	PUNCT
ma-85	66	39	max{α1	max{α1	NOUN
ma-85	66	40	,	,	PUNCT
ma-85	66	41	α2}.then	α2}.then	ADV
ma-85	66	42	,	,	PUNCT
ma-85	66	43	we	we	PRON
ma-85	66	44	can	can	AUX
ma-85	66	45	show	show	VERB
ma-85	66	46	the	the	DET
ma-85	66	47	second	second	ADJ
ma-85	66	48	result	result	NOUN
ma-85	66	49	on	on	ADP
ma-85	66	50	majorizing	majorize	VERB
ma-85	66	51	sequences	sequence	NOUN
ma-85	66	52	for	for	ADP
ma-85	66	53	method	method	NOUN
ma-85	66	54	(	(	PUNCT
ma-85	66	55	1.2	1.2	NUM
ma-85	66	56	)	)	PUNCT
ma-85	66	57	.	.	PUNCT
ma-85	67	1	lemma	lemma	PROPN
ma-85	67	2	2.2	2.2	NUM
ma-85	67	3	.	.	PUNCT
ma-85	67	4	suppose	suppose	VERB
ma-85	67	5	0	0	PUNCT
ma-85	68	1	<	<	X
ma-85	68	2	c̄	c̄	PROPN
ma-85	68	3	≤	≤	NUM
ma-85	68	4	c	c	NOUN
ma-85	68	5	≤	≤	NOUN
ma-85	68	6	α3	α3	NOUN
ma-85	68	7	≤	≤	NUM
ma-85	68	8	α	α	PROPN
ma-85	68	9	≤	≤	NUM
ma-85	68	10	1−	1−	NUM
ma-85	68	11	10	10	NUM
ma-85	68	12	3	3	NUM
ma-85	68	13	k0η	k0η	NOUN
ma-85	68	14	.	.	PUNCT
ma-85	69	1	(	(	PUNCT
ma-85	69	2	2.3	2.3	NUM
ma-85	69	3	)	)	PUNCT
ma-85	69	4	then	then	ADV
ma-85	69	5	,	,	PUNCT
ma-85	69	6	sequence	sequence	NOUN
ma-85	69	7	{	{	PUNCT
ma-85	69	8	tn	tn	NOUN
ma-85	69	9	}	}	PUNCT
ma-85	69	10	is	be	AUX
ma-85	69	11	nondecreasing	nondecrease	VERB
ma-85	69	12	,	,	PUNCT
ma-85	69	13	bounded	bound	VERB
ma-85	69	14	from	from	ADP
ma-85	69	15	above	above	ADV
ma-85	69	16	by	by	ADP
ma-85	69	17	t	t	PROPN
ma-85	69	18	=	=	SYM
ma-85	69	19	η	η	PROPN
ma-85	69	20	1−α	1−α	PROPN
ma-85	69	21	and	and	CCONJ
ma-85	69	22	as	as	ADV
ma-85	69	23	such	such	ADJ
ma-85	69	24	it	it	PRON
ma-85	69	25	converges	converge	VERB
ma-85	69	26	to	to	ADP
ma-85	69	27	its	its	PRON
ma-85	69	28	unique	unique	ADJ
ma-85	69	29	least	least	ADV
ma-85	69	30	upper	upper	ADJ
ma-85	69	31	bound	bind	VERB
ma-85	69	32	t∗	t∗	NOUN
ma-85	69	33	∈	∈	PROPN
ma-85	70	1	[	[	X
ma-85	70	2	0	0	NUM
ma-85	70	3	,	,	PUNCT
ma-85	70	4	t	t	X
ma-85	70	5	]	]	PUNCT
ma-85	70	6	.	.	PUNCT
ma-85	71	1	proof	proof	NOUN
ma-85	71	2	.	.	PUNCT
ma-85	72	1	items	item	NOUN
ma-85	72	2	0	0	NUM
ma-85	72	3	≤	≤	NUM
ma-85	72	4	2k(tk+1	2k(tk+1	NUM
ma-85	72	5	−	−	PROPN
ma-85	72	6	tk	tk	PROPN
ma-85	72	7	)	)	PUNCT
ma-85	72	8	9(1−k0tk)(1−	9(1−k0tk)(1−	PROPN
ma-85	72	9	pk	pk	NOUN
ma-85	72	10	)	)	PUNCT
ma-85	72	11	≤	≤	NOUN
ma-85	72	12	α	α	X
ma-85	72	13	,	,	PUNCT
ma-85	72	14	(	(	PUNCT
ma-85	72	15	2.4	2.4	NUM
ma-85	72	16	)	)	PUNCT
ma-85	72	17	0	0	NUM
ma-85	73	1	≤	≤	NUM
ma-85	74	1	k(tk+1	k(tk+1	NOUN
ma-85	74	2	−	−	PROPN
ma-85	74	3	tk	tk	PROPN
ma-85	74	4	+	+	CCONJ
ma-85	74	5	sk	sk	PROPN
ma-85	74	6	−	−	PROPN
ma-85	74	7	tk)(tk+1	tk)(tk+1	NOUN
ma-85	74	8	−	−	PROPN
ma-85	74	9	tk	tk	PROPN
ma-85	74	10	)	)	PUNCT
ma-85	74	11	2(1−k0tk+1	2(1−k0tk+1	NUM
ma-85	74	12	)	)	PUNCT
ma-85	74	13	≤	≤	NOUN
ma-85	74	14	α(sk	α(sk	NUM
ma-85	74	15	−	−	PROPN
ma-85	74	16	tk	tk	PROPN
ma-85	74	17	)	)	PUNCT
ma-85	74	18	,	,	PUNCT
ma-85	74	19	(	(	PUNCT
ma-85	74	20	2.5	2.5	NUM
ma-85	74	21	)	)	PUNCT
ma-85	74	22	0	0	NUM
ma-85	75	1	≤	≤	NUM
ma-85	75	2	1	1	NUM
ma-85	75	3	1−	1−	NUM
ma-85	75	4	pk	pk	NOUN
ma-85	75	5	≤	≤	ADV
ma-85	75	6	2	2	NUM
ma-85	75	7	(	(	PUNCT
ma-85	75	8	2.6)and	2.6)and	NUM
ma-85	75	9	tk	tk	PROPN
ma-85	75	10	≤	≤	NOUN
ma-85	75	11	sk	sk	VERB
ma-85	75	12	≤	≤	NUM
ma-85	75	13	tk+1	tk+1	NUM
ma-85	75	14	(	(	PUNCT
ma-85	75	15	2.7)are	2.7)are	NUM
ma-85	75	16	shown	show	VERB
ma-85	75	17	using	use	VERB
ma-85	75	18	induction	induction	NOUN
ma-85	75	19	on	on	ADP
ma-85	75	20	k.	k.	PROPN
ma-85	75	21	these	these	DET
ma-85	75	22	estimates	estimate	NOUN
ma-85	75	23	are	be	AUX
ma-85	75	24	true	true	ADJ
ma-85	75	25	for	for	ADP
ma-85	75	26	k	k	PROPN
ma-85	75	27	=	=	SYM
ma-85	75	28	0	0	NUM
ma-85	75	29	by	by	ADP
ma-85	75	30	(	(	PUNCT
ma-85	75	31	2.3	2.3	NUM
ma-85	75	32	)	)	PUNCT
ma-85	75	33	.	.	PUNCT
ma-85	76	1	suppose	suppose	VERB
ma-85	76	2	thesehold	thesehold	VERB
ma-85	76	3	for	for	ADP
ma-85	76	4	all	all	DET
ma-85	76	5	k	k	NOUN
ma-85	76	6	smaller	small	ADJ
ma-85	76	7	than	than	ADP
ma-85	76	8	n	n	CCONJ
ma-85	76	9	−	−	PROPN
ma-85	76	10	1	1	NUM
ma-85	76	11	.	.	PUNCT
ma-85	77	1	by	by	ADP
ma-85	77	2	induction	induction	NOUN
ma-85	77	3	hypotheses	hypothesis	NOUN
ma-85	77	4	and	and	CCONJ
ma-85	77	5	(	(	PUNCT
ma-85	77	6	1.2	1.2	NUM
ma-85	77	7	)	)	PUNCT
ma-85	77	8	,	,	PUNCT
ma-85	77	9	we	we	PRON
ma-85	77	10	have	have	VERB
ma-85	77	11	0	0	NUM
ma-85	77	12	≤	≤	NOUN
ma-85	77	13	sk	sk	VERB
ma-85	77	14	−	−	PROPN
ma-85	77	15	tk	tk	PROPN
ma-85	77	16	≤	≤	PROPN
ma-85	77	17	α(sk−1	α(sk−1	PROPN
ma-85	77	18	−	−	PROPN
ma-85	77	19	tk−1	tk−1	PROPN
ma-85	77	20	)	)	PUNCT
ma-85	77	21	≤	≤	NOUN
ma-85	77	22	.	.	PUNCT
ma-85	77	23	.	.	PUNCT
ma-85	77	24	.	.	PUNCT
ma-85	78	1	≤	≤	NUM
ma-85	78	2	αkη	αkη	NOUN
ma-85	78	3	,	,	PUNCT
ma-85	78	4	tk+1	tk+1	NUM
ma-85	78	5	−	−	PROPN
ma-85	78	6	tk	tk	NOUN
ma-85	78	7	=	=	SYM
ma-85	78	8	(	(	PUNCT
ma-85	78	9	tk+1	tk+1	NUM
ma-85	78	10	−	−	NOUN
ma-85	78	11	sk	sk	NOUN
ma-85	78	12	)	)	PUNCT
ma-85	78	13	+	+	CCONJ
ma-85	78	14	(	(	PUNCT
ma-85	78	15	sk	sk	INTJ
ma-85	78	16	−	−	PROPN
ma-85	78	17	tk	tk	PROPN
ma-85	78	18	)	)	PUNCT
ma-85	78	19	≤	≤	NOUN
ma-85	78	20	(	(	PUNCT
ma-85	78	21	1	1	NUM
ma-85	78	22	+	+	SYM
ma-85	78	23	α)(sk	α)(sk	NUM
ma-85	78	24	−	−	PROPN
ma-85	78	25	tk	tk	PROPN
ma-85	78	26	)	)	PUNCT
ma-85	78	27	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	PROPN
ma-85	78	28	eur	eur	PROPN
ma-85	78	29	.	.	PUNCT
ma-85	79	1	j.	j.	PROPN
ma-85	79	2	math	math	PROPN
ma-85	79	3	.	.	PUNCT
ma-85	80	1	anal	anal	PROPN
ma-85	80	2	.	.	PUNCT
ma-85	81	1	10.28924	10.28924	NUM
ma-85	81	2	/	/	SYM
ma-85	81	3	ada	ada	PROPN
ma-85	81	4	/	/	SYM
ma-85	81	5	ma.2.13	ma.2.13	PROPN
ma-85	82	1	4and	4and	NOUN
ma-85	82	2	tk+1	tk+1	NUM
ma-85	82	3	≤	≤	NUM
ma-85	82	4	(	(	PUNCT
ma-85	82	5	1−	1−	NUM
ma-85	82	6	αk+2)η	αk+2)η	NUM
ma-85	82	7	1−	1−	NUM
ma-85	82	8	α	α	NOUN
ma-85	82	9	<	<	X
ma-85	82	10	t.	t.	X
ma-85	82	11	evidently	evidently	ADV
ma-85	82	12	,	,	PUNCT
ma-85	82	13	(	(	PUNCT
ma-85	82	14	2.4	2.4	NUM
ma-85	82	15	)	)	PUNCT
ma-85	82	16	holds	hold	VERB
ma-85	82	17	if	if	SCONJ
ma-85	82	18	4k(1	4k(1	NUM
ma-85	82	19	+	+	NOUN
ma-85	82	20	α)αk−1η	α)αk−1η	PROPN
ma-85	82	21	9(1−k0	9(1−k0	NOUN
ma-85	82	22	1−α	1−α	NUM
ma-85	82	23	k+1	k+1	X
ma-85	82	24	1−α	1−α	NUM
ma-85	82	25	η	η	PROPN
ma-85	82	26	≤	≤	PROPN
ma-85	82	27	α	α	NUM
ma-85	82	28	,	,	PUNCT
ma-85	82	29	(	(	PUNCT
ma-85	82	30	2.8	2.8	NUM
ma-85	82	31	)	)	PUNCT
ma-85	82	32	where	where	SCONJ
ma-85	82	33	we	we	PRON
ma-85	82	34	used	use	VERB
ma-85	82	35	(	(	PUNCT
ma-85	82	36	2.6	2.6	NUM
ma-85	82	37	)	)	PUNCT
ma-85	82	38	.	.	PUNCT
ma-85	83	1	define	define	VERB
ma-85	83	2	recurrent	recurrent	ADJ
ma-85	83	3	polynomials	polynomial	NOUN
ma-85	83	4	f	f	X
ma-85	83	5	(	(	PUNCT
ma-85	83	6	1)k	1)k	NUM
ma-85	83	7	on	on	ADP
ma-85	83	8	the	the	DET
ma-85	83	9	interval	interval	NOUN
ma-85	83	10	(	(	PUNCT
ma-85	83	11	0	0	NUM
ma-85	83	12	,	,	PUNCT
ma-85	83	13	1	1	NUM
ma-85	83	14	)	)	PUNCT
ma-85	83	15	by	by	ADP
ma-85	83	16	f	f	PROPN
ma-85	83	17	(	(	PUNCT
ma-85	83	18	1	1	NUM
ma-85	83	19	)	)	PUNCT
ma-85	83	20	n	n	PROPN
ma-85	83	21	(	(	PUNCT
ma-85	83	22	t	t	NOUN
ma-85	83	23	)	)	PUNCT
ma-85	83	24	=	=	SYM
ma-85	83	25	4k(1	4k(1	X
ma-85	84	1	+	+	CCONJ
ma-85	84	2	t)tk−1η	t)tk−1η	ADJ
ma-85	85	1	+	+	CCONJ
ma-85	85	2	9k0(1	9k0(1	NUM
ma-85	85	3	+	+	NUM
ma-85	85	4	t	t	NOUN
ma-85	85	5	+	+	X
ma-85	85	6	.	.	PUNCT
ma-85	85	7	.	.	PUNCT
ma-85	86	1	.+	.+	NOUN
ma-85	86	2	tk−1)η	tk−1)η	PUNCT
ma-85	87	1	−	−	NOUN
ma-85	87	2	9	9	NUM
ma-85	87	3	.	.	PUNCT
ma-85	88	1	(	(	PUNCT
ma-85	88	2	2.9	2.9	NUM
ma-85	88	3	)	)	PUNCT
ma-85	88	4	then	then	ADV
ma-85	88	5	,	,	PUNCT
ma-85	88	6	estimate	estimate	INTJ
ma-85	88	7	(	(	PUNCT
ma-85	88	8	2.8	2.8	NUM
ma-85	88	9	)	)	PUNCT
ma-85	88	10	holds	hold	VERB
ma-85	88	11	if	if	SCONJ
ma-85	88	12	f	f	PROPN
ma-85	88	13	(	(	PUNCT
ma-85	88	14	1	1	NUM
ma-85	88	15	)	)	PUNCT
ma-85	88	16	n	n	PROPN
ma-85	88	17	(	(	PUNCT
ma-85	88	18	t	t	NOUN
ma-85	88	19	)	)	PUNCT
ma-85	88	20	≤	≤	NOUN
ma-85	88	21	0	0	NUM
ma-85	89	1	at	at	ADP
ma-85	89	2	t	t	NOUN
ma-85	89	3	=	=	SYM
ma-85	89	4	α1	α1	PROPN
ma-85	89	5	.	.	PUNCT
ma-85	90	1	(	(	PUNCT
ma-85	90	2	2.10	2.10	NUM
ma-85	90	3	)	)	PUNCT
ma-85	90	4	we	we	PRON
ma-85	90	5	need	need	VERB
ma-85	90	6	a	a	DET
ma-85	90	7	relationship	relationship	NOUN
ma-85	90	8	between	between	ADP
ma-85	90	9	two	two	NUM
ma-85	90	10	consecutive	consecutive	ADJ
ma-85	90	11	polynomials	polynomial	NOUN
ma-85	90	12	f	f	X
ma-85	90	13	(	(	PUNCT
ma-85	90	14	1)k	1)k	NUM
ma-85	90	15	:	:	PUNCT
ma-85	90	16	f	f	X
ma-85	90	17	(	(	PUNCT
ma-85	90	18	1	1	NUM
ma-85	90	19	)	)	PUNCT
ma-85	90	20	k+1(t	k+1(t	PROPN
ma-85	90	21	)	)	PUNCT
ma-85	91	1	=	=	SYM
ma-85	91	2	4k(1	4k(1	X
ma-85	92	1	+	+	PUNCT
ma-85	92	2	t)tkη	t)tkη	NOUN
ma-85	92	3	+	+	NOUN
ma-85	92	4	3k0(1	3k0(1	NUM
ma-85	92	5	+	+	NUM
ma-85	92	6	t	t	NOUN
ma-85	92	7	+	+	X
ma-85	92	8	.	.	PUNCT
ma-85	92	9	.	.	PUNCT
ma-85	93	1	.+	.+	NOUN
ma-85	94	1	tk)η	tk)η	NOUN
ma-85	94	2	−	−	NOUN
ma-85	94	3	9	9	NUM
ma-85	94	4	+	+	CCONJ
ma-85	94	5	f	f	X
ma-85	94	6	(	(	PUNCT
ma-85	94	7	1	1	NUM
ma-85	94	8	)	)	PUNCT
ma-85	94	9	k	k	PROPN
ma-85	94	10	(	(	PUNCT
ma-85	94	11	t	t	PROPN
ma-85	94	12	)	)	PUNCT
ma-85	94	13	−4k(1	−4k(1	NOUN
ma-85	95	1	+	+	CCONJ
ma-85	95	2	t)tk−1	t)tk−1	NOUN
ma-85	95	3	+	+	CCONJ
ma-85	95	4	3k0(1	3k0(1	NUM
ma-85	95	5	+	+	NUM
ma-85	95	6	t	t	NOUN
ma-85	96	1	+	+	X
ma-85	96	2	.	.	PUNCT
ma-85	96	3	.	.	PUNCT
ma-85	97	1	.+	.+	NOUN
ma-85	97	2	tk−1)η	tk−1)η	PUNCT
ma-85	98	1	+	+	CCONJ
ma-85	98	2	9	9	NUM
ma-85	98	3	=	=	SYM
ma-85	98	4	f	f	X
ma-85	98	5	(	(	PUNCT
ma-85	98	6	1	1	NUM
ma-85	98	7	)	)	PUNCT
ma-85	98	8	k	k	PROPN
ma-85	98	9	(	(	PUNCT
ma-85	98	10	t	t	PROPN
ma-85	98	11	)	)	PUNCT
ma-85	98	12	+	+	CCONJ
ma-85	98	13	g1(t)t	g1(t)t	X
ma-85	98	14	k−1η	k−1η	X
ma-85	98	15	.	.	PUNCT
ma-85	98	16	(	(	PUNCT
ma-85	98	17	2.11	2.11	NUM
ma-85	98	18	)	)	PUNCT
ma-85	98	19	in	in	ADP
ma-85	98	20	particular	particular	ADJ
ma-85	98	21	,	,	PUNCT
ma-85	98	22	one	one	PRON
ma-85	98	23	gets	get	VERB
ma-85	98	24	f	f	PROPN
ma-85	98	25	(	(	PUNCT
ma-85	98	26	1)k+1(α1	1)k+1(α1	NUM
ma-85	98	27	)	)	PUNCT
ma-85	99	1	=	=	SYM
ma-85	99	2	f	f	PROPN
ma-85	99	3	(	(	PUNCT
ma-85	99	4	1	1	NUM
ma-85	99	5	)	)	PUNCT
ma-85	99	6	k	k	PROPN
ma-85	99	7	(	(	PUNCT
ma-85	99	8	α1	α1	PROPN
ma-85	99	9	)	)	PUNCT
ma-85	99	10	since	since	SCONJ
ma-85	99	11	by	by	ADP
ma-85	99	12	the	the	DET
ma-85	99	13	definition	definition	NOUN
ma-85	99	14	of	of	ADP
ma-85	99	15	α1	α1	PROPN
ma-85	99	16	and	and	CCONJ
ma-85	99	17	g1	g1	NOUN
ma-85	99	18	,	,	PUNCT
ma-85	99	19	g1(α1	g1(α1	NOUN
ma-85	99	20	)	)	PUNCT
ma-85	99	21	=	=	SYM
ma-85	99	22	0.define	0.define	PRON
ma-85	99	23	function	function	VERB
ma-85	99	24	f	f	X
ma-85	99	25	(	(	PUNCT
ma-85	99	26	1)∞	1)∞	PROPN
ma-85	99	27	(	(	PUNCT
ma-85	99	28	t	t	PROPN
ma-85	99	29	)	)	PUNCT
ma-85	99	30	=	=	PROPN
ma-85	100	1	lim	lim	PROPN
ma-85	100	2	k−→∞	k−→∞	PROPN
ma-85	100	3	f	f	PROPN
ma-85	100	4	(	(	PUNCT
ma-85	100	5	1	1	NUM
ma-85	100	6	)	)	PUNCT
ma-85	100	7	k	k	PROPN
ma-85	100	8	(	(	PUNCT
ma-85	100	9	t	t	PROPN
ma-85	100	10	)	)	PUNCT
ma-85	100	11	.	.	PUNCT
ma-85	101	1	(	(	PUNCT
ma-85	101	2	2.12	2.12	NUM
ma-85	101	3	)	)	PUNCT
ma-85	101	4	then	then	ADV
ma-85	101	5	,	,	PUNCT
ma-85	101	6	(	(	PUNCT
ma-85	101	7	2.10	2.10	NUM
ma-85	101	8	)	)	PUNCT
ma-85	101	9	holds	hold	VERB
ma-85	101	10	if	if	SCONJ
ma-85	101	11	f	f	PROPN
ma-85	101	12	(	(	PUNCT
ma-85	101	13	1)∞	1)∞	PROPN
ma-85	101	14	(	(	PUNCT
ma-85	101	15	t	t	PROPN
ma-85	101	16	)	)	PUNCT
ma-85	101	17	≤	≤	NOUN
ma-85	101	18	0	0	NUM
ma-85	101	19	at	at	ADP
ma-85	101	20	t	t	NOUN
ma-85	101	21	=	=	SYM
ma-85	101	22	α1	α1	PROPN
ma-85	101	23	.	.	PUNCT
ma-85	102	1	(	(	PUNCT
ma-85	102	2	2.13	2.13	NUM
ma-85	102	3	)	)	PUNCT
ma-85	102	4	but	but	CCONJ
ma-85	102	5	by	by	ADP
ma-85	102	6	(	(	PUNCT
ma-85	102	7	2.9	2.9	NUM
ma-85	102	8	)	)	PUNCT
ma-85	102	9	and	and	CCONJ
ma-85	102	10	(	(	PUNCT
ma-85	102	11	2.12	2.12	NUM
ma-85	102	12	)	)	PUNCT
ma-85	102	13	one	one	NOUN
ma-85	102	14	gets	get	VERB
ma-85	102	15	f	f	X
ma-85	102	16	(	(	PUNCT
ma-85	102	17	1)∞	1)∞	PROPN
ma-85	102	18	(	(	PUNCT
ma-85	102	19	t	t	PROPN
ma-85	102	20	)	)	PUNCT
ma-85	103	1	=	=	SYM
ma-85	103	2	9k0η	9k0η	NOUN
ma-85	103	3	1−	1−	NUM
ma-85	103	4	t	t	NOUN
ma-85	103	5	−	−	NOUN
ma-85	103	6	9	9	NUM
ma-85	103	7	,	,	PUNCT
ma-85	103	8	(	(	PUNCT
ma-85	103	9	2.14	2.14	NUM
ma-85	103	10	)	)	PUNCT
ma-85	104	1	so	so	CCONJ
ma-85	104	2	(	(	PUNCT
ma-85	104	3	2.13	2.13	NUM
ma-85	104	4	)	)	PUNCT
ma-85	104	5	holds	hold	VERB
ma-85	104	6	if	if	SCONJ
ma-85	104	7	f	f	PROPN
ma-85	104	8	(	(	PUNCT
ma-85	104	9	1)∞	1)∞	PROPN
ma-85	104	10	(	(	PUNCT
ma-85	104	11	t	t	PROPN
ma-85	104	12	)	)	PUNCT
ma-85	104	13	≤	≤	NOUN
ma-85	104	14	0	0	NUM
ma-85	105	1	at	at	ADP
ma-85	105	2	t	t	PROPN
ma-85	105	3	=	=	SYM
ma-85	105	4	α1	α1	NOUN
ma-85	105	5	which	which	PRON
ma-85	105	6	is	be	AUX
ma-85	105	7	true	true	ADJ
ma-85	105	8	by	by	ADP
ma-85	105	9	(	(	PUNCT
ma-85	105	10	2.3).similarly	2.3).similarly	ADV
ma-85	105	11	,	,	PUNCT
ma-85	105	12	(	(	PUNCT
ma-85	105	13	2.5	2.5	NUM
ma-85	105	14	)	)	PUNCT
ma-85	105	15	holds	hold	VERB
ma-85	105	16	if	if	SCONJ
ma-85	105	17	k(2	k(2	PROPN
ma-85	105	18	+	+	NUM
ma-85	105	19	α)(1	α)(1	NUM
ma-85	106	1	+	+	CCONJ
ma-85	106	2	α)αkη	α)αkη	NUM
ma-85	106	3	2(1−k0	2(1−k0	NOUN
ma-85	106	4	1−α	1−α	NUM
ma-85	106	5	k+2	k+2	PROPN
ma-85	106	6	1−α	1−α	NUM
ma-85	106	7	η	η	NOUN
ma-85	106	8	)	)	PUNCT
ma-85	106	9	≤	≤	NOUN
ma-85	106	10	α	α	X
ma-85	106	11	.	.	PUNCT
ma-85	107	1	(	(	PUNCT
ma-85	107	2	2.15	2.15	NUM
ma-85	107	3	)	)	PUNCT
ma-85	107	4	define	define	VERB
ma-85	107	5	polynomials	polynomial	NOUN
ma-85	107	6	f	f	PROPN
ma-85	107	7	(	(	PUNCT
ma-85	107	8	2)k	2)k	NOUN
ma-85	107	9	(	(	PUNCT
ma-85	107	10	t	t	NOUN
ma-85	107	11	)	)	PUNCT
ma-85	107	12	on	on	ADP
ma-85	107	13	the	the	DET
ma-85	107	14	interval	interval	NOUN
ma-85	107	15	(	(	PUNCT
ma-85	107	16	0	0	NUM
ma-85	107	17	,	,	PUNCT
ma-85	107	18	1	1	NUM
ma-85	107	19	)	)	PUNCT
ma-85	107	20	by	by	ADP
ma-85	107	21	f	f	PROPN
ma-85	107	22	(	(	PUNCT
ma-85	107	23	2	2	NUM
ma-85	107	24	)	)	PUNCT
ma-85	107	25	k	k	NOUN
ma-85	107	26	(	(	PUNCT
ma-85	107	27	t	t	PROPN
ma-85	107	28	)	)	PUNCT
ma-85	107	29	=	=	SYM
ma-85	108	1	k(2	k(2	NOUN
ma-85	108	2	+	+	CCONJ
ma-85	108	3	t)(1	t)(1	X
ma-85	108	4	+	+	CCONJ
ma-85	108	5	t)tk−1η	t)tk−1η	ADJ
ma-85	108	6	+	+	CCONJ
ma-85	108	7	2k0(1	2k0(1	NUM
ma-85	108	8	+	+	CCONJ
ma-85	108	9	t	t	NOUN
ma-85	108	10	+	+	X
ma-85	108	11	.	.	PUNCT
ma-85	108	12	.	.	PUNCT
ma-85	109	1	.+	.+	NOUN
ma-85	109	2	tk+1)η	tk+1)η	VERB
ma-85	109	3	−	−	NOUN
ma-85	109	4	2	2	NUM
ma-85	109	5	.	.	PUNCT
ma-85	109	6	(	(	PUNCT
ma-85	109	7	2.16	2.16	NUM
ma-85	109	8	)	)	PUNCT
ma-85	109	9	then	then	ADV
ma-85	109	10	,	,	PUNCT
ma-85	109	11	(	(	PUNCT
ma-85	109	12	2.15	2.15	NUM
ma-85	109	13	)	)	PUNCT
ma-85	109	14	holds	hold	VERB
ma-85	109	15	if	if	SCONJ
ma-85	109	16	f	f	PROPN
ma-85	109	17	(	(	PUNCT
ma-85	109	18	2	2	NUM
ma-85	109	19	)	)	PUNCT
ma-85	109	20	k	k	NOUN
ma-85	109	21	(	(	PUNCT
ma-85	109	22	t	t	PROPN
ma-85	109	23	)	)	PUNCT
ma-85	109	24	≤	≤	NOUN
ma-85	109	25	0	0	NUM
ma-85	110	1	at	at	ADP
ma-85	110	2	t	t	PROPN
ma-85	110	3	=	=	SYM
ma-85	110	4	α2	α2	PROPN
ma-85	110	5	.	.	PUNCT
ma-85	111	1	(	(	PUNCT
ma-85	111	2	2.17	2.17	NUM
ma-85	111	3	)	)	PUNCT
ma-85	111	4	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	NOUN
ma-85	111	5	eur	eur	PROPN
ma-85	111	6	.	.	PUNCT
ma-85	112	1	j.	j.	PROPN
ma-85	112	2	math	math	PROPN
ma-85	112	3	.	.	PUNCT
ma-85	113	1	anal	anal	PROPN
ma-85	113	2	.	.	PUNCT
ma-85	114	1	10.28924	10.28924	NUM
ma-85	114	2	/	/	SYM
ma-85	114	3	ada	ada	PROPN
ma-85	114	4	/	/	SYM
ma-85	114	5	ma.2.13	ma.2.13	PROPN
ma-85	114	6	5we	5we	NOUN
ma-85	114	7	get	get	VERB
ma-85	114	8	f	f	X
ma-85	114	9	(	(	PUNCT
ma-85	114	10	2	2	NUM
ma-85	114	11	)	)	PUNCT
ma-85	114	12	k+1(t	k+1(t	PROPN
ma-85	114	13	)	)	PUNCT
ma-85	115	1	=	=	PUNCT
ma-85	115	2	k(2	k(2	NOUN
ma-85	115	3	+	+	CCONJ
ma-85	115	4	t)(1	t)(1	X
ma-85	115	5	+	+	ADJ
ma-85	115	6	t)tkη	t)tkη	NOUN
ma-85	115	7	+	+	NUM
ma-85	115	8	2k0(1	2k0(1	NUM
ma-85	115	9	+	+	CCONJ
ma-85	115	10	t	t	NOUN
ma-85	115	11	+	+	X
ma-85	115	12	.	.	PUNCT
ma-85	115	13	.	.	PUNCT
ma-85	116	1	.+	.+	NOUN
ma-85	117	1	tk+2)η	tk+2)η	NOUN
ma-85	117	2	−	−	NOUN
ma-85	117	3	2	2	NUM
ma-85	117	4	+	+	CCONJ
ma-85	117	5	f	f	X
ma-85	117	6	(	(	PUNCT
ma-85	117	7	2	2	NUM
ma-85	117	8	)	)	PUNCT
ma-85	117	9	k	k	NOUN
ma-85	117	10	(	(	PUNCT
ma-85	117	11	t	t	NOUN
ma-85	117	12	)	)	PUNCT
ma-85	117	13	−k(2	−k(2	PROPN
ma-85	118	1	+	+	CCONJ
ma-85	118	2	t)(1	t)(1	X
ma-85	119	1	+	+	CCONJ
ma-85	119	2	t)tk−1η	t)tk−1η	VERB
ma-85	119	3	−	−	NUM
ma-85	119	4	2k0(1	2k0(1	NUM
ma-85	120	1	+	+	CCONJ
ma-85	120	2	t	t	NOUN
ma-85	120	3	+	+	X
ma-85	120	4	.	.	PUNCT
ma-85	120	5	.	.	PUNCT
ma-85	121	1	.+	.+	NOUN
ma-85	121	2	tk+1)η	tk+1)η	VERB
ma-85	122	1	+	+	CCONJ
ma-85	122	2	2	2	NUM
ma-85	122	3	=	=	SYM
ma-85	122	4	f	f	X
ma-85	122	5	(	(	PUNCT
ma-85	122	6	2	2	NUM
ma-85	122	7	)	)	PUNCT
ma-85	122	8	k	k	NOUN
ma-85	122	9	(	(	PUNCT
ma-85	122	10	t	t	PROPN
ma-85	122	11	)	)	PUNCT
ma-85	122	12	+	+	CCONJ
ma-85	122	13	g2(t)t	g2(t)t	NOUN
ma-85	122	14	k−1η	k−1η	X
ma-85	122	15	,	,	PUNCT
ma-85	122	16	(	(	PUNCT
ma-85	122	17	2.18	2.18	NUM
ma-85	122	18	)	)	PUNCT
ma-85	122	19	and	and	CCONJ
ma-85	122	20	f	f	PROPN
ma-85	122	21	(	(	PUNCT
ma-85	122	22	2	2	NUM
ma-85	122	23	)	)	PUNCT
ma-85	122	24	k+1(α2	k+1(α2	NOUN
ma-85	122	25	)	)	PUNCT
ma-85	122	26	=	=	SYM
ma-85	122	27	f	f	PROPN
ma-85	122	28	(	(	PUNCT
ma-85	122	29	2	2	NUM
ma-85	122	30	)	)	PUNCT
ma-85	122	31	k	k	NOUN
ma-85	122	32	(	(	PUNCT
ma-85	122	33	α2	α2	PROPN
ma-85	122	34	)	)	PUNCT
ma-85	122	35	.	.	PUNCT
ma-85	123	1	(	(	PUNCT
ma-85	123	2	2.19	2.19	NUM
ma-85	123	3	)	)	PUNCT
ma-85	123	4	define	define	VERB
ma-85	123	5	function	function	NOUN
ma-85	123	6	f	f	PROPN
ma-85	123	7	(	(	PUNCT
ma-85	123	8	2)∞	2)∞	PROPN
ma-85	123	9	(	(	PUNCT
ma-85	123	10	t	t	PROPN
ma-85	123	11	)	)	PUNCT
ma-85	124	1	=	=	PROPN
ma-85	124	2	lim	lim	PROPN
ma-85	124	3	k−→∞	k−→∞	PROPN
ma-85	124	4	f	f	PROPN
ma-85	124	5	(	(	PUNCT
ma-85	124	6	2	2	NUM
ma-85	124	7	)	)	PUNCT
ma-85	124	8	k	k	NOUN
ma-85	124	9	(	(	PUNCT
ma-85	124	10	t	t	PROPN
ma-85	124	11	)	)	PUNCT
ma-85	124	12	.	.	PUNCT
ma-85	125	1	(	(	PUNCT
ma-85	125	2	2.20	2.20	NUM
ma-85	125	3	)	)	PUNCT
ma-85	125	4	then	then	ADV
ma-85	125	5	,	,	PUNCT
ma-85	125	6	(	(	PUNCT
ma-85	125	7	2.17	2.17	NUM
ma-85	125	8	)	)	PUNCT
ma-85	125	9	holds	hold	VERB
ma-85	125	10	if	if	SCONJ
ma-85	125	11	f	f	PROPN
ma-85	125	12	(	(	PUNCT
ma-85	125	13	2)∞	2)∞	PROPN
ma-85	125	14	(	(	PUNCT
ma-85	125	15	t	t	PROPN
ma-85	125	16	)	)	PUNCT
ma-85	125	17	≤	≤	NOUN
ma-85	125	18	0	0	NUM
ma-85	125	19	at	at	ADP
ma-85	125	20	t	t	PROPN
ma-85	125	21	=	=	SYM
ma-85	125	22	α2	α2	PROPN
ma-85	125	23	.	.	PUNCT
ma-85	126	1	(	(	PUNCT
ma-85	126	2	2.21	2.21	NUM
ma-85	126	3	)	)	PUNCT
ma-85	126	4	by	by	ADP
ma-85	126	5	(	(	PUNCT
ma-85	126	6	2.16	2.16	NUM
ma-85	126	7	)	)	PUNCT
ma-85	126	8	and	and	CCONJ
ma-85	126	9	(	(	PUNCT
ma-85	126	10	2.20	2.20	NUM
ma-85	126	11	)	)	PUNCT
ma-85	126	12	,	,	PUNCT
ma-85	126	13	we	we	PRON
ma-85	126	14	get	get	VERB
ma-85	126	15	f	f	X
ma-85	126	16	(	(	PUNCT
ma-85	126	17	2)∞	2)∞	PROPN
ma-85	126	18	(	(	PUNCT
ma-85	126	19	t	t	PROPN
ma-85	126	20	)	)	PUNCT
ma-85	127	1	=	=	PUNCT
ma-85	128	1	k0η	k0η	PROPN
ma-85	128	2	1−	1−	NUM
ma-85	128	3	t	t	NOUN
ma-85	128	4	−	−	NOUN
ma-85	128	5	1	1	NUM
ma-85	128	6	,	,	PUNCT
ma-85	128	7	so	so	CCONJ
ma-85	128	8	(	(	PUNCT
ma-85	128	9	2.21	2.21	NUM
ma-85	128	10	)	)	PUNCT
ma-85	128	11	holds	hold	VERB
ma-85	128	12	by	by	ADP
ma-85	128	13	(	(	PUNCT
ma-85	128	14	2.3	2.3	NUM
ma-85	128	15	)	)	PUNCT
ma-85	128	16	.	.	PUNCT
ma-85	129	1	moreover	moreover	ADV
ma-85	129	2	,	,	PUNCT
ma-85	129	3	estimate	estimate	NOUN
ma-85	129	4	(	(	PUNCT
ma-85	129	5	2.6	2.6	NUM
ma-85	129	6	)	)	PUNCT
ma-85	129	7	certainly	certainly	ADV
ma-85	129	8	holds	hold	VERB
ma-85	129	9	if	if	SCONJ
ma-85	129	10	2pk	2pk	ADJ
ma-85	129	11	=	=	SYM
ma-85	129	12	5k0	5k0	NUM
ma-85	129	13	3	3	NUM
ma-85	129	14	(	(	PUNCT
ma-85	129	15	sk+tk	sk+tk	NOUN
ma-85	129	16	)	)	PUNCT
ma-85	129	17	<	<	X
ma-85	129	18	5k0	5k0	NUM
ma-85	129	19	3	3	NUM
ma-85	129	20	(	(	PUNCT
ma-85	129	21	η	η	PROPN
ma-85	129	22	1−α+	1−α+	PROPN
ma-85	129	23	η	η	PROPN
ma-85	129	24	1−α	1−α	NUM
ma-85	129	25	)	)	PUNCT
ma-85	129	26	=	=	SYM
ma-85	129	27	10k0η	10k0η	NUM
ma-85	129	28	3(1−α	3(1−α	NUM
ma-85	129	29	)	)	PUNCT
ma-85	129	30	<	<	X
ma-85	129	31	1	1	NUM
ma-85	129	32	,	,	PUNCT
ma-85	129	33	which	which	PRON
ma-85	129	34	is	be	AUX
ma-85	129	35	true	true	ADJ
ma-85	129	36	by	by	ADP
ma-85	129	37	(	(	PUNCT
ma-85	129	38	2.3	2.3	NUM
ma-85	129	39	)	)	PUNCT
ma-85	129	40	.	.	PUNCT
ma-85	130	1	furthermore	furthermore	ADV
ma-85	130	2	,	,	PUNCT
ma-85	130	3	estimate	estimate	INTJ
ma-85	130	4	(	(	PUNCT
ma-85	130	5	2.7	2.7	NUM
ma-85	130	6	)	)	PUNCT
ma-85	130	7	holds	hold	VERB
ma-85	130	8	by	by	ADP
ma-85	130	9	(	(	PUNCT
ma-85	130	10	2.4)-(2.6	2.4)-(2.6	NUM
ma-85	130	11	)	)	PUNCT
ma-85	130	12	and	and	CCONJ
ma-85	130	13	thedefinition	thedefinition	NOUN
ma-85	130	14	of	of	ADP
ma-85	130	15	sequence	sequence	NOUN
ma-85	130	16	{	{	PUNCT
ma-85	130	17	tk	tk	PROPN
ma-85	130	18	}	}	PUNCT
ma-85	130	19	.	.	PUNCT
ma-85	131	1	hence	hence	ADV
ma-85	131	2	the	the	DET
ma-85	131	3	induction	induction	NOUN
ma-85	131	4	for	for	ADP
ma-85	131	5	estimates	estimate	NOUN
ma-85	131	6	(	(	PUNCT
ma-85	131	7	2.4)-(2.7	2.4)-(2.7	NUM
ma-85	131	8	)	)	PUNCT
ma-85	131	9	is	be	AUX
ma-85	131	10	completed	complete	VERB
ma-85	131	11	.	.	PUNCT
ma-85	132	1	it	it	PRON
ma-85	132	2	followsthat	followsthat	ADP
ma-85	132	3	sequence	sequence	NOUN
ma-85	132	4	{	{	PUNCT
ma-85	132	5	tk	tk	PROPN
ma-85	132	6	}	}	PUNCT
ma-85	132	7	is	be	AUX
ma-85	132	8	nondecreasing	nondecrease	VERB
ma-85	132	9	and	and	CCONJ
ma-85	132	10	bounded	bound	VERB
ma-85	132	11	from	from	ADP
ma-85	132	12	above	above	ADV
ma-85	132	13	by	by	ADP
ma-85	132	14	t	t	PROPN
ma-85	132	15	∗	∗	NOUN
ma-85	132	16	,	,	PUNCT
ma-85	132	17	and	and	CCONJ
ma-85	132	18	such	such	ADJ
ma-85	132	19	it	it	PRON
ma-85	132	20	converges	converge	VERB
ma-85	132	21	to	to	ADP
ma-85	132	22	t.	t.	PROPN
ma-85	132	23	�	�	PROPN
ma-85	132	24	if	if	SCONJ
ma-85	132	25	one	one	NUM
ma-85	132	26	desires	desire	NOUN
ma-85	132	27	iterates	iterate	VERB
ma-85	132	28	to	to	PART
ma-85	132	29	be	be	AUX
ma-85	132	30	given	give	VERB
ma-85	132	31	explicitly	explicitly	ADV
ma-85	132	32	in	in	ADP
ma-85	132	33	(	(	PUNCT
ma-85	132	34	2.1	2.1	NUM
ma-85	132	35	)	)	PUNCT
ma-85	132	36	,	,	PUNCT
ma-85	132	37	then	then	ADV
ma-85	132	38	define	define	VERB
ma-85	132	39	instead	instead	ADV
ma-85	132	40	sequence	sequence	NOUN
ma-85	132	41	{	{	PUNCT
ma-85	132	42	tn	tn	NOUN
ma-85	132	43	}	}	PUNCT
ma-85	132	44	as	as	SCONJ
ma-85	132	45	follows	follow	VERB
ma-85	132	46	t0	t0	PROPN
ma-85	132	47	=	=	SYM
ma-85	132	48	0	0	NUM
ma-85	132	49	,	,	PUNCT
ma-85	132	50	s0	s0	PROPN
ma-85	132	51	=	=	SYM
ma-85	132	52	η	η	PROPN
ma-85	132	53	tn+1	tn+1	PROPN
ma-85	132	54	=	=	SYM
ma-85	132	55	sn	sn	PROPN
ma-85	132	56	+	+	CCONJ
ma-85	132	57	2k(1	2k(1	NUM
ma-85	133	1	+	+	NOUN
ma-85	133	2	k0tn)(sn	k0tn)(sn	PROPN
ma-85	133	3	−	−	PROPN
ma-85	133	4	tn)2	tn)2	PROPN
ma-85	133	5	3(1−k0tn)(1−	3(1−k0tn)(1−	PROPN
ma-85	133	6	pn	pn	NOUN
ma-85	133	7	)	)	PUNCT
ma-85	133	8	(	(	PUNCT
ma-85	133	9	2.22	2.22	NUM
ma-85	133	10	)	)	PUNCT
ma-85	133	11	sn+1	sn+1	NOUN
ma-85	133	12	=	=	SYM
ma-85	133	13	tn+1	tn+1	PROPN
ma-85	133	14	+	+	CCONJ
ma-85	133	15	2k(tn+1	2k(tn+1	NUM
ma-85	133	16	−	−	PROPN
ma-85	133	17	tn	tn	NOUN
ma-85	134	1	+	+	CCONJ
ma-85	134	2	sn	sn	PROPN
ma-85	134	3	−	−	PROPN
ma-85	134	4	tn)(tn+1	tn)(tn+1	PROPN
ma-85	134	5	−	−	PROPN
ma-85	134	6	tn	tn	PROPN
ma-85	134	7	)	)	PUNCT
ma-85	134	8	2(1−k0tn+1	2(1−k0tn+1	NUM
ma-85	134	9	)	)	PUNCT
ma-85	134	10	.	.	PUNCT
ma-85	135	1	moreover	moreover	ADV
ma-85	135	2	,	,	PUNCT
ma-85	135	3	define	define	VERB
ma-85	135	4	recurrent	recurrent	ADJ
ma-85	135	5	polynomial	polynomial	NOUN
ma-85	135	6	on	on	ADP
ma-85	135	7	the	the	DET
ma-85	135	8	interval	interval	NOUN
ma-85	135	9	[	[	X
ma-85	135	10	0	0	NUM
ma-85	135	11	,	,	PUNCT
ma-85	135	12	1	1	NUM
ma-85	135	13	)	)	PUNCT
ma-85	135	14	by	by	ADP
ma-85	135	15	f	f	PROPN
ma-85	135	16	(	(	PUNCT
ma-85	135	17	1	1	NUM
ma-85	135	18	)	)	PUNCT
ma-85	135	19	n	n	PROPN
ma-85	135	20	(	(	PUNCT
ma-85	135	21	t	t	NOUN
ma-85	135	22	)	)	PUNCT
ma-85	135	23	=	=	PUNCT
ma-85	135	24	4k	4k	NOUN
ma-85	135	25	3	3	NUM
ma-85	136	1	tn−1η	tn−1η	NUM
ma-85	137	1	+	+	CCONJ
ma-85	137	2	4kk0	4kk0	NUM
ma-85	137	3	3	3	NUM
ma-85	137	4	tn−1(1	tn−1(1	SYM
ma-85	137	5	+	+	NUM
ma-85	137	6	t	t	NOUN
ma-85	137	7	+	+	X
ma-85	137	8	.	.	PUNCT
ma-85	137	9	.	.	PUNCT
ma-85	138	1	.+	.+	NOUN
ma-85	138	2	tn)η2	tn)η2	VERB
ma-85	139	1	+	+	NOUN
ma-85	139	2	k0(1	k0(1	PROPN
ma-85	139	3	+	+	CCONJ
ma-85	139	4	t	t	PROPN
ma-85	139	5	+	+	X
ma-85	139	6	.	.	PUNCT
ma-85	139	7	.	.	PUNCT
ma-85	140	1	.+	.+	NOUN
ma-85	140	2	tn)η	tn)η	NOUN
ma-85	141	1	−	−	NOUN
ma-85	141	2	1	1	X
ma-85	141	3	.	.	PUNCT
ma-85	142	1	this	this	DET
ma-85	142	2	time	time	NOUN
ma-85	142	3	we	we	PRON
ma-85	142	4	have	have	VERB
ma-85	142	5	f	f	X
ma-85	142	6	(	(	PUNCT
ma-85	142	7	1	1	X
ma-85	142	8	)	)	PUNCT
ma-85	142	9	n+1(t	n+1(t	NUM
ma-85	142	10	)	)	PUNCT
ma-85	143	1	=	=	SYM
ma-85	143	2	f	f	PROPN
ma-85	143	3	(	(	PUNCT
ma-85	143	4	1	1	NUM
ma-85	143	5	)	)	PUNCT
ma-85	143	6	n	n	PROPN
ma-85	143	7	(	(	PUNCT
ma-85	143	8	t	t	PROPN
ma-85	143	9	)	)	PUNCT
ma-85	143	10	+	+	CCONJ
ma-85	143	11	g	g	PROPN
ma-85	143	12	(	(	PUNCT
ma-85	143	13	1	1	NUM
ma-85	143	14	)	)	PUNCT
ma-85	143	15	n	n	CCONJ
ma-85	143	16	(	(	PUNCT
ma-85	143	17	t)tn−1η	t)tn−1η	PROPN
ma-85	143	18	,	,	PUNCT
ma-85	143	19	(	(	PUNCT
ma-85	143	20	2.23	2.23	NUM
ma-85	143	21	)	)	PUNCT
ma-85	144	1	where	where	SCONJ
ma-85	144	2	g	g	PROPN
ma-85	144	3	(	(	PUNCT
ma-85	144	4	1	1	NUM
ma-85	144	5	)	)	PUNCT
ma-85	144	6	n	n	PROPN
ma-85	144	7	(	(	PUNCT
ma-85	144	8	t	t	NOUN
ma-85	144	9	)	)	PUNCT
ma-85	144	10	=	=	SYM
ma-85	144	11	4kk0	4kk0	NUM
ma-85	144	12	3	3	NUM
ma-85	144	13	tn+2η	tn+2η	NOUN
ma-85	144	14	+	+	CCONJ
ma-85	144	15	4kk0	4kk0	NUM
ma-85	144	16	3	3	NUM
ma-85	144	17	tn+1η	tn+1η	NOUN
ma-85	144	18	+	+	CCONJ
ma-85	144	19	4	4	NUM
ma-85	144	20	3	3	NUM
ma-85	144	21	kt	kt	ADP
ma-85	144	22	−	−	PROPN
ma-85	144	23	4k	4k	NOUN
ma-85	144	24	3	3	NUM
ma-85	144	25	(	(	PUNCT
ma-85	144	26	1−k0η	1−k0η	NUM
ma-85	144	27	)	)	PUNCT
ma-85	144	28	.	.	PUNCT
ma-85	145	1	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	PROPN
ma-85	145	2	eur	eur	PROPN
ma-85	145	3	.	.	PUNCT
ma-85	146	1	j.	j.	PROPN
ma-85	146	2	math	math	PROPN
ma-85	146	3	.	.	PUNCT
ma-85	147	1	anal	anal	PROPN
ma-85	147	2	.	.	PUNCT
ma-85	148	1	10.28924	10.28924	NUM
ma-85	148	2	/	/	SYM
ma-85	148	3	ada	ada	PROPN
ma-85	148	4	/	/	SYM
ma-85	148	5	ma.2.13	ma.2.13	PROPN
ma-85	148	6	6	6	NUM
ma-85	148	7	we	we	PRON
ma-85	148	8	get	get	VERB
ma-85	148	9	g(1)n	g(1)n	ADP
ma-85	148	10	(	(	PUNCT
ma-85	148	11	0	0	NUM
ma-85	148	12	)	)	PUNCT
ma-85	148	13	=	=	SYM
ma-85	149	1	−4k3	−4k3	NUM
ma-85	149	2	(	(	PUNCT
ma-85	149	3	1	1	NUM
ma-85	149	4	−	−	PROPN
ma-85	149	5	k0η	k0η	PROPN
ma-85	149	6	)	)	PUNCT
ma-85	149	7	<	<	X
ma-85	149	8	0	0	NUM
ma-85	150	1	for	for	ADP
ma-85	150	2	k0η	k0η	PROPN
ma-85	150	3	<	<	X
ma-85	150	4	1	1	NUM
ma-85	150	5	,	,	PUNCT
ma-85	150	6	and	and	CCONJ
ma-85	150	7	g(1)1	g(1)1	PROPN
ma-85	150	8	(	(	PUNCT
ma-85	150	9	1	1	NUM
ma-85	150	10	)	)	PUNCT
ma-85	150	11	=	=	SYM
ma-85	151	1	4kk0η	4kk0η	NUM
ma-85	151	2	>	>	SYM
ma-85	151	3	0	0	X
ma-85	151	4	.	.	PUNCT
ma-85	152	1	denote	denote	VERB
ma-85	152	2	by	by	ADP
ma-85	152	3	rn	rn	PROPN
ma-85	152	4	thesmallest	thesmall	ADJ
ma-85	152	5	solution	solution	NOUN
ma-85	152	6	of	of	ADP
ma-85	152	7	g(1)n	g(1)n	ADP
ma-85	152	8	(	(	PUNCT
ma-85	152	9	t),respectively	t),respectively	ADV
ma-85	152	10	.	.	PUNCT
ma-85	153	1	notice	notice	VERB
ma-85	153	2	that	that	SCONJ
ma-85	153	3	these	these	DET
ma-85	153	4	solutions	solution	NOUN
ma-85	153	5	are	be	AUX
ma-85	153	6	increasing	increase	VERB
ma-85	153	7	as	as	ADP
ma-85	153	8	n	n	ADP
ma-85	153	9	increases	increase	NOUN
ma-85	153	10	,	,	PUNCT
ma-85	153	11	since	since	SCONJ
ma-85	153	12	g(1)n	g(1)n	PROPN
ma-85	153	13	(	(	PUNCT
ma-85	153	14	t	t	NOUN
ma-85	153	15	)	)	PUNCT
ma-85	153	16	≤	≤	NOUN
ma-85	153	17	g(1)n−1(t	g(1)n−1(t	PRON
ma-85	153	18	)	)	PUNCT
ma-85	153	19	.	.	PUNCT
ma-85	154	1	hence	hence	ADV
ma-85	154	2	,	,	PUNCT
ma-85	154	3	it	it	PRON
ma-85	154	4	follows	follow	VERB
ma-85	154	5	by	by	ADP
ma-85	154	6	(	(	PUNCT
ma-85	154	7	2.23	2.23	NUM
ma-85	154	8	)	)	PUNCT
ma-85	155	1	that	that	SCONJ
ma-85	156	1	f	f	X
ma-85	156	2	(	(	PUNCT
ma-85	156	3	1	1	X
ma-85	156	4	)	)	PUNCT
ma-85	156	5	n+1(t	n+1(t	PROPN
ma-85	156	6	)	)	PUNCT
ma-85	157	1	≤	≤	NUM
ma-85	157	2	f	f	X
ma-85	157	3	(	(	PUNCT
ma-85	157	4	1	1	NUM
ma-85	157	5	)	)	PUNCT
ma-85	157	6	n	n	PROPN
ma-85	157	7	(	(	PUNCT
ma-85	157	8	t	t	PROPN
ma-85	157	9	)	)	PUNCT
ma-85	157	10	+	+	CCONJ
ma-85	157	11	g	g	PROPN
ma-85	157	12	(	(	PUNCT
ma-85	157	13	1	1	NUM
ma-85	157	14	)	)	PUNCT
ma-85	157	15	1	1	NUM
ma-85	157	16	(	(	PUNCT
ma-85	157	17	t)tn−1η	t)tn−1η	PROPN
ma-85	157	18	.	.	PUNCT
ma-85	158	1	in	in	ADP
ma-85	158	2	particular	particular	ADJ
ma-85	158	3	for	for	ADP
ma-85	158	4	α1	α1	PROPN
ma-85	158	5	=	=	SYM
ma-85	158	6	r1	r1	PROPN
ma-85	158	7	,	,	PUNCT
ma-85	158	8	we	we	PRON
ma-85	158	9	get	get	VERB
ma-85	158	10	f	f	X
ma-85	158	11	(	(	PUNCT
ma-85	158	12	1	1	X
ma-85	158	13	)	)	PUNCT
ma-85	158	14	n+1(t	n+1(t	PROPN
ma-85	158	15	)	)	PUNCT
ma-85	159	1	≤	≤	NUM
ma-85	159	2	f	f	X
ma-85	159	3	(	(	PUNCT
ma-85	159	4	1	1	NUM
ma-85	159	5	)	)	PUNCT
ma-85	159	6	n	n	PROPN
ma-85	159	7	(	(	PUNCT
ma-85	159	8	t	t	NOUN
ma-85	159	9	)	)	PUNCT
ma-85	159	10	at	at	ADP
ma-85	159	11	t	t	NOUN
ma-85	159	12	=	=	SYM
ma-85	159	13	α1	α1	PROPN
ma-85	159	14	.	.	PUNCT
ma-85	160	1	hence	hence	ADV
ma-85	160	2	,	,	PUNCT
ma-85	160	3	f	f	PROPN
ma-85	160	4	(	(	PUNCT
ma-85	160	5	1	1	NUM
ma-85	160	6	)	)	PUNCT
ma-85	160	7	n	n	PROPN
ma-85	160	8	(	(	PUNCT
ma-85	160	9	t	t	NOUN
ma-85	160	10	)	)	PUNCT
ma-85	160	11	≤	≤	NOUN
ma-85	160	12	0	0	NUM
ma-85	160	13	holds	hold	VERB
ma-85	160	14	if	if	SCONJ
ma-85	160	15	f	f	PROPN
ma-85	160	16	(	(	PUNCT
ma-85	160	17	1	1	NUM
ma-85	160	18	)	)	PUNCT
ma-85	160	19	1	1	NUM
ma-85	160	20	(	(	PUNCT
ma-85	160	21	t	t	NOUN
ma-85	160	22	)	)	PUNCT
ma-85	160	23	≤	≤	NOUN
ma-85	160	24	0	0	NUM
ma-85	161	1	at	at	ADP
ma-85	161	2	t	t	PROPN
ma-85	161	3	=	=	PUNCT
ma-85	162	1	α1.but	α1.but	NUM
ma-85	162	2	f	f	PROPN
ma-85	162	3	(	(	PUNCT
ma-85	162	4	1	1	NUM
ma-85	162	5	)	)	PUNCT
ma-85	162	6	1	1	NUM
ma-85	162	7	(	(	PUNCT
ma-85	162	8	t	t	NOUN
ma-85	162	9	)	)	PUNCT
ma-85	162	10	=	=	PUNCT
ma-85	162	11	4k	4k	PUNCT
ma-85	162	12	3	3	NUM
ma-85	162	13	η	η	X
ma-85	162	14	+	+	ADP
ma-85	162	15	4	4	NUM
ma-85	162	16	3	3	NUM
ma-85	162	17	kk0η	kk0η	PROPN
ma-85	162	18	2	2	NUM
ma-85	163	1	+	+	NOUN
ma-85	163	2	k0η	k0η	NOUN
ma-85	163	3	−	−	PROPN
ma-85	163	4	1	1	X
ma-85	163	5	.	.	PUNCT
ma-85	164	1	define	define	VERB
ma-85	164	2	b	b	NOUN
ma-85	164	3	=	=	SYM
ma-85	164	4	2k(s0−t0	2k(s0−t0	NUM
ma-85	164	5	)	)	PUNCT
ma-85	164	6	3	3	NUM
ma-85	164	7	.	.	PUNCT
ma-85	165	1	then	then	ADV
ma-85	165	2	,	,	PUNCT
ma-85	165	3	we	we	PRON
ma-85	165	4	arrive	arrive	VERB
ma-85	165	5	at	at	ADP
ma-85	165	6	the	the	DET
ma-85	165	7	following	follow	VERB
ma-85	165	8	convergence	convergence	NOUN
ma-85	165	9	results	result	NOUN
ma-85	165	10	for	for	ADP
ma-85	165	11	majorizing	majorize	VERB
ma-85	165	12	sequence(2.2	sequence(2.2	ADJ
ma-85	165	13	)	)	PUNCT
ma-85	165	14	.	.	PUNCT
ma-85	166	1	lemma	lemma	PROPN
ma-85	166	2	2.3	2.3	NUM
ma-85	166	3	.	.	PUNCT
ma-85	167	1	suppose	suppose	VERB
ma-85	167	2	5(tn	5(tn	PROPN
ma-85	167	3	+	+	CCONJ
ma-85	167	4	sn	sn	NOUN
ma-85	167	5	)	)	PUNCT
ma-85	167	6	<	<	X
ma-85	167	7	6	6	NUM
ma-85	167	8	k0	k0	PROPN
ma-85	167	9	,	,	PUNCT
ma-85	167	10	where	where	SCONJ
ma-85	167	11	{	{	PUNCT
ma-85	167	12	tn	tn	NOUN
ma-85	167	13	}	}	PUNCT
ma-85	167	14	is	be	AUX
ma-85	167	15	the	the	DET
ma-85	167	16	sequence	sequence	NOUN
ma-85	167	17	defined	define	VERB
ma-85	167	18	by	by	ADP
ma-85	167	19	(	(	PUNCT
ma-85	167	20	2.22	2.22	NUM
ma-85	167	21	)	)	PUNCT
ma-85	167	22	.	.	PUNCT
ma-85	168	1	then	then	ADV
ma-85	168	2	,	,	PUNCT
ma-85	168	3	the	the	DET
ma-85	168	4	conclusions	conclusion	NOUN
ma-85	168	5	of	of	ADP
ma-85	168	6	lemma	lemma	PROPN
ma-85	168	7	2.2	2.2	NUM
ma-85	168	8	hold	hold	NOUN
ma-85	168	9	for	for	ADP
ma-85	168	10	this	this	DET
ma-85	168	11	sequence	sequence	NOUN
ma-85	168	12	.	.	PUNCT
ma-85	169	1	lemma	lemma	PROPN
ma-85	169	2	2.4	2.4	NUM
ma-85	169	3	.	.	PUNCT
ma-85	169	4	suppose	suppose	VERB
ma-85	169	5	0	0	PUNCT
ma-85	170	1	<	<	X
ma-85	170	2	c̄	c̄	PROPN
ma-85	170	3	≤	≤	NUM
ma-85	170	4	c	c	NOUN
ma-85	170	5	≤	≤	NOUN
ma-85	170	6	α3	α3	NOUN
ma-85	170	7	≤	≤	NUM
ma-85	170	8	α	α	PROPN
ma-85	170	9	≤	≤	NOUN
ma-85	170	10	1−	1−	NUM
ma-85	170	11	10k0	10k0	NUM
ma-85	170	12	3	3	NUM
ma-85	170	13	η	η	PROPN
ma-85	170	14	(	(	PUNCT
ma-85	170	15	2.24	2.24	NUM
ma-85	170	16	)	)	PUNCT
ma-85	170	17	and	and	CCONJ
ma-85	170	18	(	(	PUNCT
ma-85	170	19	4k	4k	NOUN
ma-85	170	20	3	3	NUM
ma-85	170	21	+	+	CCONJ
ma-85	170	22	4	4	NUM
ma-85	170	23	3	3	NUM
ma-85	170	24	k0kη	k0kη	PUNCT
ma-85	171	1	+	+	PROPN
ma-85	171	2	k0	k0	PROPN
ma-85	171	3	)	)	PUNCT
ma-85	171	4	η	η	PROPN
ma-85	171	5	≤	≤	PROPN
ma-85	171	6	1	1	NUM
ma-85	171	7	.	.	PUNCT
ma-85	171	8	(	(	PUNCT
ma-85	171	9	2.25	2.25	NUM
ma-85	171	10	)	)	PUNCT
ma-85	171	11	then	then	ADV
ma-85	171	12	,	,	PUNCT
ma-85	171	13	the	the	DET
ma-85	171	14	conclusions	conclusion	NOUN
ma-85	171	15	of	of	ADP
ma-85	171	16	lemma	lemma	PROPN
ma-85	171	17	2.2	2.2	NUM
ma-85	171	18	hold	hold	NOUN
ma-85	171	19	for	for	ADP
ma-85	171	20	sequence	sequence	NOUN
ma-85	171	21	{	{	PUNCT
ma-85	171	22	tn	tn	NOUN
ma-85	171	23	}	}	PUNCT
ma-85	171	24	given	give	VERB
ma-85	171	25	by	by	ADP
ma-85	171	26	(	(	PUNCT
ma-85	171	27	2.22	2.22	NUM
ma-85	171	28	)	)	PUNCT
ma-85	171	29	.	.	PUNCT
ma-85	172	1	remark	remark	VERB
ma-85	172	2	2.5	2.5	NUM
ma-85	172	3	.	.	PUNCT
ma-85	173	1	the	the	DET
ma-85	173	2	solutions	solution	NOUN
ma-85	173	3	α1	α1	PROPN
ma-85	173	4	and	and	CCONJ
ma-85	173	5	α2	α2	ADJ
ma-85	173	6	in	in	ADP
ma-85	173	7	lemma	lemma	PROPN
ma-85	173	8	2.2	2.2	NUM
ma-85	173	9	depend	depend	VERB
ma-85	173	10	only	only	ADV
ma-85	173	11	on	on	ADP
ma-85	173	12	k0	k0	PROPN
ma-85	173	13	and	and	CCONJ
ma-85	173	14	k.	k.	PROPN
ma-85	173	15	similarly	similarly	ADV
ma-85	173	16	α2	α2	ADJ
ma-85	173	17	in	in	ADP
ma-85	173	18	lemma	lemma	PROPN
ma-85	173	19	2.4	2.4	NUM
ma-85	173	20	depends	depend	VERB
ma-85	173	21	on	on	ADP
ma-85	173	22	k0	k0	PROPN
ma-85	173	23	and	and	CCONJ
ma-85	173	24	k1	k1	PROPN
ma-85	173	25	.	.	PUNCT
ma-85	174	1	but	but	CCONJ
ma-85	174	2	α1	α1	PROPN
ma-85	174	3	depends	depend	VERB
ma-85	174	4	k0	k0	PROPN
ma-85	174	5	,	,	PUNCT
ma-85	174	6	k	k	PROPN
ma-85	174	7	and	and	CCONJ
ma-85	174	8	η	η	PROPN
ma-85	174	9	.	.	PROPN
ma-85	174	10	to	to	PART
ma-85	174	11	avoid	avoid	VERB
ma-85	174	12	this	this	DET
ma-85	174	13	dependence	dependence	NOUN
ma-85	174	14	pick	pick	VERB
ma-85	174	15	any	any	DET
ma-85	174	16	γ	γ	X
ma-85	174	17	∈	∈	PROPN
ma-85	174	18	(	(	PUNCT
ma-85	174	19	0	0	NUM
ma-85	174	20	,	,	PUNCT
ma-85	174	21	1	1	NUM
ma-85	174	22	]	]	PUNCT
ma-85	174	23	and	and	CCONJ
ma-85	174	24	set	set	VERB
ma-85	174	25	γ	γ	PROPN
ma-85	174	26	=	=	SYM
ma-85	174	27	k0η	k0η	PROPN
ma-85	174	28	.	.	PUNCT
ma-85	175	1	define	define	NOUN
ma-85	175	2	functions	function	NOUN
ma-85	175	3	ḡ(1)n	ḡ(1)n	PROPN
ma-85	175	4	(	(	PUNCT
ma-85	175	5	t	t	PROPN
ma-85	175	6	)	)	PUNCT
ma-85	175	7	on	on	ADP
ma-85	175	8	[	[	X
ma-85	175	9	0	0	NUM
ma-85	175	10	,	,	PUNCT
ma-85	175	11	1	1	NUM
ma-85	175	12	)	)	PUNCT
ma-85	175	13	by	by	ADP
ma-85	175	14	ḡ	ḡ	VERB
ma-85	175	15	(	(	PUNCT
ma-85	175	16	1	1	NUM
ma-85	175	17	)	)	PUNCT
ma-85	175	18	n	n	PROPN
ma-85	175	19	(	(	PUNCT
ma-85	175	20	t	t	NOUN
ma-85	175	21	)	)	PUNCT
ma-85	175	22	=	=	PUNCT
ma-85	176	1	4kγ	4kγ	ADJ
ma-85	176	2	3	3	NUM
ma-85	176	3	tn+1	tn+1	NOUN
ma-85	177	1	+	+	CCONJ
ma-85	177	2	4kγ	4kγ	ADJ
ma-85	177	3	3	3	NUM
ma-85	177	4	tn=1	tn=1	NOUN
ma-85	177	5	+	+	CCONJ
ma-85	177	6	4	4	NUM
ma-85	177	7	3	3	NUM
ma-85	177	8	kt	kt	ADP
ma-85	177	9	−	−	PROPN
ma-85	177	10	4k	4k	NOUN
ma-85	177	11	3	3	NUM
ma-85	177	12	(	(	PUNCT
ma-85	177	13	1−	1−	NUM
ma-85	177	14	γ	γ	NOUN
ma-85	177	15	)	)	PUNCT
ma-85	177	16	.	.	PUNCT
ma-85	178	1	then	then	ADV
ma-85	178	2	,	,	PUNCT
ma-85	178	3	according	accord	VERB
ma-85	178	4	to	to	ADP
ma-85	178	5	the	the	DET
ma-85	178	6	proof	proof	NOUN
ma-85	178	7	of	of	ADP
ma-85	178	8	lemma	lemma	PROPN
ma-85	178	9	2.2	2.2	NUM
ma-85	178	10	we	we	PRON
ma-85	178	11	can	can	AUX
ma-85	178	12	set	set	VERB
ma-85	178	13	α1	α1	PROPN
ma-85	178	14	=	=	SYM
ma-85	178	15	r̄1	r̄1	NOUN
ma-85	178	16	,	,	PUNCT
ma-85	178	17	where	where	SCONJ
ma-85	178	18	r̄1	r̄1	NOUN
ma-85	178	19	is	be	AUX
ma-85	178	20	the	the	DET
ma-85	178	21	smallest	small	ADJ
ma-85	178	22	solution	solution	NOUN
ma-85	178	23	in	in	ADP
ma-85	178	24	(	(	PUNCT
ma-85	178	25	0	0	NUM
ma-85	178	26	,	,	PUNCT
ma-85	178	27	1	1	NUM
ma-85	178	28	)	)	PUNCT
ma-85	178	29	of	of	ADP
ma-85	178	30	equation	equation	NOUN
ma-85	178	31	ḡ(1)1	ḡ(1)1	PROPN
ma-85	178	32	(	(	PUNCT
ma-85	178	33	t	t	NOUN
ma-85	178	34	)	)	PUNCT
ma-85	178	35	=	=	SYM
ma-85	178	36	0	0	PUNCT
ma-85	178	37	assured	assure	VERB
ma-85	178	38	also	also	ADV
ma-85	178	39	to	to	PART
ma-85	178	40	exist	exist	VERB
ma-85	178	41	.	.	PUNCT
ma-85	179	1	finally	finally	ADV
ma-85	179	2	,	,	PUNCT
ma-85	179	3	notice	notice	VERB
ma-85	179	4	that	that	SCONJ
ma-85	179	5	the	the	DET
ma-85	179	6	first	first	ADJ
ma-85	179	7	condition	condition	NOUN
ma-85	179	8	shows	show	VERB
ma-85	179	9	implicitly	implicitly	ADV
ma-85	179	10	and	and	CCONJ
ma-85	179	11	the	the	DET
ma-85	179	12	second	second	ADJ
ma-85	179	13	explicitly	explicitly	ADV
ma-85	179	14	the	the	DET
ma-85	179	15	smallness	smallness	NOUN
ma-85	179	16	of	of	ADP
ma-85	179	17	η	η	PROPN
ma-85	179	18	.	.	PROPN
ma-85	179	19	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	PROPN
ma-85	179	20	eur	eur	PROPN
ma-85	179	21	.	.	PUNCT
ma-85	180	1	j.	j.	PROPN
ma-85	180	2	math	math	PROPN
ma-85	180	3	.	.	PUNCT
ma-85	181	1	anal	anal	PROPN
ma-85	181	2	.	.	PUNCT
ma-85	182	1	10.28924	10.28924	NUM
ma-85	182	2	/	/	SYM
ma-85	182	3	ada	ada	PROPN
ma-85	182	4	/	/	SYM
ma-85	182	5	ma.2.13	ma.2.13	PROPN
ma-85	182	6	73	73	NUM
ma-85	182	7	.	.	PUNCT
ma-85	183	1	semi	semi	ADJ
ma-85	183	2	-	-	ADJ
ma-85	183	3	local	local	ADJ
ma-85	183	4	convergence	convergence	NOUN
ma-85	183	5	the	the	DET
ma-85	183	6	following	follow	VERB
ma-85	183	7	sufficient	sufficient	ADJ
ma-85	183	8	convergence	convergence	NOUN
ma-85	183	9	criteria	criterion	NOUN
ma-85	183	10	(	(	PUNCT
ma-85	183	11	a	a	X
ma-85	183	12	)	)	PUNCT
ma-85	183	13	are	be	AUX
ma-85	183	14	used	use	VERB
ma-85	183	15	.	.	PUNCT
ma-85	184	1	suppose:(a1	suppose:(a1	VERB
ma-85	184	2	)	)	PUNCT
ma-85	184	3	there	there	PRON
ma-85	184	4	exist	exist	VERB
ma-85	184	5	x0	x0	PROPN
ma-85	184	6	∈	∈	PROPN
ma-85	184	7	d	d	PROPN
ma-85	184	8	and	and	CCONJ
ma-85	184	9	η	η	PROPN
ma-85	184	10	>	>	X
ma-85	184	11	0	0	NUM
ma-85	185	1	such	such	ADJ
ma-85	185	2	that	that	SCONJ
ma-85	185	3	f	f	PROPN
ma-85	185	4	′(x0)−1	′(x0)−1	PROPN
ma-85	185	5	exists	exist	VERB
ma-85	185	6	and	and	CCONJ
ma-85	185	7	‖f	‖f	ADJ
ma-85	185	8	′(x0)−1f	′(x0)−1f	NOUN
ma-85	185	9	(	(	PUNCT
ma-85	185	10	x0)‖	x0)‖	PROPN
ma-85	185	11	≤	≤	PROPN
ma-85	185	12	η	η	PROPN
ma-85	185	13	.	.	PROPN
ma-85	185	14	(	(	PUNCT
ma-85	185	15	a2	a2	PROPN
ma-85	185	16	)	)	PUNCT
ma-85	185	17	‖f	‖f	PUNCT
ma-85	185	18	′(x0)−1(f	′(x0)−1(f	PROPN
ma-85	185	19	′(w)−	′(w)−	VERB
ma-85	185	20	f	f	PROPN
ma-85	185	21	′(x0))‖	′(x0))‖	NUM
ma-85	185	22	≤	≤	NUM
ma-85	185	23	k0‖w	k0‖w	NOUN
ma-85	186	1	−	−	PROPN
ma-85	187	1	x0‖for	x0‖for	ADP
ma-85	187	2	all	all	DET
ma-85	187	3	w	w	PROPN
ma-85	187	4	∈	∈	PROPN
ma-85	187	5	d.	d.	NOUN
ma-85	187	6	set	set	VERB
ma-85	187	7	d0	d0	NOUN
ma-85	187	8	=	=	SYM
ma-85	188	1	d	d	PROPN
ma-85	188	2	∩	∩	ADJ
ma-85	188	3	u(x0	u(x0	NOUN
ma-85	188	4	,	,	PUNCT
ma-85	188	5	1	1	NUM
ma-85	188	6	k0	k0	PROPN
ma-85	188	7	)	)	PUNCT
ma-85	188	8	.(a3	.(a3	PROPN
ma-85	188	9	)	)	PUNCT
ma-85	188	10	‖f	‖f	PUNCT
ma-85	188	11	′(x0)−1(f	′(x0)−1(f	PROPN
ma-85	188	12	′(w)−	′(w)−	VERB
ma-85	188	13	f	f	PROPN
ma-85	188	14	′(v)‖	′(v)‖	PROPN
ma-85	188	15	≤	≤	PROPN
ma-85	188	16	k‖w	k‖w	PROPN
ma-85	188	17	−	−	PROPN
ma-85	188	18	v‖for	v‖for	ADP
ma-85	188	19	all	all	DET
ma-85	188	20	v	v	ADP
ma-85	188	21	∈	∈	NOUN
ma-85	188	22	d0	d0	NOUN
ma-85	188	23	and	and	CCONJ
ma-85	188	24	w	w	NOUN
ma-85	188	25	=	=	NOUN
ma-85	188	26	v	v	ADP
ma-85	188	27	−	−	PROPN
ma-85	188	28	f	f	PROPN
ma-85	188	29	′(v)−1f	′(v)−1f	X
ma-85	188	30	(	(	PUNCT
ma-85	188	31	v	v	NOUN
ma-85	188	32	)	)	PUNCT
ma-85	188	33	.	.	PUNCT
ma-85	189	1	denote	denote	VERB
ma-85	189	2	by	by	ADP
ma-85	189	3	l	l	PROPN
ma-85	189	4	the	the	DET
ma-85	189	5	constant	constant	ADJ
ma-85	189	6	,	,	PUNCT
ma-85	189	7	if	if	SCONJ
ma-85	189	8	(	(	PUNCT
ma-85	189	9	a3	a3	NOUN
ma-85	189	10	)	)	PUNCT
ma-85	189	11	holds	hold	VERB
ma-85	189	12	for	for	ADP
ma-85	189	13	all	all	DET
ma-85	189	14	u	u	NOUN
ma-85	189	15	,	,	PUNCT
ma-85	189	16	v	v	NOUN
ma-85	189	17	∈	∈	NOUN
ma-85	189	18	d0	d0	NOUN
ma-85	189	19	,	,	PUNCT
ma-85	189	20	and	and	CCONJ
ma-85	189	21	by	by	ADP
ma-85	189	22	l1	l1	PROPN
ma-85	189	23	the	the	DET
ma-85	189	24	constant	constant	ADJ
ma-85	189	25	for	for	ADP
ma-85	189	26	all	all	DET
ma-85	189	27	u	u	NOUN
ma-85	189	28	,	,	PUNCT
ma-85	189	29	v	v	PROPN
ma-85	189	30	∈	∈	PROPN
ma-85	189	31	d.	d.	NOUN
ma-85	189	32	it	it	PRON
ma-85	189	33	follows	follow	VERB
ma-85	189	34	that	that	SCONJ
ma-85	189	35	k	k	PROPN
ma-85	189	36	≤	≤	PROPN
ma-85	189	37	l	l	NOUN
ma-85	189	38	≤	≤	PROPN
ma-85	189	39	l1	l1	PROPN
ma-85	189	40	.	.	PUNCT
ma-85	190	1	in	in	ADP
ma-85	190	2	practicewe	practicewe	NOUN
ma-85	190	3	shall	shall	AUX
ma-85	190	4	use	use	VERB
ma-85	190	5	whichever	whichever	PRON
ma-85	190	6	of	of	ADP
ma-85	190	7	k	k	PROPN
ma-85	190	8	or	or	CCONJ
ma-85	190	9	l	l	NOUN
ma-85	190	10	is	be	AUX
ma-85	190	11	easier	easy	ADJ
ma-85	190	12	to	to	PART
ma-85	190	13	compute	compute	VERB
ma-85	190	14	(	(	PUNCT
ma-85	190	15	see	see	VERB
ma-85	190	16	also	also	ADV
ma-85	190	17	the	the	DET
ma-85	190	18	numerical	numerical	ADJ
ma-85	190	19	section).(a4	section).(a4	PROPN
ma-85	190	20	)	)	PUNCT
ma-85	190	21	hypotheses	hypothesis	NOUN
ma-85	190	22	of	of	ADP
ma-85	190	23	lemma	lemma	PROPN
ma-85	190	24	2.1	2.1	NUM
ma-85	190	25	or	or	CCONJ
ma-85	190	26	lemma	lemma	PROPN
ma-85	190	27	2.2	2.2	NUM
ma-85	190	28	hold.and(a5	hold.and(a5	ADV
ma-85	190	29	)	)	PUNCT
ma-85	190	30	u[x0	u[x0	NOUN
ma-85	190	31	,	,	PUNCT
ma-85	190	32	t	t	PROPN
ma-85	190	33	∗	∗	NOUN
ma-85	190	34	]	]	PUNCT
ma-85	191	1	⊂	⊂	PROPN
ma-85	191	2	d	d	X
ma-85	191	3	(	(	PUNCT
ma-85	191	4	or	or	CCONJ
ma-85	191	5	u[x0	u[x0	NOUN
ma-85	191	6	,	,	PUNCT
ma-85	191	7	t	t	X
ma-85	191	8	]	]	PUNCT
ma-85	191	9	⊆	⊆	X
ma-85	191	10	d).next	d).next	PROPN
ma-85	191	11	,	,	PUNCT
ma-85	191	12	the	the	DET
ma-85	191	13	semi	semi	ADJ
ma-85	191	14	-	-	ADJ
ma-85	191	15	local	local	ADJ
ma-85	191	16	convergence	convergence	NOUN
ma-85	191	17	of	of	ADP
ma-85	191	18	scheme	scheme	NOUN
ma-85	191	19	(	(	PUNCT
ma-85	191	20	1.1	1.1	NUM
ma-85	191	21	)	)	PUNCT
ma-85	191	22	is	be	AUX
ma-85	191	23	developed	develop	VERB
ma-85	191	24	based	base	VERB
ma-85	191	25	on	on	ADP
ma-85	191	26	conditions	condition	NOUN
ma-85	191	27	(	(	PUNCT
ma-85	191	28	a	a	X
ma-85	191	29	)	)	PUNCT
ma-85	191	30	and	and	CCONJ
ma-85	191	31	theaforementioned	theaforementione	VERB
ma-85	191	32	notation	notation	NOUN
ma-85	191	33	.	.	PUNCT
ma-85	192	1	theorem	theorem	VERB
ma-85	192	2	3.1	3.1	NUM
ma-85	192	3	.	.	PUNCT
ma-85	193	1	suppose	suppose	VERB
ma-85	193	2	conditions	condition	NOUN
ma-85	193	3	(	(	PUNCT
ma-85	193	4	a	a	X
ma-85	193	5	)	)	PUNCT
ma-85	193	6	hold	hold	NOUN
ma-85	193	7	.	.	PUNCT
ma-85	194	1	then	then	ADV
ma-85	194	2	,	,	PUNCT
ma-85	194	3	the	the	DET
ma-85	194	4	following	follow	VERB
ma-85	194	5	items	item	NOUN
ma-85	194	6	hold	hold	VERB
ma-85	194	7	{	{	PUNCT
ma-85	194	8	xn	xn	NOUN
ma-85	194	9	}	}	PUNCT
ma-85	194	10	∈	∈	PROPN
ma-85	194	11	u(x0	u(x0	NOUN
ma-85	194	12	,	,	PUNCT
ma-85	194	13	t	t	PROPN
ma-85	194	14	∗	∗	NOUN
ma-85	194	15	)	)	PUNCT
ma-85	194	16	(	(	PUNCT
ma-85	194	17	3.1	3.1	NUM
ma-85	194	18	)	)	PUNCT
ma-85	194	19	and	and	CCONJ
ma-85	194	20	‖x∗	‖x∗	NUM
ma-85	195	1	−	−	NOUN
ma-85	195	2	xn‖	xn‖	PROPN
ma-85	195	3	≤	≤	NOUN
ma-85	195	4	t∗	t∗	NOUN
ma-85	195	5	−	−	PROPN
ma-85	195	6	tn	tn	PROPN
ma-85	195	7	,	,	PUNCT
ma-85	195	8	(	(	PUNCT
ma-85	195	9	3.2	3.2	NUM
ma-85	195	10	)	)	PUNCT
ma-85	195	11	where	where	SCONJ
ma-85	195	12	x∗	x∗	PROPN
ma-85	195	13	=	=	SYM
ma-85	195	14	limn−→∞	limn−→∞	NOUN
ma-85	195	15	xn	xn	PROPN
ma-85	195	16	∈	∈	PROPN
ma-85	195	17	u[x0	u[x0	NOUN
ma-85	195	18	,	,	PUNCT
ma-85	195	19	t	t	PROPN
ma-85	195	20	∗	∗	NOUN
ma-85	195	21	]	]	PUNCT
ma-85	195	22	and	and	CCONJ
ma-85	195	23	f	f	PROPN
ma-85	195	24	(	(	PUNCT
ma-85	195	25	x∗	x∗	PROPN
ma-85	195	26	)	)	PUNCT
ma-85	195	27	=	=	SYM
ma-85	195	28	0	0	X
ma-85	195	29	.	.	PUNCT
ma-85	196	1	proof	proof	NOUN
ma-85	196	2	.	.	PUNCT
ma-85	197	1	mathematical	mathematical	ADJ
ma-85	197	2	induction	induction	NOUN
ma-85	197	3	is	be	AUX
ma-85	197	4	used	use	VERB
ma-85	197	5	to	to	PART
ma-85	197	6	show	show	VERB
ma-85	197	7	‖yk	‖yk	PROPN
ma-85	197	8	−	−	PROPN
ma-85	197	9	xk‖	xk‖	PROPN
ma-85	197	10	≤	≤	PROPN
ma-85	197	11	sk	sk	VERB
ma-85	197	12	−	−	PROPN
ma-85	197	13	tk	tk	PROPN
ma-85	197	14	(	(	PUNCT
ma-85	197	15	3.3	3.3	NUM
ma-85	197	16	)	)	PUNCT
ma-85	197	17	and	and	CCONJ
ma-85	197	18	‖xk+1	‖xk+1	VERB
ma-85	197	19	−	−	NUM
ma-85	197	20	yk‖	yk‖	NOUN
ma-85	197	21	≤	≤	NOUN
ma-85	198	1	tk+1	tk+1	NUM
ma-85	198	2	−	−	NOUN
ma-85	198	3	sk	sk	INTJ
ma-85	198	4	.	.	PUNCT
ma-85	199	1	(	(	PUNCT
ma-85	199	2	3.4)it	3.4)it	PROPN
ma-85	199	3	follows	follow	VERB
ma-85	199	4	from	from	ADP
ma-85	199	5	(	(	PUNCT
ma-85	199	6	a1	a1	NOUN
ma-85	199	7	)	)	PUNCT
ma-85	199	8	and	and	CCONJ
ma-85	199	9	(	(	PUNCT
ma-85	199	10	1.1	1.1	NUM
ma-85	199	11	)	)	PUNCT
ma-85	199	12	that	that	PRON
ma-85	199	13	‖y0	‖y0	VERB
ma-85	199	14	−	−	PROPN
ma-85	199	15	x0‖	x0‖	PROPN
ma-85	200	1	=	=	PUNCT
ma-85	201	1	‖f	‖f	DET
ma-85	201	2	′(x0)−1f	′(x0)−1f	NOUN
ma-85	201	3	(	(	PUNCT
ma-85	201	4	x0	x0	PROPN
ma-85	201	5	)	)	PUNCT
ma-85	201	6	≤	≤	NUM
ma-85	201	7	η	η	X
ma-85	201	8	=	=	PROPN
ma-85	201	9	≤	≤	PROPN
ma-85	201	10	s0	s0	NOUN
ma-85	201	11	−	−	PROPN
ma-85	201	12	t0	t0	PROPN
ma-85	201	13	=	=	SYM
ma-85	201	14	η	η	PROPN
ma-85	201	15	≤	≤	PROPN
ma-85	201	16	t	t	PROPN
ma-85	201	17	,	,	PUNCT
ma-85	201	18	(	(	PUNCT
ma-85	201	19	3.5	3.5	NUM
ma-85	201	20	)	)	PUNCT
ma-85	202	1	so	so	ADV
ma-85	202	2	y0	y0	PROPN
ma-85	202	3	∈	∈	PROPN
ma-85	202	4	u(x0	u(x0	NOUN
ma-85	202	5	,	,	PUNCT
ma-85	202	6	t	t	PROPN
ma-85	202	7	∗	∗	NOUN
ma-85	202	8	)	)	PUNCT
ma-85	202	9	and	and	CCONJ
ma-85	202	10	(	(	PUNCT
ma-85	202	11	3.3	3.3	NUM
ma-85	202	12	)	)	PUNCT
ma-85	202	13	hold	hold	VERB
ma-85	202	14	for	for	ADP
ma-85	202	15	k	k	PROPN
ma-85	202	16	=	=	SYM
ma-85	202	17	0	0	X
ma-85	202	18	.	.	PUNCT
ma-85	203	1	let	let	VERB
ma-85	203	2	z	z	NOUN
ma-85	203	3	∈	∈	PROPN
ma-85	203	4	u(x0	u(x0	NOUN
ma-85	203	5	,	,	PUNCT
ma-85	203	6	t	t	PROPN
ma-85	203	7	∗	∗	NOUN
ma-85	203	8	)	)	PUNCT
ma-85	203	9	.	.	PUNCT
ma-85	204	1	in	in	ADP
ma-85	204	2	view	view	NOUN
ma-85	204	3	of	of	ADP
ma-85	204	4	(	(	PUNCT
ma-85	204	5	a2	a2	PROPN
ma-85	204	6	)	)	PUNCT
ma-85	204	7	,	,	PUNCT
ma-85	204	8	one	one	PRON
ma-85	204	9	has	have	VERB
ma-85	204	10	‖f	‖f	ADP
ma-85	204	11	′(x0)−1(f	′(x0)−1(f	VERB
ma-85	204	12	′(z)−	′(z)−	PROPN
ma-85	204	13	f	f	PROPN
ma-85	204	14	′(x0	′(x0	NOUN
ma-85	204	15	)	)	PUNCT
ma-85	204	16	)	)	PUNCT
ma-85	205	1	≤	≤	NUM
ma-85	205	2	k0‖z	k0‖z	NOUN
ma-85	205	3	−	−	PROPN
ma-85	205	4	x0‖	x0‖	PROPN
ma-85	205	5	≤	≤	PROPN
ma-85	205	6	k0t∗	k0t∗	VERB
ma-85	205	7	<	<	X
ma-85	205	8	1	1	NUM
ma-85	205	9	,	,	PUNCT
ma-85	205	10	so	so	SCONJ
ma-85	205	11	f	f	PROPN
ma-85	205	12	′(z)−1	′(z)−1	PROPN
ma-85	205	13	∈	∈	PROPN
ma-85	205	14	l(e1	l(e1	ADV
ma-85	205	15	,	,	PUNCT
ma-85	205	16	e	e	NOUN
ma-85	205	17	)	)	PUNCT
ma-85	205	18	and	and	CCONJ
ma-85	205	19	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	PART
ma-85	205	20	eur	eur	PROPN
ma-85	205	21	.	.	PUNCT
ma-85	206	1	j.	j.	PROPN
ma-85	206	2	math	math	PROPN
ma-85	206	3	.	.	PUNCT
ma-85	207	1	anal	anal	PROPN
ma-85	207	2	.	.	PUNCT
ma-85	208	1	10.28924	10.28924	NUM
ma-85	208	2	/	/	SYM
ma-85	208	3	ada	ada	PROPN
ma-85	208	4	/	/	SYM
ma-85	208	5	ma.2.13	ma.2.13	PROPN
ma-85	208	6	8	8	NUM
ma-85	208	7	‖f	‖f	ADP
ma-85	208	8	′(z)−1f	′(z)−1f	NOUN
ma-85	208	9	′(x0)‖	′(x0)‖	X
ma-85	208	10	≤	≤	ADV
ma-85	208	11	1	1	NUM
ma-85	208	12	1−k0‖z	1−k0‖z	NUM
ma-85	208	13	−	−	PROPN
ma-85	208	14	x0‖	x0‖	PROPN
ma-85	208	15	.	.	PUNCT
ma-85	209	1	(	(	PUNCT
ma-85	209	2	3.6	3.6	NUM
ma-85	209	3	)	)	PUNCT
ma-85	209	4	by	by	ADP
ma-85	209	5	a	a	DET
ma-85	209	6	result	result	NOUN
ma-85	209	7	due	due	ADP
ma-85	209	8	to	to	ADP
ma-85	209	9	banach	banach	NOUN
ma-85	209	10	[	[	X
ma-85	209	11	14	14	NUM
ma-85	209	12	]	]	PUNCT
ma-85	209	13	on	on	ADP
ma-85	209	14	linear	linear	PROPN
ma-85	209	15	invertible	invertible	ADJ
ma-85	209	16	operators	operator	NOUN
ma-85	209	17	.	.	PUNCT
ma-85	210	1	operator	operator	NOUN
ma-85	210	2	mk	mk	PROPN
ma-85	210	3	can	can	AUX
ma-85	210	4	be	be	AUX
ma-85	210	5	shown	show	VERB
ma-85	210	6	to	to	AUX
ma-85	210	7	beinvertible	beinvertible	ADJ
ma-85	210	8	.	.	PUNCT
ma-85	211	1	indeed	indeed	ADV
ma-85	211	2	,	,	PUNCT
ma-85	211	3	by	by	ADP
ma-85	211	4	the	the	DET
ma-85	211	5	definition	definition	NOUN
ma-85	211	6	of	of	ADP
ma-85	211	7	operator	operator	NOUN
ma-85	211	8	mk	mk	NOUN
ma-85	211	9	,	,	PUNCT
ma-85	211	10	(	(	PUNCT
ma-85	211	11	2.2	2.2	NUM
ma-85	211	12	)	)	PUNCT
ma-85	211	13	and	and	CCONJ
ma-85	211	14	(	(	PUNCT
ma-85	211	15	a2	a2	PROPN
ma-85	211	16	)	)	PUNCT
ma-85	211	17	we	we	PRON
ma-85	211	18	obtain	obtain	VERB
ma-85	211	19	‖(3f	‖(3f	ADP
ma-85	211	20	′(x0))−1(mk	′(x0))−1(mk	PROPN
ma-85	211	21	−	−	PROPN
ma-85	211	22	3f	3f	PROPN
ma-85	211	23	′(x0))‖	′(x0))‖	NUM
ma-85	211	24	≤	≤	NUM
ma-85	211	25	1	1	NUM
ma-85	211	26	3	3	NUM
ma-85	211	27	[	[	X
ma-85	211	28	2‖f	2‖f	NUM
ma-85	211	29	′(x0)−1	′(x0)−1	NOUN
ma-85	211	30	(	(	PUNCT
ma-85	211	31	f	f	NOUN
ma-85	211	32	′	′	NOUN
ma-85	212	1	(	(	PUNCT
ma-85	212	2	3xk	3xk	ADJ
ma-85	212	3	+	+	CCONJ
ma-85	212	4	yk	yk	PROPN
ma-85	212	5	4	4	NUM
ma-85	212	6	)	)	PUNCT
ma-85	212	7	−	−	PROPN
ma-85	212	8	f	f	NOUN
ma-85	212	9	′(x0))‖	′(x0))‖	NUM
ma-85	212	10	+	+	PROPN
ma-85	212	11	‖f	‖f	ADJ
ma-85	212	12	′(x0)−1	′(x0)−1	NOUN
ma-85	212	13	(	(	PUNCT
ma-85	212	14	f	f	NOUN
ma-85	212	15	′	′	NUM
ma-85	213	1	(	(	PUNCT
ma-85	213	2	xk	xk	PROPN
ma-85	213	3	+	+	CCONJ
ma-85	213	4	yk	yk	PROPN
ma-85	213	5	2	2	NUM
ma-85	213	6	)	)	PUNCT
ma-85	213	7	−	−	PROPN
ma-85	213	8	f	f	PROPN
ma-85	213	9	′(x0	′(x0	NOUN
ma-85	213	10	)	)	PUNCT
ma-85	213	11	)	)	PUNCT
ma-85	214	1	‖	‖	PROPN
ma-85	215	1	+2‖f	+2‖f	PROPN
ma-85	215	2	′(x0)−1	′(x0)−1	PROPN
ma-85	215	3	(	(	PUNCT
ma-85	215	4	f	f	PROPN
ma-85	215	5	′	′	NUM
ma-85	216	1	(	(	PUNCT
ma-85	216	2	xk	xk	PROPN
ma-85	216	3	+	+	CCONJ
ma-85	216	4	3yk	3yk	ADJ
ma-85	216	5	4	4	NUM
ma-85	216	6	)	)	PUNCT
ma-85	216	7	−	−	PROPN
ma-85	216	8	f	f	PROPN
ma-85	216	9	′(x0	′(x0	NOUN
ma-85	216	10	)	)	PUNCT
ma-85	216	11	)	)	PUNCT
ma-85	217	1	≤	≤	ADV
ma-85	217	2	1	1	NUM
ma-85	217	3	3	3	NUM
ma-85	217	4	(	(	PUNCT
ma-85	217	5	2k0‖	2k0‖	ADP
ma-85	217	6	3xk	3xk	ADJ
ma-85	217	7	+	+	CCONJ
ma-85	217	8	yk	yk	PROPN
ma-85	217	9	4	4	NUM
ma-85	217	10	−	−	NOUN
ma-85	217	11	x0‖+k0‖	x0‖+k0‖	X
ma-85	217	12	xk	xk	PROPN
ma-85	217	13	+	+	CCONJ
ma-85	217	14	yk	yk	PROPN
ma-85	217	15	2	2	NUM
ma-85	217	16	−	−	PROPN
ma-85	217	17	x0‖	x0‖	PROPN
ma-85	218	1	+2k0‖	+2k0‖	PROPN
ma-85	218	2	xk	xk	PROPN
ma-85	219	1	+	+	CCONJ
ma-85	219	2	3yk	3yk	ADJ
ma-85	219	3	4	4	NUM
ma-85	219	4	−	−	NOUN
ma-85	219	5	x0‖	x0‖	PROPN
ma-85	219	6	)	)	PUNCT
ma-85	219	7	≤	≤	NOUN
ma-85	219	8	1	1	NUM
ma-85	219	9	3	3	NUM
ma-85	219	10	(	(	PUNCT
ma-85	219	11	2k0	2k0	NUM
ma-85	219	12	3tk	3tk	NOUN
ma-85	219	13	+	+	CCONJ
ma-85	219	14	sk	sk	PRON
ma-85	219	15	4	4	NUM
ma-85	219	16	+	+	NOUN
ma-85	219	17	k0	k0	PROPN
ma-85	219	18	sk	sk	PROPN
ma-85	219	19	+	+	PROPN
ma-85	219	20	tk	tk	PROPN
ma-85	219	21	2	2	NUM
ma-85	219	22	+	+	NUM
ma-85	219	23	2k0	2k0	NUM
ma-85	219	24	tk	tk	NOUN
ma-85	220	1	+	+	CCONJ
ma-85	220	2	3sk	3sk	ADJ
ma-85	220	3	4	4	NUM
ma-85	220	4	)	)	PUNCT
ma-85	220	5	=	=	SYM
ma-85	221	1	5k0	5k0	NUM
ma-85	221	2	6	6	NUM
ma-85	221	3	(	(	PUNCT
ma-85	221	4	tk	tk	PROPN
ma-85	221	5	+	+	CCONJ
ma-85	221	6	sk	sk	PROPN
ma-85	221	7	)	)	PUNCT
ma-85	221	8	=	=	SYM
ma-85	221	9	pk	pk	NOUN
ma-85	221	10	<	<	X
ma-85	221	11	1	1	NUM
ma-85	221	12	,	,	PUNCT
ma-85	221	13	so	so	SCONJ
ma-85	221	14	mk	mk	PROPN
ma-85	221	15	is	be	AUX
ma-85	221	16	invertible	invertible	ADJ
ma-85	221	17	and	and	CCONJ
ma-85	221	18	‖m−1k	‖m−1k	VERB
ma-85	221	19	f	f	PROPN
ma-85	222	1	′(x0)‖	′(x0)‖	NOUN
ma-85	222	2	≤	≤	NUM
ma-85	222	3	1	1	NUM
ma-85	222	4	3(1−	3(1−	NUM
ma-85	222	5	pk	pk	NOUN
ma-85	222	6	)	)	PUNCT
ma-85	222	7	,	,	PUNCT
ma-85	222	8	(	(	PUNCT
ma-85	222	9	3.7	3.7	NUM
ma-85	222	10	)	)	PUNCT
ma-85	223	1	and	and	CCONJ
ma-85	223	2	xk+1	xk+1	NUM
ma-85	223	3	is	be	AUX
ma-85	223	4	well	well	ADV
ma-85	223	5	defined	define	VERB
ma-85	223	6	by	by	ADP
ma-85	223	7	the	the	DET
ma-85	223	8	second	second	ADJ
ma-85	223	9	substep	substep	NOUN
ma-85	223	10	of	of	ADP
ma-85	223	11	method	method	NOUN
ma-85	223	12	(	(	PUNCT
ma-85	223	13	1.1	1.1	NUM
ma-85	223	14	)	)	PUNCT
ma-85	223	15	.	.	PUNCT
ma-85	224	1	then	then	ADV
ma-85	224	2	,	,	PUNCT
ma-85	224	3	we	we	PRON
ma-85	224	4	can	can	AUX
ma-85	224	5	write	write	VERB
ma-85	224	6	by	by	ADP
ma-85	224	7	method(1.1	method(1.1	NOUN
ma-85	224	8	)	)	PUNCT
ma-85	224	9	that	that	SCONJ
ma-85	224	10	xk+1	xk+1	X
ma-85	225	1	=	=	SYM
ma-85	225	2	xk	xk	PROPN
ma-85	226	1	−	−	PROPN
ma-85	226	2	f	f	PROPN
ma-85	226	3	′(xk)−1f	′(xk)−1f	PROPN
ma-85	226	4	(	(	PUNCT
ma-85	226	5	xk	xk	PROPN
ma-85	226	6	)	)	PUNCT
ma-85	226	7	+	+	CCONJ
ma-85	226	8	(	(	PUNCT
ma-85	226	9	f	f	NOUN
ma-85	226	10	′(xk)−1	′(xk)−1	NOUN
ma-85	226	11	−	−	PROPN
ma-85	226	12	3m−1k	3m−1k	NUM
ma-85	226	13	)	)	PUNCT
ma-85	226	14	f	f	PROPN
ma-85	226	15	(	(	PUNCT
ma-85	226	16	xk	xk	PROPN
ma-85	226	17	)	)	PUNCT
ma-85	226	18	=	=	SYM
ma-85	226	19	yk	yk	PROPN
ma-85	226	20	−	−	NOUN
ma-85	226	21	1	1	NUM
ma-85	226	22	3	3	NUM
ma-85	226	23	f	f	PROPN
ma-85	226	24	′(xk)−1(mk	′(xk)−1(mk	PROPN
ma-85	226	25	−	−	PROPN
ma-85	226	26	3f	3f	PROPN
ma-85	226	27	′(xk))m−1k	′(xk))m−1k	NUM
ma-85	226	28	(	(	PUNCT
ma-85	226	29	xk+1	xk+1	NUM
ma-85	226	30	−	−	PROPN
ma-85	226	31	xk	xk	PROPN
ma-85	226	32	)	)	PUNCT
ma-85	226	33	.	.	PUNCT
ma-85	227	1	(	(	PUNCT
ma-85	227	2	3.8	3.8	NUM
ma-85	227	3	)	)	PUNCT
ma-85	227	4	we	we	PRON
ma-85	227	5	need	need	VERB
ma-85	227	6	the	the	DET
ma-85	227	7	estimate	estimate	NOUN
ma-85	227	8	,	,	PUNCT
ma-85	227	9	mk	mk	PROPN
ma-85	227	10	−	−	PROPN
ma-85	227	11	3f	3f	PROPN
ma-85	227	12	′(xk	′(xk	PROPN
ma-85	227	13	)	)	PUNCT
ma-85	228	1	=	=	SYM
ma-85	228	2	2f	2f	NUM
ma-85	228	3	′	′	NOUN
ma-85	229	1	(	(	PUNCT
ma-85	229	2	3xk	3xk	ADJ
ma-85	229	3	+	+	CCONJ
ma-85	229	4	yk	yk	PROPN
ma-85	229	5	4	4	NUM
ma-85	229	6	)	)	PUNCT
ma-85	229	7	−	−	PROPN
ma-85	230	1	f	f	NOUN
ma-85	230	2	′	′	NUM
ma-85	231	1	(	(	PUNCT
ma-85	231	2	xk	xk	PROPN
ma-85	231	3	+	+	CCONJ
ma-85	231	4	yk	yk	PROPN
ma-85	231	5	2	2	NUM
ma-85	231	6	)	)	PUNCT
ma-85	231	7	+2f	+2f	NUM
ma-85	231	8	′	′	NUM
ma-85	231	9	(	(	PUNCT
ma-85	231	10	xk	xk	PROPN
ma-85	232	1	+	+	CCONJ
ma-85	232	2	3yk	3yk	ADJ
ma-85	232	3	4	4	NUM
ma-85	232	4	)	)	PUNCT
ma-85	232	5	−	−	PROPN
ma-85	232	6	3f	3f	PROPN
ma-85	232	7	′(xk	′(xk	PROPN
ma-85	232	8	)	)	PUNCT
ma-85	232	9	=	=	PUNCT
ma-85	233	1	(	(	PUNCT
ma-85	233	2	f	f	NOUN
ma-85	233	3	′	′	NOUN
ma-85	234	1	(	(	PUNCT
ma-85	234	2	3xk	3xk	ADJ
ma-85	234	3	+	+	CCONJ
ma-85	234	4	yk	yk	PROPN
ma-85	234	5	4	4	NUM
ma-85	234	6	)	)	PUNCT
ma-85	234	7	−	−	PROPN
ma-85	235	1	f	f	NOUN
ma-85	235	2	′	′	NUM
ma-85	236	1	(	(	PUNCT
ma-85	236	2	xk	xk	PROPN
ma-85	236	3	+	+	CCONJ
ma-85	236	4	yk	yk	PROPN
ma-85	236	5	2	2	NUM
ma-85	236	6	)	)	PUNCT
ma-85	236	7	)	)	PUNCT
ma-85	237	1	+	+	CCONJ
ma-85	237	2	(	(	PUNCT
ma-85	237	3	f	f	X
ma-85	237	4	′	′	NOUN
ma-85	237	5	(	(	PUNCT
ma-85	237	6	3xk	3xk	ADJ
ma-85	237	7	+	+	CCONJ
ma-85	237	8	yk	yk	PROPN
ma-85	237	9	4	4	NUM
ma-85	237	10	)	)	PUNCT
ma-85	237	11	−	−	PROPN
ma-85	237	12	f	f	PROPN
ma-85	237	13	′(xk	′(xk	PROPN
ma-85	237	14	)	)	PUNCT
ma-85	237	15	)	)	PUNCT
ma-85	238	1	+	+	CCONJ
ma-85	238	2	2	2	NUM
ma-85	238	3	(	(	PUNCT
ma-85	238	4	f	f	NOUN
ma-85	238	5	′	′	NUM
ma-85	239	1	(	(	PUNCT
ma-85	239	2	xk	xk	PROPN
ma-85	239	3	+	+	CCONJ
ma-85	239	4	3yk	3yk	ADJ
ma-85	239	5	4	4	NUM
ma-85	239	6	)	)	PUNCT
ma-85	239	7	−	−	PROPN
ma-85	239	8	f	f	PROPN
ma-85	239	9	′(xk	′(xk	PROPN
ma-85	239	10	)	)	PUNCT
ma-85	239	11	)	)	PUNCT
ma-85	239	12	,	,	PUNCT
ma-85	239	13	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	X
ma-85	239	14	eur	eur	PROPN
ma-85	239	15	.	.	PUNCT
ma-85	240	1	j.	j.	PROPN
ma-85	240	2	math	math	PROPN
ma-85	240	3	.	.	PUNCT
ma-85	241	1	anal	anal	PROPN
ma-85	241	2	.	.	PUNCT
ma-85	242	1	10.28924	10.28924	NUM
ma-85	242	2	/	/	SYM
ma-85	242	3	ada	ada	PROPN
ma-85	242	4	/	/	SYM
ma-85	242	5	ma.2.13	ma.2.13	PROPN
ma-85	242	6	9so	9so	NOUN
ma-85	242	7	by	by	ADP
ma-85	242	8	(	(	PUNCT
ma-85	242	9	a3	a3	NOUN
ma-85	242	10	)	)	PUNCT
ma-85	242	11	‖f	‖f	PRON
ma-85	242	12	′(x0)−1(mk	′(x0)−1(mk	NOUN
ma-85	242	13	−	−	PROPN
ma-85	242	14	3f	3f	PROPN
ma-85	242	15	′(xk))‖	′(xk))‖	VERB
ma-85	242	16	≤	≤	NUM
ma-85	242	17	k‖	k‖	X
ma-85	242	18	3xk	3xk	PROPN
ma-85	243	1	+	+	CCONJ
ma-85	243	2	yk	yk	PROPN
ma-85	243	3	4	4	NUM
ma-85	243	4	−	−	NOUN
ma-85	243	5	2xk	2xk	NOUN
ma-85	244	1	+	+	CCONJ
ma-85	244	2	2yk	2yk	ADJ
ma-85	244	3	4	4	NUM
ma-85	244	4	‖	‖	ADJ
ma-85	244	5	k‖	k‖	X
ma-85	244	6	3xk	3xk	PROPN
ma-85	245	1	+	+	CCONJ
ma-85	245	2	yk	yk	PROPN
ma-85	245	3	4	4	NUM
ma-85	245	4	−	−	NOUN
ma-85	245	5	4xk	4xk	ADJ
ma-85	245	6	4	4	NUM
ma-85	245	7	‖+	‖+	NUM
ma-85	245	8	2k‖	2k‖	NUM
ma-85	245	9	xk	xk	NOUN
ma-85	246	1	+	+	CCONJ
ma-85	246	2	3yk	3yk	ADJ
ma-85	246	3	4	4	NUM
ma-85	246	4	−	−	NOUN
ma-85	246	5	4xk	4xk	ADJ
ma-85	246	6	4	4	NUM
ma-85	246	7	‖	‖	PROPN
ma-85	246	8	=	=	NOUN
ma-85	246	9	2k‖yk	2k‖yk	NUM
ma-85	246	10	−	−	NOUN
ma-85	247	1	xk‖	xk‖	PROPN
ma-85	247	2	≤	≤	PROPN
ma-85	247	3	2k(sk	2k(sk	NUM
ma-85	247	4	−	−	NOUN
ma-85	247	5	tk	tk	PROPN
ma-85	247	6	)	)	PUNCT
ma-85	247	7	.	.	PUNCT
ma-85	248	1	(	(	PUNCT
ma-85	248	2	3.9	3.9	NUM
ma-85	248	3	)	)	PUNCT
ma-85	248	4	using	use	VERB
ma-85	248	5	(	(	PUNCT
ma-85	248	6	1.1	1.1	NUM
ma-85	248	7	)	)	PUNCT
ma-85	248	8	,	,	PUNCT
ma-85	248	9	(	(	PUNCT
ma-85	248	10	3.6	3.6	NUM
ma-85	248	11	)	)	PUNCT
ma-85	248	12	(	(	PUNCT
ma-85	248	13	for	for	ADP
ma-85	248	14	z	z	NOUN
ma-85	248	15	=	=	SYM
ma-85	248	16	xk	xk	PROPN
ma-85	248	17	)	)	PUNCT
ma-85	248	18	and	and	CCONJ
ma-85	248	19	(	(	PUNCT
ma-85	248	20	3.7)-(3.9	3.7)-(3.9	NUM
ma-85	248	21	)	)	PUNCT
ma-85	248	22	‖xk+1	‖xk+1	VERB
ma-85	248	23	−	−	NUM
ma-85	248	24	yk‖	yk‖	NOUN
ma-85	248	25	≤	≤	NOUN
ma-85	248	26	2k(sk	2k(sk	NUM
ma-85	248	27	−	−	NOUN
ma-85	248	28	tk)(tk+1	tk)(tk+1	NOUN
ma-85	248	29	−	−	PROPN
ma-85	248	30	tk	tk	PROPN
ma-85	248	31	)	)	PUNCT
ma-85	248	32	9(1−k0tk)(1−	9(1−k0tk)(1−	PROPN
ma-85	248	33	pk	pk	NOUN
ma-85	248	34	)	)	PUNCT
ma-85	248	35	=	=	SYM
ma-85	248	36	tk+1	tk+1	NUM
ma-85	248	37	−	−	NOUN
ma-85	248	38	sk	sk	INTJ
ma-85	248	39	.	.	PUNCT
ma-85	249	1	(	(	PUNCT
ma-85	249	2	3.10	3.10	NUM
ma-85	249	3	)	)	PUNCT
ma-85	249	4	we	we	PRON
ma-85	249	5	also	also	ADV
ma-85	249	6	have	have	VERB
ma-85	249	7	‖xk+1	‖xk+1	VERB
ma-85	249	8	−	−	PROPN
ma-85	249	9	x0‖	x0‖	PROPN
ma-85	249	10	≤	≤	PROPN
ma-85	249	11	‖xk+1	‖xk+1	VERB
ma-85	250	1	−	−	PROPN
ma-85	250	2	yk‖+	yk‖+	PROPN
ma-85	250	3	‖yk	‖yk	ADP
ma-85	250	4	−	−	PROPN
ma-85	250	5	x0‖	x0‖	PROPN
ma-85	250	6	≤	≤	PROPN
ma-85	250	7	tk+1	tk+1	NUM
ma-85	250	8	−	−	PROPN
ma-85	250	9	sk	sk	NOUN
ma-85	250	10	+	+	CCONJ
ma-85	250	11	sk	sk	PROPN
ma-85	250	12	−	−	PROPN
ma-85	250	13	t0	t0	PROPN
ma-85	250	14	=	=	PUNCT
ma-85	250	15	tk+1	tk+1	PROPN
ma-85	250	16	≤	≤	NUM
ma-85	250	17	t∗	t∗	NOUN
ma-85	250	18	,	,	PUNCT
ma-85	250	19	(	(	PUNCT
ma-85	250	20	3.11	3.11	NUM
ma-85	250	21	)	)	PUNCT
ma-85	251	1	so	so	ADV
ma-85	251	2	xk+1	xk+1	PROPN
ma-85	251	3	∈	∈	PROPN
ma-85	251	4	u(x0	u(x0	NOUN
ma-85	251	5	,	,	PUNCT
ma-85	251	6	t	t	PROPN
ma-85	251	7	∗	∗	NOUN
ma-85	251	8	)	)	PUNCT
ma-85	251	9	.	.	PUNCT
ma-85	252	1	we	we	PRON
ma-85	252	2	can	can	AUX
ma-85	252	3	write	write	VERB
ma-85	252	4	by	by	ADP
ma-85	252	5	method	method	NOUN
ma-85	252	6	(	(	PUNCT
ma-85	252	7	1.1	1.1	NUM
ma-85	252	8	)	)	PUNCT
ma-85	252	9	f	f	NOUN
ma-85	252	10	(	(	PUNCT
ma-85	252	11	xk+1	xk+1	X
ma-85	252	12	)	)	PUNCT
ma-85	252	13	=	=	SYM
ma-85	252	14	f	f	X
ma-85	252	15	(	(	PUNCT
ma-85	252	16	xk+1)−	xk+1)−	PROPN
ma-85	252	17	f	f	PROPN
ma-85	252	18	(	(	PUNCT
ma-85	252	19	xk)−	xk)−	PROPN
ma-85	252	20	1	1	NUM
ma-85	252	21	3	3	NUM
ma-85	252	22	mk(xk+1	mk(xk+1	NOUN
ma-85	252	23	−	−	NOUN
ma-85	252	24	xk	xk	NOUN
ma-85	252	25	)	)	PUNCT
ma-85	252	26	=	=	SYM
ma-85	253	1	∫	∫	PROPN
ma-85	253	2	1	1	NUM
ma-85	253	3	0	0	NUM
ma-85	254	1	(	(	PUNCT
ma-85	254	2	f	f	PROPN
ma-85	254	3	′(xk	′(xk	PROPN
ma-85	254	4	+	+	CCONJ
ma-85	254	5	θ(xk+1	θ(xk+1	VERB
ma-85	254	6	−	−	PROPN
ma-85	254	7	xk))dθ	xk))dθ	PROPN
ma-85	254	8	−	−	NOUN
ma-85	254	9	1	1	NUM
ma-85	254	10	3	3	NUM
ma-85	254	11	mk)(xk+1	mk)(xk+1	NOUN
ma-85	254	12	−	−	PROPN
ma-85	254	13	xk	xk	PROPN
ma-85	254	14	)	)	PUNCT
ma-85	254	15	.	.	PUNCT
ma-85	255	1	(	(	PUNCT
ma-85	255	2	3.12	3.12	NUM
ma-85	255	3	)	)	PUNCT
ma-85	255	4	one	one	PRON
ma-85	255	5	can	can	AUX
ma-85	255	6	obtain	obtain	VERB
ma-85	255	7	the	the	DET
ma-85	255	8	estimate∫	estimate∫	ADJ
ma-85	255	9	1	1	NUM
ma-85	255	10	0	0	NUM
ma-85	255	11	(	(	PUNCT
ma-85	255	12	f	f	PROPN
ma-85	255	13	′(xk	′(xk	PROPN
ma-85	255	14	+	+	CCONJ
ma-85	255	15	θ(xk+1	θ(xk+1	VERB
ma-85	255	16	−	−	PROPN
ma-85	255	17	xk))dθ	xk))dθ	PROPN
ma-85	255	18	−	−	NOUN
ma-85	255	19	2	2	NUM
ma-85	255	20	3	3	NUM
ma-85	255	21	f	f	NOUN
ma-85	255	22	′	′	NOUN
ma-85	256	1	(	(	PUNCT
ma-85	256	2	3xk	3xk	ADJ
ma-85	256	3	+	+	CCONJ
ma-85	256	4	yk	yk	PROPN
ma-85	256	5	4	4	NUM
ma-85	256	6	)	)	PUNCT
ma-85	257	1	+	+	CCONJ
ma-85	257	2	1	1	NUM
ma-85	257	3	3	3	NUM
ma-85	257	4	f	f	NOUN
ma-85	257	5	′	′	NUM
ma-85	258	1	(	(	PUNCT
ma-85	258	2	xk	xk	PROPN
ma-85	258	3	+	+	CCONJ
ma-85	258	4	yk	yk	PROPN
ma-85	258	5	2	2	NUM
ma-85	258	6	)	)	PUNCT
ma-85	258	7	−	−	NOUN
ma-85	259	1	2	2	NUM
ma-85	259	2	3	3	NUM
ma-85	259	3	f	f	NOUN
ma-85	259	4	′	′	NUM
ma-85	260	1	(	(	PUNCT
ma-85	260	2	xk	xk	PROPN
ma-85	261	1	+	+	CCONJ
ma-85	261	2	4yk	4yk	NOUN
ma-85	261	3	4	4	NUM
ma-85	261	4	)	)	PUNCT
ma-85	261	5	=	=	SYM
ma-85	262	1	∫	∫	PROPN
ma-85	262	2	1	1	NUM
ma-85	262	3	0	0	X
ma-85	262	4	f	f	PROPN
ma-85	262	5	′(xk	′(xk	PROPN
ma-85	262	6	+	+	CCONJ
ma-85	262	7	θ(xk+1	θ(xk+1	VERB
ma-85	262	8	−	−	PROPN
ma-85	262	9	xk))dθ	xk))dθ	PROPN
ma-85	262	10	−	−	PROPN
ma-85	262	11	f	f	PROPN
ma-85	262	12	′(xk	′(xk	PROPN
ma-85	262	13	)	)	PUNCT
ma-85	262	14	)	)	PUNCT
ma-85	263	1	+	+	CCONJ
ma-85	263	2	2	2	NUM
ma-85	263	3	3	3	NUM
ma-85	263	4	(	(	PUNCT
ma-85	263	5	f	f	PROPN
ma-85	263	6	′(xk)−	′(xk)−	PROPN
ma-85	263	7	f	f	NOUN
ma-85	263	8	′	′	NOUN
ma-85	263	9	(	(	PUNCT
ma-85	263	10	3xk	3xk	ADJ
ma-85	263	11	+	+	CCONJ
ma-85	263	12	yk	yk	PROPN
ma-85	263	13	4	4	NUM
ma-85	263	14	)	)	PUNCT
ma-85	263	15	)	)	PUNCT
ma-85	264	1	+	+	CCONJ
ma-85	264	2	1	1	NUM
ma-85	264	3	3	3	NUM
ma-85	264	4	(	(	PUNCT
ma-85	264	5	f	f	PROPN
ma-85	264	6	′(xk)−	′(xk)−	PROPN
ma-85	264	7	f	f	NOUN
ma-85	264	8	′	′	NUM
ma-85	264	9	(	(	PUNCT
ma-85	264	10	xk	xk	PROPN
ma-85	264	11	+	+	CCONJ
ma-85	264	12	3yk	3yk	ADJ
ma-85	264	13	4	4	NUM
ma-85	264	14	)	)	PUNCT
ma-85	264	15	+	+	CCONJ
ma-85	264	16	1	1	NUM
ma-85	264	17	3	3	NUM
ma-85	264	18	(	(	PUNCT
ma-85	264	19	f	f	NOUN
ma-85	264	20	′	′	NUM
ma-85	265	1	(	(	PUNCT
ma-85	265	2	xk	xk	PROPN
ma-85	265	3	+	+	CCONJ
ma-85	265	4	yk	yk	PROPN
ma-85	265	5	2	2	NUM
ma-85	265	6	)	)	PUNCT
ma-85	265	7	−	−	PROPN
ma-85	266	1	f	f	NOUN
ma-85	266	2	′	′	NUM
ma-85	267	1	(	(	PUNCT
ma-85	267	2	xk	xk	PROPN
ma-85	267	3	+	+	CCONJ
ma-85	267	4	3yk	3yk	ADJ
ma-85	267	5	4	4	NUM
ma-85	267	6	)	)	PUNCT
ma-85	267	7	)	)	PUNCT
ma-85	267	8	,	,	PUNCT
ma-85	267	9	(	(	PUNCT
ma-85	267	10	3.13	3.13	NUM
ma-85	267	11	)	)	PUNCT
ma-85	267	12	so	so	SCONJ
ma-85	267	13	‖f	‖f	ADP
ma-85	267	14	′(x0)−1	′(x0)−1	NOUN
ma-85	267	15	∫	∫	PROPN
ma-85	267	16	1	1	NUM
ma-85	267	17	0	0	NUM
ma-85	267	18	(	(	PUNCT
ma-85	267	19	f	f	PROPN
ma-85	267	20	′(xk	′(xk	PROPN
ma-85	267	21	+	+	CCONJ
ma-85	267	22	θ(xk+1	θ(xk+1	AUX
ma-85	267	23	−	−	PROPN
ma-85	267	24	xk))dθ	xk))dθ	PROPN
ma-85	267	25	−	−	NOUN
ma-85	267	26	1	1	NUM
ma-85	267	27	3	3	NUM
ma-85	267	28	mk)‖	mk)‖	PROPN
ma-85	267	29	≤	≤	PUNCT
ma-85	268	1	k	k	PROPN
ma-85	269	1	[	[	PUNCT
ma-85	269	2	‖xk+1	‖xk+1	ADP
ma-85	269	3	−	−	PROPN
ma-85	269	4	xk‖	xk‖	PROPN
ma-85	269	5	2	2	NUM
ma-85	269	6	+	+	NUM
ma-85	269	7	‖yk	‖yk	NUM
ma-85	269	8	−	−	PROPN
ma-85	269	9	xk‖	xk‖	PROPN
ma-85	269	10	6	6	NUM
ma-85	269	11	+	+	SYM
ma-85	269	12	‖yk	‖yk	NUM
ma-85	269	13	−	−	PROPN
ma-85	269	14	xk‖	xk‖	PROPN
ma-85	269	15	4	4	NUM
ma-85	269	16	+	+	SYM
ma-85	269	17	‖yk	‖yk	NUM
ma-85	269	18	−	−	PROPN
ma-85	269	19	xk‖	xk‖	PROPN
ma-85	269	20	12	12	NUM
ma-85	269	21	]	]	PUNCT
ma-85	269	22	≤	≤	NUM
ma-85	270	1	k	k	NOUN
ma-85	270	2	(	(	PUNCT
ma-85	270	3	tk+1	tk+1	PROPN
ma-85	270	4	−	−	PROPN
ma-85	270	5	tk	tk	NOUN
ma-85	270	6	2	2	NUM
ma-85	270	7	+	+	CCONJ
ma-85	270	8	sk	sk	PROPN
ma-85	270	9	−	−	PROPN
ma-85	270	10	tk	tk	PROPN
ma-85	270	11	6	6	NUM
ma-85	270	12	+	+	CCONJ
ma-85	270	13	sk	sk	PROPN
ma-85	270	14	−	−	PROPN
ma-85	270	15	tk	tk	PROPN
ma-85	270	16	4	4	NUM
ma-85	270	17	+	+	CCONJ
ma-85	270	18	sk	sk	PROPN
ma-85	270	19	−	−	PROPN
ma-85	270	20	tk	tk	PROPN
ma-85	270	21	12	12	NUM
ma-85	270	22	)	)	PUNCT
ma-85	271	1	=	=	SYM
ma-85	271	2	k	k	X
ma-85	271	3	2	2	NUM
ma-85	271	4	(	(	PUNCT
ma-85	271	5	tk+1	tk+1	NUM
ma-85	271	6	−	−	PROPN
ma-85	271	7	tk	tk	PROPN
ma-85	272	1	+	+	CCONJ
ma-85	272	2	sk	sk	PROPN
ma-85	272	3	−	−	PROPN
ma-85	272	4	tk	tk	PROPN
ma-85	272	5	)	)	PUNCT
ma-85	272	6	.	.	PUNCT
ma-85	273	1	(	(	PUNCT
ma-85	273	2	3.14	3.14	NUM
ma-85	273	3	)	)	PUNCT
ma-85	273	4	it	it	PRON
ma-85	273	5	follows	follow	VERB
ma-85	273	6	from	from	ADP
ma-85	273	7	method	method	NOUN
ma-85	273	8	(	(	PUNCT
ma-85	273	9	1.1	1.1	NUM
ma-85	273	10	)	)	PUNCT
ma-85	273	11	,	,	PUNCT
ma-85	273	12	(	(	PUNCT
ma-85	273	13	3.6	3.6	NUM
ma-85	273	14	)	)	PUNCT
ma-85	273	15	(	(	PUNCT
ma-85	273	16	for	for	ADP
ma-85	273	17	z	z	NOUN
ma-85	273	18	=	=	SYM
ma-85	273	19	xk+1	xk+1	NUM
ma-85	273	20	)	)	PUNCT
ma-85	273	21	,	,	PUNCT
ma-85	273	22	(	(	PUNCT
ma-85	273	23	3.11	3.11	NUM
ma-85	273	24	)	)	PUNCT
ma-85	273	25	and	and	CCONJ
ma-85	273	26	(	(	PUNCT
ma-85	273	27	2.10	2.10	NUM
ma-85	273	28	)	)	PUNCT
ma-85	273	29	that	that	DET
ma-85	273	30	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	AUX
ma-85	273	31	eur	eur	PROPN
ma-85	273	32	.	.	PUNCT
ma-85	274	1	j.	j.	PROPN
ma-85	274	2	math	math	PROPN
ma-85	274	3	.	.	PUNCT
ma-85	275	1	anal	anal	PROPN
ma-85	275	2	.	.	PUNCT
ma-85	276	1	10.28924	10.28924	NUM
ma-85	276	2	/	/	SYM
ma-85	276	3	ada	ada	PROPN
ma-85	276	4	/	/	SYM
ma-85	276	5	ma.2.13	ma.2.13	PROPN
ma-85	276	6	10	10	NUM
ma-85	276	7	‖yk+1	‖yk+1	NOUN
ma-85	276	8	−	−	PROPN
ma-85	276	9	xk+1‖	xk+1‖	PROPN
ma-85	276	10	≤	≤	PROPN
ma-85	276	11	‖(f	‖(f	PROPN
ma-85	276	12	′(xk+1)−1f	′(xk+1)−1f	PROPN
ma-85	276	13	′(x0)f	′(x0)f	NOUN
ma-85	276	14	′(x0)−1f	′(x0)−1f	PROPN
ma-85	276	15	(	(	PUNCT
ma-85	276	16	xk+1)‖	xk+1)‖	NOUN
ma-85	276	17	≤	≤	PUNCT
ma-85	276	18	k(tk+1	k(tk+1	NOUN
ma-85	276	19	−	−	PROPN
ma-85	276	20	tk	tk	PROPN
ma-85	276	21	+	+	CCONJ
ma-85	276	22	sk	sk	PROPN
ma-85	276	23	−	−	PROPN
ma-85	276	24	tk)(tk+1	tk)(tk+1	NOUN
ma-85	276	25	−	−	PROPN
ma-85	276	26	tk	tk	PROPN
ma-85	276	27	)	)	PUNCT
ma-85	276	28	2(1−k0tk+1	2(1−k0tk+1	NUM
ma-85	276	29	)	)	PUNCT
ma-85	276	30	=	=	SYM
ma-85	276	31	sk+1	sk+1	NUM
ma-85	276	32	−	−	NOUN
ma-85	276	33	tk+1	tk+1	NOUN
ma-85	276	34	,	,	PUNCT
ma-85	276	35	(	(	PUNCT
ma-85	276	36	3.15	3.15	NUM
ma-85	276	37	)	)	PUNCT
ma-85	276	38	showing	show	VERB
ma-85	276	39	(	(	PUNCT
ma-85	276	40	3.3	3.3	NUM
ma-85	276	41	)	)	PUNCT
ma-85	276	42	.	.	PUNCT
ma-85	277	1	moreover	moreover	ADV
ma-85	277	2	,	,	PUNCT
ma-85	277	3	we	we	PRON
ma-85	277	4	get	get	VERB
ma-85	277	5	‖yk+1	‖yk+1	PUNCT
ma-85	277	6	−	−	PROPN
ma-85	277	7	x0‖	x0‖	PROPN
ma-85	277	8	≤	≤	PROPN
ma-85	277	9	‖yk+1	‖yk+1	VERB
ma-85	277	10	−	−	PROPN
ma-85	277	11	xk+1‖+	xk+1‖+	PRON
ma-85	277	12	‖xk+1	‖xk+1	VERB
ma-85	278	1	−	−	PROPN
ma-85	278	2	x0‖	x0‖	PROPN
ma-85	278	3	≤	≤	PROPN
ma-85	278	4	sk+1	sk+1	NUM
ma-85	278	5	−	−	NUM
ma-85	278	6	tk+1	tk+1	NUM
ma-85	279	1	+	+	CCONJ
ma-85	279	2	tk+1	tk+1	NUM
ma-85	279	3	−	−	PROPN
ma-85	279	4	t0	t0	NOUN
ma-85	279	5	=	=	SYM
ma-85	279	6	sk+1	sk+1	VERB
ma-85	279	7	≤	≤	NUM
ma-85	279	8	t∗	t∗	NOUN
ma-85	279	9	,	,	PUNCT
ma-85	279	10	(	(	PUNCT
ma-85	279	11	3.16	3.16	NUM
ma-85	279	12	)	)	PUNCT
ma-85	279	13	so	so	SCONJ
ma-85	279	14	yk+1	yk+1	PRON
ma-85	279	15	∈	∈	PROPN
ma-85	279	16	u(x0	u(x0	NOUN
ma-85	279	17	,	,	PUNCT
ma-85	279	18	t	t	PROPN
ma-85	279	19	∗	∗	NOUN
ma-85	279	20	)	)	PUNCT
ma-85	279	21	.	.	PUNCT
ma-85	280	1	the	the	DET
ma-85	280	2	induction	induction	NOUN
ma-85	280	3	for	for	ADP
ma-85	280	4	(	(	PUNCT
ma-85	280	5	3.3	3.3	NUM
ma-85	280	6	)	)	PUNCT
ma-85	280	7	and	and	CCONJ
ma-85	280	8	(	(	PUNCT
ma-85	280	9	3.6	3.6	NUM
ma-85	280	10	)	)	PUNCT
ma-85	280	11	is	be	AUX
ma-85	280	12	completed	complete	VERB
ma-85	280	13	.	.	PUNCT
ma-85	281	1	it	it	PRON
ma-85	281	2	follows	follow	VERB
ma-85	281	3	from(3.3	from(3.3	NOUN
ma-85	281	4	)	)	PUNCT
ma-85	281	5	,	,	PUNCT
ma-85	281	6	(	(	PUNCT
ma-85	281	7	3.6	3.6	NUM
ma-85	281	8	)	)	PUNCT
ma-85	281	9	,	,	PUNCT
ma-85	281	10	(	(	PUNCT
ma-85	281	11	3.10)and	3.10)and	NUM
ma-85	281	12	(	(	PUNCT
ma-85	281	13	3.16	3.16	NUM
ma-85	281	14	)	)	PUNCT
ma-85	281	15	that	that	PRON
ma-85	281	16	sequence	sequence	NOUN
ma-85	281	17	{	{	PUNCT
ma-85	281	18	xn	xn	NOUN
ma-85	281	19	}	}	PUNCT
ma-85	281	20	is	be	AUX
ma-85	281	21	fundamental	fundamental	ADJ
ma-85	281	22	in	in	ADP
ma-85	281	23	banach	banach	NOUN
ma-85	281	24	space	space	NOUN
ma-85	281	25	e	e	NOUN
ma-85	281	26	,	,	PUNCT
ma-85	281	27	and	and	CCONJ
ma-85	281	28	as	as	ADP
ma-85	281	29	such	such	ADJ
ma-85	281	30	it	it	PRON
ma-85	281	31	converges	converge	VERB
ma-85	281	32	to	to	ADP
ma-85	281	33	x∗	x∗	PROPN
ma-85	281	34	∈	∈	PROPN
ma-85	281	35	u[x0	u[x0	NOUN
ma-85	281	36	,	,	PUNCT
ma-85	281	37	t	t	PROPN
ma-85	281	38	∗	∗	NOUN
ma-85	281	39	]	]	PUNCT
ma-85	281	40	.	.	PUNCT
ma-85	282	1	using	use	VERB
ma-85	282	2	(	(	PUNCT
ma-85	282	3	3.9	3.9	NUM
ma-85	282	4	)	)	PUNCT
ma-85	282	5	and	and	CCONJ
ma-85	282	6	letting	let	VERB
ma-85	282	7	k	k	X
ma-85	282	8	−→	−→	NOUN
ma-85	282	9	∞	∞	NUM
ma-85	282	10	in	in	ADP
ma-85	282	11	‖f	‖f	ADJ
ma-85	282	12	′(x0)−1f	′(x0)−1f	NOUN
ma-85	282	13	(	(	PUNCT
ma-85	282	14	xk+1)‖	xk+1)‖	NOUN
ma-85	282	15	≤	≤	X
ma-85	283	1	k	k	X
ma-85	283	2	2	2	NUM
ma-85	283	3	(	(	PUNCT
ma-85	283	4	tk+1	tk+1	NUM
ma-85	283	5	−	−	PROPN
ma-85	283	6	tk	tk	PROPN
ma-85	284	1	+	+	CCONJ
ma-85	284	2	sk	sk	INTJ
ma-85	284	3	−	−	PROPN
ma-85	284	4	tk),we	tk),we	PROPN
ma-85	284	5	obtain	obtain	VERB
ma-85	284	6	f	f	PROPN
ma-85	284	7	(	(	PUNCT
ma-85	284	8	x∗	x∗	PROPN
ma-85	284	9	)	)	PUNCT
ma-85	284	10	=	=	SYM
ma-85	284	11	0	0	X
ma-85	284	12	.	.	X
ma-85	285	1	�	�	PROPN
ma-85	285	2	next	next	ADV
ma-85	285	3	,	,	PUNCT
ma-85	285	4	a	a	DET
ma-85	285	5	uniqueness	uniqueness	NOUN
ma-85	285	6	of	of	ADP
ma-85	285	7	the	the	DET
ma-85	285	8	solution	solution	NOUN
ma-85	285	9	x∗	x∗	PROPN
ma-85	285	10	result	result	VERB
ma-85	285	11	is	be	AUX
ma-85	285	12	presented	present	VERB
ma-85	285	13	.	.	PUNCT
ma-85	286	1	proposition	proposition	NOUN
ma-85	286	2	3.2	3.2	NUM
ma-85	286	3	.	.	PUNCT
ma-85	287	1	suppose	suppose	VERB
ma-85	287	2	:	:	PUNCT
ma-85	287	3	(	(	PUNCT
ma-85	287	4	1	1	X
ma-85	287	5	)	)	PUNCT
ma-85	287	6	the	the	DET
ma-85	287	7	element	element	NOUN
ma-85	287	8	x∗	x∗	PROPN
ma-85	287	9	∈	∈	PROPN
ma-85	287	10	u(x∗	u(x∗	PROPN
ma-85	287	11	,	,	PUNCT
ma-85	287	12	s	s	PART
ma-85	287	13	∗	∗	NOUN
ma-85	287	14	)	)	PUNCT
ma-85	287	15	is	be	AUX
ma-85	287	16	a	a	DET
ma-85	287	17	simple	simple	ADJ
ma-85	287	18	solution	solution	NOUN
ma-85	287	19	of	of	ADP
ma-85	287	20	(	(	PUNCT
ma-85	287	21	1.2	1.2	NUM
ma-85	287	22	)	)	PUNCT
ma-85	287	23	,	,	PUNCT
ma-85	287	24	and	and	CCONJ
ma-85	287	25	(	(	PUNCT
ma-85	287	26	a2	a2	NOUN
ma-85	287	27	)	)	PUNCT
ma-85	287	28	holds	hold	VERB
ma-85	287	29	.	.	PUNCT
ma-85	288	1	(	(	PUNCT
ma-85	288	2	2	2	X
ma-85	288	3	)	)	PUNCT
ma-85	288	4	there	there	PRON
ma-85	288	5	exists	exist	VERB
ma-85	288	6	δ	δ	PROPN
ma-85	288	7	≥	≥	PRON
ma-85	288	8	s∗	s∗	VERB
ma-85	288	9	so	so	SCONJ
ma-85	288	10	that	that	SCONJ
ma-85	288	11	k0(s	k0(s	PROPN
ma-85	288	12	∗	∗	VERB
ma-85	288	13	+	+	CCONJ
ma-85	288	14	δ	δ	NOUN
ma-85	288	15	)	)	PUNCT
ma-85	288	16	<	<	X
ma-85	289	1	2	2	X
ma-85	289	2	.	.	PUNCT
ma-85	289	3	(	(	PUNCT
ma-85	289	4	3.17	3.17	NUM
ma-85	289	5	)	)	PUNCT
ma-85	289	6	set	set	VERB
ma-85	289	7	d1	d1	NOUN
ma-85	289	8	=	=	PUNCT
ma-85	290	1	d	d	PROPN
ma-85	290	2	∩	∩	X
ma-85	290	3	u[x∗	u[x∗	PROPN
ma-85	290	4	,	,	PUNCT
ma-85	290	5	δ	δ	PROPN
ma-85	290	6	]	]	PUNCT
ma-85	290	7	.	.	PUNCT
ma-85	291	1	then	then	ADV
ma-85	291	2	,	,	PUNCT
ma-85	291	3	x∗	x∗	PROPN
ma-85	291	4	is	be	AUX
ma-85	291	5	the	the	DET
ma-85	291	6	unique	unique	ADJ
ma-85	291	7	solution	solution	NOUN
ma-85	291	8	of	of	ADP
ma-85	291	9	equation	equation	NOUN
ma-85	291	10	(	(	PUNCT
ma-85	291	11	1.2	1.2	NUM
ma-85	291	12	)	)	PUNCT
ma-85	291	13	in	in	ADP
ma-85	291	14	the	the	DET
ma-85	291	15	domain	domain	NOUN
ma-85	291	16	d1	d1	NOUN
ma-85	291	17	.	.	PUNCT
ma-85	292	1	proof	proof	NOUN
ma-85	292	2	.	.	PUNCT
ma-85	293	1	let	let	VERB
ma-85	293	2	q	q	NOUN
ma-85	293	3	∈	∈	PROPN
ma-85	293	4	d1	d1	PROPN
ma-85	293	5	with	with	ADP
ma-85	293	6	f	f	PROPN
ma-85	293	7	(	(	PUNCT
ma-85	293	8	q	q	X
ma-85	293	9	)	)	PUNCT
ma-85	293	10	=	=	SYM
ma-85	294	1	0	0	X
ma-85	294	2	.	.	PUNCT
ma-85	294	3	define	define	VERB
ma-85	294	4	s	s	PART
ma-85	294	5	=	=	PUNCT
ma-85	294	6	∫	∫	PROPN
ma-85	294	7	1	1	NUM
ma-85	294	8	0	0	NUM
ma-85	294	9	f	f	NOUN
ma-85	294	10	′(q	′(q	NOUN
ma-85	294	11	+	+	CCONJ
ma-85	294	12	θ(x∗	θ(x∗	NOUN
ma-85	294	13	−	−	NOUN
ma-85	294	14	q))dθ	q))dθ	NOUN
ma-85	294	15	.	.	PUNCT
ma-85	295	1	using	use	VERB
ma-85	295	2	(	(	PUNCT
ma-85	295	3	h2	h2	NOUN
ma-85	295	4	)	)	PUNCT
ma-85	295	5	and	and	CCONJ
ma-85	295	6	(	(	PUNCT
ma-85	295	7	3.17)one	3.17)one	NOUN
ma-85	295	8	obtains	obtain	VERB
ma-85	295	9	‖f	‖f	PUNCT
ma-85	295	10	′(x0)−1(s	′(x0)−1(s	PUNCT
ma-85	295	11	−	−	PROPN
ma-85	295	12	f	f	SYM
ma-85	295	13	′(x0))‖	′(x0))‖	NUM
ma-85	295	14	≤	≤	PROPN
ma-85	295	15	k0	k0	PROPN
ma-85	295	16	∫	∫	PROPN
ma-85	295	17	1	1	NUM
ma-85	295	18	0	0	NUM
ma-85	295	19	(	(	PUNCT
ma-85	295	20	(	(	PUNCT
ma-85	295	21	1−	1−	NUM
ma-85	295	22	θ)‖q	θ)‖q	NOUN
ma-85	295	23	−	−	PROPN
ma-85	295	24	x0‖+	x0‖+	SYM
ma-85	295	25	θ‖x∗	θ‖x∗	NOUN
ma-85	295	26	−	−	PROPN
ma-85	295	27	x0‖)dθ	x0‖)dθ	NOUN
ma-85	295	28	≤	≤	PROPN
ma-85	296	1	k0	k0	PROPN
ma-85	296	2	2	2	NUM
ma-85	296	3	(	(	PUNCT
ma-85	296	4	s∗	s∗	PROPN
ma-85	296	5	+	+	CCONJ
ma-85	296	6	δ	δ	X
ma-85	296	7	)	)	PUNCT
ma-85	296	8	<	<	X
ma-85	296	9	1	1	NUM
ma-85	296	10	,	,	PUNCT
ma-85	296	11	so	so	ADV
ma-85	296	12	q	q	NOUN
ma-85	296	13	=	=	SYM
ma-85	296	14	x∗	x∗	NOUN
ma-85	296	15	,	,	PUNCT
ma-85	296	16	follows	follow	VERB
ma-85	296	17	from	from	ADP
ma-85	296	18	the	the	DET
ma-85	296	19	invertability	invertability	NOUN
ma-85	296	20	of	of	ADP
ma-85	296	21	s	s	PRON
ma-85	296	22	and	and	CCONJ
ma-85	296	23	the	the	DET
ma-85	296	24	identity	identity	NOUN
ma-85	296	25	s(q−x∗	s(q−x∗	PROPN
ma-85	296	26	)	)	PUNCT
ma-85	297	1	=	=	SYM
ma-85	297	2	f	f	PROPN
ma-85	297	3	(	(	PUNCT
ma-85	297	4	q)−f	q)−f	X
ma-85	297	5	(	(	PUNCT
ma-85	297	6	x∗	x∗	PROPN
ma-85	297	7	)	)	PUNCT
ma-85	297	8	=	=	SYM
ma-85	297	9	0−0	0−0	X
ma-85	298	1	=	=	SYM
ma-85	298	2	0	0	X
ma-85	298	3	.	.	PUNCT
ma-85	298	4	�	�	PROPN
ma-85	298	5	remark	remark	VERB
ma-85	298	6	3.3	3.3	NUM
ma-85	298	7	.	.	PUNCT
ma-85	299	1	(	(	PUNCT
ma-85	299	2	i	i	NOUN
ma-85	299	3	)	)	PUNCT
ma-85	299	4	point	point	NOUN
ma-85	299	5	t	t	NOUN
ma-85	299	6	given	give	VERB
ma-85	299	7	in	in	ADP
ma-85	299	8	closed	closed	ADJ
ma-85	299	9	form	form	NOUN
ma-85	299	10	can	can	AUX
ma-85	299	11	repalce	repalce	VERB
ma-85	299	12	t∗	t∗	NOUN
ma-85	299	13	in	in	ADP
ma-85	299	14	theorem	theorem	PROPN
ma-85	299	15	3.1	3.1	NUM
ma-85	299	16	.	.	PUNCT
ma-85	300	1	(	(	PUNCT
ma-85	300	2	ii	ii	NOUN
ma-85	300	3	)	)	PUNCT
ma-85	300	4	we	we	PRON
ma-85	300	5	used	use	VERB
ma-85	300	6	majorizing	majorize	VERB
ma-85	300	7	sequence	sequence	NOUN
ma-85	300	8	{	{	PUNCT
ma-85	300	9	tn	tn	NOUN
ma-85	300	10	}	}	PUNCT
ma-85	300	11	given	give	VERB
ma-85	300	12	by	by	ADP
ma-85	300	13	(	(	PUNCT
ma-85	300	14	2.1	2.1	NUM
ma-85	300	15	)	)	PUNCT
ma-85	300	16	and	and	CCONJ
ma-85	300	17	lemma	lemma	PROPN
ma-85	300	18	2.2	2.2	NUM
ma-85	300	19	to	to	PART
ma-85	300	20	prove	prove	VERB
ma-85	300	21	theorem	theorem	ADJ
ma-85	300	22	3.1	3.1	NUM
ma-85	300	23	.	.	PUNCT
ma-85	301	1	but	but	CCONJ
ma-85	301	2	we	we	PRON
ma-85	301	3	can	can	AUX
ma-85	301	4	also	also	ADV
ma-85	301	5	use	use	VERB
ma-85	301	6	majorizing	majorize	VERB
ma-85	301	7	sequence	sequence	NOUN
ma-85	301	8	{	{	PUNCT
ma-85	301	9	tn	tn	NOUN
ma-85	301	10	}	}	PUNCT
ma-85	301	11	given	give	VERB
ma-85	301	12	by	by	ADP
ma-85	301	13	(	(	PUNCT
ma-85	301	14	2.22	2.22	NUM
ma-85	301	15	)	)	PUNCT
ma-85	301	16	and	and	CCONJ
ma-85	301	17	lemma	lemma	PROPN
ma-85	301	18	2.3	2.3	NUM
ma-85	301	19	to	to	PART
ma-85	301	20	arrive	arrive	VERB
ma-85	301	21	at	at	ADP
ma-85	301	22	the	the	DET
ma-85	301	23	conclusions	conclusion	NOUN
ma-85	301	24	of	of	ADP
ma-85	301	25	the	the	DET
ma-85	301	26	theorem	theorem	NOUN
ma-85	301	27	3.1	3.1	NUM
ma-85	301	28	.	.	PUNCT
ma-85	302	1	simply	simply	ADV
ma-85	302	2	notice	notice	VERB
ma-85	302	3	that	that	SCONJ
ma-85	302	4	in	in	ADP
ma-85	302	5	the	the	DET
ma-85	302	6	proof	proof	NOUN
ma-85	302	7	of	of	ADP
ma-85	302	8	this	this	DET
ma-85	302	9	theorem	theorem	NOUN
ma-85	302	10	we	we	PRON
ma-85	302	11	got	get	AUX
ma-85	302	12	using	use	VERB
ma-85	302	13	the	the	DET
ma-85	302	14	second	second	ADJ
ma-85	302	15	substep	substep	NOUN
ma-85	302	16	of	of	ADP
ma-85	302	17	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	PROPN
ma-85	302	18	eur	eur	PROPN
ma-85	302	19	.	.	PUNCT
ma-85	303	1	j.	j.	PROPN
ma-85	303	2	math	math	PROPN
ma-85	303	3	.	.	PUNCT
ma-85	304	1	anal	anal	PROPN
ma-85	304	2	.	.	PUNCT
ma-85	305	1	10.28924	10.28924	NUM
ma-85	305	2	/	/	SYM
ma-85	305	3	ada	ada	PROPN
ma-85	305	4	/	/	SYM
ma-85	305	5	ma.2.13	ma.2.13	PROPN
ma-85	305	6	11	11	NUM
ma-85	305	7	scheme	scheme	NOUN
ma-85	305	8	(	(	PUNCT
ma-85	305	9	1.1	1.1	NUM
ma-85	305	10	)	)	PUNCT
ma-85	305	11	,	,	PUNCT
ma-85	305	12	(	(	PUNCT
ma-85	305	13	3.8	3.8	NUM
ma-85	305	14	)	)	PUNCT
ma-85	305	15	and	and	CCONJ
ma-85	305	16	(	(	PUNCT
ma-85	305	17	3.9	3.9	NUM
ma-85	305	18	)	)	PUNCT
ma-85	305	19	estimate	estimate	NOUN
ma-85	305	20	(	(	PUNCT
ma-85	305	21	3.10	3.10	NUM
ma-85	305	22	)	)	PUNCT
ma-85	305	23	leading	lead	VERB
ma-85	305	24	to	to	ADP
ma-85	305	25	the	the	DET
ma-85	305	26	definition	definition	NOUN
ma-85	305	27	of	of	ADP
ma-85	305	28	the	the	DET
ma-85	305	29	first	first	ADJ
ma-85	305	30	substep	substep	NOUN
ma-85	305	31	of	of	ADP
ma-85	305	32	sequence	sequence	NOUN
ma-85	305	33	(	(	PUNCT
ma-85	305	34	2.1	2.1	NUM
ma-85	305	35	)	)	PUNCT
ma-85	305	36	.	.	PUNCT
ma-85	306	1	but	but	CCONJ
ma-85	306	2	we	we	PRON
ma-85	306	3	can	can	AUX
ma-85	306	4	use	use	VERB
ma-85	306	5	the	the	DET
ma-85	306	6	first	first	ADJ
ma-85	306	7	substep	substep	NOUN
ma-85	306	8	of	of	ADP
ma-85	306	9	scheme	scheme	NOUN
ma-85	306	10	(	(	PUNCT
ma-85	306	11	1.1	1.1	NUM
ma-85	306	12	)	)	PUNCT
ma-85	306	13	to	to	PART
ma-85	306	14	write	write	VERB
ma-85	306	15	instead	instead	ADV
ma-85	306	16	of	of	ADP
ma-85	306	17	(	(	PUNCT
ma-85	306	18	3.8	3.8	NUM
ma-85	306	19	)	)	PUNCT
ma-85	307	1	that	that	PRON
ma-85	307	2	xk+1	xk+1	VERB
ma-85	308	1	=	=	SYM
ma-85	308	2	yk	yk	PROPN
ma-85	308	3	−	−	PROPN
ma-85	309	1	f	f	PROPN
ma-85	309	2	′(xk)−1(mk	′(xk)−1(mk	PROPN
ma-85	309	3	−	−	PROPN
ma-85	309	4	3f	3f	PROPN
ma-85	309	5	′(xk))m−1k	′(xk))m−1k	PROPN
ma-85	310	1	f	f	X
ma-85	310	2	(	(	PUNCT
ma-85	310	3	xk)(yk	xk)(yk	PROPN
ma-85	310	4	−	−	PROPN
ma-85	310	5	xk	xk	NOUN
ma-85	310	6	)	)	PUNCT
ma-85	310	7	leading	lead	VERB
ma-85	310	8	to	to	ADP
ma-85	310	9	‖xk+1	‖xk+1	NOUN
ma-85	310	10	−	−	NUM
ma-85	310	11	yk‖	yk‖	NOUN
ma-85	310	12	≤	≤	NOUN
ma-85	310	13	2k(1	2k(1	NOUN
ma-85	311	1	+	+	ADP
ma-85	311	2	k0tk)(sk	k0tk)(sk	PROPN
ma-85	311	3	−	−	PROPN
ma-85	311	4	tk)2	tk)2	PROPN
ma-85	311	5	3(1−k0tk)(1−	3(1−k0tk)(1−	PROPN
ma-85	311	6	pk	pk	NOUN
ma-85	311	7	)	)	PUNCT
ma-85	311	8	=	=	SYM
ma-85	312	1	tk+1	tk+1	NUM
ma-85	312	2	−	−	NOUN
ma-85	312	3	sk	sk	INTJ
ma-85	312	4	,	,	PUNCT
ma-85	312	5	where	where	SCONJ
ma-85	312	6	,	,	PUNCT
ma-85	312	7	we	we	PRON
ma-85	312	8	also	also	ADV
ma-85	312	9	used	use	VERB
ma-85	312	10	‖f	‖f	ADJ
ma-85	312	11	′(x0)−1f	′(x0)−1f	NOUN
ma-85	312	12	(	(	PUNCT
ma-85	312	13	xk)‖	xk)‖	NOUN
ma-85	312	14	=	=	SYM
ma-85	312	15	‖f	‖f	ADP
ma-85	312	16	′(x0)−1((f	′(x0)−1((f	VERB
ma-85	312	17	′(xk)−	′(xk)−	PROPN
ma-85	312	18	f	f	X
ma-85	312	19	(	(	PUNCT
ma-85	312	20	x0	x0	PROPN
ma-85	312	21	)	)	PUNCT
ma-85	312	22	)	)	PUNCT
ma-85	313	1	+	+	CCONJ
ma-85	313	2	f	f	PROPN
ma-85	313	3	′(x0))‖	′(x0))‖	NUM
ma-85	313	4	≤	≤	NUM
ma-85	313	5	1	1	NUM
ma-85	314	1	+	+	NOUN
ma-85	314	2	k0‖xk	k0‖xk	PROPN
ma-85	314	3	−	−	PROPN
ma-85	314	4	x0‖	x0‖	PROPN
ma-85	314	5	≤	≤	NUM
ma-85	314	6	1	1	NUM
ma-85	314	7	+	+	NOUN
ma-85	314	8	k0tk	k0tk	X
ma-85	314	9	.	.	PUNCT
ma-85	315	1	hence	hence	ADV
ma-85	315	2	,	,	PUNCT
ma-85	315	3	we	we	PRON
ma-85	315	4	arrive	arrive	VERB
ma-85	315	5	at	at	ADP
ma-85	315	6	the	the	DET
ma-85	315	7	second	second	ADJ
ma-85	315	8	semi	semi	ADJ
ma-85	315	9	-	-	ADJ
ma-85	315	10	local	local	ADJ
ma-85	315	11	convergence	convergence	NOUN
ma-85	315	12	rsult	rsult	NOUN
ma-85	315	13	for	for	ADP
ma-85	315	14	scheme	scheme	NOUN
ma-85	315	15	(	(	PUNCT
ma-85	315	16	1.1	1.1	NUM
ma-85	315	17	)	)	PUNCT
ma-85	315	18	.	.	PUNCT
ma-85	316	1	theorem	theorem	VERB
ma-85	316	2	3.4	3.4	NUM
ma-85	316	3	.	.	PUNCT
ma-85	317	1	suppose	suppose	VERB
ma-85	317	2	:	:	PUNCT
ma-85	317	3	conditions	condition	NOUN
ma-85	317	4	(	(	PUNCT
ma-85	317	5	a	a	X
ma-85	317	6	)	)	PUNCT
ma-85	317	7	hold	hold	NOUN
ma-85	317	8	with	with	ADP
ma-85	317	9	(	(	PUNCT
ma-85	317	10	a4	a4	NOUN
ma-85	317	11	)	)	PUNCT
ma-85	317	12	replaced	replace	VERB
ma-85	317	13	by	by	ADP
ma-85	317	14	(	(	PUNCT
ma-85	317	15	a4	a4	NOUN
ma-85	317	16	)	)	PUNCT
ma-85	317	17	’	'	PUNCT
ma-85	317	18	hypotheses	hypothesis	NOUN
ma-85	317	19	of	of	ADP
ma-85	317	20	lemma	lemma	PROPN
ma-85	317	21	2.3	2.3	NUM
ma-85	317	22	or	or	CCONJ
ma-85	317	23	lemma	lemma	PROPN
ma-85	317	24	2.4	2.4	NUM
ma-85	317	25	hold	hold	NOUN
ma-85	317	26	.	.	PUNCT
ma-85	318	1	then	then	ADV
ma-85	318	2	,	,	PUNCT
ma-85	318	3	the	the	DET
ma-85	318	4	conclusions	conclusion	NOUN
ma-85	318	5	of	of	ADP
ma-85	318	6	theorem	theorem	ADJ
ma-85	318	7	3.1	3.1	NUM
ma-85	318	8	hold	hold	NOUN
ma-85	318	9	with	with	ADP
ma-85	318	10	(	(	PUNCT
ma-85	318	11	2.22	2.22	NUM
ma-85	318	12	)	)	PUNCT
ma-85	318	13	replacing	replace	VERB
ma-85	318	14	(	(	PUNCT
ma-85	318	15	2.1	2.1	NUM
ma-85	318	16	)	)	PUNCT
ma-85	318	17	.	.	PUNCT
ma-85	319	1	in	in	ADP
ma-85	319	2	practice	practice	NOUN
ma-85	319	3	we	we	PRON
ma-85	319	4	shall	shall	AUX
ma-85	319	5	use	use	VERB
ma-85	319	6	the	the	DET
ma-85	319	7	theorem	theorem	NOUN
ma-85	319	8	providing	provide	VERB
ma-85	319	9	the	the	DET
ma-85	319	10	best	good	ADJ
ma-85	319	11	results	result	NOUN
ma-85	319	12	.	.	PUNCT
ma-85	320	1	4	4	X
ma-85	320	2	.	.	NOUN
ma-85	320	3	numerical	numerical	ADJ
ma-85	320	4	experiments	experiment	NOUN
ma-85	320	5	lipschitz	lipschitz	NOUN
ma-85	320	6	parameters	parameter	NOUN
ma-85	320	7	are	be	AUX
ma-85	320	8	determinded	determinded	ADJ
ma-85	320	9	and	and	CCONJ
ma-85	320	10	convegence	convegence	NOUN
ma-85	320	11	criteria	criterion	NOUN
ma-85	320	12	are	be	AUX
ma-85	320	13	tested	test	VERB
ma-85	320	14	for	for	ADP
ma-85	320	15	some	some	DET
ma-85	320	16	numericalexperiments	numericalexperiment	NOUN
ma-85	320	17	.	.	PUNCT
ma-85	321	1	example	example	NOUN
ma-85	321	2	4.1	4.1	NUM
ma-85	321	3	.	.	PUNCT
ma-85	322	1	define	define	VERB
ma-85	322	2	scalar	scalar	ADJ
ma-85	322	3	function	function	NOUN
ma-85	322	4	ζ(t	ζ(t	VERB
ma-85	322	5	)	)	PUNCT
ma-85	323	1	=	=	SYM
ma-85	323	2	ξ0	ξ0	PROPN
ma-85	323	3	t	t	NOUN
ma-85	323	4	+	+	CCONJ
ma-85	323	5	ξ1	ξ1	NOUN
ma-85	323	6	+	+	CCONJ
ma-85	323	7	ξ2	ξ2	ADJ
ma-85	323	8	sin	sin	NOUN
ma-85	323	9	ξ3	ξ3	PROPN
ma-85	323	10	t	t	PROPN
ma-85	323	11	,	,	PUNCT
ma-85	323	12	x0	x0	PROPN
ma-85	323	13	=	=	PUNCT
ma-85	323	14	0	0	PROPN
ma-85	323	15	,	,	PUNCT
ma-85	323	16	where	where	SCONJ
ma-85	323	17	ξj	ξj	NOUN
ma-85	323	18	,	,	PUNCT
ma-85	323	19	j	j	PROPN
ma-85	323	20	=	=	SYM
ma-85	323	21	0	0	NUM
ma-85	323	22	,	,	PUNCT
ma-85	323	23	1	1	NUM
ma-85	323	24	,	,	PUNCT
ma-85	323	25	2	2	NUM
ma-85	323	26	,	,	PUNCT
ma-85	323	27	3	3	NUM
ma-85	323	28	are	be	AUX
ma-85	323	29	parameters	parameter	NOUN
ma-85	323	30	.	.	PUNCT
ma-85	324	1	then	then	ADV
ma-85	324	2	,	,	PUNCT
ma-85	324	3	clearly	clearly	ADV
ma-85	324	4	for	for	ADP
ma-85	324	5	ξ3	ξ3	PROPN
ma-85	324	6	large	large	ADJ
ma-85	324	7	and	and	CCONJ
ma-85	324	8	ξ2	ξ2	ADJ
ma-85	324	9	small	small	ADJ
ma-85	324	10	,	,	PUNCT
ma-85	324	11	k0l1	k0l1	X
ma-85	324	12	can	can	AUX
ma-85	324	13	be	be	AUX
ma-85	324	14	small	small	ADJ
ma-85	324	15	(	(	PUNCT
ma-85	324	16	arbitrarily	arbitrarily	ADV
ma-85	324	17	)	)	PUNCT
ma-85	324	18	.	.	PUNCT
ma-85	325	1	in	in	ADP
ma-85	325	2	particular	particular	ADJ
ma-85	325	3	,	,	PUNCT
ma-85	325	4	notice	notice	VERB
ma-85	325	5	that	that	SCONJ
ma-85	325	6	k	k	PROPN
ma-85	325	7	l1	l1	PROPN
ma-85	325	8	−→	−→	PROPN
ma-85	325	9	0	0	NUM
ma-85	325	10	.	.	PUNCT
ma-85	325	11	example	example	NOUN
ma-85	326	1	4.2	4.2	NUM
ma-85	326	2	.	.	PUNCT
ma-85	327	1	let	let	VERB
ma-85	327	2	e	e	NOUN
ma-85	327	3	=	=	NOUN
ma-85	327	4	e1	e1	PROPN
ma-85	327	5	=	=	SYM
ma-85	327	6	c[0	c[0	PROPN
ma-85	327	7	,	,	PUNCT
ma-85	327	8	1	1	NUM
ma-85	327	9	]	]	PUNCT
ma-85	327	10	and	and	CCONJ
ma-85	327	11	d	d	PROPN
ma-85	327	12	=	=	SYM
ma-85	327	13	u[0	u[0	PROPN
ma-85	327	14	,	,	PUNCT
ma-85	327	15	1	1	NUM
ma-85	327	16	]	]	PUNCT
ma-85	327	17	.	.	PUNCT
ma-85	328	1	it	it	PRON
ma-85	328	2	is	be	AUX
ma-85	328	3	well	well	ADV
ma-85	328	4	known	know	VERB
ma-85	328	5	that	that	SCONJ
ma-85	328	6	the	the	DET
ma-85	328	7	boundary	boundary	ADJ
ma-85	328	8	value	value	NOUN
ma-85	328	9	problem	problem	NOUN
ma-85	328	10	[	[	X
ma-85	328	11	12	12	NUM
ma-85	328	12	]	]	PUNCT
ma-85	328	13	.	.	PUNCT
ma-85	329	1	ς(0	ς(0	PROPN
ma-85	329	2	)	)	PUNCT
ma-85	329	3	=	=	SYM
ma-85	329	4	0	0	NUM
ma-85	329	5	,	,	PUNCT
ma-85	329	6	ς(1	ς(1	NOUN
ma-85	329	7	)	)	PUNCT
ma-85	329	8	=	=	SYM
ma-85	329	9	1	1	NUM
ma-85	329	10	,	,	PUNCT
ma-85	329	11	ς	ς	PROPN
ma-85	329	12	′′	′′	PROPN
ma-85	329	13	=	=	PUNCT
ma-85	329	14	−ς	−ς	PROPN
ma-85	329	15	−	−	PROPN
ma-85	329	16	σς2	σς2	NOUN
ma-85	329	17	can	can	AUX
ma-85	329	18	be	be	AUX
ma-85	329	19	given	give	VERB
ma-85	329	20	as	as	ADP
ma-85	329	21	a	a	DET
ma-85	329	22	hammerstein	hammerstein	NOUN
ma-85	329	23	-	-	PUNCT
ma-85	329	24	like	like	ADJ
ma-85	329	25	nonlinear	nonlinear	ADJ
ma-85	329	26	integral	integral	ADJ
ma-85	329	27	equation	equation	NOUN
ma-85	329	28	ς(s	ς(s	PROPN
ma-85	329	29	)	)	PUNCT
ma-85	330	1	=	=	SYM
ma-85	330	2	s	s	PART
ma-85	331	1	+	+	NUM
ma-85	331	2	∫	∫	PROPN
ma-85	331	3	1	1	NUM
ma-85	331	4	0	0	NUM
ma-85	331	5	q(s	q(s	X
ma-85	331	6	,	,	PUNCT
ma-85	331	7	t)(ς3(t	t)(ς3(t	PRON
ma-85	331	8	)	)	PUNCT
ma-85	331	9	+	+	NUM
ma-85	331	10	σς2(t))dt	σς2(t))dt	NOUN
ma-85	331	11	where	where	SCONJ
ma-85	331	12	σ	σ	PROPN
ma-85	331	13	is	be	AUX
ma-85	331	14	a	a	DET
ma-85	331	15	parameter	parameter	NOUN
ma-85	331	16	.	.	PUNCT
ma-85	332	1	then	then	ADV
ma-85	332	2	,	,	PUNCT
ma-85	332	3	define	define	VERB
ma-85	332	4	f	f	X
ma-85	332	5	:	:	PUNCT
ma-85	332	6	d	d	ADP
ma-85	332	7	−→	−→	NOUN
ma-85	332	8	e1	e1	NOUN
ma-85	332	9	by	by	ADP
ma-85	332	10	[	[	X
ma-85	332	11	f	f	X
ma-85	332	12	(	(	PUNCT
ma-85	332	13	x)](s	x)](s	PROPN
ma-85	332	14	)	)	PUNCT
ma-85	333	1	=	=	PUNCT
ma-85	334	1	x(s)−	x(s)−	PROPN
ma-85	334	2	s	s	PART
ma-85	334	3	−	−	NOUN
ma-85	334	4	∫	∫	PROPN
ma-85	334	5	1	1	NUM
ma-85	334	6	0	0	NUM
ma-85	334	7	q(s	q(s	PROPN
ma-85	334	8	,	,	PUNCT
ma-85	334	9	t)(x3(t	t)(x3(t	NOUN
ma-85	334	10	)	)	PUNCT
ma-85	334	11	+	+	NUM
ma-85	334	12	σx2(t))dt	σx2(t))dt	NOUN
ma-85	334	13	.	.	PUNCT
ma-85	335	1	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	PROPN
ma-85	335	2	eur	eur	PROPN
ma-85	335	3	.	.	PUNCT
ma-85	336	1	j.	j.	PROPN
ma-85	336	2	math	math	PROPN
ma-85	336	3	.	.	PUNCT
ma-85	337	1	anal	anal	PROPN
ma-85	337	2	.	.	PUNCT
ma-85	338	1	10.28924	10.28924	NUM
ma-85	338	2	/	/	SYM
ma-85	338	3	ada	ada	PROPN
ma-85	338	4	/	/	SYM
ma-85	338	5	ma.2.13	ma.2.13	PROPN
ma-85	338	6	12	12	NUM
ma-85	338	7	choose	choose	NOUN
ma-85	338	8	ς0(s	ς0(s	PROPN
ma-85	338	9	)	)	PUNCT
ma-85	338	10	=	=	SYM
ma-85	338	11	s	s	PROPN
ma-85	338	12	and	and	CCONJ
ma-85	338	13	d	d	NOUN
ma-85	338	14	=	=	PUNCT
ma-85	338	15	u(ς0	u(ς0	NOUN
ma-85	338	16	,	,	PUNCT
ma-85	338	17	ρ0	ρ0	PROPN
ma-85	338	18	)	)	PUNCT
ma-85	338	19	.	.	PUNCT
ma-85	339	1	then	then	ADV
ma-85	339	2	,	,	PUNCT
ma-85	339	3	clearly	clearly	ADV
ma-85	339	4	u(ς0	u(ς0	ADJ
ma-85	339	5	,	,	PUNCT
ma-85	339	6	ρ0	ρ0	PROPN
ma-85	339	7	)	)	PUNCT
ma-85	339	8	⊂	⊂	PROPN
ma-85	340	1	u(0	u(0	PROPN
ma-85	340	2	,	,	PUNCT
ma-85	340	3	ρ0	ρ0	PROPN
ma-85	340	4	+	+	PROPN
ma-85	340	5	1	1	NUM
ma-85	340	6	)	)	PUNCT
ma-85	340	7	,	,	PUNCT
ma-85	340	8	since	since	SCONJ
ma-85	340	9	‖ς0‖	‖ς0‖	NOUN
ma-85	340	10	=	=	SYM
ma-85	340	11	1	1	X
ma-85	340	12	.	.	PUNCT
ma-85	340	13	suppose	suppose	VERB
ma-85	340	14	2σ	2σ	PRON
ma-85	340	15	<	<	X
ma-85	340	16	5	5	X
ma-85	340	17	.	.	PUNCT
ma-85	341	1	then	then	ADV
ma-85	341	2	,	,	PUNCT
ma-85	341	3	conditions	condition	NOUN
ma-85	341	4	(	(	PUNCT
ma-85	341	5	a	a	X
ma-85	341	6	)	)	PUNCT
ma-85	341	7	are	be	AUX
ma-85	341	8	satisfied	satisfied	ADJ
ma-85	341	9	for	for	ADP
ma-85	341	10	k0	k0	PROPN
ma-85	341	11	=	=	PROPN
ma-85	341	12	2σ	2σ	NOUN
ma-85	342	1	+	+	CCONJ
ma-85	342	2	3ρ0	3ρ0	NUM
ma-85	342	3	+	+	CCONJ
ma-85	342	4	6	6	NUM
ma-85	342	5	8	8	NUM
ma-85	342	6	,	,	PUNCT
ma-85	342	7	l	l	NOUN
ma-85	342	8	=	=	PUNCT
ma-85	342	9	σ	σ	NOUN
ma-85	343	1	+	+	NUM
ma-85	343	2	6ρ0	6ρ0	NUM
ma-85	343	3	+	+	CCONJ
ma-85	343	4	3	3	NUM
ma-85	343	5	4	4	NUM
ma-85	343	6	,	,	PUNCT
ma-85	343	7	and	and	CCONJ
ma-85	343	8	η	η	PROPN
ma-85	343	9	=	=	SYM
ma-85	343	10	1+σ	1+σ	NUM
ma-85	343	11	5−2σ	5−2σ	NUM
ma-85	343	12	.	.	PUNCT
ma-85	344	1	notice	notice	VERB
ma-85	344	2	that	that	SCONJ
ma-85	344	3	k0	k0	PROPN
ma-85	344	4	<	<	X
ma-85	344	5	l.	l.	PROPN
ma-85	344	6	example	example	NOUN
ma-85	344	7	4.3	4.3	NUM
ma-85	344	8	.	.	PUNCT
ma-85	345	1	let	let	VERB
ma-85	345	2	us	we	PRON
ma-85	345	3	consider	consider	VERB
ma-85	345	4	a	a	DET
ma-85	345	5	scalar	scalar	ADJ
ma-85	345	6	function	function	NOUN
ma-85	345	7	ψ	ψ	NOUN
ma-85	345	8	defined	define	VERB
ma-85	345	9	on	on	ADP
ma-85	345	10	the	the	DET
ma-85	345	11	set	set	NOUN
ma-85	345	12	d	d	PROPN
ma-85	345	13	=	=	SYM
ma-85	345	14	u[x0	u[x0	NOUN
ma-85	345	15	,	,	PUNCT
ma-85	345	16	1	1	NUM
ma-85	345	17	−	−	PROPN
ma-85	345	18	q	q	X
ma-85	345	19	]	]	X
ma-85	345	20	for	for	ADP
ma-85	345	21	q	q	PROPN
ma-85	345	22	∈	∈	PROPN
ma-85	345	23	(	(	PUNCT
ma-85	345	24	0	0	NUM
ma-85	345	25	,	,	PUNCT
ma-85	345	26	12	12	NUM
ma-85	345	27	)	)	PUNCT
ma-85	345	28	,	,	PUNCT
ma-85	345	29	by	by	ADP
ma-85	345	30	ψ(x	ψ(x	NOUN
ma-85	345	31	)	)	PUNCT
ma-85	345	32	=	=	SYM
ma-85	346	1	x3	x3	ADJ
ma-85	346	2	−	−	PROPN
ma-85	347	1	q.	q.	PROPN
ma-85	347	2	choose	choose	VERB
ma-85	347	3	x0	x0	PROPN
ma-85	347	4	=	=	SYM
ma-85	348	1	1	1	X
ma-85	348	2	.	.	PUNCT
ma-85	348	3	then	then	ADV
ma-85	348	4	,	,	PUNCT
ma-85	348	5	we	we	PRON
ma-85	348	6	obtain	obtain	VERB
ma-85	348	7	the	the	DET
ma-85	348	8	estiamtes	estiamte	NOUN
ma-85	348	9	|ψ′(x0)−1(ψ′(x)−	|ψ′(x0)−1(ψ′(x)−	PROPN
ma-85	348	10	ψ′(x0))|	ψ′(x0))|	PROPN
ma-85	349	1	=	=	PUNCT
ma-85	349	2	|x2	|x2	ADJ
ma-85	349	3	−	−	NUM
ma-85	349	4	x20	x20	NOUN
ma-85	349	5	|	|	CCONJ
ma-85	349	6	≤	≤	NUM
ma-85	349	7	|x	|x	NOUN
ma-85	349	8	+	+	CCONJ
ma-85	349	9	x0||x	x0||x	PROPN
ma-85	349	10	−	−	PROPN
ma-85	349	11	x0|	x0|	PROPN
ma-85	349	12	≤	≤	PROPN
ma-85	349	13	(	(	PUNCT
ma-85	349	14	|x	|x	X
ma-85	349	15	−	−	PROPN
ma-85	349	16	x0|+	x0|+	PROPN
ma-85	349	17	2|x0|)|x	2|x0|)|x	NUM
ma-85	349	18	−	−	NOUN
ma-85	349	19	x0|	x0|	PROPN
ma-85	349	20	=	=	PRON
ma-85	349	21	(	(	PUNCT
ma-85	349	22	1−	1−	NUM
ma-85	349	23	q	q	NOUN
ma-85	349	24	+	+	NUM
ma-85	349	25	2)|x	2)|x	NUM
ma-85	349	26	−	−	NOUN
ma-85	349	27	x0|	x0|	PROPN
ma-85	350	1	=	=	PRON
ma-85	351	1	(	(	PUNCT
ma-85	351	2	3−	3−	NUM
ma-85	351	3	q)|x	q)|x	NOUN
ma-85	351	4	−	−	PROPN
ma-85	351	5	x0|	x0|	PROPN
ma-85	351	6	,	,	PUNCT
ma-85	351	7	for	for	ADP
ma-85	351	8	all	all	DET
ma-85	351	9	x	x	SYM
ma-85	351	10	∈	∈	PROPN
ma-85	351	11	d	d	NOUN
ma-85	351	12	,	,	PUNCT
ma-85	351	13	so	so	ADV
ma-85	351	14	k0	k0	PROPN
ma-85	351	15	=	=	PROPN
ma-85	351	16	3−	3−	PROPN
ma-85	351	17	q	q	NOUN
ma-85	351	18	,	,	PUNCT
ma-85	351	19	d0	d0	NOUN
ma-85	351	20	=	=	SYM
ma-85	351	21	u(x0	u(x0	NOUN
ma-85	351	22	,	,	PUNCT
ma-85	351	23	1	1	NUM
ma-85	351	24	k0	k0	PROPN
ma-85	351	25	)	)	PUNCT
ma-85	351	26	∩d	∩d	VERB
ma-85	352	1	=	=	PUNCT
ma-85	352	2	u(x0	u(x0	NOUN
ma-85	352	3	,	,	PUNCT
ma-85	352	4	1	1	NUM
ma-85	352	5	k0	k0	PROPN
ma-85	352	6	)	)	PUNCT
ma-85	352	7	,	,	PUNCT
ma-85	352	8	|ψ′(x0)−1(ψ′(y)−	|ψ′(x0)−1(ψ′(y)−	NOUN
ma-85	352	9	ψ′(x)|	ψ′(x)|	NOUN
ma-85	352	10	=	=	PUNCT
ma-85	352	11	|y2	|y2	ADJ
ma-85	352	12	−	−	NOUN
ma-85	352	13	x2|	x2|	PROPN
ma-85	352	14	≤	≤	NOUN
ma-85	352	15	|y	|y	NOUN
ma-85	352	16	+	+	CCONJ
ma-85	352	17	x	x	SYM
ma-85	352	18	||y	||y	ADJ
ma-85	352	19	−	−	NOUN
ma-85	352	20	x	x	SYM
ma-85	352	21	|	|	ADV
ma-85	352	22	≤	≤	X
ma-85	352	23	(	(	PUNCT
ma-85	352	24	|y	|y	NOUN
ma-85	352	25	−	−	X
ma-85	352	26	x0	x0	PROPN
ma-85	353	1	+	+	CCONJ
ma-85	354	1	x	x	SYM
ma-85	354	2	−	−	NOUN
ma-85	354	3	x0	x0	PROPN
ma-85	355	1	+	+	CCONJ
ma-85	356	1	2x0)||y	2x0)||y	NUM
ma-85	356	2	−	−	NOUN
ma-85	357	1	x	x	SYM
ma-85	357	2	|	|	ADV
ma-85	357	3	=	=	SYM
ma-85	357	4	(	(	PUNCT
ma-85	357	5	|y	|y	NOUN
ma-85	357	6	−	−	PROPN
ma-85	357	7	x0|+	x0|+	PROPN
ma-85	357	8	|x	|x	PROPN
ma-85	357	9	−	−	PROPN
ma-85	357	10	x0|+	x0|+	PROPN
ma-85	358	1	2|x0|)|y	2|x0|)|y	NOUN
ma-85	359	1	−	−	NOUN
ma-85	359	2	x	x	SYM
ma-85	359	3	|	|	ADV
ma-85	359	4	≤	≤	NUM
ma-85	359	5	(	(	PUNCT
ma-85	359	6	1	1	NUM
ma-85	359	7	k0	k0	PROPN
ma-85	359	8	+	+	CCONJ
ma-85	359	9	1	1	NUM
ma-85	359	10	k0	k0	PROPN
ma-85	359	11	+	+	PROPN
ma-85	360	1	2)|y	2)|y	NUM
ma-85	360	2	−	−	NOUN
ma-85	360	3	x	x	SYM
ma-85	360	4	|	|	NOUN
ma-85	360	5	=	=	SYM
ma-85	360	6	2(1	2(1	NUM
ma-85	360	7	+	+	CCONJ
ma-85	360	8	1	1	NUM
ma-85	360	9	k0	k0	NOUN
ma-85	360	10	)	)	PUNCT
ma-85	360	11	|y	|y	NOUN
ma-85	360	12	−	−	NOUN
ma-85	360	13	x	x	PUNCT
ma-85	360	14	|	|	ADV
ma-85	360	15	,	,	PUNCT
ma-85	360	16	for	for	ADP
ma-85	360	17	all	all	DET
ma-85	360	18	x	x	NOUN
ma-85	360	19	,	,	PUNCT
ma-85	360	20	y	y	PROPN
ma-85	360	21	∈	∈	PROPN
ma-85	360	22	d0	d0	NOUN
ma-85	360	23	,	,	PUNCT
ma-85	360	24	so	so	SCONJ
ma-85	360	25	l	l	NOUN
ma-85	360	26	=	=	SYM
ma-85	360	27	2(1	2(1	NUM
ma-85	360	28	+	+	CCONJ
ma-85	360	29	1	1	NUM
ma-85	360	30	k0	k0	PROPN
ma-85	360	31	)	)	PUNCT
ma-85	360	32	,	,	PUNCT
ma-85	360	33	|ψ′(x0)−1(ψ′(y)−	|ψ′(x0)−1(ψ′(y)−	NOUN
ma-85	360	34	ψ′(x)|	ψ′(x)|	NOUN
ma-85	360	35	=	=	PUNCT
ma-85	360	36	(	(	PUNCT
ma-85	360	37	|y	|y	NOUN
ma-85	360	38	−	−	PROPN
ma-85	360	39	x0|+	x0|+	PROPN
ma-85	360	40	|x	|x	PROPN
ma-85	360	41	−	−	PROPN
ma-85	360	42	x0|+	x0|+	PROPN
ma-85	360	43	2|x0|)|y	2|x0|)|y	NOUN
ma-85	361	1	−	−	NOUN
ma-85	361	2	x	x	SYM
ma-85	361	3	|	|	ADV
ma-85	361	4	≤	≤	NUM
ma-85	361	5	(	(	PUNCT
ma-85	361	6	1−	1−	NUM
ma-85	361	7	q	q	NOUN
ma-85	362	1	+	+	NUM
ma-85	362	2	1−	1−	NUM
ma-85	362	3	q	q	NOUN
ma-85	363	1	+	+	NUM
ma-85	363	2	2)|y	2)|y	NUM
ma-85	363	3	−	−	NOUN
ma-85	364	1	x	x	SYM
ma-85	365	1	|	|	ADV
ma-85	365	2	=	=	SYM
ma-85	365	3	2(2−	2(2−	NUM
ma-85	365	4	q)|y	q)|y	NOUN
ma-85	365	5	−	−	NOUN
ma-85	365	6	x	x	SYM
ma-85	365	7	|	|	ADV
ma-85	365	8	,	,	PUNCT
ma-85	365	9	for	for	ADP
ma-85	365	10	all	all	DET
ma-85	365	11	x	x	NOUN
ma-85	365	12	,	,	PUNCT
ma-85	365	13	y	y	PROPN
ma-85	365	14	∈	∈	PROPN
ma-85	365	15	d	d	PROPN
ma-85	365	16	and	and	CCONJ
ma-85	365	17	l1	l1	PROPN
ma-85	365	18	=	=	PUNCT
ma-85	366	1	2(2−	2(2−	NUM
ma-85	366	2	q	q	NOUN
ma-85	366	3	)	)	PUNCT
ma-85	366	4	.	.	PUNCT
ma-85	367	1	notice	notice	VERB
ma-85	367	2	that	that	SCONJ
ma-85	367	3	for	for	ADP
ma-85	367	4	all	all	DET
ma-85	367	5	q	q	PROPN
ma-85	367	6	∈	∈	PROPN
ma-85	367	7	(	(	PUNCT
ma-85	367	8	0	0	NUM
ma-85	367	9	,	,	PUNCT
ma-85	367	10	12	12	NUM
ma-85	367	11	)	)	PUNCT
ma-85	367	12	k0	k0	PROPN
ma-85	367	13	<	<	X
ma-85	367	14	l	l	X
ma-85	367	15	<	<	X
ma-85	367	16	l1	l1	PROPN
ma-85	367	17	.	.	PUNCT
ma-85	368	1	next	next	ADV
ma-85	368	2	,	,	PUNCT
ma-85	368	3	set	set	VERB
ma-85	368	4	y	y	PROPN
ma-85	368	5	=	=	PUNCT
ma-85	368	6	x	x	SYM
ma-85	368	7	−	−	PROPN
ma-85	368	8	ψ′(x)−1ψ(x	ψ′(x)−1ψ(x	NOUN
ma-85	368	9	)	)	PUNCT
ma-85	368	10	,	,	PUNCT
ma-85	368	11	x	x	PROPN
ma-85	368	12	∈	∈	PROPN
ma-85	368	13	d.	d.	NOUN
ma-85	368	14	then	then	ADV
ma-85	368	15	,	,	PUNCT
ma-85	368	16	we	we	PRON
ma-85	368	17	have	have	VERB
ma-85	368	18	y	y	NOUN
ma-85	369	1	+	+	NOUN
ma-85	369	2	x	x	SYM
ma-85	369	3	=	=	PUNCT
ma-85	369	4	x	x	SYM
ma-85	369	5	−	−	NOUN
ma-85	369	6	ψ′(x)−1ψ(x	ψ′(x)−1ψ(x	NOUN
ma-85	369	7	)	)	PUNCT
ma-85	370	1	+	+	NUM
ma-85	370	2	x	x	SYM
ma-85	370	3	=	=	SYM
ma-85	370	4	5x3	5x3	NUM
ma-85	370	5	+	+	CCONJ
ma-85	370	6	q	q	NOUN
ma-85	370	7	3x2	3x2	NUM
ma-85	370	8	.	.	PUNCT
ma-85	371	1	define	define	VERB
ma-85	371	2	fundtion	fundtion	NOUN
ma-85	371	3	ψ̄	ψ̄	NOUN
ma-85	371	4	on	on	ADP
ma-85	371	5	the	the	DET
ma-85	371	6	interval	interval	NOUN
ma-85	372	1	d	d	NOUN
ma-85	372	2	=	=	PUNCT
ma-85	373	1	[	[	X
ma-85	373	2	q	q	X
ma-85	373	3	,	,	PUNCT
ma-85	373	4	2−	2−	NUM
ma-85	373	5	q	q	NOUN
ma-85	373	6	]	]	PUNCT
ma-85	373	7	by	by	ADP
ma-85	373	8	ψ̄(x	ψ̄(x	PROPN
ma-85	373	9	)	)	PUNCT
ma-85	373	10	=	=	PUNCT
ma-85	373	11	5x3	5x3	NUM
ma-85	374	1	+	+	CCONJ
ma-85	374	2	q	q	NOUN
ma-85	374	3	3x2	3x2	NUM
ma-85	374	4	.	.	PUNCT
ma-85	375	1	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	AUX
ma-85	375	2	eur	eur	PROPN
ma-85	375	3	.	.	PUNCT
ma-85	376	1	j.	j.	PROPN
ma-85	376	2	math	math	PROPN
ma-85	376	3	.	.	PUNCT
ma-85	377	1	anal	anal	PROPN
ma-85	377	2	.	.	PUNCT
ma-85	378	1	10.28924	10.28924	NUM
ma-85	378	2	/	/	SYM
ma-85	378	3	ada	ada	PROPN
ma-85	378	4	/	/	SYM
ma-85	378	5	ma.2.13	ma.2.13	PROPN
ma-85	378	6	13	13	NUM
ma-85	378	7	then	then	ADV
ma-85	378	8	,	,	PUNCT
ma-85	378	9	we	we	PRON
ma-85	378	10	get	get	VERB
ma-85	378	11	by	by	ADP
ma-85	378	12	this	this	DET
ma-85	378	13	definition	definition	NOUN
ma-85	378	14	that	that	SCONJ
ma-85	378	15	ψ̄′(x	ψ̄′(x	VERB
ma-85	378	16	)	)	PUNCT
ma-85	378	17	=	=	PUNCT
ma-85	379	1	15x4	15x4	NUM
ma-85	380	1	−	−	NUM
ma-85	380	2	6xq	6xq	NOUN
ma-85	380	3	9x4	9x4	NUM
ma-85	380	4	=	=	SYM
ma-85	380	5	5(x	5(x	NUM
ma-85	380	6	−	−	NOUN
ma-85	380	7	q)(x2	q)(x2	NOUN
ma-85	380	8	+	+	CCONJ
ma-85	380	9	xq	xq	PROPN
ma-85	380	10	+	+	CCONJ
ma-85	380	11	q2	q2	NOUN
ma-85	380	12	)	)	PUNCT
ma-85	380	13	3x3	3x3	NUM
ma-85	380	14	,	,	PUNCT
ma-85	381	1	where	where	SCONJ
ma-85	381	2	p	p	NOUN
ma-85	381	3	=	=	NOUN
ma-85	381	4	3	3	NUM
ma-85	381	5	√	√	NOUN
ma-85	381	6	2q	2q	NUM
ma-85	381	7	5	5	NUM
ma-85	381	8	is	be	AUX
ma-85	381	9	the	the	DET
ma-85	381	10	critical	critical	ADJ
ma-85	381	11	point	point	NOUN
ma-85	381	12	of	of	ADP
ma-85	381	13	function	function	NOUN
ma-85	381	14	ψ̄.	ψ̄.	PUNCT
ma-85	381	15	notice	notice	VERB
ma-85	381	16	that	that	SCONJ
ma-85	381	17	q	q	PUNCT
ma-85	381	18	<	<	X
ma-85	381	19	p	p	X
ma-85	381	20	<	<	X
ma-85	381	21	2	2	NUM
ma-85	381	22	−	−	NOUN
ma-85	381	23	q.	q.	NOUN
ma-85	381	24	it	it	PRON
ma-85	381	25	follows	follow	VERB
ma-85	381	26	that	that	SCONJ
ma-85	381	27	this	this	DET
ma-85	381	28	function	function	NOUN
ma-85	381	29	is	be	AUX
ma-85	381	30	decreasing	decrease	VERB
ma-85	381	31	on	on	ADP
ma-85	381	32	the	the	DET
ma-85	381	33	interval	interval	NOUN
ma-85	381	34	(	(	PUNCT
ma-85	381	35	q	q	X
ma-85	381	36	,	,	PUNCT
ma-85	381	37	p	p	NOUN
ma-85	381	38	)	)	PUNCT
ma-85	381	39	and	and	CCONJ
ma-85	381	40	increasing	increase	VERB
ma-85	381	41	on	on	ADP
ma-85	381	42	the	the	DET
ma-85	381	43	interval	interval	NOUN
ma-85	381	44	(	(	PUNCT
ma-85	381	45	q	q	NOUN
ma-85	381	46	,	,	PUNCT
ma-85	381	47	2	2	NUM
ma-85	381	48	−	−	NOUN
ma-85	381	49	q	q	NOUN
ma-85	381	50	)	)	PUNCT
ma-85	381	51	,	,	PUNCT
ma-85	381	52	since	since	SCONJ
ma-85	381	53	x2	x2	PROPN
ma-85	382	1	+	+	CCONJ
ma-85	382	2	xq	xq	PROPN
ma-85	382	3	+	+	CCONJ
ma-85	382	4	q2	q2	X
ma-85	382	5	>	>	X
ma-85	382	6	0	0	PUNCT
ma-85	382	7	and	and	CCONJ
ma-85	382	8	x3	x3	VERB
ma-85	382	9	>	>	X
ma-85	382	10	0	0	X
ma-85	382	11	.	.	PUNCT
ma-85	383	1	so	so	ADV
ma-85	383	2	,	,	PUNCT
ma-85	383	3	we	we	PRON
ma-85	383	4	can	can	AUX
ma-85	383	5	set	set	VERB
ma-85	383	6	k1	k1	NOUN
ma-85	383	7	=	=	SYM
ma-85	383	8	5(2−	5(2−	NUM
ma-85	383	9	q)2	q)2	PROPN
ma-85	383	10	+	+	CCONJ
ma-85	383	11	q	q	ADJ
ma-85	383	12	9(2−	9(2−	NUM
ma-85	383	13	q)2	q)2	PROPN
ma-85	383	14	,	,	PUNCT
ma-85	383	15	η	η	PROPN
ma-85	383	16	=	=	PROPN
ma-85	384	1	1−	1−	NUM
ma-85	384	2	q	q	NOUN
ma-85	384	3	3	3	NUM
ma-85	384	4	and	and	CCONJ
ma-85	384	5	k1	k1	NOUN
ma-85	384	6	<	<	X
ma-85	384	7	k0	k0	PROPN
ma-85	384	8	.	.	PUNCT
ma-85	385	1	but	but	CCONJ
ma-85	385	2	if	if	SCONJ
ma-85	385	3	x	x	SYM
ma-85	385	4	∈	∈	NOUN
ma-85	385	5	d0	d0	NOUN
ma-85	385	6	=	=	PUNCT
ma-85	386	1	[	[	X
ma-85	386	2	1−	1−	NUM
ma-85	386	3	1	1	NUM
ma-85	386	4	k0	k0	PROPN
ma-85	386	5	,	,	PUNCT
ma-85	386	6	1	1	NUM
ma-85	386	7	+	+	SYM
ma-85	386	8	1	1	NUM
ma-85	386	9	k0	k0	PROPN
ma-85	386	10	]	]	PUNCT
ma-85	386	11	,	,	PUNCT
ma-85	386	12	then	then	ADV
ma-85	386	13	k	k	PROPN
ma-85	386	14	=	=	PUNCT
ma-85	386	15	5%3	5%3	NUM
ma-85	386	16	+	+	CCONJ
ma-85	386	17	q	q	X
ma-85	386	18	9%2	9%2	X
ma-85	386	19	,	,	PUNCT
ma-85	386	20	where	where	SCONJ
ma-85	386	21	%	%	NOUN
ma-85	386	22	=	=	SYM
ma-85	386	23	4−q	4−q	NUM
ma-85	386	24	3−q	3−q	NUM
ma-85	386	25	and	and	CCONJ
ma-85	386	26	k	k	X
ma-85	386	27	<	<	X
ma-85	386	28	k1	k1	PROPN
ma-85	386	29	for	for	ADP
ma-85	386	30	all	all	DET
ma-85	386	31	q	q	PROPN
ma-85	386	32	∈	∈	PROPN
ma-85	386	33	(	(	PUNCT
ma-85	386	34	0	0	NUM
ma-85	386	35	,	,	PUNCT
ma-85	386	36	12	12	NUM
ma-85	386	37	)	)	PUNCT
ma-85	386	38	.	.	PUNCT
ma-85	387	1	next	next	ADV
ma-85	387	2	,	,	PUNCT
ma-85	387	3	we	we	PRON
ma-85	387	4	verify	verify	VERB
ma-85	387	5	conditions	condition	NOUN
ma-85	387	6	(	(	PUNCT
ma-85	387	7	2.2	2.2	NUM
ma-85	387	8	)	)	PUNCT
ma-85	387	9	,	,	PUNCT
ma-85	387	10	(	(	PUNCT
ma-85	387	11	2.3	2.3	NUM
ma-85	387	12	)	)	PUNCT
ma-85	387	13	,	,	PUNCT
ma-85	387	14	(	(	PUNCT
ma-85	387	15	2.24	2.24	NUM
ma-85	387	16	)	)	PUNCT
ma-85	387	17	and	and	CCONJ
ma-85	387	18	(	(	PUNCT
ma-85	387	19	2.25	2.25	NUM
ma-85	387	20	)	)	PUNCT
ma-85	387	21	.	.	PUNCT
ma-85	388	1	then	then	ADV
ma-85	388	2	for	for	ADP
ma-85	388	3	q	q	NOUN
ma-85	388	4	=	=	NOUN
ma-85	388	5	0.95	0.95	NUM
ma-85	388	6	,	,	PUNCT
ma-85	388	7	6k0	6k0	NUM
ma-85	388	8	=	=	NOUN
ma-85	388	9	2.9268	2.9268	NUM
ma-85	388	10	and	and	CCONJ
ma-85	388	11	n	n	NUM
ma-85	388	12	1	1	NUM
ma-85	388	13	2	2	NUM
ma-85	388	14	3	3	NUM
ma-85	388	15	4	4	NUM
ma-85	388	16	5	5	NUM
ma-85	388	17	tn	tn	NOUN
ma-85	388	18	0.1683	0.1683	NUM
ma-85	388	19	0.1694	0.1694	NUM
ma-85	388	20	0.1694	0.1694	NUM
ma-85	388	21	0.1694	0.1694	NUM
ma-85	388	22	0.1694	0.1694	NUM
ma-85	388	23	α1	α1	NOUN
ma-85	388	24	=	=	SYM
ma-85	388	25	0.1643	0.1643	NUM
ma-85	388	26	=	=	SYM
ma-85	388	27	α3	α3	ADJ
ma-85	388	28	,	,	PUNCT
ma-85	388	29	α2	α2	PROPN
ma-85	388	30	=	=	SYM
ma-85	388	31	0.6588	0.6588	NUM
ma-85	388	32	=	=	SYM
ma-85	388	33	α	α	PROPN
ma-85	388	34	,	,	PUNCT
ma-85	388	35	a	a	DET
ma-85	388	36	=	=	SYM
ma-85	388	37	0.0030	0.0030	NUM
ma-85	388	38	=	=	SYM
ma-85	388	39	c̄	c̄	PROPN
ma-85	388	40	,	,	PUNCT
ma-85	388	41	b	b	NOUN
ma-85	388	42	=	=	SYM
ma-85	388	43	0.0136	0.0136	NUM
ma-85	388	44	=	=	SYM
ma-85	388	45	c	c	X
ma-85	388	46	,	,	PUNCT
ma-85	388	47	1	1	NUM
ma-85	388	48	−	−	PROPN
ma-85	388	49	10k0η3	10k0η3	PROPN
ma-85	388	50	=	=	SYM
ma-85	388	51	0.8861	0.8861	NUM
ma-85	388	52	,	,	PUNCT
ma-85	388	53	and	and	CCONJ
ma-85	388	54	(	(	PUNCT
ma-85	388	55	4k3	4k3	NUM
ma-85	389	1	+	+	CCONJ
ma-85	389	2	4	4	NUM
ma-85	389	3	3k0kη	3k0kη	NUM
ma-85	389	4	+	+	CCONJ
ma-85	389	5	k0)η	k0)η	NOUN
ma-85	389	6	=	=	PUNCT
ma-85	389	7	0.0521	0.0521	NUM
ma-85	389	8	<	<	X
ma-85	389	9	1	1	NUM
ma-85	389	10	.	.	PUNCT
ma-85	390	1	hence	hence	ADV
ma-85	390	2	,	,	PUNCT
ma-85	390	3	conditions	condition	NOUN
ma-85	390	4	(	(	PUNCT
ma-85	390	5	2.2),(2.3	2.2),(2.3	NUM
ma-85	390	6	)	)	PUNCT
ma-85	390	7	,	,	PUNCT
ma-85	390	8	(	(	PUNCT
ma-85	390	9	2.24	2.24	NUM
ma-85	390	10	)	)	PUNCT
ma-85	390	11	and	and	CCONJ
ma-85	390	12	(	(	PUNCT
ma-85	390	13	2.25	2.25	NUM
ma-85	390	14	)	)	PUNCT
ma-85	390	15	hold	hold	VERB
ma-85	390	16	.	.	PUNCT
ma-85	391	1	5	5	X
ma-85	391	2	.	.	X
ma-85	391	3	conclusion	conclusion	NOUN
ma-85	391	4	the	the	DET
ma-85	391	5	semi	semi	ADJ
ma-85	391	6	-	-	ADJ
ma-85	391	7	local	local	ADJ
ma-85	391	8	convergence	convergence	NOUN
ma-85	391	9	of	of	ADP
ma-85	391	10	scheme	scheme	NOUN
ma-85	391	11	(	(	PUNCT
ma-85	391	12	1.1	1.1	NUM
ma-85	391	13	)	)	PUNCT
ma-85	391	14	with	with	ADP
ma-85	391	15	order	order	NOUN
ma-85	391	16	three	three	NUM
ma-85	391	17	is	be	AUX
ma-85	391	18	extended	extend	VERB
ma-85	391	19	using	use	VERB
ma-85	391	20	general	general	ADJ
ma-85	391	21	conditionson	conditionson	NOUN
ma-85	391	22	f	f	PROPN
ma-85	392	1	′	′	NOUN
ma-85	392	2	and	and	CCONJ
ma-85	392	3	recurrent	recurrent	ADJ
ma-85	392	4	majorizing	majorize	VERB
ma-85	392	5	sequences	sequence	NOUN
ma-85	392	6	.	.	PUNCT
ma-85	393	1	references	reference	NOUN
ma-85	393	2	[	[	X
ma-85	393	3	1	1	NUM
ma-85	393	4	]	]	X
ma-85	393	5	i.k	i.k	PROPN
ma-85	393	6	.	.	PROPN
ma-85	393	7	argyros	argyros	PROPN
ma-85	393	8	,	,	PUNCT
ma-85	393	9	on	on	ADP
ma-85	393	10	the	the	DET
ma-85	393	11	newton	newton	PROPN
ma-85	393	12	kantorovich	kantorovich	PROPN
ma-85	393	13	hypothesis	hypothesis	NOUN
ma-85	393	14	for	for	ADP
ma-85	393	15	solving	solve	VERB
ma-85	393	16	equations	equation	NOUN
ma-85	393	17	,	,	PUNCT
ma-85	393	18	j.	j.	PROPN
ma-85	393	19	comput	comput	PROPN
ma-85	393	20	.	.	PUNCT
ma-85	394	1	math	math	NOUN
ma-85	394	2	.	.	PUNCT
ma-85	395	1	169	169	NUM
ma-85	395	2	(	(	PUNCT
ma-85	395	3	2004	2004	NUM
ma-85	395	4	)	)	PUNCT
ma-85	395	5	315	315	NUM
ma-85	395	6	-	-	SYM
ma-85	395	7	332	332	NUM
ma-85	395	8	.	.	PUNCT
ma-85	396	1	https://doi.org/10.1016/j.cam.2004.01.029[2	https://doi.org/10.1016/j.cam.2004.01.029[2	PROPN
ma-85	396	2	]	]	X
ma-85	396	3	i.k	i.k	PROPN
ma-85	396	4	.	.	PROPN
ma-85	396	5	argyros	argyros	PROPN
ma-85	396	6	,	,	PUNCT
ma-85	396	7	computational	computational	ADJ
ma-85	396	8	theory	theory	NOUN
ma-85	396	9	of	of	ADP
ma-85	396	10	iterative	iterative	NOUN
ma-85	396	11	schemes	scheme	NOUN
ma-85	396	12	.	.	PUNCT
ma-85	397	1	series	series	NOUN
ma-85	397	2	:	:	PUNCT
ma-85	397	3	studies	study	NOUN
ma-85	397	4	in	in	ADP
ma-85	397	5	computational	computational	ADJ
ma-85	397	6	mathematics	mathematic	NOUN
ma-85	397	7	,	,	PUNCT
ma-85	397	8	15	15	NUM
ma-85	397	9	,	,	PUNCT
ma-85	397	10	editors	editor	NOUN
ma-85	397	11	:	:	PUNCT
ma-85	397	12	c.k.chui	c.k.chui	PROPN
ma-85	397	13	and	and	CCONJ
ma-85	397	14	l.	l.	PROPN
ma-85	397	15	wuytack	wuytack	PROPN
ma-85	397	16	,	,	PUNCT
ma-85	397	17	elsevier	elsevier	PROPN
ma-85	397	18	publ	publ	PROPN
ma-85	397	19	.	.	PUNCT
ma-85	398	1	co.	co.	PROPN
ma-85	398	2	new	new	PROPN
ma-85	398	3	york	york	PROPN
ma-85	398	4	,	,	PUNCT
ma-85	398	5	u.s.a	u.s.a	PROPN
ma-85	398	6	,	,	PUNCT
ma-85	398	7	2007.[3	2007.[3	NUM
ma-85	398	8	]	]	X
ma-85	398	9	i.k	i.k	PROPN
ma-85	398	10	.	.	PROPN
ma-85	398	11	argyros	argyros	PROPN
ma-85	398	12	,	,	PUNCT
ma-85	398	13	convergence	convergence	NOUN
ma-85	398	14	and	and	CCONJ
ma-85	398	15	applications	application	NOUN
ma-85	398	16	of	of	ADP
ma-85	398	17	newton	newton	NOUN
ma-85	398	18	-	-	PUNCT
ma-85	398	19	type	type	NOUN
ma-85	398	20	iterations	iteration	NOUN
ma-85	398	21	,	,	PUNCT
ma-85	398	22	springer	springer	NOUN
ma-85	398	23	verlag	verlag	PROPN
ma-85	398	24	,	,	PUNCT
ma-85	398	25	berlin	berlin	PROPN
ma-85	398	26	,	,	PUNCT
ma-85	398	27	germany	germany	PROPN
ma-85	398	28	,	,	PUNCT
ma-85	398	29	(	(	PUNCT
ma-85	398	30	2008).[4	2008).[4	NOUN
ma-85	398	31	]	]	X
ma-85	398	32	i.k	i.k	PROPN
ma-85	398	33	.	.	PROPN
ma-85	398	34	argyros	argyros	PROPN
ma-85	398	35	,	,	PUNCT
ma-85	398	36	s.	s.	PROPN
ma-85	398	37	hilout	hilout	PROPN
ma-85	398	38	,	,	PUNCT
ma-85	398	39	weaker	weak	ADJ
ma-85	398	40	conditions	condition	NOUN
ma-85	398	41	for	for	ADP
ma-85	398	42	the	the	DET
ma-85	398	43	convergence	convergence	NOUN
ma-85	398	44	of	of	ADP
ma-85	398	45	newton	newton	PROPN
ma-85	398	46	’s	’s	PART
ma-85	398	47	scheme	scheme	NOUN
ma-85	398	48	,	,	PUNCT
ma-85	398	49	j.	j.	PROPN
ma-85	398	50	complex	complex	PROPN
ma-85	398	51	.	.	PUNCT
ma-85	399	1	28	28	NUM
ma-85	399	2	(	(	PUNCT
ma-85	399	3	2012	2012	NUM
ma-85	399	4	)	)	PUNCT
ma-85	400	1	364–387	364–387	NUM
ma-85	400	2	.	.	PUNCT
ma-85	401	1	https://doi.org/10.1016/j.jco.2011.12.003.[5	https://doi.org/10.1016/j.jco.2011.12.003.[5	PRON
ma-85	401	2	]	]	X
ma-85	401	3	i.k	i.k	PROPN
ma-85	401	4	.	.	PROPN
ma-85	401	5	argyros	argyros	PROPN
ma-85	401	6	,	,	PUNCT
ma-85	401	7	s.	s.	PROPN
ma-85	401	8	hilout	hilout	PROPN
ma-85	401	9	,	,	PUNCT
ma-85	401	10	on	on	ADP
ma-85	401	11	an	an	DET
ma-85	401	12	improved	improved	ADJ
ma-85	401	13	convergence	convergence	NOUN
ma-85	401	14	analysis	analysis	NOUN
ma-85	401	15	of	of	ADP
ma-85	401	16	newton	newton	PROPN
ma-85	401	17	’s	’s	PART
ma-85	401	18	scheme	scheme	NOUN
ma-85	401	19	,	,	PUNCT
ma-85	401	20	appl	appl	PROPN
ma-85	401	21	.	.	PROPN
ma-85	401	22	math	math	NOUN
ma-85	401	23	.	.	PUNCT
ma-85	402	1	comput	comput	NOUN
ma-85	402	2	.	.	PUNCT
ma-85	403	1	225	225	NUM
ma-85	403	2	(	(	PUNCT
ma-85	403	3	2013)372	2013)372	PROPN
ma-85	403	4	-	-	PUNCT
ma-85	403	5	386	386	NUM
ma-85	403	6	.	.	PUNCT
ma-85	404	1	https://doi.org/10.1016/j.amc.2013.09.049	https://doi.org/10.1016/j.amc.2013.09.049	PROPN
ma-85	404	2	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	PROPN
ma-85	405	1	https://doi.org/10.1016/j.cam.2004.01.029	https://doi.org/10.1016/j.cam.2004.01.029	PROPN
ma-85	406	1	https://doi.org/10.1016/j.jco.2011.12.003	https://doi.org/10.1016/j.jco.2011.12.003	PROPN
ma-85	406	2	https://doi.org/10.1016/j.amc.2013.09.049	https://doi.org/10.1016/j.amc.2013.09.049	PROPN
ma-85	406	3	eur	eur	PROPN
ma-85	406	4	.	.	PUNCT
ma-85	407	1	j.	j.	PROPN
ma-85	407	2	math	math	PROPN
ma-85	407	3	.	.	PUNCT
ma-85	408	1	anal	anal	PROPN
ma-85	408	2	.	.	PUNCT
ma-85	409	1	10.28924	10.28924	NUM
ma-85	409	2	/	/	SYM
ma-85	409	3	ada	ada	PROPN
ma-85	409	4	/	/	SYM
ma-85	409	5	ma.2.13	ma.2.13	PROPN
ma-85	409	6	14	14	NUM
ma-85	410	1	[	[	X
ma-85	410	2	6	6	NUM
ma-85	410	3	]	]	X
ma-85	410	4	i.k	i.k	PROPN
ma-85	410	5	.	.	PROPN
ma-85	410	6	argyros	argyros	PROPN
ma-85	410	7	,	,	PUNCT
ma-85	410	8	a.a	a.a	PROPN
ma-85	410	9	.	.	PROPN
ma-85	410	10	magréñan	magréñan	PROPN
ma-85	410	11	,	,	PUNCT
ma-85	410	12	iterative	iterative	ADJ
ma-85	410	13	schemes	scheme	NOUN
ma-85	410	14	and	and	CCONJ
ma-85	410	15	their	their	PRON
ma-85	410	16	dynamics	dynamic	NOUN
ma-85	410	17	with	with	ADP
ma-85	410	18	applications	application	NOUN
ma-85	410	19	,	,	PUNCT
ma-85	410	20	crc	crc	NOUN
ma-85	410	21	press	press	NOUN
ma-85	410	22	,	,	PUNCT
ma-85	410	23	new	new	PROPN
ma-85	410	24	york	york	PROPN
ma-85	410	25	,	,	PUNCT
ma-85	410	26	usa,2017.[7	usa,2017.[7	NOUN
ma-85	410	27	]	]	X
ma-85	410	28	i.k	i.k	PROPN
ma-85	410	29	.	.	PROPN
ma-85	410	30	argyros	argyros	PROPN
ma-85	410	31	,	,	PUNCT
ma-85	410	32	a.a	a.a	PROPN
ma-85	410	33	.	.	PROPN
ma-85	410	34	magréñan	magréñan	PROPN
ma-85	410	35	,	,	PUNCT
ma-85	410	36	a	a	DET
ma-85	410	37	contemporary	contemporary	ADJ
ma-85	410	38	study	study	NOUN
ma-85	410	39	of	of	ADP
ma-85	410	40	iterative	iterative	NOUN
ma-85	410	41	schemes	scheme	NOUN
ma-85	410	42	,	,	PUNCT
ma-85	410	43	elsevier	elsevier	NOUN
ma-85	410	44	(	(	PUNCT
ma-85	410	45	academic	academic	ADJ
ma-85	410	46	press	press	NOUN
ma-85	410	47	)	)	PUNCT
ma-85	410	48	,	,	PUNCT
ma-85	410	49	new	new	PROPN
ma-85	410	50	york,2018.[8	york,2018.[8	PROPN
ma-85	410	51	]	]	X
ma-85	410	52	r.	r.	PROPN
ma-85	410	53	behl	behl	PROPN
ma-85	410	54	,	,	PUNCT
ma-85	410	55	p.	p.	PROPN
ma-85	410	56	maroju	maroju	PROPN
ma-85	410	57	,	,	PUNCT
ma-85	410	58	e.	e.	PROPN
ma-85	410	59	martinez	martinez	PROPN
ma-85	410	60	,	,	PUNCT
ma-85	410	61	s.	s.	PROPN
ma-85	410	62	singh	singh	PROPN
ma-85	410	63	,	,	PUNCT
ma-85	410	64	a	a	DET
ma-85	410	65	study	study	NOUN
ma-85	410	66	of	of	ADP
ma-85	410	67	the	the	DET
ma-85	410	68	local	local	ADJ
ma-85	410	69	convergence	convergence	NOUN
ma-85	410	70	of	of	ADP
ma-85	410	71	a	a	DET
ma-85	410	72	fifth	fifth	ADJ
ma-85	410	73	order	order	NOUN
ma-85	410	74	iterative	iterative	NOUN
ma-85	410	75	scheme	scheme	NOUN
ma-85	410	76	,	,	PUNCT
ma-85	410	77	indianj	indianj	ADJ
ma-85	410	78	.	.	PUNCT
ma-85	411	1	pure	pure	ADJ
ma-85	411	2	appl	appl	PROPN
ma-85	411	3	.	.	PUNCT
ma-85	411	4	math	math	NOUN
ma-85	411	5	.	.	PUNCT
ma-85	412	1	51	51	NUM
ma-85	412	2	(	(	PUNCT
ma-85	412	3	2020	2020	NUM
ma-85	412	4	)	)	PUNCT
ma-85	412	5	439	439	NUM
ma-85	412	6	-	-	SYM
ma-85	412	7	455	455	NUM
ma-85	412	8	.	.	PUNCT
ma-85	413	1	https://doi.org/10.1007/s13226-020-0409-5.[9	https://doi.org/10.1007/s13226-020-0409-5.[9	PRON
ma-85	413	2	]	]	X
ma-85	413	3	e.	e.	PROPN
ma-85	413	4	cătinaş	cătinaş	PROPN
ma-85	413	5	,	,	PUNCT
ma-85	413	6	the	the	DET
ma-85	413	7	inexact	inexact	ADJ
ma-85	413	8	,	,	PUNCT
ma-85	413	9	inexact	inexact	ADJ
ma-85	413	10	perturbed	perturb	VERB
ma-85	413	11	,	,	PUNCT
ma-85	413	12	and	and	CCONJ
ma-85	413	13	quasi	quasi	ADJ
ma-85	413	14	-	-	ADJ
ma-85	413	15	newton	newton	PROPN
ma-85	413	16	schemes	scheme	NOUN
ma-85	413	17	are	be	AUX
ma-85	413	18	equivalent	equivalent	ADJ
ma-85	413	19	models	model	NOUN
ma-85	413	20	,	,	PUNCT
ma-85	413	21	math	math	NOUN
ma-85	413	22	.	.	PUNCT
ma-85	414	1	comput	comput	NOUN
ma-85	414	2	.	.	PUNCT
ma-85	415	1	74(2005	74(2005	NUM
ma-85	415	2	)	)	PUNCT
ma-85	416	1	291–301	291–301	NUM
ma-85	416	2	.	.	PUNCT
ma-85	417	1	https://doi.org/10.1090/s0025-5718-04-01646-1.[10	https://doi.org/10.1090/s0025-5718-04-01646-1.[10	PROPN
ma-85	417	2	]	]	PUNCT
ma-85	417	3	a.	a.	PROPN
ma-85	417	4	cordero	cordero	PROPN
ma-85	417	5	,	,	PUNCT
ma-85	417	6	j.r	j.r	PROPN
ma-85	417	7	.	.	PROPN
ma-85	417	8	torregrosa	torregrosa	PROPN
ma-85	417	9	,	,	PUNCT
ma-85	417	10	variants	variant	NOUN
ma-85	417	11	of	of	ADP
ma-85	417	12	newton	newton	PROPN
ma-85	417	13	’s	’s	PART
ma-85	417	14	method	method	NOUN
ma-85	417	15	using	use	VERB
ma-85	417	16	fifth	fifth	ADJ
ma-85	417	17	-	-	PUNCT
ma-85	417	18	order	order	NOUN
ma-85	417	19	quadrature	quadrature	NOUN
ma-85	417	20	formulas	formula	NOUN
ma-85	417	21	,	,	PUNCT
ma-85	417	22	appl	appl	PROPN
ma-85	417	23	.	.	PROPN
ma-85	417	24	math	math	NOUN
ma-85	417	25	.	.	PUNCT
ma-85	418	1	comput.190	comput.190	NOUN
ma-85	418	2	(	(	PUNCT
ma-85	418	3	2007	2007	NUM
ma-85	418	4	)	)	PUNCT
ma-85	418	5	686–698	686–698	NUM
ma-85	418	6	.	.	PUNCT
ma-85	419	1	https://doi.org/10.1016/j.amc.2007.01.062.[11	https://doi.org/10.1016/j.amc.2007.01.062.[11	PROPN
ma-85	419	2	]	]	PUNCT
ma-85	419	3	j.a	j.a	PROPN
ma-85	419	4	.	.	PROPN
ma-85	419	5	ezquerro	ezquerro	PROPN
ma-85	419	6	,	,	PUNCT
ma-85	419	7	j.m	j.m	PROPN
ma-85	419	8	.	.	PROPN
ma-85	419	9	gutiérrez	gutiérrez	PROPN
ma-85	419	10	,	,	PUNCT
ma-85	419	11	m.a	m.a	PROPN
ma-85	419	12	.	.	PROPN
ma-85	419	13	hernández	hernández	PROPN
ma-85	419	14	,	,	PUNCT
ma-85	419	15	n.	n.	PROPN
ma-85	419	16	romero	romero	PROPN
ma-85	419	17	,	,	PUNCT
ma-85	419	18	m.j	m.j	PROPN
ma-85	419	19	.	.	PROPN
ma-85	419	20	rubio	rubio	PROPN
ma-85	419	21	,	,	PUNCT
ma-85	419	22	the	the	DET
ma-85	419	23	newton	newton	PROPN
ma-85	419	24	scheme	scheme	NOUN
ma-85	419	25	:	:	PUNCT
ma-85	419	26	from	from	ADP
ma-85	419	27	newton	newton	PROPN
ma-85	419	28	tokantorovich	tokantorovich	PROPN
ma-85	419	29	(	(	PUNCT
ma-85	419	30	spanish	spanish	ADJ
ma-85	419	31	)	)	PUNCT
ma-85	419	32	,	,	PUNCT
ma-85	419	33	gac	gac	PROPN
ma-85	419	34	.	.	PUNCT
ma-85	420	1	r.	r.	PROPN
ma-85	420	2	soc	soc	PROPN
ma-85	420	3	.	.	PUNCT
ma-85	421	1	mat	mat	PROPN
ma-85	421	2	.	.	PUNCT
ma-85	422	1	esp	esp	PROPN
ma-85	422	2	.	.	PUNCT
ma-85	423	1	13	13	NUM
ma-85	423	2	(	(	PUNCT
ma-85	423	3	2010	2010	NUM
ma-85	423	4	)	)	PUNCT
ma-85	423	5	53	53	NUM
ma-85	423	6	-	-	SYM
ma-85	423	7	76.[12	76.[12	PROPN
ma-85	423	8	]	]	X
ma-85	423	9	j.a	j.a	PROPN
ma-85	423	10	.	.	PROPN
ma-85	423	11	ezquerro	ezquerro	PROPN
ma-85	423	12	,	,	PUNCT
ma-85	423	13	m.a	m.a	PROPN
ma-85	423	14	.	.	PROPN
ma-85	423	15	hernandez	hernandez	PROPN
ma-85	423	16	,	,	PUNCT
ma-85	423	17	newton	newton	PROPN
ma-85	423	18	’s	’s	PART
ma-85	423	19	scheme	scheme	NOUN
ma-85	423	20	:	:	PUNCT
ma-85	423	21	an	an	DET
ma-85	423	22	updated	update	VERB
ma-85	423	23	approach	approach	NOUN
ma-85	423	24	of	of	ADP
ma-85	423	25	kantorovich	kantorovich	PROPN
ma-85	423	26	’s	’s	PART
ma-85	423	27	theory	theory	NOUN
ma-85	423	28	,	,	PUNCT
ma-85	423	29	cham	cham	PROPN
ma-85	423	30	.	.	PUNCT
ma-85	424	1	switzerland,(2018).[13	switzerland,(2018).[13	PROPN
ma-85	424	2	]	]	PUNCT
ma-85	424	3	m.	m.	NOUN
ma-85	424	4	grau	grau	PROPN
ma-85	424	5	-	-	PUNCT
ma-85	424	6	sánchez	sánchez	PROPN
ma-85	424	7	,	,	PUNCT
ma-85	424	8	à	à	X
ma-85	424	9	.	.	PUNCT
ma-85	424	10	grau	grau	PROPN
ma-85	424	11	,	,	PUNCT
ma-85	424	12	m.	m.	NOUN
ma-85	424	13	noguera	noguera	PROPN
ma-85	424	14	,	,	PUNCT
ma-85	424	15	ostrowski	ostrowski	ADJ
ma-85	424	16	type	type	NOUN
ma-85	424	17	methods	method	NOUN
ma-85	424	18	for	for	ADP
ma-85	424	19	solving	solve	VERB
ma-85	424	20	systems	system	NOUN
ma-85	424	21	of	of	ADP
ma-85	424	22	nonlinear	nonlinear	ADJ
ma-85	424	23	equations	equation	NOUN
ma-85	424	24	,	,	PUNCT
ma-85	425	1	appl.math	appl.math	PROPN
ma-85	425	2	.	.	PUNCT
ma-85	425	3	comput	comput	NOUN
ma-85	425	4	.	.	PUNCT
ma-85	426	1	218	218	NUM
ma-85	426	2	(	(	PUNCT
ma-85	426	3	2011	2011	NUM
ma-85	426	4	)	)	PUNCT
ma-85	426	5	2377–2385	2377–2385	NUM
ma-85	426	6	.	.	PUNCT
ma-85	427	1	https://doi.org/10.1016/j.amc.2011.08.011.[14	https://doi.org/10.1016/j.amc.2011.08.011.[14	PROPN
ma-85	427	2	]	]	PUNCT
ma-85	427	3	l.v	l.v	PROPN
ma-85	427	4	.	.	PROPN
ma-85	427	5	kantorovich	kantorovich	PROPN
ma-85	427	6	,	,	PUNCT
ma-85	427	7	g.p	g.p	PROPN
ma-85	427	8	.	.	PROPN
ma-85	427	9	akilov	akilov	PROPN
ma-85	427	10	,	,	PUNCT
ma-85	427	11	functional	functional	ADJ
ma-85	427	12	analysis	analysis	NOUN
ma-85	427	13	,	,	PUNCT
ma-85	427	14	pergamon	pergamon	PROPN
ma-85	427	15	press	press	PROPN
ma-85	427	16	,	,	PUNCT
ma-85	427	17	oxford	oxford	PROPN
ma-85	427	18	,	,	PUNCT
ma-85	427	19	(	(	PUNCT
ma-85	427	20	1982).[15	1982).[15	NUM
ma-85	427	21	]	]	SYM
ma-85	427	22	a.a	a.a	PROPN
ma-85	427	23	.	.	PROPN
ma-85	427	24	magréñan	magréñan	PROPN
ma-85	427	25	,	,	PUNCT
ma-85	427	26	i.k	i.k	PROPN
ma-85	427	27	.	.	PROPN
ma-85	427	28	argyros	argyros	PROPN
ma-85	427	29	,	,	PUNCT
ma-85	427	30	j.j	j.j	PROPN
ma-85	427	31	.	.	PROPN
ma-85	427	32	rainer	rainer	PROPN
ma-85	427	33	,	,	PUNCT
ma-85	427	34	j.a	j.a	PROPN
ma-85	427	35	.	.	PROPN
ma-85	427	36	sicilia	sicilia	PROPN
ma-85	427	37	,	,	PUNCT
ma-85	427	38	ball	ball	NOUN
ma-85	427	39	convergence	convergence	NOUN
ma-85	427	40	of	of	ADP
ma-85	427	41	a	a	DET
ma-85	427	42	sixth	sixth	ADJ
ma-85	427	43	-	-	PUNCT
ma-85	427	44	order	order	NOUN
ma-85	427	45	newton	newton	NOUN
ma-85	427	46	-	-	PUNCT
ma-85	427	47	like	like	NOUN
ma-85	427	48	schemebased	schemebase	VERB
ma-85	427	49	on	on	ADP
ma-85	427	50	means	mean	NOUN
ma-85	427	51	under	under	ADP
ma-85	427	52	weak	weak	ADJ
ma-85	427	53	conditions	condition	NOUN
ma-85	427	54	,	,	PUNCT
ma-85	427	55	j.	j.	PROPN
ma-85	427	56	math	math	PROPN
ma-85	427	57	.	.	PUNCT
ma-85	428	1	chem	chem	PROPN
ma-85	428	2	.	.	PUNCT
ma-85	429	1	56	56	NUM
ma-85	429	2	(	(	PUNCT
ma-85	429	3	2018	2018	NUM
ma-85	429	4	)	)	PUNCT
ma-85	429	5	2117	2117	NUM
ma-85	429	6	-	-	SYM
ma-85	429	7	2131	2131	NUM
ma-85	429	8	.	.	PUNCT
ma-85	430	1	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-85	430	2	s10910	s10910	PROPN
ma-85	430	3	-	-	PUNCT
ma-85	430	4	018	018	NUM
ma-85	430	5	-	-	PUNCT
ma-85	430	6	0856	0856	NUM
ma-85	430	7	-	-	PUNCT
ma-85	430	8	y.[16	y.[16	PROPN
ma-85	430	9	]	]	PUNCT
ma-85	430	10	a.a	a.a	PROPN
ma-85	430	11	.	.	PROPN
ma-85	430	12	magréñan	magréñan	PROPN
ma-85	430	13	,	,	PUNCT
ma-85	430	14	j.m	j.m	PROPN
ma-85	430	15	.	.	PROPN
ma-85	430	16	gutiérrez	gutiérrez	PROPN
ma-85	430	17	,	,	PUNCT
ma-85	430	18	real	real	ADJ
ma-85	430	19	dynamics	dynamic	NOUN
ma-85	430	20	for	for	ADP
ma-85	430	21	damped	damped	PROPN
ma-85	430	22	newton	newton	PROPN
ma-85	430	23	’s	’s	PART
ma-85	430	24	scheme	scheme	NOUN
ma-85	430	25	applied	apply	VERB
ma-85	430	26	to	to	ADP
ma-85	430	27	cubic	cubic	ADJ
ma-85	430	28	polynomials	polynomial	NOUN
ma-85	430	29	,	,	PUNCT
ma-85	430	30	j.	j.	PROPN
ma-85	430	31	comput.appl	comput.appl	PROPN
ma-85	430	32	.	.	PUNCT
ma-85	430	33	math	math	NOUN
ma-85	430	34	.	.	PUNCT
ma-85	431	1	275	275	NUM
ma-85	431	2	(	(	PUNCT
ma-85	431	3	2015	2015	NUM
ma-85	431	4	)	)	PUNCT
ma-85	432	1	527–538	527–538	NUM
ma-85	432	2	.	.	PUNCT
ma-85	433	1	https://doi.org/10.1016/j.cam.2013.11.019.[17	https://doi.org/10.1016/j.cam.2013.11.019.[17	PROPN
ma-85	433	2	]	]	X
ma-85	433	3	l.m	l.m	PROPN
ma-85	433	4	.	.	PROPN
ma-85	433	5	ortega	ortega	PROPN
ma-85	433	6	,	,	PUNCT
ma-85	433	7	w.c	w.c	PROPN
ma-85	433	8	.	.	PROPN
ma-85	433	9	rheinboldt	rheinboldt	ADJ
ma-85	433	10	,	,	PUNCT
ma-85	433	11	iterative	iterative	ADJ
ma-85	433	12	solution	solution	NOUN
ma-85	433	13	of	of	ADP
ma-85	433	14	nonlinear	nonlinear	ADJ
ma-85	433	15	equations	equation	NOUN
ma-85	433	16	in	in	ADP
ma-85	433	17	several	several	ADJ
ma-85	433	18	variables	variable	NOUN
ma-85	433	19	,	,	PUNCT
ma-85	433	20	academic	academic	ADJ
ma-85	433	21	press	press	NOUN
ma-85	433	22	,	,	PUNCT
ma-85	433	23	newyork	newyork	NOUN
ma-85	433	24	,	,	PUNCT
ma-85	433	25	(	(	PUNCT
ma-85	433	26	1970).[18	1970).[18	NUM
ma-85	433	27	]	]	X
ma-85	433	28	a.m.	a.m.	NOUN
ma-85	433	29	ostrowski	ostrowski	PROPN
ma-85	433	30	,	,	PUNCT
ma-85	433	31	solution	solution	NOUN
ma-85	433	32	of	of	ADP
ma-85	433	33	equations	equation	NOUN
ma-85	433	34	in	in	ADP
ma-85	433	35	euclidean	euclidean	NOUN
ma-85	433	36	and	and	CCONJ
ma-85	433	37	banach	banach	NOUN
ma-85	433	38	spaces	space	NOUN
ma-85	433	39	,	,	PUNCT
ma-85	433	40	elsevier	elsevier	NOUN
ma-85	433	41	,	,	PUNCT
ma-85	433	42	amsterdam	amsterdam	PROPN
ma-85	433	43	,	,	PUNCT
ma-85	433	44	1973.[19	1973.[19	NUM
ma-85	433	45	]	]	X
ma-85	433	46	f.a	f.a	PROPN
ma-85	433	47	.	.	PROPN
ma-85	433	48	potra	potra	PROPN
ma-85	433	49	,	,	PUNCT
ma-85	433	50	v.	v.	ADP
ma-85	433	51	pták	pták	ADJ
ma-85	433	52	,	,	PUNCT
ma-85	433	53	nondiscrete	nondiscrete	ADJ
ma-85	433	54	induction	induction	NOUN
ma-85	433	55	and	and	CCONJ
ma-85	433	56	iterative	iterative	NOUN
ma-85	433	57	processes	process	NOUN
ma-85	433	58	,	,	PUNCT
ma-85	433	59	research	research	NOUN
ma-85	433	60	notes	note	NOUN
ma-85	433	61	in	in	ADP
ma-85	433	62	mathematics	mathematic	NOUN
ma-85	433	63	,	,	PUNCT
ma-85	433	64	103	103	NUM
ma-85	433	65	.	.	PUNCT
ma-85	434	1	pitman(advanced	pitman(advance	VERB
ma-85	434	2	publishing	publishing	NOUN
ma-85	434	3	program	program	NOUN
ma-85	434	4	)	)	PUNCT
ma-85	434	5	,	,	PUNCT
ma-85	434	6	boston	boston	PROPN
ma-85	434	7	,	,	PUNCT
ma-85	434	8	ma	ma	PROPN
ma-85	434	9	.	.	PROPN
ma-85	435	1	(	(	PUNCT
ma-85	435	2	1984).[20	1984).[20	NUM
ma-85	435	3	]	]	X
ma-85	435	4	p.d	p.d	PROPN
ma-85	435	5	.	.	PROPN
ma-85	435	6	proinov	proinov	PROPN
ma-85	435	7	,	,	PUNCT
ma-85	435	8	general	general	ADJ
ma-85	435	9	local	local	ADJ
ma-85	435	10	convergence	convergence	NOUN
ma-85	435	11	theory	theory	NOUN
ma-85	435	12	for	for	ADP
ma-85	435	13	a	a	DET
ma-85	435	14	class	class	NOUN
ma-85	435	15	of	of	ADP
ma-85	435	16	iterative	iterative	NOUN
ma-85	435	17	processes	process	NOUN
ma-85	435	18	and	and	CCONJ
ma-85	435	19	its	its	PRON
ma-85	435	20	applications	application	NOUN
ma-85	435	21	to	to	ADP
ma-85	435	22	newton’sscheme	newton’sscheme	NOUN
ma-85	435	23	,	,	PUNCT
ma-85	435	24	j.	j.	PROPN
ma-85	435	25	complex	complex	PROPN
ma-85	435	26	.	.	PUNCT
ma-85	436	1	25	25	NUM
ma-85	436	2	(	(	PUNCT
ma-85	436	3	2009	2009	NUM
ma-85	436	4	)	)	PUNCT
ma-85	436	5	38	38	NUM
ma-85	436	6	-	-	SYM
ma-85	436	7	62	62	NUM
ma-85	436	8	.	.	PUNCT
ma-85	437	1	https://doi.org/10.1016/j.jco.2008.05.006[21	https://doi.org/10.1016/j.jco.2008.05.006[21	PROPN
ma-85	437	2	]	]	PUNCT
ma-85	437	3	p.d	p.d	PROPN
ma-85	437	4	.	.	PROPN
ma-85	437	5	proinov	proinov	PROPN
ma-85	437	6	,	,	PUNCT
ma-85	437	7	new	new	ADJ
ma-85	437	8	general	general	ADJ
ma-85	437	9	convergence	convergence	NOUN
ma-85	437	10	theory	theory	NOUN
ma-85	437	11	for	for	ADP
ma-85	437	12	iterative	iterative	NOUN
ma-85	437	13	processes	process	NOUN
ma-85	437	14	and	and	CCONJ
ma-85	437	15	its	its	PRON
ma-85	437	16	applications	application	NOUN
ma-85	437	17	to	to	ADP
ma-85	437	18	newton	newton	PROPN
ma-85	437	19	-	-	PUNCT
ma-85	437	20	kantorovichtype	kantorovichtype	NOUN
ma-85	437	21	theorems	theorems	PROPN
ma-85	437	22	,	,	PUNCT
ma-85	437	23	j.	j.	PROPN
ma-85	437	24	complex	complex	PROPN
ma-85	437	25	.	.	PUNCT
ma-85	438	1	26	26	NUM
ma-85	438	2	(	(	PUNCT
ma-85	438	3	2010	2010	NUM
ma-85	438	4	)	)	PUNCT
ma-85	438	5	3	3	NUM
ma-85	438	6	-	-	SYM
ma-85	438	7	42	42	NUM
ma-85	438	8	.	.	PUNCT
ma-85	439	1	https://doi.org/10.1016/j.jco.2009.05.001[22	https://doi.org/10.1016/j.jco.2009.05.001[22	NOUN
ma-85	439	2	]	]	PUNCT
ma-85	439	3	w.c	w.c	PROPN
ma-85	439	4	.	.	PROPN
ma-85	439	5	rheinboldt	rheinboldt	PROPN
ma-85	439	6	,	,	PUNCT
ma-85	439	7	an	an	DET
ma-85	439	8	adaptive	adaptive	ADJ
ma-85	439	9	continuation	continuation	NOUN
ma-85	439	10	process	process	NOUN
ma-85	439	11	of	of	ADP
ma-85	439	12	solving	solve	VERB
ma-85	439	13	systems	system	NOUN
ma-85	439	14	of	of	ADP
ma-85	439	15	nonlinear	nonlinear	ADJ
ma-85	439	16	equations	equation	NOUN
ma-85	439	17	,	,	PUNCT
ma-85	439	18	banach	banach	NOUN
ma-85	439	19	center	center	NOUN
ma-85	439	20	publ.3	publ.3	NOUN
ma-85	439	21	(	(	PUNCT
ma-85	439	22	1978	1978	NUM
ma-85	439	23	)	)	PUNCT
ma-85	439	24	129	129	NUM
ma-85	439	25	-	-	SYM
ma-85	439	26	142.[23	142.[23	NUM
ma-85	439	27	]	]	X
ma-85	439	28	s.m	s.m	PROPN
ma-85	439	29	.	.	PROPN
ma-85	439	30	shakhno	shakhno	PROPN
ma-85	439	31	,	,	PUNCT
ma-85	439	32	o.p	o.p	PROPN
ma-85	439	33	.	.	PROPN
ma-85	439	34	gnatyshyn	gnatyshyn	PROPN
ma-85	439	35	,	,	PUNCT
ma-85	439	36	on	on	ADP
ma-85	439	37	an	an	DET
ma-85	439	38	iterative	iterative	ADJ
ma-85	439	39	algorithm	algorithm	NOUN
ma-85	439	40	of	of	ADP
ma-85	439	41	order	order	NOUN
ma-85	439	42	1.839	1.839	NUM
ma-85	439	43	.	.	PUNCT
ma-85	439	44	.	.	PUNCT
ma-85	439	45	.	.	PUNCT
ma-85	440	1	for	for	ADP
ma-85	440	2	solving	solve	VERB
ma-85	440	3	the	the	DET
ma-85	440	4	nonlinear	nonlinear	ADJ
ma-85	440	5	least	least	ADJ
ma-85	440	6	squaresproblems	squaresproblem	NOUN
ma-85	440	7	,	,	PUNCT
ma-85	440	8	appl	appl	PROPN
ma-85	440	9	.	.	PROPN
ma-85	440	10	math	math	PROPN
ma-85	440	11	.	.	PUNCT
ma-85	441	1	comput	comput	NOUN
ma-85	441	2	.	.	PUNCT
ma-85	442	1	161	161	NUM
ma-85	442	2	(	(	PUNCT
ma-85	442	3	2005	2005	NUM
ma-85	442	4	)	)	PUNCT
ma-85	442	5	253–264	253–264	NUM
ma-85	442	6	.	.	PUNCT
ma-85	443	1	https://doi.org/10.1016/j.amc.2003.12.025.[24	https://doi.org/10.1016/j.amc.2003.12.025.[24	PROPN
ma-85	443	2	]	]	PUNCT
ma-85	443	3	s.m	s.m	PROPN
ma-85	443	4	.	.	PROPN
ma-85	443	5	shakhno	shakhno	PROPN
ma-85	443	6	,	,	PUNCT
ma-85	443	7	r.p	r.p	PROPN
ma-85	443	8	.	.	PROPN
ma-85	443	9	iakymchuk	iakymchuk	PROPN
ma-85	443	10	,	,	PUNCT
ma-85	443	11	h.p	h.p	PROPN
ma-85	443	12	.	.	PROPN
ma-85	443	13	yarmola	yarmola	PROPN
ma-85	443	14	,	,	PUNCT
ma-85	443	15	convergence	convergence	NOUN
ma-85	443	16	analysis	analysis	NOUN
ma-85	443	17	of	of	ADP
ma-85	443	18	a	a	DET
ma-85	443	19	two	two	NUM
ma-85	443	20	step	step	NOUN
ma-85	443	21	scheme	scheme	NOUN
ma-85	443	22	for	for	ADP
ma-85	443	23	the	the	DET
ma-85	443	24	nonlinear	nonlinear	ADJ
ma-85	443	25	squaresproblem	squaresproblem	NOUN
ma-85	443	26	with	with	ADP
ma-85	443	27	decomposition	decomposition	NOUN
ma-85	443	28	of	of	ADP
ma-85	443	29	operator	operator	NOUN
ma-85	443	30	,	,	PUNCT
ma-85	443	31	j.	j.	PROPN
ma-85	443	32	numer	numer	PROPN
ma-85	443	33	.	.	PUNCT
ma-85	443	34	appl	appl	PROPN
ma-85	443	35	.	.	PROPN
ma-85	443	36	math	math	PROPN
ma-85	443	37	.	.	PUNCT
ma-85	444	1	128	128	NUM
ma-85	444	2	(	(	PUNCT
ma-85	444	3	2018	2018	NUM
ma-85	444	4	)	)	PUNCT
ma-85	444	5	82	82	NUM
ma-85	444	6	-	-	SYM
ma-85	444	7	95.[25	95.[25	PROPN
ma-85	444	8	]	]	X
ma-85	444	9	j.r	j.r	PROPN
ma-85	444	10	.	.	PROPN
ma-85	444	11	sharma	sharma	PROPN
ma-85	444	12	,	,	PUNCT
ma-85	444	13	r.k	r.k	PROPN
ma-85	444	14	.	.	PROPN
ma-85	444	15	guha	guha	PROPN
ma-85	444	16	,	,	PUNCT
ma-85	444	17	r.	r.	PROPN
ma-85	444	18	sharma	sharma	PROPN
ma-85	444	19	,	,	PUNCT
ma-85	444	20	an	an	DET
ma-85	444	21	efficient	efficient	ADJ
ma-85	444	22	fourth	fourth	ADJ
ma-85	444	23	order	order	NOUN
ma-85	444	24	weighted	weight	VERB
ma-85	444	25	newton	newton	PROPN
ma-85	444	26	scheme	scheme	NOUN
ma-85	444	27	for	for	ADP
ma-85	444	28	systems	system	NOUN
ma-85	444	29	of	of	ADP
ma-85	444	30	nonlinearequations	nonlinearequation	NOUN
ma-85	444	31	,	,	PUNCT
ma-85	444	32	numer	numer	NOUN
ma-85	444	33	.	.	PROPN
ma-85	445	1	algorithms	algorithms	PROPN
ma-85	445	2	,	,	PUNCT
ma-85	445	3	62	62	NUM
ma-85	445	4	(	(	PUNCT
ma-85	445	5	2013	2013	NUM
ma-85	445	6	)	)	PUNCT
ma-85	445	7	307–323	307–323	NUM
ma-85	445	8	,	,	PUNCT
ma-85	445	9	https://doi.org/10.1007/s11075-012-9585-7.[26	https://doi.org/10.1007/s11075-012-9585-7.[26	PROPN
ma-85	445	10	]	]	X
ma-85	445	11	j.f	j.f	PROPN
ma-85	445	12	.	.	PROPN
ma-85	445	13	traub	traub	PROPN
ma-85	445	14	,	,	PUNCT
ma-85	445	15	iterative	iterative	NOUN
ma-85	445	16	schemes	scheme	NOUN
ma-85	445	17	for	for	ADP
ma-85	445	18	the	the	DET
ma-85	445	19	solution	solution	NOUN
ma-85	445	20	of	of	ADP
ma-85	445	21	equations	equation	NOUN
ma-85	445	22	,	,	PUNCT
ma-85	445	23	prentice	prentice	NOUN
ma-85	445	24	hall	hall	PROPN
ma-85	445	25	,	,	PUNCT
ma-85	445	26	new	new	PROPN
ma-85	445	27	jersey	jersey	PROPN
ma-85	445	28	,	,	PUNCT
ma-85	445	29	u.s.a	u.s.a	PROPN
ma-85	445	30	.	.	PUNCT
ma-85	446	1	(	(	PUNCT
ma-85	446	2	1964).[27	1964).[27	NUM
ma-85	446	3	]	]	X
ma-85	446	4	r.	r.	PROPN
ma-85	446	5	verma	verma	PROPN
ma-85	446	6	,	,	PUNCT
ma-85	446	7	new	new	ADJ
ma-85	446	8	trends	trend	NOUN
ma-85	446	9	in	in	ADP
ma-85	446	10	fractional	fractional	ADJ
ma-85	446	11	programming	programming	NOUN
ma-85	446	12	,	,	PUNCT
ma-85	446	13	nova	nova	PROPN
ma-85	446	14	science	science	NOUN
ma-85	446	15	publisher	publisher	NOUN
ma-85	446	16	,	,	PUNCT
ma-85	446	17	new	new	PROPN
ma-85	446	18	york	york	PROPN
ma-85	446	19	,	,	PUNCT
ma-85	446	20	usa	usa	PROPN
ma-85	446	21	,	,	PUNCT
ma-85	446	22	(	(	PUNCT
ma-85	446	23	2019	2019	NUM
ma-85	446	24	)	)	PUNCT
ma-85	446	25	.	.	PUNCT
ma-85	447	1	https://doi.org/10.28924/ada/ma.2.13	https://doi.org/10.28924/ada/ma.2.13	PROPN
ma-85	447	2	https://doi.org/10.1007/s13226-020-0409-5	https://doi.org/10.1007/s13226-020-0409-5	NUM
ma-85	447	3	https://doi.org/10.1090/s0025-5718-04-01646-1	https://doi.org/10.1090/s0025-5718-04-01646-1	NUM
ma-85	447	4	https://doi.org/10.1016/j.amc.2007.01.062	https://doi.org/10.1016/j.amc.2007.01.062	PRON
ma-85	448	1	https://doi.org/10.1016/j.amc.2011.08.011	https://doi.org/10.1016/j.amc.2011.08.011	AUX
ma-85	448	2	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-85	448	3	s10910	s10910	PROPN
ma-85	448	4	-	-	PUNCT
ma-85	448	5	018	018	NUM
ma-85	448	6	-	-	PUNCT
ma-85	448	7	0856	0856	NUM
ma-85	448	8	-	-	PUNCT
ma-85	448	9	y	y	PROPN
ma-85	448	10	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-85	448	11	s10910	s10910	PROPN
ma-85	448	12	-	-	PUNCT
ma-85	448	13	018	018	NUM
ma-85	448	14	-	-	PUNCT
ma-85	448	15	0856	0856	NUM
ma-85	448	16	-	-	PUNCT
ma-85	448	17	y	y	PROPN
ma-85	448	18	https://doi.org/10.1016/j.cam.2013.11.019	https://doi.org/10.1016/j.cam.2013.11.019	PROPN
ma-85	448	19	https://doi.org/10.1016/j.jco.2008.05.006	https://doi.org/10.1016/j.jco.2008.05.006	PROPN
ma-85	448	20	https://doi.org/10.1016/j.jco.2009.05.001	https://doi.org/10.1016/j.jco.2009.05.001	PROPN
ma-85	448	21	https://doi.org/10.1016/j.amc.2003.12.025	https://doi.org/10.1016/j.amc.2003.12.025	PROPN
ma-85	448	22	https://doi.org/10.1007/s11075-012-9585-7	https://doi.org/10.1007/s11075-012-9585-7	PROPN
ma-85	448	23	1	1	NUM
ma-85	448	24	.	.	PUNCT
ma-85	449	1	introduction	introduction	NOUN
ma-85	449	2	2	2	NUM
ma-85	449	3	.	.	PUNCT
ma-85	449	4	majorizing	majorize	VERB
ma-85	449	5	sequences	sequence	NOUN
ma-85	449	6	3	3	NUM
ma-85	449	7	.	.	PUNCT
ma-85	449	8	semi	semi	ADJ
ma-85	449	9	-	-	ADJ
ma-85	449	10	local	local	ADJ
ma-85	449	11	convergence	convergence	NOUN
ma-85	449	12	4	4	NUM
ma-85	449	13	.	.	PUNCT
ma-85	449	14	numerical	numerical	ADJ
ma-85	449	15	experiments	experiment	NOUN
ma-85	449	16	5	5	NUM
ma-85	449	17	.	.	PUNCT
ma-85	450	1	conclusion	conclusion	NOUN
ma-85	450	2	references	reference	NOUN