id	sid	tid	token	lemma	pos
ma-17	1	1	2021	2021	NUM
ma-17	1	2	ada	ada	PROPN
ma-17	1	3	academica	academica	PROPN
ma-17	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-17	1	5	.	.	PUNCT
ma-17	2	1	j.	j.	PROPN
ma-17	2	2	math	math	PROPN
ma-17	2	3	.	.	PUNCT
ma-17	3	1	anal	anal	ADJ
ma-17	3	2	.	.	PUNCT
ma-17	4	1	1	1	NUM
ma-17	4	2	(	(	PUNCT
ma-17	4	3	2021	2021	NUM
ma-17	4	4	)	)	PUNCT
ma-17	4	5	68	68	NUM
ma-17	4	6	-	-	PUNCT
ma-17	4	7	85doi	85doi	NUM
ma-17	4	8	:	:	PUNCT
ma-17	4	9	10.28924	10.28924	NUM
ma-17	4	10	/	/	SYM
ma-17	4	11	ada	ada	PROPN
ma-17	4	12	/	/	SYM
ma-17	4	13	ma.1.68	ma.1.68	PROPN
ma-17	4	14	unified	unified	ADJ
ma-17	4	15	convergence	convergence	NOUN
ma-17	4	16	analysis	analysis	NOUN
ma-17	4	17	of	of	ADP
ma-17	4	18	two	two	NUM
ma-17	4	19	-	-	PUNCT
ma-17	4	20	step	step	NOUN
ma-17	4	21	iterative	iterative	NOUN
ma-17	4	22	methods	method	NOUN
ma-17	4	23	for	for	ADP
ma-17	4	24	solving	solve	VERB
ma-17	4	25	equations	equation	NOUN
ma-17	4	26	ioannis	ioannis	PROPN
ma-17	4	27	k.	k.	PROPN
ma-17	4	28	argyros	argyros	PROPN
ma-17	4	29	department	department	PROPN
ma-17	4	30	of	of	ADP
ma-17	4	31	mathematical	mathematical	ADJ
ma-17	4	32	sciences	sciences	PROPN
ma-17	4	33	,	,	PUNCT
ma-17	4	34	cameron	cameron	PROPN
ma-17	4	35	university	university	PROPN
ma-17	4	36	,	,	PUNCT
ma-17	4	37	lawton	lawton	PROPN
ma-17	4	38	,	,	PUNCT
ma-17	4	39	ok	ok	PROPN
ma-17	4	40	73505	73505	NUM
ma-17	4	41	,	,	PUNCT
ma-17	4	42	usa	usa	PROPN
ma-17	4	43	correspondence	correspondence	NOUN
ma-17	4	44	:	:	PUNCT
ma-17	4	45	iargyros@cameron.edu	iargyros@cameron.edu	X
ma-17	5	1	abstract	abstract	ADJ
ma-17	5	2	.	.	PUNCT
ma-17	6	1	in	in	ADP
ma-17	6	2	this	this	DET
ma-17	6	3	paper	paper	NOUN
ma-17	6	4	we	we	PRON
ma-17	6	5	consider	consider	VERB
ma-17	6	6	unified	unified	ADJ
ma-17	6	7	convergence	convergence	NOUN
ma-17	6	8	analysis	analysis	NOUN
ma-17	6	9	of	of	ADP
ma-17	6	10	two	two	NUM
ma-17	6	11	-	-	PUNCT
ma-17	6	12	step	step	NOUN
ma-17	6	13	iterative	iterative	NOUN
ma-17	6	14	methods	method	NOUN
ma-17	6	15	forsolving	forsolve	VERB
ma-17	6	16	equations	equation	NOUN
ma-17	6	17	in	in	ADP
ma-17	6	18	the	the	DET
ma-17	6	19	banach	banach	NOUN
ma-17	6	20	space	space	NOUN
ma-17	6	21	setting	setting	NOUN
ma-17	6	22	.	.	PUNCT
ma-17	7	1	the	the	DET
ma-17	7	2	convergence	convergence	NOUN
ma-17	7	3	order	order	NOUN
ma-17	7	4	four	four	NUM
ma-17	7	5	was	be	AUX
ma-17	7	6	shown	show	VERB
ma-17	7	7	using	use	VERB
ma-17	7	8	taylorexpansions	taylorexpansion	NOUN
ma-17	7	9	requiring	require	VERB
ma-17	7	10	the	the	DET
ma-17	7	11	existence	existence	NOUN
ma-17	7	12	of	of	ADP
ma-17	7	13	the	the	DET
ma-17	7	14	fifth	fifth	ADJ
ma-17	7	15	derivative	derivative	NOUN
ma-17	7	16	not	not	PART
ma-17	7	17	on	on	ADP
ma-17	7	18	this	this	DET
ma-17	7	19	method	method	NOUN
ma-17	7	20	.	.	PUNCT
ma-17	8	1	but	but	CCONJ
ma-17	8	2	these	these	PRON
ma-17	8	3	hypotheseslimit	hypotheseslimit	VERB
ma-17	8	4	the	the	DET
ma-17	8	5	utilization	utilization	NOUN
ma-17	8	6	of	of	ADP
ma-17	8	7	it	it	PRON
ma-17	8	8	to	to	ADP
ma-17	8	9	functions	function	NOUN
ma-17	8	10	which	which	PRON
ma-17	8	11	are	be	AUX
ma-17	8	12	at	at	ADV
ma-17	8	13	least	least	ADV
ma-17	8	14	five	five	NUM
ma-17	8	15	times	time	NOUN
ma-17	8	16	differentiable	differentiable	ADJ
ma-17	8	17	although	although	SCONJ
ma-17	8	18	the	the	DET
ma-17	8	19	methodmay	methodmay	NOUN
ma-17	8	20	converge	converge	VERB
ma-17	8	21	.	.	PUNCT
ma-17	9	1	as	as	ADV
ma-17	9	2	far	far	ADV
ma-17	9	3	as	as	SCONJ
ma-17	9	4	we	we	PRON
ma-17	9	5	know	know	VERB
ma-17	9	6	no	no	DET
ma-17	9	7	semi	semi	ADJ
ma-17	9	8	-	-	ADJ
ma-17	9	9	local	local	ADJ
ma-17	9	10	convergence	convergence	NOUN
ma-17	9	11	has	have	AUX
ma-17	9	12	been	be	AUX
ma-17	9	13	given	give	VERB
ma-17	9	14	in	in	ADP
ma-17	9	15	this	this	DET
ma-17	9	16	setting	setting	NOUN
ma-17	9	17	.	.	PUNCT
ma-17	10	1	ourgoal	ourgoal	PROPN
ma-17	10	2	is	be	AUX
ma-17	10	3	to	to	PART
ma-17	10	4	extend	extend	VERB
ma-17	10	5	the	the	DET
ma-17	10	6	applicability	applicability	NOUN
ma-17	10	7	of	of	ADP
ma-17	10	8	this	this	DET
ma-17	10	9	method	method	NOUN
ma-17	10	10	in	in	ADP
ma-17	10	11	both	both	CCONJ
ma-17	10	12	the	the	DET
ma-17	10	13	local	local	ADJ
ma-17	10	14	and	and	CCONJ
ma-17	10	15	semi	semi	ADJ
ma-17	10	16	-	-	ADJ
ma-17	10	17	local	local	ADJ
ma-17	10	18	convergence	convergence	NOUN
ma-17	10	19	caseand	caseand	NOUN
ma-17	10	20	in	in	ADP
ma-17	10	21	the	the	DET
ma-17	10	22	more	more	ADV
ma-17	10	23	general	general	ADJ
ma-17	10	24	setting	setting	NOUN
ma-17	10	25	of	of	ADP
ma-17	10	26	banach	banach	NOUN
ma-17	10	27	space	space	NOUN
ma-17	10	28	valued	value	VERB
ma-17	10	29	operators	operator	NOUN
ma-17	10	30	.	.	PUNCT
ma-17	11	1	moreover	moreover	ADV
ma-17	11	2	,	,	PUNCT
ma-17	11	3	we	we	PRON
ma-17	11	4	use	use	VERB
ma-17	11	5	our	our	PRON
ma-17	11	6	idea	idea	NOUN
ma-17	11	7	ofrecurrent	ofrecurrent	NOUN
ma-17	11	8	functions	function	NOUN
ma-17	11	9	and	and	CCONJ
ma-17	11	10	conditions	condition	NOUN
ma-17	11	11	only	only	ADV
ma-17	11	12	on	on	ADP
ma-17	11	13	the	the	DET
ma-17	11	14	first	first	ADJ
ma-17	11	15	derivative	derivative	ADJ
ma-17	11	16	and	and	CCONJ
ma-17	11	17	divided	divide	VERB
ma-17	11	18	differences	difference	NOUN
ma-17	11	19	which	which	PRON
ma-17	11	20	appearon	appearon	VERB
ma-17	11	21	the	the	DET
ma-17	11	22	method	method	NOUN
ma-17	11	23	.	.	PUNCT
ma-17	12	1	this	this	DET
ma-17	12	2	idea	idea	NOUN
ma-17	12	3	can	can	AUX
ma-17	12	4	be	be	AUX
ma-17	12	5	used	use	VERB
ma-17	12	6	to	to	PART
ma-17	12	7	extend	extend	VERB
ma-17	12	8	other	other	ADJ
ma-17	12	9	high	high	ADJ
ma-17	12	10	convergence	convergence	NOUN
ma-17	12	11	multipoint	multipoint	NOUN
ma-17	12	12	and	and	CCONJ
ma-17	12	13	multistepmethods	multistepmethod	NOUN
ma-17	12	14	.	.	PUNCT
ma-17	13	1	numerical	numerical	ADJ
ma-17	13	2	experiments	experiment	NOUN
ma-17	13	3	testing	test	VERB
ma-17	13	4	the	the	DET
ma-17	13	5	convergence	convergence	NOUN
ma-17	13	6	criteria	criterion	NOUN
ma-17	13	7	complement	complement	VERB
ma-17	13	8	this	this	DET
ma-17	13	9	study	study	NOUN
ma-17	13	10	.	.	PUNCT
ma-17	14	1	1	1	X
ma-17	14	2	.	.	X
ma-17	14	3	introduction	introduction	NOUN
ma-17	14	4	we	we	PRON
ma-17	14	5	consider	consider	VERB
ma-17	14	6	the	the	DET
ma-17	14	7	problem	problem	NOUN
ma-17	14	8	of	of	ADP
ma-17	14	9	approximating	approximate	VERB
ma-17	14	10	a	a	DET
ma-17	14	11	solution	solution	NOUN
ma-17	14	12	x∗	x∗	NOUN
ma-17	14	13	of	of	ADP
ma-17	14	14	equation	equation	NOUN
ma-17	14	15	f	f	X
ma-17	14	16	(	(	PUNCT
ma-17	14	17	x	x	X
ma-17	14	18	)	)	PUNCT
ma-17	14	19	=	=	SYM
ma-17	14	20	0	0	NUM
ma-17	14	21	,	,	PUNCT
ma-17	14	22	(	(	PUNCT
ma-17	14	23	1.1	1.1	NUM
ma-17	14	24	)	)	PUNCT
ma-17	14	25	where	where	SCONJ
ma-17	14	26	f	f	X
ma-17	14	27	:	:	PUNCT
ma-17	15	1	ω	ω	NUM
ma-17	15	2	⊂	⊂	PROPN
ma-17	15	3	b	b	X
ma-17	15	4	−→	−→	ADJ
ma-17	15	5	b1	b1	NOUN
ma-17	15	6	is	be	AUX
ma-17	15	7	a	a	DET
ma-17	15	8	continuous	continuous	ADJ
ma-17	15	9	operator	operator	NOUN
ma-17	15	10	acting	act	VERB
ma-17	15	11	between	between	ADP
ma-17	15	12	banach	banach	NOUN
ma-17	15	13	spaces	space	NOUN
ma-17	15	14	b	b	NOUN
ma-17	15	15	and	and	CCONJ
ma-17	15	16	b1	b1	VERB
ma-17	15	17	with	with	ADP
ma-17	15	18	ω	ω	PROPN
ma-17	15	19	6=	6=	ADP
ma-17	15	20	∅.	∅.	NOUN
ma-17	15	21	since	since	SCONJ
ma-17	15	22	a	a	DET
ma-17	15	23	closed	closed	ADJ
ma-17	15	24	form	form	NOUN
ma-17	15	25	solution	solution	NOUN
ma-17	15	26	is	be	AUX
ma-17	15	27	not	not	PART
ma-17	15	28	possible	possible	ADJ
ma-17	15	29	in	in	ADP
ma-17	15	30	general	general	ADJ
ma-17	15	31	,	,	PUNCT
ma-17	15	32	iterative	iterative	ADJ
ma-17	15	33	methods	method	NOUN
ma-17	15	34	are	be	AUX
ma-17	15	35	used	use	VERB
ma-17	15	36	forsolving	forsolve	VERB
ma-17	15	37	(	(	PUNCT
ma-17	15	38	1.1	1.1	NUM
ma-17	15	39	)	)	PUNCT
ma-17	15	40	.	.	PUNCT
ma-17	16	1	many	many	ADJ
ma-17	16	2	iterative	iterative	NOUN
ma-17	16	3	methods	method	NOUN
ma-17	16	4	are	be	AUX
ma-17	16	5	studied	study	VERB
ma-17	16	6	for	for	ADP
ma-17	16	7	approximating	approximate	VERB
ma-17	16	8	x∗.	x∗.	NOUN
ma-17	17	1	in	in	ADP
ma-17	17	2	this	this	DET
ma-17	17	3	paper	paper	NOUN
ma-17	17	4	,	,	PUNCT
ma-17	17	5	we	we	PRON
ma-17	17	6	considerthe	considerthe	VERB
ma-17	17	7	iterative	iterative	NOUN
ma-17	17	8	methods	method	NOUN
ma-17	17	9	,	,	PUNCT
ma-17	17	10	defined	define	VERB
ma-17	17	11	for	for	ADP
ma-17	17	12	n	n	NOUN
ma-17	17	13	=	=	SYM
ma-17	17	14	0	0	NUM
ma-17	17	15	,	,	PUNCT
ma-17	17	16	1	1	NUM
ma-17	17	17	,	,	PUNCT
ma-17	17	18	2	2	NUM
ma-17	17	19	,	,	PUNCT
ma-17	17	20	.	.	PUNCT
ma-17	17	21	.	.	PUNCT
ma-17	17	22	.	.	PUNCT
ma-17	18	1	,	,	PUNCT
ma-17	18	2	by	by	ADP
ma-17	18	3	yn	yn	X
ma-17	18	4	=	=	PUNCT
ma-17	18	5	xn	xn	PROPN
ma-17	19	1	−	−	PROPN
ma-17	19	2	f	f	PROPN
ma-17	19	3	′(xn)−1f	′(xn)−1f	PROPN
ma-17	19	4	(	(	PUNCT
ma-17	19	5	xn	xn	PROPN
ma-17	19	6	)	)	PUNCT
ma-17	19	7	xn+1	xn+1	PUNCT
ma-17	19	8	=	=	SYM
ma-17	20	1	yn	yn	PROPN
ma-17	20	2	−	−	PROPN
ma-17	20	3	anf	anf	PROPN
ma-17	20	4	′(xn)−1f	′(xn)−1f	PROPN
ma-17	20	5	(	(	PUNCT
ma-17	20	6	yn	yn	PROPN
ma-17	20	7	)	)	PUNCT
ma-17	20	8	,	,	PUNCT
ma-17	20	9	(	(	PUNCT
ma-17	20	10	1.2	1.2	NUM
ma-17	20	11	)	)	PUNCT
ma-17	20	12	an	an	DET
ma-17	20	13	=	=	SYM
ma-17	20	14	a(xn	a(xn	PROPN
ma-17	20	15	,	,	PUNCT
ma-17	20	16	yn	yn	PROPN
ma-17	20	17	)	)	PUNCT
ma-17	20	18	,	,	PUNCT
ma-17	20	19	a	a	PRON
ma-17	20	20	:	:	PUNCT
ma-17	20	21	ω×ω	ω×ω	NUM
ma-17	20	22	−→	−→	ADJ
ma-17	20	23	l(b	l(b	PROPN
ma-17	20	24	,	,	PUNCT
ma-17	20	25	b1	b1	NOUN
ma-17	20	26	)	)	PUNCT
ma-17	20	27	,	,	PUNCT
ma-17	20	28	where	where	SCONJ
ma-17	20	29	a−1	a−1	PROPN
ma-17	20	30	∈	∈	PROPN
ma-17	20	31	l(b1	l(b1	NOUN
ma-17	20	32	,	,	PUNCT
ma-17	20	33	b	b	NOUN
ma-17	20	34	)	)	PUNCT
ma-17	20	35	.	.	PUNCT
ma-17	21	1	many	many	ADJ
ma-17	21	2	methods	method	NOUN
ma-17	21	3	are	be	AUX
ma-17	21	4	special	special	ADJ
ma-17	21	5	casesof	casesof	NOUN
ma-17	21	6	(	(	PUNCT
ma-17	21	7	1.2	1.2	NUM
ma-17	21	8	)	)	PUNCT
ma-17	21	9	.	.	PUNCT
ma-17	22	1	for	for	ADP
ma-17	22	2	example	example	NOUN
ma-17	22	3	:	:	PUNCT
ma-17	22	4	received	receive	VERB
ma-17	22	5	:	:	PUNCT
ma-17	22	6	31	31	NUM
ma-17	22	7	aug	aug	PROPN
ma-17	22	8	2021	2021	NUM
ma-17	22	9	.	.	PUNCT
ma-17	23	1	key	key	ADJ
ma-17	23	2	words	word	NOUN
ma-17	23	3	and	and	CCONJ
ma-17	23	4	phrases	phrase	NOUN
ma-17	23	5	.	.	PUNCT
ma-17	24	1	iterative	iterative	NOUN
ma-17	24	2	methods	method	NOUN
ma-17	24	3	;	;	PUNCT
ma-17	24	4	banach	banach	NOUN
ma-17	24	5	space	space	NOUN
ma-17	24	6	;	;	PUNCT
ma-17	24	7	convergence	convergence	NOUN
ma-17	24	8	criterion	criterion	NOUN
ma-17	24	9	;	;	PUNCT
ma-17	24	10	continuous	continuous	ADJ
ma-17	24	11	functions.68	functions.68	PROPN
ma-17	24	12	https://adac.ee	https://adac.ee	PROPN
ma-17	24	13	https://doi.org/10.28924/ada/ma.1.68	https://doi.org/10.28924/ada/ma.1.68	PROPN
ma-17	24	14	eur	eur	PROPN
ma-17	24	15	.	.	PUNCT
ma-17	25	1	j.	j.	PROPN
ma-17	25	2	math	math	PROPN
ma-17	25	3	.	.	PUNCT
ma-17	26	1	anal	anal	ADJ
ma-17	26	2	.	.	PUNCT
ma-17	27	1	1	1	NUM
ma-17	27	2	(	(	PUNCT
ma-17	27	3	2021	2021	NUM
ma-17	27	4	)	)	PUNCT
ma-17	27	5	69	69	NUM
ma-17	27	6	traub	traub	NOUN
ma-17	28	1	[	[	X
ma-17	28	2	35	35	NUM
ma-17	28	3	]	]	X
ma-17	28	4	yn	yn	PROPN
ma-17	28	5	=	=	PUNCT
ma-17	28	6	xn	xn	PROPN
ma-17	29	1	−	−	PROPN
ma-17	29	2	f	f	PROPN
ma-17	29	3	′(xn)−1f	′(xn)−1f	PROPN
ma-17	29	4	(	(	PUNCT
ma-17	29	5	xn	xn	PROPN
ma-17	29	6	)	)	PUNCT
ma-17	29	7	xn+1	xn+1	PUNCT
ma-17	29	8	=	=	SYM
ma-17	30	1	yn	yn	PROPN
ma-17	30	2	−	−	PROPN
ma-17	30	3	f	f	PROPN
ma-17	30	4	′(xn)−1f	′(xn)−1f	PROPN
ma-17	30	5	(	(	PUNCT
ma-17	30	6	yn	yn	PROPN
ma-17	30	7	)	)	PUNCT
ma-17	30	8	,	,	PUNCT
ma-17	30	9	(	(	PUNCT
ma-17	30	10	1.3	1.3	NUM
ma-17	30	11	)	)	PUNCT
ma-17	30	12	newton	newton	NOUN
ma-17	31	1	[	[	X
ma-17	31	2	6	6	NUM
ma-17	31	3	]	]	PUNCT
ma-17	31	4	yn	yn	PROPN
ma-17	31	5	=	=	PUNCT
ma-17	31	6	xn	xn	PROPN
ma-17	32	1	−	−	PROPN
ma-17	32	2	f	f	PROPN
ma-17	32	3	′(xn)−1f	′(xn)−1f	PROPN
ma-17	32	4	(	(	PUNCT
ma-17	32	5	xn	xn	PROPN
ma-17	32	6	)	)	PUNCT
ma-17	32	7	xn+1	xn+1	PUNCT
ma-17	32	8	=	=	SYM
ma-17	33	1	yn	yn	PROPN
ma-17	33	2	−	−	PROPN
ma-17	33	3	f	f	PROPN
ma-17	33	4	′(yn)−1f	′(yn)−1f	X
ma-17	33	5	(	(	PUNCT
ma-17	33	6	yn	yn	PROPN
ma-17	33	7	)	)	PUNCT
ma-17	33	8	,	,	PUNCT
ma-17	33	9	(	(	PUNCT
ma-17	33	10	1.4	1.4	NUM
ma-17	33	11	)	)	PUNCT
ma-17	33	12	ostrowski	ostrowski	NOUN
ma-17	34	1	[	[	X
ma-17	34	2	25	25	NUM
ma-17	34	3	]	]	X
ma-17	34	4	yn	yn	PROPN
ma-17	34	5	=	=	PUNCT
ma-17	34	6	xn	xn	PROPN
ma-17	35	1	−	−	PROPN
ma-17	35	2	f	f	PROPN
ma-17	35	3	′(xn)−1f	′(xn)−1f	PROPN
ma-17	35	4	(	(	PUNCT
ma-17	35	5	xn	xn	PROPN
ma-17	35	6	)	)	PUNCT
ma-17	35	7	xn+1	xn+1	PUNCT
ma-17	35	8	=	=	SYM
ma-17	36	1	yn	yn	INTJ
ma-17	36	2	−	−	PROPN
ma-17	37	1	(	(	PUNCT
ma-17	37	2	2[xn	2[xn	NUM
ma-17	37	3	,	,	PUNCT
ma-17	37	4	yn;f	yn;f	NOUN
ma-17	37	5	]	]	PUNCT
ma-17	37	6	−	−	X
ma-17	37	7	f	f	PROPN
ma-17	37	8	′(xn))−1f	′(xn))−1f	PROPN
ma-17	37	9	(	(	PUNCT
ma-17	37	10	yn	yn	PROPN
ma-17	37	11	)	)	PUNCT
ma-17	37	12	,	,	PUNCT
ma-17	37	13	(	(	PUNCT
ma-17	37	14	1.5	1.5	NUM
ma-17	37	15	)	)	PUNCT
ma-17	37	16	kung	kung	ADJ
ma-17	37	17	-	-	PUNCT
ma-17	37	18	traub	traub	NOUN
ma-17	38	1	[	[	X
ma-17	38	2	35–37	35–37	NOUN
ma-17	38	3	]	]	X
ma-17	38	4	yn	yn	X
ma-17	39	1	=	=	PUNCT
ma-17	39	2	xn	xn	PROPN
ma-17	40	1	−	−	PROPN
ma-17	40	2	f	f	PROPN
ma-17	40	3	′(xn)−1f	′(xn)−1f	PROPN
ma-17	40	4	(	(	PUNCT
ma-17	40	5	xn	xn	PROPN
ma-17	40	6	)	)	PUNCT
ma-17	40	7	xn+1	xn+1	PUNCT
ma-17	40	8	=	=	SYM
ma-17	41	1	yn	yn	INTJ
ma-17	41	2	−	−	PROPN
ma-17	42	1	[	[	X
ma-17	42	2	xn	xn	X
ma-17	42	3	,	,	PUNCT
ma-17	42	4	yn;f	yn;f	NOUN
ma-17	42	5	]	]	PUNCT
ma-17	42	6	−1f	−1f	PROPN
ma-17	42	7	′(xn)[xn	′(xn)[xn	PROPN
ma-17	42	8	,	,	PUNCT
ma-17	42	9	yn;f	yn;f	NOUN
ma-17	42	10	]	]	X
ma-17	42	11	−1f	−1f	PROPN
ma-17	42	12	(	(	PUNCT
ma-17	42	13	yn	yn	PROPN
ma-17	42	14	)	)	PUNCT
ma-17	42	15	,	,	PUNCT
ma-17	42	16	(	(	PUNCT
ma-17	42	17	1.6	1.6	NUM
ma-17	42	18	)	)	PUNCT
ma-17	42	19	ostrowski	ostrowski	NOUN
ma-17	42	20	-	-	PUNCT
ma-17	42	21	type	type	NOUN
ma-17	42	22	[	[	X
ma-17	42	23	25	25	NUM
ma-17	42	24	]	]	X
ma-17	42	25	yn	yn	PROPN
ma-17	43	1	=	=	PUNCT
ma-17	43	2	xn	xn	PROPN
ma-17	44	1	−	−	PROPN
ma-17	44	2	f	f	PROPN
ma-17	44	3	′(xn)−1f	′(xn)−1f	PROPN
ma-17	44	4	(	(	PUNCT
ma-17	44	5	xn	xn	PROPN
ma-17	44	6	)	)	PUNCT
ma-17	44	7	xn+1	xn+1	PUNCT
ma-17	44	8	=	=	SYM
ma-17	45	1	yn	yn	INTJ
ma-17	45	2	−	−	PROPN
ma-17	46	1	(	(	PUNCT
ma-17	46	2	2[xn	2[xn	NUM
ma-17	46	3	,	,	PUNCT
ma-17	46	4	yn;f	yn;f	NOUN
ma-17	46	5	]	]	SYM
ma-17	46	6	−1	−1	NOUN
ma-17	46	7	−	−	PROPN
ma-17	46	8	f	f	X
ma-17	46	9	′(xn)−1)f	′(xn)−1)f	PROPN
ma-17	46	10	(	(	PUNCT
ma-17	46	11	yn	yn	PROPN
ma-17	46	12	)	)	PUNCT
ma-17	46	13	,	,	PUNCT
ma-17	46	14	(	(	PUNCT
ma-17	46	15	1.7	1.7	NUM
ma-17	46	16	)	)	PUNCT
ma-17	46	17	sharma	sharma	NOUN
ma-17	46	18	type	type	NOUN
ma-17	47	1	[	[	X
ma-17	47	2	32	32	NUM
ma-17	47	3	]	]	X
ma-17	47	4	yn	yn	PROPN
ma-17	47	5	=	=	PUNCT
ma-17	47	6	xn	xn	PROPN
ma-17	48	1	−	−	PROPN
ma-17	48	2	f	f	PROPN
ma-17	48	3	′(xn)−1f	′(xn)−1f	PROPN
ma-17	48	4	(	(	PUNCT
ma-17	48	5	xn	xn	PROPN
ma-17	48	6	)	)	PUNCT
ma-17	48	7	xn+1	xn+1	PUNCT
ma-17	48	8	=	=	SYM
ma-17	49	1	yn	yn	PROPN
ma-17	49	2	−	−	PROPN
ma-17	49	3	p	p	X
ma-17	49	4	(	(	PUNCT
ma-17	49	5	xn	xn	PROPN
ma-17	49	6	,	,	PUNCT
ma-17	49	7	yn)f	yn)f	PROPN
ma-17	49	8	′(xn)−1f	′(xn)−1f	PROPN
ma-17	49	9	(	(	PUNCT
ma-17	49	10	yn	yn	PROPN
ma-17	49	11	)	)	PUNCT
ma-17	49	12	.	.	PUNCT
ma-17	50	1	(	(	PUNCT
ma-17	50	2	1.8	1.8	NUM
ma-17	50	3	)	)	PUNCT
ma-17	50	4	to	to	PART
ma-17	50	5	obtain	obtain	VERB
ma-17	50	6	all	all	DET
ma-17	50	7	these	these	DET
ma-17	50	8	special	special	ADJ
ma-17	50	9	cases	case	NOUN
ma-17	50	10	choose	choose	VERB
ma-17	50	11	,	,	PUNCT
ma-17	50	12	an	an	DET
ma-17	50	13	=	=	X
ma-17	50	14	i	i	PROPN
ma-17	50	15	,	,	PUNCT
ma-17	50	16	an	an	DET
ma-17	50	17	=	=	SYM
ma-17	50	18	f	f	PROPN
ma-17	50	19	′(yn)−1f	′(yn)−1f	NOUN
ma-17	50	20	′(xn	′(xn	NOUN
ma-17	50	21	)	)	PUNCT
ma-17	50	22	,	,	PUNCT
ma-17	50	23	an	an	PRON
ma-17	50	24	=	=	X
ma-17	50	25	(	(	PUNCT
ma-17	50	26	2[xn	2[xn	NUM
ma-17	50	27	,	,	PUNCT
ma-17	50	28	yn;f	yn;f	ADJ
ma-17	50	29	]	]	PUNCT
ma-17	51	1	−	−	PROPN
ma-17	51	2	f	f	X
ma-17	51	3	′(xn))f	′(xn))f	PUNCT
ma-17	52	1	′(xn	′(xn	PROPN
ma-17	52	2	)	)	PUNCT
ma-17	52	3	,	,	PUNCT
ma-17	52	4	an	an	PRON
ma-17	52	5	=	=	X
ma-17	53	1	[	[	X
ma-17	53	2	xn	xn	X
ma-17	53	3	,	,	PUNCT
ma-17	53	4	yn;f	yn;f	NOUN
ma-17	53	5	]	]	PUNCT
ma-17	53	6	−1f	−1f	PROPN
ma-17	53	7	′(xn)[xn	′(xn)[xn	PROPN
ma-17	53	8	,	,	PUNCT
ma-17	53	9	yn;f	yn;f	NOUN
ma-17	53	10	]	]	PUNCT
ma-17	53	11	−1f	−1f	PROPN
ma-17	53	12	′(xn	′(xn	PROPN
ma-17	53	13	)	)	PUNCT
ma-17	53	14	,	,	PUNCT
ma-17	53	15	an	an	PRON
ma-17	53	16	=	=	X
ma-17	53	17	(	(	PUNCT
ma-17	53	18	2[xn	2[xn	NUM
ma-17	53	19	,	,	PUNCT
ma-17	53	20	yn;f	yn;f	NOUN
ma-17	53	21	]	]	PUNCT
ma-17	53	22	−1−f	−1−f	PROPN
ma-17	53	23	′(xn)−1)f	′(xn)−1)f	VERB
ma-17	53	24	′(xn	′(xn	PROPN
ma-17	53	25	)	)	PUNCT
ma-17	53	26	,	,	PUNCT
ma-17	53	27	an	an	PRON
ma-17	53	28	=	=	X
ma-17	53	29	p	p	X
ma-17	53	30	(	(	PUNCT
ma-17	53	31	xn	xn	PROPN
ma-17	53	32	,	,	PUNCT
ma-17	53	33	yn	yn	PROPN
ma-17	53	34	)	)	PUNCT
ma-17	53	35	,	,	PUNCT
ma-17	53	36	respectively	respectively	ADV
ma-17	53	37	,	,	PUNCT
ma-17	53	38	where	where	SCONJ
ma-17	53	39	[	[	X
ma-17	53	40	.	.	PUNCT
ma-17	53	41	,	,	PUNCT
ma-17	53	42	.;f	.;f	PUNCT
ma-17	53	43	]	]	PUNCT
ma-17	53	44	:	:	PUNCT
ma-17	53	45	ω	ω	NUM
ma-17	53	46	×	×	PROPN
ma-17	53	47	ω	ω	NUM
ma-17	53	48	−→	−→	PROPN
ma-17	53	49	l(b	l(b	PROPN
ma-17	53	50	,	,	PUNCT
ma-17	53	51	b1	b1	NOUN
ma-17	53	52	)	)	PUNCT
ma-17	53	53	is	be	AUX
ma-17	53	54	a	a	DET
ma-17	53	55	divided	divided	ADJ
ma-17	53	56	difference	difference	NOUN
ma-17	53	57	of	of	ADP
ma-17	53	58	orderone	orderone	NOUN
ma-17	53	59	and	and	CCONJ
ma-17	53	60	p	p	NOUN
ma-17	53	61	:	:	PUNCT
ma-17	53	62	ω×ω	ω×ω	NUM
ma-17	53	63	−→	−→	ADJ
ma-17	53	64	l(b	l(b	PROPN
ma-17	53	65	,	,	PUNCT
ma-17	53	66	b1	b1	NOUN
ma-17	53	67	)	)	PUNCT
ma-17	53	68	is	be	AUX
ma-17	53	69	weight	weight	NOUN
ma-17	53	70	operator	operator	NOUN
ma-17	53	71	[	[	X
ma-17	53	72	32	32	NUM
ma-17	53	73	]	]	PUNCT
ma-17	53	74	(	(	PUNCT
ma-17	53	75	see	see	VERB
ma-17	53	76	also	also	ADV
ma-17	53	77	[	[	X
ma-17	53	78	15,28,40	15,28,40	NUM
ma-17	53	79	]	]	PUNCT
ma-17	53	80	and	and	CCONJ
ma-17	53	81	reference	reference	NOUN
ma-17	53	82	therein).these	therein).these	ADJ
ma-17	53	83	special	special	ADJ
ma-17	53	84	methods	method	NOUN
ma-17	53	85	were	be	AUX
ma-17	53	86	shown	show	VERB
ma-17	53	87	to	to	PART
ma-17	53	88	be	be	AUX
ma-17	53	89	of	of	ADP
ma-17	53	90	order	order	NOUN
ma-17	53	91	four	four	NUM
ma-17	53	92	using	use	VERB
ma-17	53	93	taylor	taylor	NOUN
ma-17	53	94	expansion	expansion	NOUN
ma-17	53	95	and	and	CCONJ
ma-17	53	96	assumptions	assumption	VERB
ma-17	53	97	onthe	onthe	ADJ
ma-17	53	98	fifth	fifth	ADJ
ma-17	53	99	order	order	NOUN
ma-17	53	100	derivative	derivative	NOUN
ma-17	53	101	of	of	ADP
ma-17	53	102	f	f	PROPN
ma-17	53	103	,	,	PUNCT
ma-17	53	104	which	which	PRON
ma-17	53	105	is	be	AUX
ma-17	53	106	not	not	PART
ma-17	53	107	on	on	ADP
ma-17	53	108	these	these	DET
ma-17	53	109	methods	method	NOUN
ma-17	53	110	.	.	PUNCT
ma-17	54	1	so	so	ADV
ma-17	54	2	,	,	PUNCT
ma-17	54	3	the	the	DET
ma-17	54	4	assumptions	assumption	NOUN
ma-17	54	5	on	on	ADP
ma-17	54	6	the	the	DET
ma-17	54	7	fifthderivative	fifthderivative	ADJ
ma-17	54	8	reduce	reduce	VERB
ma-17	54	9	the	the	DET
ma-17	54	10	applicability	applicability	NOUN
ma-17	54	11	of	of	ADP
ma-17	54	12	these	these	DET
ma-17	54	13	methods	method	NOUN
ma-17	54	14	[	[	PUNCT
ma-17	54	15	1–41].for	1–41].for	NUM
ma-17	54	16	example	example	NOUN
ma-17	54	17	:	:	PUNCT
ma-17	54	18	let	let	VERB
ma-17	54	19	b	b	NOUN
ma-17	54	20	=	=	SYM
ma-17	54	21	b1	b1	NOUN
ma-17	54	22	=	=	SYM
ma-17	54	23	r	r	PROPN
ma-17	54	24	,	,	PUNCT
ma-17	54	25	ω	ω	NOUN
ma-17	54	26	=	=	PUNCT
ma-17	55	1	[	[	X
ma-17	55	2	−0.5	−0.5	PROPN
ma-17	55	3	,	,	PUNCT
ma-17	55	4	1.5	1.5	NUM
ma-17	55	5	]	]	PUNCT
ma-17	55	6	.	.	PUNCT
ma-17	56	1	define	define	VERB
ma-17	56	2	λ	λ	PROPN
ma-17	56	3	on	on	ADP
ma-17	56	4	ω	ω	NUM
ma-17	56	5	by	by	ADP
ma-17	56	6	λ(t	λ(t	NOUN
ma-17	56	7	)	)	PUNCT
ma-17	56	8	=	=	PRON
ma-17	56	9	{	{	PUNCT
ma-17	56	10	t3	t3	PROPN
ma-17	56	11	log	log	NOUN
ma-17	56	12	t2	t2	PROPN
ma-17	56	13	+	+	CCONJ
ma-17	56	14	t5	t5	PROPN
ma-17	56	15	−	−	PROPN
ma-17	57	1	t4	t4	PROPN
ma-17	58	1	i	i	PRON
ma-17	58	2	f	f	PROPN
ma-17	58	3	t	t	PROPN
ma-17	58	4	6=	6=	PROPN
ma-17	58	5	0	0	NUM
ma-17	58	6	0	0	NUM
ma-17	59	1	i	i	PRON
ma-17	59	2	f	f	NOUN
ma-17	59	3	t	t	PROPN
ma-17	59	4	=	=	PUNCT
ma-17	59	5	0.then	0.then	NUM
ma-17	59	6	,	,	PUNCT
ma-17	59	7	we	we	PRON
ma-17	59	8	get	get	VERB
ma-17	59	9	t∗	t∗	NOUN
ma-17	59	10	=	=	SYM
ma-17	59	11	1	1	NUM
ma-17	59	12	,	,	PUNCT
ma-17	59	13	and	and	CCONJ
ma-17	59	14	λ′′′(t	λ′′′(t	PROPN
ma-17	59	15	)	)	PUNCT
ma-17	60	1	=	=	SYM
ma-17	60	2	6	6	NUM
ma-17	60	3	log	log	NOUN
ma-17	60	4	t2	t2	NOUN
ma-17	60	5	+	+	CCONJ
ma-17	60	6	60t2	60t2	NUM
ma-17	60	7	−	−	NUM
ma-17	60	8	24	24	NUM
ma-17	60	9	t	t	NOUN
ma-17	60	10	+	+	NOUN
ma-17	60	11	22	22	NUM
ma-17	60	12	.	.	PUNCT
ma-17	61	1	eur	eur	PROPN
ma-17	61	2	.	.	PUNCT
ma-17	62	1	j.	j.	PROPN
ma-17	62	2	math	math	PROPN
ma-17	62	3	.	.	PUNCT
ma-17	63	1	anal	anal	ADJ
ma-17	63	2	.	.	PUNCT
ma-17	64	1	1	1	NUM
ma-17	64	2	(	(	PUNCT
ma-17	64	3	2021	2021	NUM
ma-17	64	4	)	)	PUNCT
ma-17	65	1	70obviously	70obviously	ADV
ma-17	65	2	λ′′′(t	λ′′′(t	VERB
ma-17	65	3	)	)	PUNCT
ma-17	65	4	is	be	AUX
ma-17	65	5	not	not	PART
ma-17	65	6	bounded	bound	VERB
ma-17	65	7	on	on	ADP
ma-17	65	8	ω	ω	PROPN
ma-17	65	9	.	.	PUNCT
ma-17	66	1	so	so	ADV
ma-17	66	2	,	,	PUNCT
ma-17	66	3	the	the	DET
ma-17	66	4	convergence	convergence	NOUN
ma-17	66	5	of	of	ADP
ma-17	66	6	method	method	NOUN
ma-17	66	7	(	(	PUNCT
ma-17	66	8	1.2	1.2	NUM
ma-17	66	9	)	)	PUNCT
ma-17	66	10	is	be	AUX
ma-17	66	11	not	not	PART
ma-17	66	12	guaranteed	guarantee	VERB
ma-17	66	13	bythe	bythe	ADP
ma-17	66	14	previous	previous	ADJ
ma-17	66	15	analyses	analysis	NOUN
ma-17	66	16	in	in	ADP
ma-17	66	17	[	[	X
ma-17	66	18	1–41].in	1–41].in	NUM
ma-17	66	19	this	this	DET
ma-17	66	20	paper	paper	NOUN
ma-17	66	21	we	we	PRON
ma-17	66	22	introduce	introduce	VERB
ma-17	66	23	a	a	DET
ma-17	66	24	majorant	majorant	NOUN
ma-17	66	25	sequence	sequence	NOUN
ma-17	66	26	and	and	CCONJ
ma-17	66	27	use	use	VERB
ma-17	66	28	our	our	PRON
ma-17	66	29	idea	idea	NOUN
ma-17	66	30	of	of	ADP
ma-17	66	31	recurrent	recurrent	ADJ
ma-17	66	32	functions	function	NOUN
ma-17	66	33	to	to	ADP
ma-17	66	34	extendthe	extendthe	DET
ma-17	66	35	applicability	applicability	NOUN
ma-17	66	36	of	of	ADP
ma-17	66	37	method	method	NOUN
ma-17	66	38	(	(	PUNCT
ma-17	66	39	1.2	1.2	NUM
ma-17	66	40	)	)	PUNCT
ma-17	66	41	.	.	PUNCT
ma-17	67	1	our	our	PRON
ma-17	67	2	analysis	analysis	NOUN
ma-17	67	3	includes	include	VERB
ma-17	67	4	error	error	NOUN
ma-17	67	5	bounds	bound	NOUN
ma-17	67	6	and	and	CCONJ
ma-17	67	7	results	result	NOUN
ma-17	67	8	on	on	ADP
ma-17	67	9	uniqueness	uniqueness	NOUN
ma-17	67	10	of	of	ADP
ma-17	67	11	x∗	x∗	PROPN
ma-17	67	12	based	base	VERB
ma-17	67	13	on	on	ADP
ma-17	67	14	computable	computable	ADJ
ma-17	67	15	lipschitz	lipschitz	NOUN
ma-17	67	16	constants	constant	NOUN
ma-17	67	17	not	not	PART
ma-17	67	18	given	give	VERB
ma-17	67	19	before	before	ADV
ma-17	67	20	in	in	ADP
ma-17	67	21	[	[	X
ma-17	67	22	1–41	1–41	NOUN
ma-17	67	23	]	]	PUNCT
ma-17	67	24	and	and	CCONJ
ma-17	67	25	in	in	ADP
ma-17	67	26	other	other	ADJ
ma-17	67	27	similar	similar	ADJ
ma-17	67	28	studiesusing	studiesuse	VERB
ma-17	67	29	taylor	taylor	PROPN
ma-17	67	30	series	series	PROPN
ma-17	67	31	.	.	PUNCT
ma-17	68	1	our	our	PRON
ma-17	68	2	idea	idea	NOUN
ma-17	68	3	is	be	AUX
ma-17	68	4	very	very	ADV
ma-17	68	5	general	general	ADJ
ma-17	68	6	.	.	PUNCT
ma-17	69	1	so	so	ADV
ma-17	69	2	,	,	PUNCT
ma-17	69	3	it	it	PRON
ma-17	69	4	applies	apply	VERB
ma-17	69	5	on	on	ADP
ma-17	69	6	other	other	ADJ
ma-17	69	7	methods	method	NOUN
ma-17	69	8	too.the	too.the	DET
ma-17	69	9	rest	rest	NOUN
ma-17	69	10	of	of	ADP
ma-17	69	11	the	the	DET
ma-17	69	12	paper	paper	NOUN
ma-17	69	13	is	be	AUX
ma-17	69	14	set	set	VERB
ma-17	69	15	up	up	ADP
ma-17	69	16	as	as	SCONJ
ma-17	69	17	follows	follow	VERB
ma-17	69	18	:	:	PUNCT
ma-17	69	19	in	in	ADP
ma-17	69	20	section	section	NOUN
ma-17	69	21	2	2	NUM
ma-17	69	22	we	we	PRON
ma-17	69	23	present	present	VERB
ma-17	69	24	results	result	NOUN
ma-17	69	25	on	on	ADP
ma-17	69	26	majorizing	majorize	VERB
ma-17	69	27	sequences.sections	sequences.section	NOUN
ma-17	69	28	3,4	3,4	NUM
ma-17	69	29	contain	contain	VERB
ma-17	69	30	the	the	DET
ma-17	69	31	semi	semi	ADJ
ma-17	69	32	-	-	ADJ
ma-17	69	33	local	local	ADJ
ma-17	69	34	and	and	CCONJ
ma-17	69	35	local	local	ADJ
ma-17	69	36	convergence	convergence	NOUN
ma-17	69	37	,	,	PUNCT
ma-17	69	38	respectively	respectively	ADV
ma-17	69	39	,	,	PUNCT
ma-17	69	40	where	where	SCONJ
ma-17	69	41	in	in	ADP
ma-17	69	42	section	section	NOUN
ma-17	69	43	4	4	NUM
ma-17	69	44	thenumerical	thenumerical	ADJ
ma-17	69	45	experiments	experiment	NOUN
ma-17	69	46	are	be	AUX
ma-17	69	47	presented	present	VERB
ma-17	69	48	.	.	PUNCT
ma-17	70	1	concluding	conclude	VERB
ma-17	70	2	remarks	remark	NOUN
ma-17	70	3	are	be	AUX
ma-17	70	4	given	give	VERB
ma-17	70	5	in	in	ADP
ma-17	70	6	the	the	DET
ma-17	70	7	last	last	ADJ
ma-17	70	8	section	section	NOUN
ma-17	70	9	5	5	NUM
ma-17	70	10	.	.	NOUN
ma-17	70	11	2	2	NUM
ma-17	70	12	.	.	NOUN
ma-17	70	13	results	result	NOUN
ma-17	70	14	on	on	ADP
ma-17	70	15	majorizing	majorize	VERB
ma-17	70	16	sequences	sequence	NOUN
ma-17	70	17	we	we	PRON
ma-17	70	18	recall	recall	VERB
ma-17	70	19	the	the	DET
ma-17	70	20	definition	definition	NOUN
ma-17	70	21	followed	follow	VERB
ma-17	70	22	by	by	ADP
ma-17	70	23	convergence	convergence	NOUN
ma-17	70	24	results	result	NOUN
ma-17	70	25	.	.	PUNCT
ma-17	71	1	definition	definition	NOUN
ma-17	71	2	2.1	2.1	NUM
ma-17	71	3	.	.	PUNCT
ma-17	72	1	let	let	AUX
ma-17	72	2	{	{	PUNCT
ma-17	72	3	w̄n	w̄n	NOUN
ma-17	72	4	}	}	PUNCT
ma-17	72	5	be	be	AUX
ma-17	72	6	a	a	DET
ma-17	72	7	sequence	sequence	NOUN
ma-17	72	8	in	in	ADP
ma-17	72	9	a	a	DET
ma-17	72	10	banach	banach	NOUN
ma-17	72	11	space	space	NOUN
ma-17	72	12	.	.	PUNCT
ma-17	73	1	then	then	ADV
ma-17	73	2	,	,	PUNCT
ma-17	73	3	a	a	DET
ma-17	73	4	nondecreasing	nondecrease	VERB
ma-17	73	5	scalar	scalar	ADJ
ma-17	73	6	sequence	sequence	NOUN
ma-17	73	7	{	{	PUNCT
ma-17	73	8	wn	wn	PROPN
ma-17	73	9	}	}	PUNCT
ma-17	73	10	is	be	AUX
ma-17	73	11	called	call	VERB
ma-17	73	12	majorizing	majorize	VERB
ma-17	73	13	for	for	ADP
ma-17	73	14	{	{	PUNCT
ma-17	73	15	w̄n	w̄n	PROPN
ma-17	73	16	}	}	PUNCT
ma-17	73	17	if	if	SCONJ
ma-17	73	18	‖w̄n+1	‖w̄n+1	VERB
ma-17	73	19	−	−	PROPN
ma-17	73	20	w̄n‖	w̄n‖	PROPN
ma-17	73	21	≤	≤	PROPN
ma-17	73	22	wn+1	wn+1	VERB
ma-17	73	23	−	−	PROPN
ma-17	73	24	wn	wn	NOUN
ma-17	73	25	for	for	ADP
ma-17	73	26	each	each	DET
ma-17	73	27	n	n	NOUN
ma-17	73	28	=	=	SYM
ma-17	73	29	0	0	NUM
ma-17	73	30	,	,	PUNCT
ma-17	73	31	1	1	NUM
ma-17	73	32	,	,	PUNCT
ma-17	73	33	2	2	NUM
ma-17	73	34	,	,	PUNCT
ma-17	73	35	.	.	PUNCT
ma-17	73	36	.	.	PUNCT
ma-17	73	37	.	.	PUNCT
ma-17	73	38	.	.	PUNCT
ma-17	74	1	(	(	PUNCT
ma-17	74	2	2.1	2.1	NUM
ma-17	74	3	)	)	PUNCT
ma-17	74	4	sequence	sequence	NOUN
ma-17	74	5	{	{	PUNCT
ma-17	74	6	wn	wn	NOUN
ma-17	74	7	}	}	PUNCT
ma-17	74	8	is	be	AUX
ma-17	74	9	used	use	VERB
ma-17	74	10	instead	instead	ADV
ma-17	74	11	to	to	PART
ma-17	74	12	study	study	VERB
ma-17	74	13	the	the	DET
ma-17	74	14	convergence	convergence	NOUN
ma-17	74	15	of	of	ADP
ma-17	74	16	{	{	PUNCT
ma-17	74	17	w̄n	w̄n	PROPN
ma-17	74	18	}	}	PUNCT
ma-17	74	19	[	[	X
ma-17	74	20	23–25	23–25	NUM
ma-17	74	21	]	]	PUNCT
ma-17	74	22	.	.	PUNCT
ma-17	75	1	set	set	VERB
ma-17	75	2	m	m	NOUN
ma-17	75	3	=	=	PUNCT
ma-17	76	1	[	[	X
ma-17	76	2	0,∞).let	0,∞).let	X
ma-17	76	3	η	η	PROPN
ma-17	76	4	>	>	X
ma-17	76	5	0	0	PROPN
ma-17	76	6	,	,	PUNCT
ma-17	76	7	p0	p0	NOUN
ma-17	76	8	:	:	PUNCT
ma-17	76	9	m	m	VERB
ma-17	76	10	−→	−→	ADJ
ma-17	76	11	r	r	NOUN
ma-17	76	12	,	,	PUNCT
ma-17	76	13	p	p	X
ma-17	76	14	:	:	PUNCT
ma-17	76	15	m	m	VERB
ma-17	77	1	−→	−→	ADJ
ma-17	77	2	r	r	NOUN
ma-17	77	3	,	,	PUNCT
ma-17	77	4	a	a	PRON
ma-17	77	5	:	:	PUNCT
ma-17	77	6	m	m	VERB
ma-17	77	7	×	×	NOUN
ma-17	77	8	m	m	VERB
ma-17	77	9	×	×	NOUN
ma-17	77	10	m	m	VERB
ma-17	77	11	−→	−→	NOUN
ma-17	77	12	r	r	NOUN
ma-17	77	13	,	,	PUNCT
ma-17	77	14	ā	ā	NOUN
ma-17	77	15	:	:	PUNCT
ma-17	77	16	m	m	VERB
ma-17	77	17	×	×	VERB
ma-17	77	18	m	m	VERB
ma-17	77	19	×	×	NOUN
ma-17	77	20	m	m	NOUN
ma-17	77	21	−→	−→	ADJ
ma-17	77	22	rand	rand	NOUN
ma-17	77	23	b	b	NOUN
ma-17	77	24	:	:	PUNCT
ma-17	77	25	m	m	VERB
ma-17	77	26	×m	×m	NOUN
ma-17	77	27	×m	×m	NOUN
ma-17	77	28	×m	×m	NOUN
ma-17	77	29	−→	−→	NOUN
ma-17	77	30	r	r	NOUN
ma-17	77	31	be	be	VERB
ma-17	77	32	continuous	continuous	ADJ
ma-17	77	33	and	and	CCONJ
ma-17	77	34	nondecreasing	nondecreasing	ADJ
ma-17	77	35	functions	function	NOUN
ma-17	77	36	.	.	PUNCT
ma-17	78	1	set	set	VERB
ma-17	78	2	an	an	DET
ma-17	78	3	=	=	NOUN
ma-17	78	4	a(n	a(n	NOUN
ma-17	78	5	)	)	PUNCT
ma-17	78	6	and	and	CCONJ
ma-17	78	7	ξn	ξn	PROPN
ma-17	78	8	=	=	SYM
ma-17	78	9	b(n	b(n	PROPN
ma-17	78	10	)	)	PUNCT
ma-17	78	11	.	.	PUNCT
ma-17	79	1	define	define	VERB
ma-17	79	2	scalar	scalar	ADJ
ma-17	79	3	sequences	sequence	NOUN
ma-17	79	4	{	{	PUNCT
ma-17	79	5	sn	sn	NOUN
ma-17	79	6	}	}	PUNCT
ma-17	79	7	,	,	PUNCT
ma-17	79	8	{	{	PUNCT
ma-17	79	9	tn	tn	NOUN
ma-17	79	10	}	}	PUNCT
ma-17	79	11	for	for	ADP
ma-17	79	12	each	each	DET
ma-17	79	13	n	n	NOUN
ma-17	79	14	=	=	SYM
ma-17	79	15	0	0	NUM
ma-17	79	16	,	,	PUNCT
ma-17	79	17	1	1	NUM
ma-17	79	18	,	,	PUNCT
ma-17	79	19	2	2	NUM
ma-17	79	20	,	,	PUNCT
ma-17	79	21	.	.	PUNCT
ma-17	79	22	.	.	PUNCT
ma-17	79	23	.	.	PUNCT
ma-17	80	1	by	by	ADP
ma-17	80	2	t0	t0	PROPN
ma-17	80	3	=	=	SYM
ma-17	80	4	0	0	NUM
ma-17	80	5	,	,	PUNCT
ma-17	80	6	s0	s0	PROPN
ma-17	80	7	=	=	SYM
ma-17	80	8	η	η	PROPN
ma-17	80	9	,	,	PUNCT
ma-17	80	10	tn+1	tn+1	NOUN
ma-17	80	11	=	=	SYM
ma-17	80	12	sn	sn	PROPN
ma-17	80	13	+	+	CCONJ
ma-17	80	14	ᾱn(sn	ᾱn(sn	ADJ
ma-17	80	15	−	−	PROPN
ma-17	80	16	tn	tn	NOUN
ma-17	80	17	)	)	PUNCT
ma-17	80	18	sn+1	sn+1	PROPN
ma-17	80	19	=	=	SYM
ma-17	80	20	tn+1	tn+1	PROPN
ma-17	80	21	+	+	CCONJ
ma-17	80	22	βn(tn+1	βn(tn+1	NOUN
ma-17	80	23	−	−	PROPN
ma-17	80	24	sn	sn	NOUN
ma-17	80	25	)	)	PUNCT
ma-17	80	26	,	,	PUNCT
ma-17	80	27	(	(	PUNCT
ma-17	80	28	2.2	2.2	NUM
ma-17	80	29	)	)	PUNCT
ma-17	80	30	where	where	SCONJ
ma-17	80	31	ᾱn	ᾱn	NOUN
ma-17	80	32	=	=	SYM
ma-17	80	33	ān	ān	PROPN
ma-17	80	34	∫	∫	PROPN
ma-17	80	35	1	1	NUM
ma-17	80	36	0	0	NUM
ma-17	80	37	p̄	p̄	NOUN
ma-17	80	38	(	(	PUNCT
ma-17	80	39	(	(	PUNCT
ma-17	80	40	1−	1−	X
ma-17	80	41	θ)(sn	θ)(sn	NUM
ma-17	80	42	−	−	PROPN
ma-17	80	43	tn))dθ	tn))dθ	NOUN
ma-17	80	44	and	and	CCONJ
ma-17	80	45	βn	βn	VERB
ma-17	80	46	=	=	SYM
ma-17	80	47	ξn	ξn	PROPN
ma-17	80	48	1−	1−	NUM
ma-17	80	49	p0(tn+1	p0(tn+1	NOUN
ma-17	80	50	)	)	PUNCT
ma-17	80	51	,	,	PUNCT
ma-17	80	52	ān	ān	PROPN
ma-17	80	53	=	=	NOUN
ma-17	80	54	{	{	PUNCT
ma-17	80	55	ā	ā	NOUN
ma-17	80	56	,	,	PUNCT
ma-17	80	57	i	i	PRON
ma-17	80	58	f	f	PROPN
ma-17	80	59	n	n	PROPN
ma-17	80	60	=	=	SYM
ma-17	80	61	0	0	PROPN
ma-17	81	1	a	a	PRON
ma-17	81	2	,	,	PUNCT
ma-17	81	3	i	i	PRON
ma-17	81	4	f	f	PROPN
ma-17	81	5	n	n	NOUN
ma-17	81	6	=	=	SYM
ma-17	81	7	1	1	NUM
ma-17	81	8	,	,	PUNCT
ma-17	81	9	2	2	NUM
ma-17	81	10	,	,	PUNCT
ma-17	81	11	.	.	PUNCT
ma-17	81	12	.	.	PUNCT
ma-17	81	13	.	.	PUNCT
ma-17	82	1	,	,	PUNCT
ma-17	82	2	p̄	p̄	NOUN
ma-17	82	3	=	=	PRON
ma-17	82	4	{	{	PUNCT
ma-17	82	5	p0	p0	NOUN
ma-17	82	6	,	,	PUNCT
ma-17	83	1	i	i	PRON
ma-17	83	2	f	f	PROPN
ma-17	84	1	n	n	NOUN
ma-17	84	2	=	=	SYM
ma-17	84	3	0	0	NUM
ma-17	85	1	p	p	X
ma-17	85	2	,	,	PUNCT
ma-17	85	3	i	i	PRON
ma-17	85	4	f	f	PROPN
ma-17	85	5	n	n	NOUN
ma-17	85	6	=	=	SYM
ma-17	85	7	1	1	NUM
ma-17	85	8	,	,	PUNCT
ma-17	85	9	2	2	NUM
ma-17	85	10	,	,	PUNCT
ma-17	85	11	.	.	PUNCT
ma-17	85	12	.	.	PUNCT
ma-17	86	1	.next	.next	INTJ
ma-17	86	2	,	,	PUNCT
ma-17	86	3	we	we	PRON
ma-17	86	4	present	present	VERB
ma-17	86	5	results	result	NOUN
ma-17	86	6	on	on	ADP
ma-17	86	7	the	the	DET
ma-17	86	8	convergence	convergence	NOUN
ma-17	86	9	of	of	ADP
ma-17	86	10	sequence	sequence	NOUN
ma-17	86	11	{	{	PUNCT
ma-17	86	12	sn	sn	NOUN
ma-17	86	13	}	}	PUNCT
ma-17	86	14	,	,	PUNCT
ma-17	86	15	{	{	PUNCT
ma-17	86	16	tn	tn	NOUN
ma-17	86	17	}	}	PUNCT
ma-17	86	18	.	.	PUNCT
ma-17	87	1	lemma	lemma	PROPN
ma-17	87	2	2.2	2.2	NUM
ma-17	87	3	.	.	PUNCT
ma-17	87	4	suppose	suppose	VERB
ma-17	87	5	that	that	SCONJ
ma-17	87	6	there	there	PRON
ma-17	87	7	exists	exist	VERB
ma-17	87	8	µ	µ	X
ma-17	87	9	>	>	X
ma-17	87	10	0	0	NUM
ma-17	87	11	such	such	ADJ
ma-17	87	12	that	that	DET
ma-17	87	13	for	for	ADP
ma-17	87	14	each	each	DET
ma-17	87	15	n	n	NOUN
ma-17	87	16	=	=	SYM
ma-17	87	17	0	0	NUM
ma-17	87	18	,	,	PUNCT
ma-17	87	19	1	1	NUM
ma-17	87	20	,	,	PUNCT
ma-17	87	21	2	2	NUM
ma-17	87	22	,	,	PUNCT
ma-17	87	23	.	.	PUNCT
ma-17	87	24	.	.	PUNCT
ma-17	88	1	.	.	PUNCT
ma-17	89	1	,	,	PUNCT
ma-17	89	2	tn	tn	PROPN
ma-17	89	3	≤	≤	PROPN
ma-17	89	4	µ	µ	X
ma-17	89	5	(	(	PUNCT
ma-17	89	6	2.3	2.3	NUM
ma-17	89	7	)	)	PUNCT
ma-17	89	8	and	and	CCONJ
ma-17	89	9	p0(µ	p0(µ	NUM
ma-17	89	10	)	)	PUNCT
ma-17	89	11	<	<	X
ma-17	89	12	1	1	NUM
ma-17	89	13	.	.	PUNCT
ma-17	89	14	(	(	PUNCT
ma-17	89	15	2.4	2.4	NUM
ma-17	89	16	)	)	PUNCT
ma-17	89	17	eur	eur	NOUN
ma-17	89	18	.	.	PUNCT
ma-17	90	1	j.	j.	PROPN
ma-17	90	2	math	math	PROPN
ma-17	90	3	.	.	PUNCT
ma-17	91	1	anal	anal	ADJ
ma-17	91	2	.	.	PUNCT
ma-17	92	1	1	1	NUM
ma-17	92	2	(	(	PUNCT
ma-17	92	3	2021	2021	NUM
ma-17	92	4	)	)	PUNCT
ma-17	92	5	71	71	NUM
ma-17	93	1	then	then	ADV
ma-17	93	2	,	,	PUNCT
ma-17	93	3	sequences	sequence	NOUN
ma-17	93	4	{	{	PUNCT
ma-17	93	5	sn	sn	NOUN
ma-17	93	6	}	}	PUNCT
ma-17	93	7	,	,	PUNCT
ma-17	93	8	{	{	PUNCT
ma-17	93	9	tn	tn	NOUN
ma-17	93	10	}	}	PUNCT
ma-17	93	11	converge	converge	VERB
ma-17	93	12	to	to	ADP
ma-17	93	13	their	their	PRON
ma-17	93	14	unique	unique	ADJ
ma-17	93	15	least	least	ADV
ma-17	93	16	upper	upper	ADJ
ma-17	93	17	bound	bind	VERB
ma-17	93	18	t∗	t∗	NOUN
ma-17	93	19	∈	∈	PROPN
ma-17	93	20	[	[	X
ma-17	93	21	η	η	PROPN
ma-17	93	22	,	,	PUNCT
ma-17	93	23	µ	µ	X
ma-17	93	24	]	]	PUNCT
ma-17	93	25	and	and	CCONJ
ma-17	93	26	tn	tn	PROPN
ma-17	93	27	≤	≤	PROPN
ma-17	93	28	sn	sn	PROPN
ma-17	93	29	≤	≤	PROPN
ma-17	93	30	tn+1	tn+1	NOUN
ma-17	93	31	.	.	PUNCT
ma-17	94	1	proof	proof	NOUN
ma-17	94	2	.	.	PUNCT
ma-17	95	1	it	it	PRON
ma-17	95	2	follows	follow	VERB
ma-17	95	3	from	from	ADP
ma-17	95	4	(	(	PUNCT
ma-17	95	5	2.2)-(2.4	2.2)-(2.4	NUM
ma-17	95	6	)	)	PUNCT
ma-17	95	7	that	that	SCONJ
ma-17	95	8	these	these	DET
ma-17	95	9	sequences	sequence	NOUN
ma-17	95	10	are	be	AUX
ma-17	95	11	nondecreasing	nondecrease	VERB
ma-17	95	12	,	,	PUNCT
ma-17	95	13	bounded	bound	VERB
ma-17	95	14	from	from	ADP
ma-17	95	15	aboveby	aboveby	PROPN
ma-17	95	16	µ	µ	NUM
ma-17	95	17	,	,	PUNCT
ma-17	95	18	and	and	CCONJ
ma-17	95	19	as	as	ADP
ma-17	95	20	such	such	ADJ
ma-17	95	21	they	they	PRON
ma-17	95	22	converge	converge	VERB
ma-17	95	23	to	to	ADP
ma-17	95	24	t∗.	t∗.	PROPN
ma-17	95	25	�	�	PROPN
ma-17	95	26	lemma	lemma	PROPN
ma-17	95	27	2.3	2.3	NUM
ma-17	95	28	.	.	PUNCT
ma-17	96	1	if	if	SCONJ
ma-17	96	2	function	function	NOUN
ma-17	96	3	p0	p0	NOUN
ma-17	96	4	is	be	AUX
ma-17	96	5	increasing	increase	VERB
ma-17	96	6	then	then	ADV
ma-17	96	7	conditions	condition	NOUN
ma-17	96	8	(	(	PUNCT
ma-17	96	9	2.3	2.3	NUM
ma-17	96	10	)	)	PUNCT
ma-17	96	11	and	and	CCONJ
ma-17	96	12	(	(	PUNCT
ma-17	96	13	2.4	2.4	NUM
ma-17	96	14	)	)	PUNCT
ma-17	96	15	can	can	AUX
ma-17	96	16	be	be	AUX
ma-17	96	17	replaced	replace	VERB
ma-17	96	18	by	by	ADP
ma-17	96	19	tn	tn	NOUN
ma-17	96	20	≤	≤	NOUN
ma-17	96	21	p−10	p−10	NOUN
ma-17	96	22	(	(	PUNCT
ma-17	96	23	1	1	NUM
ma-17	96	24	)	)	PUNCT
ma-17	96	25	.	.	PUNCT
ma-17	97	1	(	(	PUNCT
ma-17	97	2	2.5	2.5	NUM
ma-17	97	3	)	)	PUNCT
ma-17	97	4	proof	proof	NOUN
ma-17	97	5	.	.	PUNCT
ma-17	98	1	set	set	VERB
ma-17	98	2	µ	µ	NOUN
ma-17	98	3	=	=	PUNCT
ma-17	98	4	p−10	p−10	NOUN
ma-17	98	5	(	(	PUNCT
ma-17	98	6	1	1	NUM
ma-17	98	7	)	)	PUNCT
ma-17	98	8	in	in	ADP
ma-17	98	9	lemma	lemma	PROPN
ma-17	98	10	2.2	2.2	NUM
ma-17	98	11	.	.	PUNCT
ma-17	99	1	�	�	PROPN
ma-17	99	2	remark	remark	VERB
ma-17	99	3	2.4	2.4	NUM
ma-17	99	4	.	.	PUNCT
ma-17	100	1	conditions	condition	NOUN
ma-17	100	2	(	(	PUNCT
ma-17	100	3	2.3)-(2.5	2.3)-(2.5	NUM
ma-17	100	4	)	)	PUNCT
ma-17	100	5	are	be	AUX
ma-17	100	6	very	very	ADV
ma-17	100	7	general	general	ADJ
ma-17	100	8	and	and	CCONJ
ma-17	100	9	can	can	AUX
ma-17	100	10	be	be	AUX
ma-17	100	11	verified	verify	VERB
ma-17	100	12	only	only	ADV
ma-17	100	13	in	in	ADP
ma-17	100	14	special	special	ADJ
ma-17	100	15	cases	case	NOUN
ma-17	100	16	.	.	PUNCT
ma-17	101	1	that	that	PRON
ma-17	101	2	is	be	AUX
ma-17	101	3	why	why	SCONJ
ma-17	101	4	we	we	PRON
ma-17	101	5	present	present	VERB
ma-17	101	6	stronger	strong	ADJ
ma-17	101	7	conditions	condition	NOUN
ma-17	101	8	that	that	PRON
ma-17	101	9	are	be	AUX
ma-17	101	10	easier	easy	ADJ
ma-17	101	11	to	to	PART
ma-17	101	12	verify	verify	VERB
ma-17	101	13	.	.	PUNCT
ma-17	102	1	define	define	VERB
ma-17	102	2	functions	function	NOUN
ma-17	102	3	f	f	PROPN
ma-17	102	4	and	and	CCONJ
ma-17	102	5	g	g	NOUN
ma-17	102	6	on	on	ADP
ma-17	102	7	the	the	DET
ma-17	102	8	interval	interval	NOUN
ma-17	102	9	[	[	X
ma-17	102	10	0	0	NUM
ma-17	102	11	,	,	PUNCT
ma-17	102	12	1	1	NUM
ma-17	102	13	)	)	PUNCT
ma-17	102	14	by	by	ADP
ma-17	102	15	f	f	PROPN
ma-17	102	16	(	(	PUNCT
ma-17	102	17	t	t	PROPN
ma-17	102	18	)	)	PUNCT
ma-17	102	19	=	=	SYM
ma-17	103	1	a	a	PROPN
ma-17	103	2	(	(	PUNCT
ma-17	103	3	η	η	PROPN
ma-17	103	4	1−	1−	PROPN
ma-17	103	5	t	t	PROPN
ma-17	103	6	,	,	PUNCT
ma-17	103	7	η	η	PROPN
ma-17	103	8	1−	1−	PROPN
ma-17	103	9	t	t	PROPN
ma-17	103	10	,	,	PUNCT
ma-17	103	11	t	t	PROPN
ma-17	103	12	2η	2η	NUM
ma-17	103	13	)	)	PUNCT
ma-17	103	14	∫	∫	PROPN
ma-17	104	1	1	1	NUM
ma-17	104	2	0	0	NUM
ma-17	104	3	p	p	NOUN
ma-17	104	4	(	(	PUNCT
ma-17	104	5	(	(	PUNCT
ma-17	104	6	1−	1−	NUM
ma-17	104	7	θ)t2η)dθ	θ)t2η)dθ	NUM
ma-17	104	8	−	−	PROPN
ma-17	104	9	t	t	PROPN
ma-17	104	10	and	and	CCONJ
ma-17	104	11	g(t	g(t	PROPN
ma-17	104	12	)	)	PUNCT
ma-17	104	13	=	=	SYM
ma-17	105	1	b	b	X
ma-17	105	2	(	(	PUNCT
ma-17	105	3	η	η	PROPN
ma-17	105	4	1−	1−	PROPN
ma-17	105	5	t	t	PROPN
ma-17	105	6	,	,	PUNCT
ma-17	105	7	η	η	PROPN
ma-17	105	8	1−	1−	PROPN
ma-17	105	9	t	t	PROPN
ma-17	105	10	,	,	PUNCT
ma-17	105	11	t	t	PROPN
ma-17	105	12	2η	2η	NUM
ma-17	105	13	,	,	PUNCT
ma-17	105	14	t3η	t3η	PUNCT
ma-17	105	15	)	)	PUNCT
ma-17	105	16	+	+	CCONJ
ma-17	105	17	tp0	tp0	NUM
ma-17	105	18	(	(	PUNCT
ma-17	105	19	η	η	PROPN
ma-17	105	20	1−	1−	NUM
ma-17	105	21	t	t	PROPN
ma-17	105	22	)	)	PUNCT
ma-17	105	23	−	−	PROPN
ma-17	106	1	t.	t.	PROPN
ma-17	106	2	suppose	suppose	VERB
ma-17	106	3	that	that	SCONJ
ma-17	106	4	these	these	DET
ma-17	106	5	functions	function	NOUN
ma-17	106	6	have	have	VERB
ma-17	106	7	minimal	minimal	ADJ
ma-17	106	8	zeros	zero	NOUN
ma-17	106	9	λf	λf	X
ma-17	106	10	and	and	CCONJ
ma-17	106	11	λg	λg	X
ma-17	106	12	in	in	ADP
ma-17	106	13	(	(	PUNCT
ma-17	106	14	0	0	NUM
ma-17	106	15	,	,	PUNCT
ma-17	106	16	1	1	NUM
ma-17	106	17	)	)	PUNCT
ma-17	106	18	,	,	PUNCT
ma-17	106	19	respectively	respectively	ADV
ma-17	106	20	.	.	PUNCT
ma-17	107	1	set	set	VERB
ma-17	107	2	λ	λ	PROPN
ma-17	107	3	=	=	SYM
ma-17	107	4	min{λf	min{λf	X
ma-17	107	5	,	,	PUNCT
ma-17	107	6	λg	λg	NOUN
ma-17	107	7	}	}	PUNCT
ma-17	107	8	and	and	CCONJ
ma-17	107	9	λ0	λ0	NOUN
ma-17	107	10	=	=	SYM
ma-17	107	11	max{α0	max{α0	NOUN
ma-17	107	12	,	,	PUNCT
ma-17	107	13	β0	β0	NOUN
ma-17	107	14	}	}	PUNCT
ma-17	107	15	.	.	PUNCT
ma-17	108	1	then	then	ADV
ma-17	108	2	,	,	PUNCT
ma-17	108	3	we	we	PRON
ma-17	108	4	can	can	AUX
ma-17	108	5	show	show	VERB
ma-17	108	6	the	the	DET
ma-17	108	7	third	third	ADJ
ma-17	108	8	result	result	NOUN
ma-17	108	9	on	on	ADP
ma-17	108	10	majorizing	majorize	VERB
ma-17	108	11	sequencefor	sequencefor	ADP
ma-17	108	12	method	method	NOUN
ma-17	108	13	(	(	PUNCT
ma-17	108	14	1.2	1.2	NUM
ma-17	108	15	)	)	PUNCT
ma-17	108	16	.	.	PUNCT
ma-17	109	1	lemma	lemma	PROPN
ma-17	109	2	2.5	2.5	NUM
ma-17	109	3	.	.	PUNCT
ma-17	109	4	suppose	suppose	VERB
ma-17	109	5	that	that	SCONJ
ma-17	109	6	µ0	µ0	NOUN
ma-17	109	7	≤	≤	NOUN
ma-17	109	8	λ0	λ0	NOUN
ma-17	109	9	≤	≤	PUNCT
ma-17	109	10	λ	λ	PROPN
ma-17	109	11	.	.	PUNCT
ma-17	109	12	(	(	PUNCT
ma-17	109	13	2.6	2.6	NUM
ma-17	109	14	)	)	PUNCT
ma-17	109	15	then	then	ADV
ma-17	109	16	,	,	PUNCT
ma-17	109	17	sequences	sequence	NOUN
ma-17	109	18	{	{	PUNCT
ma-17	109	19	sn	sn	NOUN
ma-17	109	20	}	}	PUNCT
ma-17	109	21	,	,	PUNCT
ma-17	109	22	{	{	PUNCT
ma-17	109	23	tn	tn	NOUN
ma-17	109	24	}	}	PUNCT
ma-17	109	25	are	be	AUX
ma-17	109	26	nondecreasing	nondecrease	VERB
ma-17	109	27	,	,	PUNCT
ma-17	109	28	bounded	bound	VERB
ma-17	109	29	from	from	ADP
ma-17	109	30	above	above	ADV
ma-17	109	31	by	by	ADP
ma-17	109	32	t∗∗	t∗∗	X
ma-17	109	33	=	=	PUNCT
ma-17	109	34	η	η	X
ma-17	109	35	1−λ	1−λ	NUM
ma-17	109	36	,	,	PUNCT
ma-17	109	37	and	and	CCONJ
ma-17	109	38	converge	converge	VERB
ma-17	109	39	to	to	ADP
ma-17	109	40	t∗	t∗	NOUN
ma-17	109	41	∈	∈	PROPN
ma-17	110	1	[	[	X
ma-17	110	2	0	0	NUM
ma-17	110	3	,	,	PUNCT
ma-17	110	4	t∗∗	t∗∗	NOUN
ma-17	110	5	]	]	PUNCT
ma-17	110	6	.	.	PUNCT
ma-17	111	1	moreover	moreover	ADV
ma-17	111	2	,	,	PUNCT
ma-17	111	3	the	the	DET
ma-17	111	4	following	follow	VERB
ma-17	111	5	estimates	estimate	NOUN
ma-17	111	6	hold	hold	VERB
ma-17	111	7	for	for	ADP
ma-17	111	8	each	each	DET
ma-17	111	9	n	n	NOUN
ma-17	111	10	=	=	SYM
ma-17	111	11	1	1	NUM
ma-17	111	12	,	,	PUNCT
ma-17	111	13	2	2	NUM
ma-17	111	14	,	,	PUNCT
ma-17	111	15	.	.	PUNCT
ma-17	111	16	.	.	PUNCT
ma-17	112	1	.	.	PUNCT
ma-17	113	1	0	0	NUM
ma-17	114	1	≤	≤	NUM
ma-17	114	2	sn	sn	PROPN
ma-17	114	3	−	−	PROPN
ma-17	114	4	tn	tn	NOUN
ma-17	114	5	≤	≤	PUNCT
ma-17	114	6	λ(tn	λ(tn	PART
ma-17	114	7	−	−	NOUN
ma-17	114	8	sn−1	sn−1	PROPN
ma-17	114	9	)	)	PUNCT
ma-17	114	10	≤	≤	NOUN
ma-17	114	11	λ2nη	λ2nη	PUNCT
ma-17	114	12	,	,	PUNCT
ma-17	114	13	(	(	PUNCT
ma-17	114	14	2.7	2.7	NUM
ma-17	114	15	)	)	PUNCT
ma-17	114	16	0	0	NUM
ma-17	115	1	≤	≤	NUM
ma-17	115	2	tn+1	tn+1	PROPN
ma-17	115	3	−	−	PROPN
ma-17	115	4	sn	sn	PROPN
ma-17	115	5	≤	≤	PROPN
ma-17	115	6	λ(sn	λ(sn	PROPN
ma-17	115	7	−	−	PROPN
ma-17	115	8	tn	tn	PROPN
ma-17	115	9	)	)	PUNCT
ma-17	115	10	≤	≤	NOUN
ma-17	115	11	λ2n+1η	λ2n+1η	NOUN
ma-17	115	12	,	,	PUNCT
ma-17	115	13	(	(	PUNCT
ma-17	115	14	2.8	2.8	NUM
ma-17	115	15	)	)	PUNCT
ma-17	115	16	0	0	NUM
ma-17	115	17	≤	≤	NUM
ma-17	115	18	sn	sn	PROPN
ma-17	115	19	≤	≤	PROPN
ma-17	115	20	1−	1−	NUM
ma-17	115	21	λ2n+1	λ2n+1	PROPN
ma-17	115	22	1−	1−	NUM
ma-17	115	23	λ	λ	PROPN
ma-17	115	24	η	η	PROPN
ma-17	115	25	(	(	PUNCT
ma-17	115	26	2.9	2.9	NUM
ma-17	115	27	)	)	PUNCT
ma-17	115	28	and	and	CCONJ
ma-17	115	29	0	0	NUM
ma-17	115	30	≤	≤	NUM
ma-17	115	31	tn+1	tn+1	VERB
ma-17	115	32	≤	≤	NUM
ma-17	115	33	1−	1−	NUM
ma-17	115	34	λ2n+1	λ2n+1	PROPN
ma-17	115	35	1−	1−	NUM
ma-17	115	36	λ	λ	PROPN
ma-17	115	37	η	η	PROPN
ma-17	115	38	.	.	PROPN
ma-17	115	39	(	(	PUNCT
ma-17	115	40	2.10	2.10	NUM
ma-17	115	41	)	)	PUNCT
ma-17	115	42	eur	eur	NOUN
ma-17	115	43	.	.	PUNCT
ma-17	116	1	j.	j.	PROPN
ma-17	116	2	math	math	PROPN
ma-17	116	3	.	.	PUNCT
ma-17	117	1	anal	anal	ADJ
ma-17	117	2	.	.	PUNCT
ma-17	118	1	1	1	NUM
ma-17	118	2	(	(	PUNCT
ma-17	118	3	2021	2021	NUM
ma-17	118	4	)	)	PUNCT
ma-17	118	5	72	72	NUM
ma-17	118	6	proof	proof	NOUN
ma-17	118	7	.	.	PUNCT
ma-17	119	1	estimates	estimate	NOUN
ma-17	119	2	(	(	PUNCT
ma-17	119	3	2.7)-(2.10	2.7)-(2.10	NOUN
ma-17	119	4	)	)	PUNCT
ma-17	119	5	hold	hold	VERB
ma-17	119	6	if	if	SCONJ
ma-17	119	7	0	0	NUM
ma-17	119	8	≤	≤	NUM
ma-17	119	9	αm	αm	NOUN
ma-17	119	10	≤	≤	PROPN
ma-17	119	11	λ	λ	PROPN
ma-17	119	12	,	,	PUNCT
ma-17	119	13	(	(	PUNCT
ma-17	119	14	2.11	2.11	NUM
ma-17	119	15	)	)	PUNCT
ma-17	119	16	0	0	NUM
ma-17	119	17	≤	≤	NUM
ma-17	119	18	βm	βm	VERB
ma-17	119	19	≤	≤	PROPN
ma-17	119	20	λ	λ	PROPN
ma-17	119	21	,	,	PUNCT
ma-17	119	22	(	(	PUNCT
ma-17	119	23	2.12)and	2.12)and	NUM
ma-17	119	24	tm	tm	NOUN
ma-17	119	25	≤	≤	PROPN
ma-17	120	1	sm	sm	VERB
ma-17	120	2	≤	≤	PROPN
ma-17	120	3	tm+1	tm+1	X
ma-17	120	4	,	,	PUNCT
ma-17	120	5	(	(	PUNCT
ma-17	120	6	2.13)are	2.13)are	NOUN
ma-17	120	7	true	true	ADJ
ma-17	120	8	for	for	ADP
ma-17	120	9	m	m	PROPN
ma-17	120	10	=	=	SYM
ma-17	120	11	0	0	NUM
ma-17	120	12	,	,	PUNCT
ma-17	120	13	1	1	NUM
ma-17	120	14	,	,	PUNCT
ma-17	120	15	2	2	NUM
ma-17	120	16	,	,	PUNCT
ma-17	120	17	.	.	PUNCT
ma-17	120	18	.	.	PUNCT
ma-17	120	19	.	.	PUNCT
ma-17	121	1	.	.	PUNCT
ma-17	122	1	these	these	DET
ma-17	122	2	estimates	estimate	NOUN
ma-17	122	3	hold	hold	VERB
ma-17	122	4	for	for	ADP
ma-17	122	5	m	m	NOUN
ma-17	122	6	=	=	SYM
ma-17	122	7	0	0	NUM
ma-17	122	8	by	by	ADP
ma-17	122	9	(	(	PUNCT
ma-17	122	10	2.6	2.6	NUM
ma-17	122	11	)	)	PUNCT
ma-17	122	12	.	.	PUNCT
ma-17	123	1	we	we	PRON
ma-17	123	2	suppose	suppose	VERB
ma-17	123	3	that	that	SCONJ
ma-17	123	4	(	(	PUNCT
ma-17	123	5	2.11)-(2.13	2.11)-(2.13	NUM
ma-17	123	6	)	)	PUNCT
ma-17	123	7	are	be	AUX
ma-17	123	8	true	true	ADJ
ma-17	123	9	for	for	ADP
ma-17	123	10	m	m	PROPN
ma-17	123	11	=	=	SYM
ma-17	123	12	1	1	NUM
ma-17	123	13	,	,	PUNCT
ma-17	123	14	2	2	NUM
ma-17	123	15	,	,	PUNCT
ma-17	123	16	.	.	PUNCT
ma-17	123	17	.	.	PUNCT
ma-17	123	18	.	.	PUNCT
ma-17	124	1	n.	n.	NOUN
ma-17	124	2	by	by	ADP
ma-17	124	3	induction	induction	NOUN
ma-17	124	4	hypotheses	hypothesis	NOUN
ma-17	124	5	,	,	PUNCT
ma-17	124	6	(	(	PUNCT
ma-17	124	7	2.7	2.7	NUM
ma-17	124	8	)	)	PUNCT
ma-17	124	9	and	and	CCONJ
ma-17	124	10	(	(	PUNCT
ma-17	124	11	2.8	2.8	NUM
ma-17	124	12	)	)	PUNCT
ma-17	124	13	,	,	PUNCT
ma-17	124	14	we	we	PRON
ma-17	124	15	have	have	VERB
ma-17	124	16	sm	sm	ADJ
ma-17	124	17	≤	≤	PROPN
ma-17	124	18	tm	tm	PROPN
ma-17	124	19	+	+	CCONJ
ma-17	124	20	λ2mη	λ2mη	VERB
ma-17	124	21	≤	≤	ADJ
ma-17	124	22	sm−1	sm−1	NOUN
ma-17	124	23	+	+	CCONJ
ma-17	124	24	λ2m−1η	λ2m−1η	X
ma-17	125	1	+	+	CCONJ
ma-17	125	2	λ2mη	λ2mη	X
ma-17	125	3	≤	≤	NUM
ma-17	125	4	η	η	PROPN
ma-17	125	5	+	+	PROPN
ma-17	125	6	λη	λη	X
ma-17	125	7	+	+	NOUN
ma-17	125	8	.	.	PUNCT
ma-17	125	9	.	.	PUNCT
ma-17	126	1	.+	.+	NOUN
ma-17	126	2	λ2mη	λ2mη	PUNCT
ma-17	127	1	=	=	SYM
ma-17	127	2	1−	1−	NUM
ma-17	127	3	λ2m+1	λ2m+1	PUNCT
ma-17	127	4	1−	1−	NUM
ma-17	127	5	λ	λ	PROPN
ma-17	127	6	η	η	PROPN
ma-17	127	7	<	<	X
ma-17	127	8	η	η	PROPN
ma-17	127	9	1−	1−	NUM
ma-17	127	10	λ	λ	PROPN
ma-17	127	11	=	=	SYM
ma-17	127	12	t∗∗	t∗∗	NOUN
ma-17	127	13	,	,	PUNCT
ma-17	127	14	and	and	CCONJ
ma-17	127	15	tm+1	tm+1	PRON
ma-17	127	16	≤	≤	NOUN
ma-17	127	17	sm	sm	X
ma-17	127	18	+	+	CCONJ
ma-17	127	19	λ2m+1η	λ2m+1η	ADJ
ma-17	127	20	≤	≤	NUM
ma-17	127	21	tm	tm	NOUN
ma-17	127	22	+	+	X
ma-17	127	23	λ2mη	λ2mη	X
ma-17	127	24	+	+	NUM
ma-17	127	25	λ2m+1η	λ2m+1η	ADJ
ma-17	127	26	≤	≤	NUM
ma-17	127	27	η	η	PROPN
ma-17	127	28	+	+	PROPN
ma-17	127	29	λη	λη	X
ma-17	127	30	+	+	NOUN
ma-17	127	31	.	.	PUNCT
ma-17	127	32	.	.	PUNCT
ma-17	128	1	.+	.+	NOUN
ma-17	129	1	λ2m+1η	λ2m+1η	PRON
ma-17	129	2	=	=	SYM
ma-17	129	3	1−	1−	NUM
ma-17	129	4	λ2m+2	λ2m+2	NOUN
ma-17	129	5	1−	1−	NUM
ma-17	129	6	λ	λ	SYM
ma-17	129	7	η	η	PROPN
ma-17	129	8	<	<	X
ma-17	129	9	η	η	PROPN
ma-17	129	10	1−	1−	NUM
ma-17	129	11	λ	λ	PROPN
ma-17	129	12	=	=	SYM
ma-17	129	13	t∗∗.	t∗∗.	NOUN
ma-17	129	14	therefore	therefore	ADV
ma-17	129	15	,	,	PUNCT
ma-17	129	16	by	by	ADP
ma-17	129	17	(	(	PUNCT
ma-17	129	18	2.13	2.13	NUM
ma-17	129	19	)	)	PUNCT
ma-17	129	20	and	and	CCONJ
ma-17	129	21	the	the	DET
ma-17	129	22	induction	induction	NOUN
ma-17	129	23	hypotheses	hypothese	VERB
ma-17	129	24	,	,	PUNCT
ma-17	129	25	we	we	PRON
ma-17	129	26	see	see	VERB
ma-17	129	27	that	that	SCONJ
ma-17	129	28	sequences	sequence	NOUN
ma-17	129	29	{	{	PUNCT
ma-17	129	30	sm	sm	X
ma-17	129	31	}	}	PUNCT
ma-17	129	32	and	and	CCONJ
ma-17	129	33	{	{	PUNCT
ma-17	129	34	tm	tm	NOUN
ma-17	129	35	}	}	PUNCT
ma-17	129	36	arenondecreasing	arenondecreasing	NOUN
ma-17	129	37	.	.	PUNCT
ma-17	130	1	then	then	ADV
ma-17	130	2	,	,	PUNCT
ma-17	130	3	(	(	PUNCT
ma-17	130	4	2.11	2.11	NUM
ma-17	130	5	)	)	PUNCT
ma-17	130	6	shall	shall	AUX
ma-17	130	7	be	be	AUX
ma-17	130	8	true	true	ADJ
ma-17	130	9	if	if	SCONJ
ma-17	130	10	a(tm	a(tm	NOUN
ma-17	130	11	,	,	PUNCT
ma-17	130	12	sm	sm	INTJ
ma-17	130	13	,	,	PUNCT
ma-17	130	14	sm	sm	PROPN
ma-17	130	15	−	−	PROPN
ma-17	130	16	tm	tm	PROPN
ma-17	130	17	)	)	PUNCT
ma-17	130	18	∫	∫	PROPN
ma-17	131	1	1	1	NUM
ma-17	131	2	0	0	NUM
ma-17	131	3	ψ((1−	ψ((1−	PRON
ma-17	131	4	θ)(sm	θ)(sm	NOUN
ma-17	131	5	−	−	NOUN
ma-17	131	6	tm))dθ	tm))dθ	PROPN
ma-17	131	7	≤	≤	ADJ
ma-17	131	8	λ	λ	PROPN
ma-17	131	9	or	or	CCONJ
ma-17	131	10	a	a	DET
ma-17	131	11	(	(	PUNCT
ma-17	131	12	1−	1−	NUM
ma-17	131	13	λ2	λ2	NOUN
ma-17	131	14	m	m	PROPN
ma-17	131	15	1−	1−	NUM
ma-17	131	16	λ	λ	PROPN
ma-17	131	17	η	η	PROPN
ma-17	131	18	,	,	PUNCT
ma-17	131	19	1−	1−	NUM
ma-17	131	20	λ2m+1	λ2m+1	PUNCT
ma-17	131	21	1−	1−	NUM
ma-17	131	22	λ	λ	PROPN
ma-17	131	23	η	η	PROPN
ma-17	131	24	,	,	PUNCT
ma-17	131	25	λ2mη	λ2mη	PUNCT
ma-17	131	26	)	)	PUNCT
ma-17	131	27	∫	∫	PROPN
ma-17	132	1	1	1	NUM
ma-17	132	2	0	0	NUM
ma-17	133	1	p	p	NOUN
ma-17	133	2	(	(	PUNCT
ma-17	133	3	(	(	PUNCT
ma-17	133	4	1−	1−	NUM
ma-17	133	5	θ)λ2mη)dθ	θ)λ2mη)dθ	PROPN
ma-17	133	6	≤	≤	PROPN
ma-17	133	7	λor	λor	VERB
ma-17	133	8	a	a	PRON
ma-17	133	9	(	(	PUNCT
ma-17	133	10	η	η	PROPN
ma-17	133	11	1−	1−	PROPN
ma-17	133	12	λ	λ	PROPN
ma-17	133	13	,	,	PUNCT
ma-17	133	14	η	η	PROPN
ma-17	133	15	1−	1−	NUM
ma-17	133	16	λ	λ	PROPN
ma-17	133	17	,	,	PUNCT
ma-17	133	18	λ	λ	PROPN
ma-17	133	19	2η	2η	NUM
ma-17	133	20	)	)	PUNCT
ma-17	133	21	∫	∫	PROPN
ma-17	134	1	1	1	NUM
ma-17	134	2	0	0	NUM
ma-17	134	3	ψ((1−	ψ((1−	PUNCT
ma-17	134	4	θ)λ2η)dθ	θ)λ2η)dθ	ADP
ma-17	134	5	≤	≤	NUM
ma-17	134	6	λor	λor	VERB
ma-17	134	7	f	f	PROPN
ma-17	134	8	(	(	PUNCT
ma-17	134	9	λ	λ	NOUN
ma-17	134	10	)	)	PUNCT
ma-17	134	11	≤	≤	NOUN
ma-17	134	12	0,which	0,which	PRON
ma-17	134	13	is	be	AUX
ma-17	134	14	true	true	ADJ
ma-17	134	15	by	by	ADP
ma-17	134	16	the	the	DET
ma-17	134	17	definition	definition	NOUN
ma-17	134	18	of	of	ADP
ma-17	134	19	λf	λf	PROPN
ma-17	134	20	and	and	CCONJ
ma-17	134	21	λ	λ	PROPN
ma-17	134	22	.	.	PROPN
ma-17	134	23	similarly	similarly	ADV
ma-17	134	24	,	,	PUNCT
ma-17	134	25	(	(	PUNCT
ma-17	134	26	2.12	2.12	NUM
ma-17	134	27	)	)	PUNCT
ma-17	134	28	shall	shall	AUX
ma-17	134	29	be	be	AUX
ma-17	134	30	true	true	ADJ
ma-17	134	31	if	if	SCONJ
ma-17	134	32	b	b	X
ma-17	134	33	(	(	PUNCT
ma-17	134	34	1−	1−	NUM
ma-17	134	35	λ2	λ2	NOUN
ma-17	134	36	m	m	PROPN
ma-17	134	37	1−	1−	NUM
ma-17	134	38	λ	λ	PROPN
ma-17	134	39	η	η	PROPN
ma-17	134	40	,	,	PUNCT
ma-17	134	41	1−	1−	NUM
ma-17	134	42	λ2	λ2	NUM
ma-17	134	43	m	m	PROPN
ma-17	134	44	1−	1−	NUM
ma-17	134	45	λ	λ	SYM
ma-17	134	46	η	η	PROPN
ma-17	134	47	,	,	PUNCT
ma-17	134	48	λ2mη	λ2mη	X
ma-17	134	49	,	,	PUNCT
ma-17	134	50	λ2m+1η	λ2m+1η	NUM
ma-17	134	51	)	)	PUNCT
ma-17	135	1	+	+	VERB
ma-17	135	2	λp0	λp0	PROPN
ma-17	135	3	(	(	PUNCT
ma-17	135	4	1−	1−	NUM
ma-17	135	5	λ2m+2	λ2m+2	NOUN
ma-17	135	6	1−	1−	NUM
ma-17	135	7	λ	λ	SYM
ma-17	135	8	η	η	PROPN
ma-17	135	9	)	)	PUNCT
ma-17	135	10	≤	≤	PROPN
ma-17	135	11	λ	λ	PROPN
ma-17	135	12	,	,	PUNCT
ma-17	135	13	or	or	CCONJ
ma-17	135	14	b	b	X
ma-17	135	15	(	(	PUNCT
ma-17	135	16	η	η	PROPN
ma-17	135	17	1−	1−	PROPN
ma-17	135	18	λ	λ	PROPN
ma-17	135	19	,	,	PUNCT
ma-17	135	20	η	η	PROPN
ma-17	135	21	1−	1−	NUM
ma-17	135	22	λ	λ	PROPN
ma-17	135	23	,	,	PUNCT
ma-17	135	24	λ	λ	PROPN
ma-17	135	25	2η	2η	NUM
ma-17	135	26	,	,	PUNCT
ma-17	135	27	λ3η	λ3η	PROPN
ma-17	135	28	)	)	PUNCT
ma-17	135	29	+	+	CCONJ
ma-17	135	30	λp0	λp0	PROPN
ma-17	135	31	(	(	PUNCT
ma-17	135	32	η	η	PROPN
ma-17	135	33	1−	1−	NUM
ma-17	135	34	λ	λ	PROPN
ma-17	135	35	)	)	PUNCT
ma-17	135	36	≤	≤	NUM
ma-17	135	37	λ	λ	PROPN
ma-17	135	38	eur	eur	PROPN
ma-17	135	39	.	.	PUNCT
ma-17	136	1	j.	j.	PROPN
ma-17	136	2	math	math	PROPN
ma-17	136	3	.	.	PUNCT
ma-17	137	1	anal	anal	ADJ
ma-17	137	2	.	.	PUNCT
ma-17	138	1	1	1	NUM
ma-17	138	2	(	(	PUNCT
ma-17	138	3	2021	2021	NUM
ma-17	138	4	)	)	PUNCT
ma-17	138	5	73or	73or	NOUN
ma-17	138	6	g(λ	g(λ	PROPN
ma-17	138	7	)	)	PUNCT
ma-17	138	8	≤	≤	NOUN
ma-17	138	9	0	0	NUM
ma-17	138	10	,	,	PUNCT
ma-17	138	11	which	which	PRON
ma-17	138	12	is	be	AUX
ma-17	138	13	also	also	ADV
ma-17	138	14	true	true	ADJ
ma-17	138	15	by	by	ADP
ma-17	138	16	the	the	DET
ma-17	138	17	definition	definition	NOUN
ma-17	138	18	of	of	ADP
ma-17	138	19	λg	λg	PROPN
ma-17	138	20	and	and	CCONJ
ma-17	138	21	λ	λ	NOUN
ma-17	138	22	.	.	PROPN
ma-17	139	1	hence	hence	ADV
ma-17	139	2	,	,	PUNCT
ma-17	139	3	we	we	PRON
ma-17	139	4	conclude	conclude	VERB
ma-17	139	5	(	(	PUNCT
ma-17	139	6	2.13	2.13	NUM
ma-17	139	7	)	)	PUNCT
ma-17	139	8	holds	hold	VERB
ma-17	139	9	and	and	CCONJ
ma-17	139	10	limm−→∞	limm−→∞	NOUN
ma-17	139	11	sm	sm	NOUN
ma-17	139	12	=	=	PUNCT
ma-17	139	13	limm−→∞	limm−→∞	NOUN
ma-17	139	14	tm	tm	PROPN
ma-17	139	15	=	=	PROPN
ma-17	139	16	t∗.	t∗.	PROPN
ma-17	139	17	�	�	PROPN
ma-17	139	18	3	3	NUM
ma-17	139	19	.	.	PUNCT
ma-17	139	20	semi	semi	ADJ
ma-17	139	21	-	-	ADJ
ma-17	139	22	local	local	ADJ
ma-17	139	23	convergence	convergence	NOUN
ma-17	139	24	let	let	VERB
ma-17	139	25	u(x0	u(x0	NOUN
ma-17	139	26	,	,	PUNCT
ma-17	139	27	r	r	NOUN
ma-17	139	28	)	)	PUNCT
ma-17	139	29	=	=	SYM
ma-17	139	30	{	{	PUNCT
ma-17	139	31	x	x	PUNCT
ma-17	139	32	∈	∈	PROPN
ma-17	139	33	b	b	PROPN
ma-17	139	34	:	:	PUNCT
ma-17	139	35	‖x	‖x	NOUN
ma-17	140	1	−	−	PROPN
ma-17	141	1	x0‖	x0‖	PROPN
ma-17	141	2	<	<	X
ma-17	142	1	r	r	PROPN
ma-17	142	2	,	,	PUNCT
ma-17	142	3	r	r	NOUN
ma-17	142	4	>	>	NOUN
ma-17	142	5	0	0	NUM
ma-17	142	6	}	}	PUNCT
ma-17	142	7	and	and	CCONJ
ma-17	142	8	u[x0	u[x0	ADJ
ma-17	142	9	,	,	PUNCT
ma-17	142	10	r	r	NOUN
ma-17	142	11	]	]	PUNCT
ma-17	142	12	=	=	PUNCT
ma-17	142	13	{	{	PUNCT
ma-17	142	14	x	x	PROPN
ma-17	142	15	∈	∈	PROPN
ma-17	142	16	b	b	PROPN
ma-17	142	17	:	:	PUNCT
ma-17	142	18	‖x	‖x	NOUN
ma-17	143	1	−	−	PROPN
ma-17	144	1	x0‖	x0‖	PROPN
ma-17	144	2	≤	≤	NUM
ma-17	145	1	r	r	NOUN
ma-17	145	2	,	,	PUNCT
ma-17	145	3	r	r	NOUN
ma-17	145	4	>	>	X
ma-17	145	5	0}.we	0}.we	NUM
ma-17	145	6	use	use	VERB
ma-17	145	7	some	some	DET
ma-17	145	8	parameters	parameter	NOUN
ma-17	145	9	and	and	CCONJ
ma-17	145	10	functions	function	NOUN
ma-17	145	11	.	.	PUNCT
ma-17	146	1	consider	consider	VERB
ma-17	146	2	m	m	NOUN
ma-17	146	3	=	=	PUNCT
ma-17	147	1	[	[	X
ma-17	147	2	0,∞	0,∞	NUM
ma-17	147	3	)	)	PUNCT
ma-17	147	4	.	.	PUNCT
ma-17	148	1	suppose	suppose	VERB
ma-17	148	2	that	that	SCONJ
ma-17	148	3	there	there	PRON
ma-17	148	4	exists	exist	VERB
ma-17	148	5	function	function	NOUN
ma-17	148	6	p0	p0	NOUN
ma-17	148	7	:	:	PUNCT
ma-17	148	8	m	m	VERB
ma-17	148	9	−→	−→	ADJ
ma-17	148	10	m	m	VERB
ma-17	148	11	which	which	PRON
ma-17	148	12	is	be	AUX
ma-17	148	13	continuous	continuous	ADJ
ma-17	148	14	and	and	CCONJ
ma-17	148	15	nondecreasing	nondecrease	VERB
ma-17	148	16	such	such	ADJ
ma-17	148	17	that	that	DET
ma-17	148	18	functions	function	NOUN
ma-17	148	19	p0(t	p0(t	NOUN
ma-17	148	20	)	)	PUNCT
ma-17	148	21	−	−	PROPN
ma-17	149	1	1	1	NUM
ma-17	149	2	=	=	SYM
ma-17	149	3	0	0	PROPN
ma-17	149	4	has	have	VERB
ma-17	149	5	aminimal	aminimal	ADJ
ma-17	149	6	zero	zero	NUM
ma-17	149	7	s	s	NOUN
ma-17	149	8	∈	∈	PROPN
ma-17	149	9	(	(	PUNCT
ma-17	149	10	0,∞	0,∞	NOUN
ma-17	149	11	)	)	PUNCT
ma-17	149	12	.	.	PUNCT
ma-17	150	1	set	set	VERB
ma-17	150	2	m0	m0	NOUN
ma-17	150	3	=	=	PUNCT
ma-17	151	1	[	[	X
ma-17	151	2	0	0	NUM
ma-17	151	3	,	,	PUNCT
ma-17	151	4	s	s	NOUN
ma-17	151	5	)	)	PUNCT
ma-17	151	6	.	.	PUNCT
ma-17	152	1	suppose	suppose	VERB
ma-17	152	2	function	function	NOUN
ma-17	152	3	p0	p0	NOUN
ma-17	152	4	:	:	PUNCT
ma-17	152	5	m0	m0	PROPN
ma-17	152	6	−→	−→	NOUN
ma-17	152	7	m	m	VERB
ma-17	152	8	is	be	AUX
ma-17	152	9	continuous	continuous	ADJ
ma-17	152	10	andnondecreasing	andnondecreasing	NOUN
ma-17	152	11	.	.	PUNCT
ma-17	153	1	the	the	DET
ma-17	153	2	following	follow	VERB
ma-17	153	3	conditions	condition	NOUN
ma-17	153	4	(	(	PUNCT
ma-17	153	5	c	c	X
ma-17	153	6	)	)	PUNCT
ma-17	153	7	are	be	AUX
ma-17	153	8	needed:(c1	needed:(c1	NUM
ma-17	153	9	)	)	PUNCT
ma-17	153	10	there	there	PRON
ma-17	153	11	exists	exist	VERB
ma-17	153	12	x0	x0	PROPN
ma-17	153	13	∈	∈	PROPN
ma-17	153	14	ω	ω	PROPN
ma-17	153	15	and	and	CCONJ
ma-17	153	16	η	η	PROPN
ma-17	153	17	>	>	X
ma-17	153	18	0	0	NUM
ma-17	153	19	such	such	ADJ
ma-17	153	20	that	that	SCONJ
ma-17	153	21	f	f	PROPN
ma-17	153	22	′(x0)−1	′(x0)−1	PROPN
ma-17	153	23	∈	∈	PROPN
ma-17	153	24	l(b1	l(b1	NOUN
ma-17	153	25	,	,	PUNCT
ma-17	153	26	b	b	NOUN
ma-17	153	27	)	)	PUNCT
ma-17	153	28	and	and	CCONJ
ma-17	153	29	‖f	‖f	ADJ
ma-17	153	30	′(x0)−1f	′(x0)−1f	NOUN
ma-17	153	31	(	(	PUNCT
ma-17	153	32	x0)‖	x0)‖	PROPN
ma-17	153	33	≤	≤	PROPN
ma-17	153	34	η	η	PROPN
ma-17	153	35	.	.	PROPN
ma-17	154	1	(	(	PUNCT
ma-17	154	2	c2	c2	PROPN
ma-17	154	3	)	)	PUNCT
ma-17	154	4	for	for	ADP
ma-17	154	5	each	each	DET
ma-17	154	6	x	x	SYM
ma-17	154	7	∈	∈	PROPN
ma-17	154	8	ω	ω	NOUN
ma-17	154	9	‖f	‖f	PRON
ma-17	154	10	′(x0)−1(f	′(x0)−1(f	PROPN
ma-17	154	11	′(u)−	′(u)−	PROPN
ma-17	155	1	f	f	PROPN
ma-17	155	2	′(x0))‖	′(x0))‖	NUM
ma-17	155	3	≤	≤	NOUN
ma-17	155	4	p0(‖u	p0(‖u	NOUN
ma-17	155	5	−	−	PROPN
ma-17	155	6	x0‖	x0‖	PROPN
ma-17	155	7	)	)	PUNCT
ma-17	155	8	.	.	PUNCT
ma-17	156	1	set	set	VERB
ma-17	156	2	s0	s0	PROPN
ma-17	156	3	=	=	PUNCT
ma-17	156	4	u(x0	u(x0	PROPN
ma-17	156	5	,	,	PUNCT
ma-17	156	6	s	s	PART
ma-17	156	7	)	)	PUNCT
ma-17	156	8	∩ω.(c3	∩ω.(c3	NUM
ma-17	156	9	)	)	PUNCT
ma-17	156	10	for	for	ADP
ma-17	156	11	each	each	DET
ma-17	156	12	x	x	NOUN
ma-17	156	13	,	,	PUNCT
ma-17	156	14	y	y	PROPN
ma-17	156	15	∈	∈	PROPN
ma-17	156	16	s0	s0	NOUN
ma-17	156	17	the	the	DET
ma-17	156	18	following	follow	VERB
ma-17	156	19	hold	hold	NOUN
ma-17	156	20	‖f	‖f	SCONJ
ma-17	156	21	′(x0)−1(f	′(x0)−1(f	PROPN
ma-17	156	22	′(y)−	′(y)−	VERB
ma-17	156	23	f	f	PROPN
ma-17	156	24	′(x))‖	′(x))‖	PROPN
ma-17	156	25	≤	≤	ADJ
ma-17	156	26	p	p	X
ma-17	156	27	(	(	PUNCT
ma-17	156	28	‖y	‖y	NOUN
ma-17	156	29	−	−	NOUN
ma-17	156	30	x‖	x‖	PROPN
ma-17	156	31	)	)	PUNCT
ma-17	156	32	(	(	PUNCT
ma-17	156	33	c4	c4	NOUN
ma-17	156	34	)	)	PUNCT
ma-17	156	35	for	for	ADP
ma-17	156	36	each	each	DET
ma-17	156	37	n	n	NOUN
ma-17	156	38	=	=	SYM
ma-17	156	39	0	0	NUM
ma-17	156	40	,	,	PUNCT
ma-17	156	41	1	1	NUM
ma-17	156	42	,	,	PUNCT
ma-17	156	43	2	2	NUM
ma-17	156	44	,	,	PUNCT
ma-17	156	45	.	.	PUNCT
ma-17	156	46	.	.	PUNCT
ma-17	156	47	.	.	PUNCT
ma-17	157	1	‖anf	‖anf	PRON
ma-17	157	2	′(xn)−1f	′(xn)−1f	NOUN
ma-17	157	3	′(x0)‖	′(x0)‖	PART
ma-17	157	4	≤	≤	NOUN
ma-17	157	5	an	an	DET
ma-17	157	6	f	f	NOUN
ma-17	157	7	′(x0	′(x0	NOUN
ma-17	157	8	)	)	PUNCT
ma-17	157	9	−1([y	−1([y	NOUN
ma-17	157	10	,	,	PUNCT
ma-17	157	11	x	x	PROPN
ma-17	157	12	;	;	PUNCT
ma-17	157	13	f	f	X
ma-17	157	14	]	]	X
ma-17	157	15	−	−	X
ma-17	157	16	f	f	PROPN
ma-17	157	17	′(x))‖	′(x))‖	PROPN
ma-17	157	18	≤	≤	VERB
ma-17	157	19	l2‖y	l2‖y	NOUN
ma-17	158	1	−	−	PROPN
ma-17	158	2	x‖and	x‖and	PUNCT
ma-17	159	1	‖f	‖f	PRON
ma-17	159	2	′(x0)−1hn‖	′(x0)−1hn‖	VERB
ma-17	159	3	≤	≤	NUM
ma-17	159	4	ξn	ξn	NOUN
ma-17	159	5	,	,	PUNCT
ma-17	159	6	where	where	SCONJ
ma-17	159	7	hn	hn	PROPN
ma-17	159	8	=	=	SYM
ma-17	159	9	f	f	PROPN
ma-17	159	10	′(x0	′(x0	NOUN
ma-17	159	11	)	)	PUNCT
ma-17	160	1	−1	−1	NOUN
ma-17	160	2	∫	∫	NOUN
ma-17	160	3	1	1	NUM
ma-17	160	4	0	0	NUM
ma-17	161	1	(	(	PUNCT
ma-17	161	2	f	f	X
ma-17	161	3	′(yn	′(yn	ADV
ma-17	161	4	+	+	CCONJ
ma-17	161	5	θ(xn+1	θ(xn+1	NUM
ma-17	161	6	−	−	NUM
ma-17	161	7	yn))−	yn))−	NOUN
ma-17	161	8	f	f	PROPN
ma-17	161	9	′(xn)a−1n	′(xn)a−1n	PROPN
ma-17	161	10	)	)	PUNCT
ma-17	161	11	dθ	dθ	PROPN
ma-17	161	12	.	.	PUNCT
ma-17	162	1	(	(	PUNCT
ma-17	162	2	c5	c5	PROPN
ma-17	162	3	)	)	PUNCT
ma-17	162	4	conditions	condition	NOUN
ma-17	162	5	of	of	ADP
ma-17	162	6	lemma	lemma	PROPN
ma-17	162	7	2.2	2.2	NUM
ma-17	162	8	or	or	CCONJ
ma-17	162	9	lemma	lemma	PROPN
ma-17	162	10	2.3	2.3	NUM
ma-17	162	11	or	or	CCONJ
ma-17	162	12	lemma	lemma	PROPN
ma-17	162	13	2.5	2.5	NUM
ma-17	162	14	hold.and(c6	hold.and(c6	NOUN
ma-17	162	15	)	)	PUNCT
ma-17	162	16	u[x0	u[x0	NOUN
ma-17	162	17	,	,	PUNCT
ma-17	162	18	t	t	PROPN
ma-17	162	19	∗	∗	NOUN
ma-17	162	20	]	]	X
ma-17	163	1	⊂	⊂	PROPN
ma-17	163	2	ω.then	ω.then	PROPN
ma-17	163	3	,	,	PUNCT
ma-17	163	4	we	we	PRON
ma-17	163	5	can	can	AUX
ma-17	163	6	show	show	VERB
ma-17	163	7	the	the	DET
ma-17	163	8	semi	semi	ADJ
ma-17	163	9	-	-	ADJ
ma-17	163	10	local	local	ADJ
ma-17	163	11	convergence	convergence	NOUN
ma-17	163	12	of	of	ADP
ma-17	163	13	method	method	NOUN
ma-17	163	14	(	(	PUNCT
ma-17	163	15	1.2	1.2	NUM
ma-17	163	16	)	)	PUNCT
ma-17	163	17	using	use	VERB
ma-17	163	18	the	the	DET
ma-17	163	19	conditions	condition	NOUN
ma-17	163	20	(	(	PUNCT
ma-17	163	21	c	c	NOUN
ma-17	163	22	)	)	PUNCT
ma-17	163	23	and	and	CCONJ
ma-17	163	24	thepreceding	theprecede	VERB
ma-17	163	25	notation	notation	NOUN
ma-17	163	26	.	.	PUNCT
ma-17	164	1	eur	eur	PROPN
ma-17	164	2	.	.	PUNCT
ma-17	165	1	j.	j.	PROPN
ma-17	165	2	math	math	PROPN
ma-17	165	3	.	.	PUNCT
ma-17	166	1	anal	anal	ADJ
ma-17	166	2	.	.	PUNCT
ma-17	167	1	1	1	NUM
ma-17	167	2	(	(	PUNCT
ma-17	167	3	2021	2021	NUM
ma-17	167	4	)	)	PUNCT
ma-17	167	5	74	74	NUM
ma-17	167	6	theorem	theorem	VERB
ma-17	167	7	3.1	3.1	NUM
ma-17	167	8	.	.	PUNCT
ma-17	168	1	under	under	ADP
ma-17	168	2	the	the	DET
ma-17	168	3	conditions	condition	NOUN
ma-17	168	4	(	(	PUNCT
ma-17	168	5	c	c	NOUN
ma-17	168	6	)	)	PUNCT
ma-17	168	7	,	,	PUNCT
ma-17	168	8	sequences	sequence	NOUN
ma-17	168	9	{	{	PUNCT
ma-17	168	10	yn	yn	PROPN
ma-17	168	11	}	}	PUNCT
ma-17	168	12	,	,	PUNCT
ma-17	168	13	{	{	PUNCT
ma-17	168	14	xn	xn	X
ma-17	168	15	}	}	PUNCT
ma-17	168	16	generated	generate	VERB
ma-17	168	17	by	by	ADP
ma-17	168	18	method	method	NOUN
ma-17	168	19	(	(	PUNCT
ma-17	168	20	1.2	1.2	NUM
ma-17	168	21	)	)	PUNCT
ma-17	168	22	are	be	AUX
ma-17	168	23	well	well	ADV
ma-17	168	24	defined	define	VERB
ma-17	168	25	in	in	ADP
ma-17	168	26	u[x0	u[x0	NOUN
ma-17	168	27	,	,	PUNCT
ma-17	168	28	t	t	PROPN
ma-17	168	29	∗	∗	NOUN
ma-17	168	30	]	]	PUNCT
ma-17	168	31	,	,	PUNCT
ma-17	168	32	remain	remain	VERB
ma-17	168	33	in	in	ADP
ma-17	168	34	u[x0	u[x0	NOUN
ma-17	168	35	,	,	PUNCT
ma-17	168	36	t	t	PROPN
ma-17	168	37	∗	∗	NOUN
ma-17	168	38	]	]	PUNCT
ma-17	168	39	for	for	ADP
ma-17	168	40	each	each	DET
ma-17	168	41	n	n	NOUN
ma-17	168	42	=	=	SYM
ma-17	168	43	0	0	NUM
ma-17	168	44	,	,	PUNCT
ma-17	168	45	1	1	NUM
ma-17	168	46	,	,	PUNCT
ma-17	168	47	2	2	NUM
ma-17	168	48	,	,	PUNCT
ma-17	168	49	.	.	PUNCT
ma-17	168	50	.	.	PUNCT
ma-17	169	1	.	.	PUNCT
ma-17	170	1	and	and	CCONJ
ma-17	170	2	converge	converge	VERB
ma-17	170	3	to	to	ADP
ma-17	170	4	a	a	DET
ma-17	170	5	solution	solution	NOUN
ma-17	170	6	x∗	x∗	PROPN
ma-17	170	7	∈	∈	PROPN
ma-17	170	8	u[x0	u[x0	NOUN
ma-17	170	9	,	,	PUNCT
ma-17	170	10	t	t	PROPN
ma-17	170	11	∗	∗	NOUN
ma-17	170	12	]	]	PUNCT
ma-17	170	13	of	of	ADP
ma-17	170	14	equation	equation	NOUN
ma-17	170	15	f	f	X
ma-17	170	16	(	(	PUNCT
ma-17	170	17	x	x	X
ma-17	170	18	)	)	PUNCT
ma-17	170	19	=	=	SYM
ma-17	171	1	0	0	X
ma-17	171	2	.	.	PUNCT
ma-17	172	1	moreover	moreover	ADV
ma-17	172	2	,	,	PUNCT
ma-17	172	3	the	the	DET
ma-17	172	4	following	follow	VERB
ma-17	172	5	error	error	NOUN
ma-17	172	6	estimates	estimate	NOUN
ma-17	172	7	hold	hold	VERB
ma-17	172	8	for	for	ADP
ma-17	172	9	each	each	DET
ma-17	172	10	n	n	NOUN
ma-17	172	11	=	=	SYM
ma-17	172	12	0	0	NUM
ma-17	172	13	,	,	PUNCT
ma-17	172	14	1	1	NUM
ma-17	172	15	,	,	PUNCT
ma-17	172	16	2	2	NUM
ma-17	172	17	,	,	PUNCT
ma-17	172	18	.	.	PUNCT
ma-17	172	19	.	.	PUNCT
ma-17	172	20	.	.	PUNCT
ma-17	173	1	‖x∗	‖x∗	PUNCT
ma-17	174	1	−	−	NOUN
ma-17	175	1	xn‖	xn‖	PROPN
ma-17	175	2	≤	≤	NOUN
ma-17	175	3	t∗	t∗	NOUN
ma-17	175	4	−	−	PROPN
ma-17	175	5	tn	tn	PROPN
ma-17	175	6	.	.	PUNCT
ma-17	175	7	proof	proof	NOUN
ma-17	175	8	.	.	PUNCT
ma-17	176	1	we	we	PRON
ma-17	176	2	shall	shall	AUX
ma-17	176	3	show	show	VERB
ma-17	176	4	items(pm	items(pm	NOUN
ma-17	176	5	)	)	PUNCT
ma-17	176	6	‖ym	‖ym	NUM
ma-17	176	7	−	−	PROPN
ma-17	176	8	xm‖	xm‖	PROPN
ma-17	176	9	≤	≤	PROPN
ma-17	177	1	sm	sm	VERB
ma-17	177	2	−	−	PROPN
ma-17	177	3	tm(qm	tm(qm	NOUN
ma-17	177	4	)	)	PUNCT
ma-17	177	5	‖xm+1	‖xm+1	PUNCT
ma-17	178	1	−	−	PROPN
ma-17	178	2	ym‖	ym‖	PROPN
ma-17	178	3	≤	≤	NOUN
ma-17	179	1	tm+1	tm+1	AUX
ma-17	179	2	−	−	NOUN
ma-17	179	3	smusing	smuse	VERB
ma-17	179	4	mathematical	mathematical	ADJ
ma-17	179	5	induction	induction	NOUN
ma-17	179	6	on	on	ADP
ma-17	179	7	integer	integer	NOUN
ma-17	179	8	m.	m.	NOUN
ma-17	179	9	by	by	ADP
ma-17	179	10	the	the	DET
ma-17	179	11	first	first	ADJ
ma-17	179	12	substep	substep	NOUN
ma-17	179	13	of	of	ADP
ma-17	179	14	method	method	NOUN
ma-17	179	15	(	(	PUNCT
ma-17	179	16	1.2	1.2	NUM
ma-17	179	17	)	)	PUNCT
ma-17	179	18	for	for	ADP
ma-17	179	19	n	n	NOUN
ma-17	179	20	=	=	SYM
ma-17	179	21	0	0	PROPN
ma-17	179	22	and	and	CCONJ
ma-17	179	23	(	(	PUNCT
ma-17	179	24	c1),we	c1),we	PROPN
ma-17	179	25	have	have	VERB
ma-17	179	26	‖y0	‖y0	VERB
ma-17	179	27	−	−	PROPN
ma-17	179	28	x0‖	x0‖	PROPN
ma-17	179	29	=	=	PUNCT
ma-17	179	30	‖f	‖f	DET
ma-17	179	31	′(x0)−1f	′(x0)−1f	NOUN
ma-17	179	32	(	(	PUNCT
ma-17	179	33	x0)‖	x0)‖	PROPN
ma-17	179	34	≤	≤	NUM
ma-17	179	35	η	η	PROPN
ma-17	179	36	=	=	PROPN
ma-17	179	37	s0	s0	PROPN
ma-17	179	38	−	−	PROPN
ma-17	179	39	t0	t0	PROPN
ma-17	179	40	=	=	PROPN
ma-17	179	41	s0	s0	PROPN
ma-17	179	42	≤	≤	NUM
ma-17	179	43	t∗,so	t∗,so	NUM
ma-17	179	44	y0	y0	PROPN
ma-17	179	45	∈	∈	PROPN
ma-17	179	46	u[x0	u[x0	NOUN
ma-17	179	47	,	,	PUNCT
ma-17	179	48	t	t	PROPN
ma-17	179	49	∗	∗	NOUN
ma-17	179	50	]	]	PUNCT
ma-17	179	51	and	and	CCONJ
ma-17	179	52	(	(	PUNCT
ma-17	179	53	p0	p0	NOUN
ma-17	179	54	)	)	PUNCT
ma-17	179	55	holds	hold	VERB
ma-17	179	56	.	.	PUNCT
ma-17	180	1	we	we	PRON
ma-17	180	2	can	can	AUX
ma-17	180	3	write	write	VERB
ma-17	180	4	by	by	ADP
ma-17	180	5	the	the	DET
ma-17	180	6	first	first	ADJ
ma-17	180	7	sustep	sustep	NOUN
ma-17	180	8	of	of	ADP
ma-17	180	9	method	method	NOUN
ma-17	180	10	(	(	PUNCT
ma-17	180	11	1.2	1.2	NUM
ma-17	180	12	)	)	PUNCT
ma-17	181	1	that	that	SCONJ
ma-17	181	2	f	f	X
ma-17	181	3	(	(	PUNCT
ma-17	181	4	y0	y0	NOUN
ma-17	181	5	)	)	PUNCT
ma-17	181	6	=	=	SYM
ma-17	181	7	f	f	X
ma-17	181	8	(	(	PUNCT
ma-17	181	9	y0)−	y0)−	PROPN
ma-17	181	10	f	f	PROPN
ma-17	181	11	(	(	PUNCT
ma-17	181	12	x0)−	x0)−	PROPN
ma-17	181	13	f	f	PROPN
ma-17	181	14	′(x0)(y0	′(x0)(y0	NOUN
ma-17	181	15	−	−	PROPN
ma-17	181	16	x0	x0	PROPN
ma-17	181	17	)	)	PUNCT
ma-17	182	1	=	=	SYM
ma-17	182	2	∫	∫	PROPN
ma-17	183	1	1	1	NUM
ma-17	183	2	0	0	NUM
ma-17	184	1	(	(	PUNCT
ma-17	184	2	f	f	PROPN
ma-17	184	3	′(x0	′(x0	NOUN
ma-17	184	4	+	+	CCONJ
ma-17	184	5	θ(y0	θ(y0	PROPN
ma-17	184	6	−	−	PROPN
ma-17	185	1	x0))−	x0))−	NOUN
ma-17	186	1	f	f	X
ma-17	187	1	′(x0))(y0	′(x0))(y0	ADV
ma-17	187	2	−	−	PROPN
ma-17	187	3	x0)dθ	x0)dθ	PROPN
ma-17	187	4	,	,	PUNCT
ma-17	187	5	leading	lead	VERB
ma-17	187	6	by	by	ADP
ma-17	187	7	(	(	PUNCT
ma-17	187	8	c2	c2	PROPN
ma-17	187	9	)	)	PUNCT
ma-17	187	10	and	and	CCONJ
ma-17	187	11	(	(	PUNCT
ma-17	187	12	p0	p0	NOUN
ma-17	187	13	)	)	PUNCT
ma-17	187	14	to	to	ADP
ma-17	187	15	‖f	‖f	ADJ
ma-17	187	16	′(x0)−1f	′(x0)−1f	NOUN
ma-17	187	17	(	(	PUNCT
ma-17	187	18	y0)‖	y0)‖	PROPN
ma-17	187	19	≤	≤	NUM
ma-17	187	20	∫	∫	PROPN
ma-17	187	21	1	1	NUM
ma-17	187	22	0	0	NUM
ma-17	188	1	p0(θ‖y0	p0(θ‖y0	PROPN
ma-17	188	2	−	−	PROPN
ma-17	188	3	x0‖)dθ‖y0	x0‖)dθ‖y0	PUNCT
ma-17	189	1	−	−	PROPN
ma-17	189	2	x0‖	x0‖	PROPN
ma-17	189	3	≤	≤	NUM
ma-17	189	4	∫	∫	PROPN
ma-17	190	1	1	1	NUM
ma-17	190	2	0	0	NUM
ma-17	190	3	p̄	p̄	NOUN
ma-17	190	4	(	(	PUNCT
ma-17	190	5	θ(s0	θ(s0	PROPN
ma-17	190	6	−	−	PROPN
ma-17	190	7	t0))dθ(s0	t0))dθ(s0	PROPN
ma-17	190	8	−	−	PROPN
ma-17	190	9	t0	t0	PROPN
ma-17	190	10	)	)	PUNCT
ma-17	190	11	.	.	PUNCT
ma-17	191	1	(	(	PUNCT
ma-17	191	2	3.1	3.1	NUM
ma-17	191	3	)	)	PUNCT
ma-17	191	4	let	let	VERB
ma-17	191	5	z	z	NOUN
ma-17	191	6	∈	∈	PROPN
ma-17	191	7	u(x0	u(x0	NOUN
ma-17	191	8	,	,	PUNCT
ma-17	191	9	t	t	PROPN
ma-17	191	10	∗	∗	NOUN
ma-17	191	11	)	)	PUNCT
ma-17	191	12	.	.	PUNCT
ma-17	192	1	in	in	ADP
ma-17	192	2	view	view	NOUN
ma-17	192	3	of	of	ADP
ma-17	192	4	(	(	PUNCT
ma-17	192	5	c2	c2	PROPN
ma-17	192	6	)	)	PUNCT
ma-17	192	7	,	,	PUNCT
ma-17	192	8	we	we	PRON
ma-17	192	9	get	get	VERB
ma-17	192	10	‖f	‖f	PUNCT
ma-17	192	11	′(x0)−1(f	′(x0)−1(f	VERB
ma-17	193	1	′(z)−	′(z)−	PROPN
ma-17	193	2	f	f	X
ma-17	193	3	′(x0))‖	′(x0))‖	NUM
ma-17	193	4	≤	≤	NOUN
ma-17	194	1	p0(‖z	p0(‖z	ADJ
ma-17	194	2	−	−	PROPN
ma-17	194	3	x0‖	x0‖	PROPN
ma-17	194	4	)	)	PUNCT
ma-17	194	5	≤	≤	NOUN
ma-17	195	1	p0(t	p0(t	CCONJ
ma-17	195	2	∗	∗	NOUN
ma-17	195	3	)	)	PUNCT
ma-17	195	4	<	<	X
ma-17	195	5	1	1	NUM
ma-17	195	6	,	,	PUNCT
ma-17	195	7	(	(	PUNCT
ma-17	195	8	3.2	3.2	NUM
ma-17	195	9	)	)	PUNCT
ma-17	196	1	so	so	SCONJ
ma-17	196	2	‖f	‖f	ADP
ma-17	196	3	′(z)−1f	′(z)−1f	NOUN
ma-17	197	1	′(x0)‖	′(x0)‖	ADP
ma-17	197	2	≤	≤	NUM
ma-17	197	3	1	1	NUM
ma-17	197	4	1−	1−	NUM
ma-17	198	1	p0(‖z	p0(‖z	NOUN
ma-17	198	2	−	−	PROPN
ma-17	198	3	x0‖	x0‖	PROPN
ma-17	198	4	)	)	PUNCT
ma-17	198	5	(	(	PUNCT
ma-17	198	6	3.3	3.3	NUM
ma-17	198	7	)	)	PUNCT
ma-17	198	8	holds	hold	VERB
ma-17	198	9	by	by	ADP
ma-17	198	10	a	a	DET
ma-17	198	11	lemma	lemma	PROPN
ma-17	198	12	on	on	ADP
ma-17	198	13	invertible	invertible	ADJ
ma-17	198	14	linear	linear	PROPN
ma-17	198	15	operators	operator	NOUN
ma-17	198	16	due	due	ADP
ma-17	198	17	to	to	ADP
ma-17	198	18	banach	banach	NOUN
ma-17	198	19	[	[	X
ma-17	198	20	24	24	NUM
ma-17	198	21	]	]	PUNCT
ma-17	198	22	and	and	CCONJ
ma-17	198	23	(	(	PUNCT
ma-17	198	24	3.2	3.2	NUM
ma-17	198	25	)	)	PUNCT
ma-17	198	26	.	.	PUNCT
ma-17	199	1	therefore	therefore	ADV
ma-17	199	2	,	,	PUNCT
ma-17	199	3	iterate	iterate	NOUN
ma-17	199	4	x1is	x1is	PUNCT
ma-17	199	5	well	well	ADV
ma-17	199	6	defined	define	VERB
ma-17	199	7	and	and	CCONJ
ma-17	199	8	we	we	PRON
ma-17	199	9	can	can	AUX
ma-17	199	10	write	write	VERB
ma-17	199	11	in	in	ADP
ma-17	199	12	turn	turn	NOUN
ma-17	199	13	by	by	ADP
ma-17	199	14	(	(	PUNCT
ma-17	199	15	c3	c3	PROPN
ma-17	199	16	)	)	PUNCT
ma-17	199	17	and	and	CCONJ
ma-17	199	18	(	(	PUNCT
ma-17	199	19	3.3	3.3	NUM
ma-17	199	20	)	)	PUNCT
ma-17	199	21	(	(	PUNCT
ma-17	199	22	for	for	ADP
ma-17	199	23	z	z	NOUN
ma-17	199	24	=	=	SYM
ma-17	199	25	x0	x0	PROPN
ma-17	199	26	,	,	PUNCT
ma-17	199	27	y0	y0	NOUN
ma-17	199	28	)	)	PUNCT
ma-17	199	29	‖x1	‖x1	NOUN
ma-17	199	30	−	−	PROPN
ma-17	199	31	y0‖	y0‖	NOUN
ma-17	199	32	=	=	SYM
ma-17	199	33	‖a0f	‖a0f	PROPN
ma-17	199	34	′(x0)−1f	′(x0)−1f	NOUN
ma-17	199	35	(	(	PUNCT
ma-17	199	36	y0)‖	y0)‖	NOUN
ma-17	199	37	≤	≤	PROPN
ma-17	199	38	‖a0f	‖a0f	PROPN
ma-17	199	39	′(x0)−1f	′(x0)−1f	PROPN
ma-17	199	40	′(x0)‖‖	′(x0)‖‖	NOUN
ma-17	199	41	∫	∫	PROPN
ma-17	199	42	1	1	NUM
ma-17	199	43	0	0	NUM
ma-17	199	44	f	f	PROPN
ma-17	199	45	′(x0	′(x0	NOUN
ma-17	199	46	)	)	PUNCT
ma-17	199	47	−1(f	−1(f	PROPN
ma-17	199	48	′(x0	′(x0	NOUN
ma-17	199	49	+	+	CCONJ
ma-17	199	50	θ(y0	θ(y0	PROPN
ma-17	200	1	−	−	PROPN
ma-17	200	2	x0))−	x0))−	PROPN
ma-17	201	1	f	f	PROPN
ma-17	201	2	′(x0))dθ(y0	′(x0))dθ(y0	PROPN
ma-17	202	1	−	−	PROPN
ma-17	202	2	x0)‖	x0)‖	PROPN
ma-17	202	3	≤	≤	PROPN
ma-17	202	4	a0	a0	NOUN
ma-17	202	5	∫	∫	PROPN
ma-17	202	6	1	1	NUM
ma-17	202	7	0	0	NUM
ma-17	202	8	p̄	p̄	NOUN
ma-17	202	9	(	(	PUNCT
ma-17	202	10	(	(	PUNCT
ma-17	202	11	1−	1−	NUM
ma-17	202	12	θ)‖y0	θ)‖y0	NOUN
ma-17	202	13	−	−	PROPN
ma-17	202	14	x0‖)dθ‖y0	x0‖)dθ‖y0	PUNCT
ma-17	203	1	−	−	PROPN
ma-17	204	1	x0‖	x0‖	PROPN
ma-17	204	2	1−	1−	NUM
ma-17	205	1	p0(‖x0	p0(‖x0	PROPN
ma-17	205	2	−	−	PROPN
ma-17	205	3	x0‖	x0‖	PROPN
ma-17	205	4	)	)	PUNCT
ma-17	205	5	≤	≤	NOUN
ma-17	206	1	a0	a0	PROPN
ma-17	206	2	∫	∫	PROPN
ma-17	206	3	1	1	NUM
ma-17	206	4	0	0	NUM
ma-17	206	5	p̄	p̄	NOUN
ma-17	206	6	(	(	PUNCT
ma-17	206	7	(	(	PUNCT
ma-17	206	8	1−	1−	NUM
ma-17	206	9	θ)(s0	θ)(s0	PROPN
ma-17	206	10	−	−	PROPN
ma-17	206	11	t0))dθ	t0))dθ	NOUN
ma-17	206	12	1−	1−	NUM
ma-17	206	13	p0(0	p0(0	NOUN
ma-17	206	14	)	)	PUNCT
ma-17	206	15	(	(	PUNCT
ma-17	206	16	s0	s0	PROPN
ma-17	206	17	−	−	PROPN
ma-17	206	18	t0	t0	PROPN
ma-17	206	19	)	)	PUNCT
ma-17	207	1	=	=	PUNCT
ma-17	207	2	t1	t1	NOUN
ma-17	207	3	−	−	PROPN
ma-17	207	4	s0	s0	PROPN
ma-17	207	5	,	,	PUNCT
ma-17	207	6	(	(	PUNCT
ma-17	207	7	3.4	3.4	NUM
ma-17	207	8	)	)	PUNCT
ma-17	207	9	eur	eur	PROPN
ma-17	207	10	.	.	PUNCT
ma-17	208	1	j.	j.	PROPN
ma-17	208	2	math	math	PROPN
ma-17	208	3	.	.	PUNCT
ma-17	209	1	anal	anal	ADJ
ma-17	209	2	.	.	PUNCT
ma-17	210	1	1	1	NUM
ma-17	210	2	(	(	PUNCT
ma-17	210	3	2021	2021	NUM
ma-17	210	4	)	)	PUNCT
ma-17	211	1	75showing	75showing	NOUN
ma-17	211	2	(	(	PUNCT
ma-17	211	3	q0	q0	PROPN
ma-17	211	4	)	)	PUNCT
ma-17	211	5	.	.	PUNCT
ma-17	212	1	then	then	ADV
ma-17	212	2	,	,	PUNCT
ma-17	212	3	we	we	PRON
ma-17	212	4	have	have	VERB
ma-17	212	5	‖x1	‖x1	NOUN
ma-17	212	6	−	−	PROPN
ma-17	212	7	x0‖	x0‖	PROPN
ma-17	212	8	≤	≤	PROPN
ma-17	213	1	‖x0	‖x0	NOUN
ma-17	214	1	−	−	PROPN
ma-17	214	2	y0‖+	y0‖+	NOUN
ma-17	215	1	‖y0	‖y0	NOUN
ma-17	215	2	−	−	PROPN
ma-17	215	3	x0‖	x0‖	PROPN
ma-17	215	4	≤	≤	PROPN
ma-17	215	5	t1	t1	NOUN
ma-17	215	6	−	−	PROPN
ma-17	216	1	s0	s0	PROPN
ma-17	216	2	+	+	CCONJ
ma-17	216	3	s0	s0	PROPN
ma-17	216	4	−	−	PROPN
ma-17	216	5	t0	t0	PROPN
ma-17	216	6	=	=	PUNCT
ma-17	216	7	t1	t1	PROPN
ma-17	216	8	≤	≤	ADJ
ma-17	216	9	t∗	t∗	NOUN
ma-17	216	10	,	,	PUNCT
ma-17	216	11	so	so	CCONJ
ma-17	216	12	x1	x1	PROPN
ma-17	216	13	∈	∈	PROPN
ma-17	216	14	u[x0	u[x0	NOUN
ma-17	216	15	,	,	PUNCT
ma-17	216	16	t	t	PROPN
ma-17	216	17	∗	∗	NOUN
ma-17	216	18	]	]	PUNCT
ma-17	216	19	.	.	PUNCT
ma-17	217	1	moreover	moreover	ADV
ma-17	217	2	,	,	PUNCT
ma-17	217	3	we	we	PRON
ma-17	217	4	can	can	AUX
ma-17	217	5	write	write	VERB
ma-17	217	6	f	f	PROPN
ma-17	217	7	(	(	PUNCT
ma-17	217	8	x1	x1	PROPN
ma-17	217	9	)	)	PUNCT
ma-17	218	1	=	=	SYM
ma-17	218	2	f	f	PROPN
ma-17	218	3	(	(	PUNCT
ma-17	218	4	x1)−	x1)−	PROPN
ma-17	218	5	f	f	PROPN
ma-17	218	6	(	(	PUNCT
ma-17	218	7	y0	y0	NOUN
ma-17	218	8	)	)	PUNCT
ma-17	219	1	+	+	NUM
ma-17	219	2	f	f	X
ma-17	219	3	(	(	PUNCT
ma-17	219	4	y0	y0	NOUN
ma-17	219	5	)	)	PUNCT
ma-17	219	6	=	=	SYM
ma-17	219	7	f	f	X
ma-17	219	8	(	(	PUNCT
ma-17	219	9	x1)−	x1)−	PROPN
ma-17	219	10	f	f	PROPN
ma-17	219	11	(	(	PUNCT
ma-17	219	12	y0)−	y0)−	PROPN
ma-17	219	13	f	f	X
ma-17	219	14	′(x0)a−10	′(x0)a−10	PROPN
ma-17	219	15	(	(	PUNCT
ma-17	219	16	x1	x1	PROPN
ma-17	219	17	−	−	PROPN
ma-17	219	18	y0	y0	NUM
ma-17	219	19	)	)	PUNCT
ma-17	219	20	=	=	SYM
ma-17	219	21	∫	∫	PROPN
ma-17	219	22	1	1	NUM
ma-17	219	23	0	0	NUM
ma-17	219	24	(	(	PUNCT
ma-17	219	25	f	f	PROPN
ma-17	219	26	′(y0	′(y0	NUM
ma-17	219	27	+	+	CCONJ
ma-17	219	28	θ(x1	θ(x1	ADJ
ma-17	219	29	−	−	PROPN
ma-17	219	30	x0))−	x0))−	PROPN
ma-17	220	1	f	f	PROPN
ma-17	220	2	′(x0)a−10	′(x0)a−10	PROPN
ma-17	220	3	)	)	PUNCT
ma-17	220	4	dθ(x1	dθ(x1	VERB
ma-17	220	5	−	−	PROPN
ma-17	220	6	y0	y0	PROPN
ma-17	220	7	)	)	PUNCT
ma-17	220	8	=	=	PUNCT
ma-17	221	1	h0(x1	h0(x1	NOUN
ma-17	221	2	−	−	PROPN
ma-17	221	3	y0	y0	NOUN
ma-17	221	4	)	)	PUNCT
ma-17	221	5	,	,	PUNCT
ma-17	221	6	(	(	PUNCT
ma-17	221	7	3.5	3.5	NUM
ma-17	221	8	)	)	PUNCT
ma-17	221	9	since	since	SCONJ
ma-17	221	10	by	by	ADP
ma-17	221	11	the	the	DET
ma-17	221	12	second	second	ADJ
ma-17	221	13	substep	substep	NOUN
ma-17	221	14	of	of	ADP
ma-17	221	15	method	method	NOUN
ma-17	221	16	(	(	PUNCT
ma-17	221	17	1.2	1.2	NUM
ma-17	221	18	)	)	PUNCT
ma-17	221	19	,	,	PUNCT
ma-17	221	20	we	we	PRON
ma-17	221	21	have	have	VERB
ma-17	221	22	f	f	X
ma-17	221	23	(	(	PUNCT
ma-17	221	24	y0	y0	NOUN
ma-17	221	25	)	)	PUNCT
ma-17	221	26	=	=	SYM
ma-17	222	1	−f	−f	PROPN
ma-17	222	2	′(x0)a−10	′(x0)a−10	PROPN
ma-17	222	3	(	(	PUNCT
ma-17	222	4	x1−	x1−	PROPN
ma-17	222	5	y0	y0	PROPN
ma-17	222	6	)	)	PUNCT
ma-17	222	7	.	.	PUNCT
ma-17	223	1	by	by	ADP
ma-17	223	2	(	(	PUNCT
ma-17	223	3	c3	c3	PROPN
ma-17	223	4	)	)	PUNCT
ma-17	223	5	,	,	PUNCT
ma-17	223	6	(	(	PUNCT
ma-17	223	7	3.4)and	3.4)and	NUM
ma-17	223	8	(	(	PUNCT
ma-17	223	9	3.5	3.5	NUM
ma-17	223	10	)	)	PUNCT
ma-17	223	11	,	,	PUNCT
ma-17	223	12	we	we	PRON
ma-17	223	13	obtain	obtain	VERB
ma-17	223	14	‖f	‖f	DET
ma-17	223	15	′(x0)−1f	′(x0)−1f	NOUN
ma-17	223	16	(	(	PUNCT
ma-17	223	17	x1)‖	x1)‖	PROPN
ma-17	223	18	≤	≤	NOUN
ma-17	223	19	‖f	‖f	PRON
ma-17	223	20	′(x0)−1h0‖‖x1	′(x0)−1h0‖‖x1	NOUN
ma-17	223	21	−	−	PROPN
ma-17	223	22	y0‖	y0‖	PROPN
ma-17	223	23	≤	≤	NOUN
ma-17	224	1	ξ0(t1	ξ0(t1	NUM
ma-17	224	2	−	−	PROPN
ma-17	224	3	s0	s0	PROPN
ma-17	224	4	)	)	PUNCT
ma-17	224	5	,	,	PUNCT
ma-17	224	6	(	(	PUNCT
ma-17	224	7	3.6	3.6	NUM
ma-17	224	8	)	)	PUNCT
ma-17	225	1	so	so	ADV
ma-17	225	2	‖y1	‖y1	DET
ma-17	225	3	−	−	NOUN
ma-17	225	4	x1‖	x1‖	PROPN
ma-17	225	5	≤	≤	NOUN
ma-17	225	6	‖f	‖f	PUNCT
ma-17	226	1	′(x1)−1f	′(x1)−1f	PROPN
ma-17	226	2	′(x0)‖‖f	′(x0)‖‖f	X
ma-17	226	3	′(x0)−1f	′(x0)−1f	NOUN
ma-17	226	4	(	(	PUNCT
ma-17	226	5	x1)‖	x1)‖	PROPN
ma-17	226	6	≤	≤	PROPN
ma-17	226	7	ξ0(t1	ξ0(t1	NUM
ma-17	226	8	−	−	PROPN
ma-17	226	9	s0	s0	PROPN
ma-17	226	10	)	)	PUNCT
ma-17	226	11	1−	1−	NUM
ma-17	226	12	p0(t1	p0(t1	NOUN
ma-17	226	13	)	)	PUNCT
ma-17	226	14	=	=	SYM
ma-17	226	15	s1	s1	PROPN
ma-17	226	16	−	−	PROPN
ma-17	226	17	t1	t1	PROPN
ma-17	226	18	,	,	PUNCT
ma-17	226	19	(	(	PUNCT
ma-17	226	20	3.7	3.7	NUM
ma-17	226	21	)	)	PUNCT
ma-17	226	22	showing	show	VERB
ma-17	226	23	(	(	PUNCT
ma-17	226	24	p1	p1	NOUN
ma-17	226	25	)	)	PUNCT
ma-17	226	26	for	for	ADP
ma-17	226	27	m	m	PROPN
ma-17	226	28	=	=	SYM
ma-17	226	29	1	1	X
ma-17	226	30	.	.	PUNCT
ma-17	226	31	suppose	suppose	VERB
ma-17	226	32	(	(	PUNCT
ma-17	226	33	pm	pm	NOUN
ma-17	226	34	)	)	PUNCT
ma-17	226	35	,	,	PUNCT
ma-17	226	36	(	(	PUNCT
ma-17	226	37	qm	qm	PROPN
ma-17	226	38	)	)	PUNCT
ma-17	226	39	hold	hold	VERB
ma-17	226	40	ym	ym	PRON
ma-17	226	41	and	and	CCONJ
ma-17	226	42	xm+1	xm+1	PROPN
ma-17	226	43	∈	∈	PROPN
ma-17	226	44	u[x0	u[x0	NOUN
ma-17	226	45	,	,	PUNCT
ma-17	226	46	t	t	PROPN
ma-17	226	47	∗	∗	NOUN
ma-17	226	48	]	]	PUNCT
ma-17	226	49	.	.	PUNCT
ma-17	227	1	then	then	ADV
ma-17	227	2	,	,	PUNCT
ma-17	227	3	by	by	ADP
ma-17	227	4	repeatingthese	repeatingthese	ADJ
ma-17	227	5	computations	computation	NOUN
ma-17	227	6	with	with	ADP
ma-17	227	7	xm	xm	PROPN
ma-17	227	8	,	,	PUNCT
ma-17	227	9	ym	ym	PROPN
ma-17	227	10	,	,	PUNCT
ma-17	227	11	xm+1	xm+1	PROPN
ma-17	227	12	replacing	replace	VERB
ma-17	227	13	x0	x0	PRON
ma-17	227	14	,	,	PUNCT
ma-17	227	15	y0	y0	PROPN
ma-17	227	16	,	,	PUNCT
ma-17	227	17	x1	x1	PROPN
ma-17	227	18	,	,	PUNCT
ma-17	227	19	respectively	respectively	ADV
ma-17	227	20	,	,	PUNCT
ma-17	227	21	we	we	PRON
ma-17	227	22	complete	complete	VERB
ma-17	227	23	the	the	DET
ma-17	227	24	induction.moreover	induction.moreover	PROPN
ma-17	227	25	,	,	PUNCT
ma-17	227	26	sequence	sequence	NOUN
ma-17	227	27	{	{	PUNCT
ma-17	227	28	xm	xm	NOUN
ma-17	227	29	}	}	PUNCT
ma-17	227	30	is	be	AUX
ma-17	227	31	complete	complete	ADJ
ma-17	227	32	in	in	ADP
ma-17	227	33	a	a	DET
ma-17	227	34	banach	banach	NOUN
ma-17	227	35	space	space	NOUN
ma-17	227	36	,	,	PUNCT
ma-17	227	37	so	so	SCONJ
ma-17	227	38	it	it	PRON
ma-17	227	39	converges	converge	VERB
ma-17	227	40	to	to	ADP
ma-17	227	41	some	some	DET
ma-17	227	42	x∗	x∗	PROPN
ma-17	227	43	∈	∈	PROPN
ma-17	227	44	u[x0	u[x0	NOUN
ma-17	227	45	,	,	PUNCT
ma-17	227	46	t	t	PROPN
ma-17	227	47	∗].finally	∗].finally	ADV
ma-17	227	48	,	,	PUNCT
ma-17	227	49	by	by	ADP
ma-17	227	50	letting	let	VERB
ma-17	227	51	m	m	PRON
ma-17	227	52	−→∞	−→∞	PROPN
ma-17	227	53	in	in	ADP
ma-17	227	54	the	the	DET
ma-17	227	55	estimation	estimation	NOUN
ma-17	227	56	‖f	‖f	ADP
ma-17	227	57	′(x0)−1f	′(x0)−1f	NOUN
ma-17	227	58	(	(	PUNCT
ma-17	227	59	xm+1)‖	xm+1)‖	PROPN
ma-17	227	60	≤	≤	PROPN
ma-17	228	1	ξm(tm+1	ξm(tm+1	ADJ
ma-17	228	2	−	−	PROPN
ma-17	228	3	sm	sm	PROPN
ma-17	228	4	)	)	PUNCT
ma-17	228	5	(	(	PUNCT
ma-17	228	6	3.8	3.8	NUM
ma-17	228	7	)	)	PUNCT
ma-17	228	8	and	and	CCONJ
ma-17	228	9	using	use	VERB
ma-17	228	10	the	the	DET
ma-17	228	11	continuity	continuity	NOUN
ma-17	228	12	of	of	ADP
ma-17	228	13	f	f	PROPN
ma-17	228	14	,	,	PUNCT
ma-17	228	15	we	we	PRON
ma-17	228	16	conclude	conclude	VERB
ma-17	228	17	f	f	X
ma-17	228	18	(	(	PUNCT
ma-17	228	19	x∗	x∗	X
ma-17	228	20	)	)	PUNCT
ma-17	228	21	=	=	SYM
ma-17	229	1	0	0	X
ma-17	229	2	.	.	X
ma-17	229	3	�	�	PROPN
ma-17	229	4	next	next	ADV
ma-17	229	5	,	,	PUNCT
ma-17	229	6	we	we	PRON
ma-17	229	7	present	present	VERB
ma-17	229	8	a	a	DET
ma-17	229	9	result	result	NOUN
ma-17	229	10	for	for	ADP
ma-17	229	11	uniqueness	uniqueness	NOUN
ma-17	229	12	of	of	ADP
ma-17	229	13	the	the	DET
ma-17	229	14	solution	solution	NOUN
ma-17	229	15	x∗.	x∗.	PUNCT
ma-17	230	1	proposition	proposition	NOUN
ma-17	230	2	3.2	3.2	NUM
ma-17	230	3	.	.	PUNCT
ma-17	231	1	suppose	suppose	VERB
ma-17	231	2	(	(	PUNCT
ma-17	231	3	a	a	X
ma-17	231	4	)	)	PUNCT
ma-17	231	5	x∗	x∗	PROPN
ma-17	231	6	is	be	AUX
ma-17	231	7	a	a	DET
ma-17	231	8	solution	solution	NOUN
ma-17	231	9	of	of	ADP
ma-17	231	10	f	f	PROPN
ma-17	231	11	(	(	PUNCT
ma-17	231	12	x	x	NOUN
ma-17	231	13	)	)	PUNCT
ma-17	232	1	=	=	SYM
ma-17	232	2	0	0	PUNCT
ma-17	232	3	(	(	PUNCT
ma-17	232	4	b	b	X
ma-17	232	5	)	)	PUNCT
ma-17	232	6	there	there	PRON
ma-17	232	7	exists	exist	VERB
ma-17	232	8	s̃	s̃	PROPN
ma-17	232	9	≥	≥	AUX
ma-17	232	10	t∗	t∗	NOUN
ma-17	232	11	such	such	ADJ
ma-17	232	12	that	that	DET
ma-17	232	13	∫	∫	PROPN
ma-17	232	14	1	1	NUM
ma-17	232	15	0	0	NUM
ma-17	232	16	p0((1−	p0((1−	PROPN
ma-17	232	17	θ)s̃	θ)s̃	NOUN
ma-17	232	18	+	+	CCONJ
ma-17	232	19	θt∗)dθ	θt∗)dθ	X
ma-17	232	20	<	<	X
ma-17	232	21	1	1	NUM
ma-17	232	22	.	.	PUNCT
ma-17	232	23	(	(	PUNCT
ma-17	232	24	3.9	3.9	NUM
ma-17	232	25	)	)	PUNCT
ma-17	232	26	set	set	NOUN
ma-17	232	27	s1	s1	NOUN
ma-17	232	28	=	=	SYM
ma-17	232	29	u[x0	u[x0	NOUN
ma-17	232	30	,	,	PUNCT
ma-17	232	31	s̃	s̃	PROPN
ma-17	232	32	]	]	X
ma-17	232	33	∩ω	∩ω	INTJ
ma-17	232	34	.	.	PUNCT
ma-17	233	1	then	then	ADV
ma-17	233	2	,	,	PUNCT
ma-17	233	3	the	the	DET
ma-17	233	4	only	only	ADJ
ma-17	233	5	solution	solution	NOUN
ma-17	233	6	of	of	ADP
ma-17	233	7	equation	equation	NOUN
ma-17	233	8	f	f	X
ma-17	233	9	(	(	PUNCT
ma-17	233	10	x	x	X
ma-17	233	11	)	)	PUNCT
ma-17	233	12	=	=	SYM
ma-17	233	13	0	0	NUM
ma-17	233	14	in	in	ADP
ma-17	233	15	the	the	DET
ma-17	233	16	region	region	NOUN
ma-17	233	17	s1	s1	NOUN
ma-17	233	18	is	be	AUX
ma-17	233	19	x∗.	x∗.	PROPN
ma-17	233	20	eur	eur	PROPN
ma-17	233	21	.	.	PUNCT
ma-17	234	1	j.	j.	PROPN
ma-17	234	2	math	math	PROPN
ma-17	234	3	.	.	PUNCT
ma-17	235	1	anal	anal	ADJ
ma-17	235	2	.	.	PUNCT
ma-17	236	1	1	1	NUM
ma-17	236	2	(	(	PUNCT
ma-17	236	3	2021	2021	NUM
ma-17	236	4	)	)	PUNCT
ma-17	237	1	76	76	NUM
ma-17	237	2	proof	proof	NOUN
ma-17	237	3	.	.	PUNCT
ma-17	238	1	set	set	VERB
ma-17	238	2	t	t	PROPN
ma-17	238	3	=	=	SYM
ma-17	238	4	∫	∫	PROPN
ma-17	238	5	1	1	NUM
ma-17	238	6	0	0	NUM
ma-17	238	7	f	f	NOUN
ma-17	238	8	′(x̃	′(x̃	PUNCT
ma-17	239	1	+	+	PUNCT
ma-17	239	2	θ(x∗	θ(x∗	NOUN
ma-17	239	3	−	−	PROPN
ma-17	239	4	x̃))dθ	x̃))dθ	PROPN
ma-17	239	5	for	for	ADP
ma-17	239	6	some	some	DET
ma-17	239	7	x̃	x̃	PROPN
ma-17	239	8	∈	∈	PROPN
ma-17	239	9	s1	s1	NOUN
ma-17	239	10	with	with	ADP
ma-17	239	11	f	f	PROPN
ma-17	239	12	(	(	PUNCT
ma-17	239	13	x̃	x̃	PROPN
ma-17	239	14	)	)	PUNCT
ma-17	239	15	=	=	PUNCT
ma-17	240	1	0	0	X
ma-17	240	2	.	.	X
ma-17	240	3	using	use	VERB
ma-17	240	4	(	(	PUNCT
ma-17	240	5	c2	c2	PROPN
ma-17	240	6	)	)	PUNCT
ma-17	240	7	and	and	CCONJ
ma-17	240	8	(	(	PUNCT
ma-17	240	9	3.9),we	3.9),we	NUM
ma-17	240	10	get	get	VERB
ma-17	240	11	‖f	‖f	PRON
ma-17	240	12	′(x0)−1(t	′(x0)−1(t	PUNCT
ma-17	241	1	−	−	PROPN
ma-17	241	2	f	f	PROPN
ma-17	241	3	′(x0))‖	′(x0))‖	NUM
ma-17	241	4	≤	≤	NUM
ma-17	241	5	∫	∫	PROPN
ma-17	241	6	1	1	NUM
ma-17	241	7	0	0	NUM
ma-17	241	8	p0(‖x̃	p0(‖x̃	ADJ
ma-17	241	9	+	+	NUM
ma-17	241	10	θ(x∗	θ(x∗	NOUN
ma-17	241	11	−	−	PROPN
ma-17	241	12	x̃)−	x̃)−	PROPN
ma-17	241	13	x0‖dθ	x0‖dθ	PROPN
ma-17	242	1	≤	≤	NUM
ma-17	242	2	∫	∫	PROPN
ma-17	242	3	1	1	NUM
ma-17	242	4	0	0	NUM
ma-17	242	5	p0((1−	p0((1−	PROPN
ma-17	242	6	θ)‖x̃	θ)‖x̃	PROPN
ma-17	242	7	−	−	PROPN
ma-17	242	8	x0‖+	x0‖+	SYM
ma-17	242	9	θ‖x∗	θ‖x∗	NOUN
ma-17	242	10	−	−	PROPN
ma-17	242	11	x0‖)dθ	x0‖)dθ	NOUN
ma-17	242	12	≤	≤	NUM
ma-17	242	13	∫	∫	PROPN
ma-17	242	14	1	1	NUM
ma-17	242	15	0	0	NUM
ma-17	242	16	p0((1−	p0((1−	PROPN
ma-17	242	17	θ)s̃	θ)s̃	NOUN
ma-17	242	18	+	+	CCONJ
ma-17	242	19	θt∗)dθ	θt∗)dθ	X
ma-17	242	20	<	<	X
ma-17	242	21	1	1	NUM
ma-17	242	22	,	,	PUNCT
ma-17	242	23	leading	lead	VERB
ma-17	242	24	to	to	ADP
ma-17	242	25	x̃	x̃	PROPN
ma-17	242	26	=	=	SYM
ma-17	242	27	x∗	x∗	PROPN
ma-17	242	28	,	,	PUNCT
ma-17	242	29	where	where	SCONJ
ma-17	242	30	we	we	PRON
ma-17	242	31	used	use	VERB
ma-17	242	32	the	the	DET
ma-17	242	33	identity	identity	NOUN
ma-17	242	34	t	t	NOUN
ma-17	242	35	(	(	PUNCT
ma-17	242	36	x∗	x∗	PROPN
ma-17	242	37	−	−	PROPN
ma-17	242	38	x̃	x̃	PROPN
ma-17	242	39	)	)	PUNCT
ma-17	243	1	=	=	SYM
ma-17	243	2	f	f	PROPN
ma-17	243	3	(	(	PUNCT
ma-17	243	4	x∗	x∗	PROPN
ma-17	243	5	)	)	PUNCT
ma-17	243	6	−	−	PROPN
ma-17	244	1	f	f	PROPN
ma-17	244	2	(	(	PUNCT
ma-17	244	3	x̃	x̃	PROPN
ma-17	244	4	)	)	PUNCT
ma-17	244	5	=	=	PUNCT
ma-17	244	6	0	0	NUM
ma-17	245	1	−	−	NOUN
ma-17	245	2	0	0	NUM
ma-17	246	1	=	=	SYM
ma-17	246	2	0	0	NUM
ma-17	246	3	and	and	CCONJ
ma-17	246	4	theinvertability	theinvertability	NOUN
ma-17	246	5	of	of	ADP
ma-17	246	6	t.	t.	PROPN
ma-17	246	7	�	�	PROPN
ma-17	246	8	remark	remark	VERB
ma-17	246	9	3.3	3.3	NUM
ma-17	246	10	.	.	PUNCT
ma-17	247	1	let	let	VERB
ma-17	247	2	us	we	PRON
ma-17	247	3	specialize	specialize	VERB
ma-17	247	4	operators	operator	NOUN
ma-17	247	5	an	an	PRON
ma-17	247	6	to	to	PART
ma-17	247	7	see	see	VERB
ma-17	247	8	how	how	SCONJ
ma-17	247	9	sequences	sequence	NOUN
ma-17	247	10	{	{	PUNCT
ma-17	247	11	sn	sn	NOUN
ma-17	247	12	}	}	PUNCT
ma-17	247	13	,	,	PUNCT
ma-17	247	14	{	{	PUNCT
ma-17	247	15	tn	tn	NOUN
ma-17	247	16	}	}	PUNCT
ma-17	247	17	,	,	PUNCT
ma-17	247	18	{	{	PUNCT
ma-17	247	19	an	an	X
ma-17	247	20	}	}	PUNCT
ma-17	247	21	,	,	PUNCT
ma-17	247	22	{	{	PUNCT
ma-17	247	23	ξn	ξn	NOUN
ma-17	247	24	}	}	PUNCT
ma-17	247	25	,	,	PUNCT
ma-17	247	26	{	{	PUNCT
ma-17	247	27	αn	αn	VERB
ma-17	247	28	}	}	PUNCT
ma-17	247	29	and	and	CCONJ
ma-17	247	30	{	{	PUNCT
ma-17	247	31	βn	βn	VERB
ma-17	247	32	}	}	PUNCT
ma-17	247	33	are	be	AUX
ma-17	247	34	defined	define	VERB
ma-17	247	35	.	.	PUNCT
ma-17	248	1	choose	choose	VERB
ma-17	248	2	the	the	DET
ma-17	248	3	case	case	NOUN
ma-17	248	4	of	of	ADP
ma-17	248	5	newton	newton	PROPN
ma-17	248	6	’s	’s	PART
ma-17	248	7	method	method	NOUN
ma-17	248	8	(	(	PUNCT
ma-17	248	9	1.4	1.4	NUM
ma-17	248	10	)	)	PUNCT
ma-17	248	11	.	.	PUNCT
ma-17	249	1	then	then	ADV
ma-17	249	2	,	,	PUNCT
ma-17	249	3	we	we	PRON
ma-17	249	4	have	have	VERB
ma-17	249	5	‖anf	‖anf	ADP
ma-17	249	6	′(xn)−1f	′(xn)−1f	NOUN
ma-17	249	7	′(x0)‖	′(x0)‖	NOUN
ma-17	249	8	=	=	SYM
ma-17	249	9	‖f	‖f	ADP
ma-17	249	10	′(yn)−1f	′(yn)−1f	NOUN
ma-17	249	11	′(x0)‖	′(x0)‖	NOUN
ma-17	249	12	≤	≤	NUM
ma-17	249	13	1	1	NUM
ma-17	249	14	1−	1−	NUM
ma-17	249	15	p0(‖yn	p0(‖yn	NOUN
ma-17	249	16	−	−	PROPN
ma-17	249	17	x0‖	x0‖	PROPN
ma-17	249	18	)	)	PUNCT
ma-17	249	19	,	,	PUNCT
ma-17	249	20	and	and	CCONJ
ma-17	249	21	‖f	‖f	ADP
ma-17	249	22	′(x0)−1hn‖	′(x0)−1hn‖	NOUN
ma-17	249	23	=	=	SYM
ma-17	249	24	‖	‖	PROPN
ma-17	249	25	∫	∫	PROPN
ma-17	249	26	1	1	NUM
ma-17	249	27	0	0	NUM
ma-17	249	28	f	f	PROPN
ma-17	249	29	′(x0	′(x0	NOUN
ma-17	249	30	)	)	PUNCT
ma-17	249	31	−1(f	−1(f	PUNCT
ma-17	250	1	′(yn	′(yn	ADV
ma-17	250	2	+	+	CCONJ
ma-17	250	3	θ(xn+1	θ(xn+1	NUM
ma-17	250	4	−	−	NUM
ma-17	250	5	yn))−	yn))−	NOUN
ma-17	250	6	f	f	PROPN
ma-17	250	7	′(xn)a−1n	′(xn)a−1n	ADJ
ma-17	250	8	)	)	PUNCT
ma-17	250	9	dθ‖	dθ‖	NOUN
ma-17	250	10	=	=	SYM
ma-17	250	11	‖	‖	PROPN
ma-17	250	12	∫	∫	PROPN
ma-17	250	13	1	1	NUM
ma-17	250	14	0	0	NUM
ma-17	250	15	f	f	PROPN
ma-17	250	16	′(x0	′(x0	NOUN
ma-17	250	17	)	)	PUNCT
ma-17	250	18	−1(f	−1(f	PUNCT
ma-17	251	1	′(yn	′(yn	ADV
ma-17	251	2	+	+	CCONJ
ma-17	251	3	θ(xn+1	θ(xn+1	NUM
ma-17	251	4	−	−	NUM
ma-17	251	5	yn))−	yn))−	NOUN
ma-17	251	6	f	f	PROPN
ma-17	251	7	′(yn))dθ‖	′(yn))dθ‖	PROPN
ma-17	251	8	≤	≤	NUM
ma-17	251	9	∫	∫	PROPN
ma-17	251	10	1	1	NUM
ma-17	251	11	0	0	NUM
ma-17	251	12	p̄	p̄	NOUN
ma-17	251	13	(	(	PUNCT
ma-17	251	14	θ‖xn+1	θ‖xn+1	ADJ
ma-17	251	15	−	−	PRON
ma-17	252	1	yn‖)dθ	yn‖)dθ	PROPN
ma-17	252	2	≤	≤	PROPN
ma-17	252	3	∫	∫	PROPN
ma-17	252	4	1	1	NUM
ma-17	252	5	0	0	NUM
ma-17	252	6	p̄	p̄	NOUN
ma-17	252	7	(	(	PUNCT
ma-17	252	8	θ(tn+1	θ(tn+1	ADJ
ma-17	252	9	−	−	PRON
ma-17	252	10	sn))dθ	sn))dθ	PROPN
ma-17	252	11	,	,	PUNCT
ma-17	252	12	so	so	SCONJ
ma-17	252	13	we	we	PRON
ma-17	252	14	can	can	AUX
ma-17	252	15	choose	choose	VERB
ma-17	252	16	an	an	PRON
ma-17	252	17	=	=	SYM
ma-17	252	18	1	1	NUM
ma-17	252	19	1−	1−	NUM
ma-17	252	20	p0(sn	p0(sn	PROPN
ma-17	252	21	)	)	PUNCT
ma-17	252	22	(	(	PUNCT
ma-17	252	23	3.10	3.10	NUM
ma-17	252	24	)	)	PUNCT
ma-17	252	25	and	and	CCONJ
ma-17	252	26	ξn	ξn	X
ma-17	252	27	=	=	SYM
ma-17	252	28	∫	∫	PROPN
ma-17	252	29	1	1	NUM
ma-17	252	30	0	0	NUM
ma-17	252	31	p̄	p̄	NOUN
ma-17	252	32	(	(	PUNCT
ma-17	252	33	θ(tn+1	θ(tn+1	ADJ
ma-17	252	34	−	−	DET
ma-17	252	35	sn))dθ	sn))dθ	PROPN
ma-17	252	36	.	.	PUNCT
ma-17	253	1	(	(	PUNCT
ma-17	253	2	3.11	3.11	NUM
ma-17	253	3	)	)	PUNCT
ma-17	253	4	in	in	ADP
ma-17	253	5	this	this	DET
ma-17	253	6	case	case	NOUN
ma-17	253	7	we	we	PRON
ma-17	253	8	can	can	AUX
ma-17	253	9	show	show	VERB
ma-17	253	10	another	another	DET
ma-17	253	11	result	result	NOUN
ma-17	253	12	on	on	ADP
ma-17	253	13	majorizing	majorize	VERB
ma-17	253	14	sequences	sequence	NOUN
ma-17	253	15	which	which	PRON
ma-17	253	16	is	be	AUX
ma-17	253	17	weaker	weak	ADJ
ma-17	253	18	than	than	ADP
ma-17	253	19	lemma	lemma	PROPN
ma-17	253	20	2.5	2.5	NUM
ma-17	253	21	for	for	ADP
ma-17	253	22	the	the	DET
ma-17	253	23	interesting	interesting	ADJ
ma-17	253	24	case	case	NOUN
ma-17	253	25	p0(t	p0(t	NOUN
ma-17	253	26	)	)	PUNCT
ma-17	253	27	=	=	SYM
ma-17	253	28	l0	l0	PROPN
ma-17	253	29	t	t	PROPN
ma-17	253	30	and	and	CCONJ
ma-17	253	31	p	p	PROPN
ma-17	253	32	(	(	PUNCT
ma-17	253	33	t	t	PROPN
ma-17	253	34	)	)	PUNCT
ma-17	253	35	=	=	SYM
ma-17	254	1	lt	lt	NOUN
ma-17	254	2	.	.	PROPN
ma-17	255	1	we	we	PRON
ma-17	255	2	get	get	VERB
ma-17	255	3	in	in	ADP
ma-17	255	4	this	this	DET
ma-17	255	5	special	special	ADJ
ma-17	255	6	case	case	NOUN
ma-17	255	7	that	that	SCONJ
ma-17	255	8	αn	αn	NOUN
ma-17	255	9	=	=	PUNCT
ma-17	255	10	l(sn	l(sn	ADJ
ma-17	255	11	−	−	PROPN
ma-17	255	12	tn	tn	NOUN
ma-17	255	13	)	)	PUNCT
ma-17	255	14	2(1−	2(1−	NUM
ma-17	255	15	l0sn	l0sn	X
ma-17	255	16	)	)	PUNCT
ma-17	255	17	(	(	PUNCT
ma-17	255	18	3.12	3.12	NUM
ma-17	255	19	)	)	PUNCT
ma-17	255	20	and	and	CCONJ
ma-17	255	21	βn	βn	X
ma-17	255	22	=	=	SYM
ma-17	255	23	l(tn+1	l(tn+1	ADJ
ma-17	255	24	−	−	PROPN
ma-17	255	25	sn	sn	NOUN
ma-17	255	26	)	)	PUNCT
ma-17	255	27	2(1−	2(1−	NUM
ma-17	255	28	l0tn+1	l0tn+1	NOUN
ma-17	255	29	)	)	PUNCT
ma-17	255	30	.	.	PUNCT
ma-17	256	1	(	(	PUNCT
ma-17	256	2	3.13	3.13	NUM
ma-17	256	3	)	)	PUNCT
ma-17	256	4	eur	eur	PROPN
ma-17	256	5	.	.	PUNCT
ma-17	257	1	j.	j.	PROPN
ma-17	257	2	math	math	PROPN
ma-17	257	3	.	.	PUNCT
ma-17	258	1	anal	anal	ADJ
ma-17	258	2	.	.	PUNCT
ma-17	259	1	1	1	NUM
ma-17	259	2	(	(	PUNCT
ma-17	259	3	2021	2021	NUM
ma-17	259	4	)	)	PUNCT
ma-17	259	5	77	77	NUM
ma-17	259	6	define	define	VERB
ma-17	259	7	sequences	sequence	NOUN
ma-17	259	8	of	of	ADP
ma-17	259	9	function	function	NOUN
ma-17	259	10	{	{	PUNCT
ma-17	259	11	f	f	X
ma-17	259	12	(	(	PUNCT
ma-17	259	13	1)n	1)n	X
ma-17	259	14	}	}	PUNCT
ma-17	259	15	,	,	PUNCT
ma-17	259	16	{	{	PUNCT
ma-17	259	17	f	f	X
ma-17	259	18	(	(	PUNCT
ma-17	259	19	2)n	2)n	NUM
ma-17	259	20	}	}	PUNCT
ma-17	259	21	on	on	ADP
ma-17	259	22	the	the	DET
ma-17	259	23	interval	interval	NOUN
ma-17	259	24	[	[	X
ma-17	259	25	0	0	NUM
ma-17	259	26	,	,	PUNCT
ma-17	259	27	1	1	NUM
ma-17	259	28	)	)	PUNCT
ma-17	259	29	by	by	ADP
ma-17	259	30	f	f	PROPN
ma-17	259	31	(	(	PUNCT
ma-17	259	32	1	1	NUM
ma-17	259	33	)	)	PUNCT
ma-17	259	34	n	n	PROPN
ma-17	259	35	(	(	PUNCT
ma-17	259	36	t	t	NOUN
ma-17	259	37	)	)	PUNCT
ma-17	259	38	=	=	PUNCT
ma-17	260	1	l	l	NOUN
ma-17	260	2	2	2	NUM
ma-17	260	3	t2n−1η	t2n−1η	NOUN
ma-17	260	4	+	+	CCONJ
ma-17	260	5	l0(1	l0(1	PROPN
ma-17	260	6	+	+	CCONJ
ma-17	260	7	t	t	NOUN
ma-17	260	8	+	+	X
ma-17	260	9	.	.	PUNCT
ma-17	260	10	.	.	PUNCT
ma-17	261	1	.+	.+	NOUN
ma-17	262	1	t2n)η	t2n)η	X
ma-17	263	1	−	−	PROPN
ma-17	263	2	1	1	NUM
ma-17	263	3	,	,	PUNCT
ma-17	263	4	f	f	PROPN
ma-17	263	5	(	(	PUNCT
ma-17	263	6	2	2	NUM
ma-17	263	7	)	)	PUNCT
ma-17	263	8	n	n	PROPN
ma-17	263	9	(	(	PUNCT
ma-17	263	10	t	t	NOUN
ma-17	263	11	)	)	PUNCT
ma-17	263	12	=	=	PUNCT
ma-17	264	1	l	l	NOUN
ma-17	264	2	2	2	NUM
ma-17	264	3	t2nη	t2nη	SYM
ma-17	264	4	+	+	CCONJ
ma-17	264	5	l0(1	l0(1	PROPN
ma-17	264	6	+	+	CCONJ
ma-17	264	7	t	t	NOUN
ma-17	264	8	+	+	X
ma-17	264	9	.	.	PUNCT
ma-17	264	10	.	.	PUNCT
ma-17	265	1	.+	.+	NOUN
ma-17	265	2	t2n+1)η	t2n+1)η	VERB
ma-17	265	3	−	−	PROPN
ma-17	266	1	1,and	1,and	NUM
ma-17	266	2	polynomial	polynomial	ADJ
ma-17	266	3	ϕ	ϕ	NOUN
ma-17	266	4	by	by	ADP
ma-17	266	5	ϕ(t	ϕ(t	NUM
ma-17	266	6	)	)	PUNCT
ma-17	267	1	=	=	SYM
ma-17	267	2	l0	l0	PROPN
ma-17	267	3	t	t	NOUN
ma-17	267	4	3	3	NUM
ma-17	267	5	+	+	CCONJ
ma-17	267	6	(	(	PUNCT
ma-17	267	7	l0	l0	INTJ
ma-17	267	8	+	+	NUM
ma-17	267	9	l	l	NOUN
ma-17	267	10	2	2	X
ma-17	267	11	)	)	PUNCT
ma-17	267	12	t2	t2	NOUN
ma-17	267	13	−	−	PROPN
ma-17	267	14	l	l	NOUN
ma-17	267	15	2	2	NUM
ma-17	267	16	.notice	.notice	NOUN
ma-17	267	17	that	that	PRON
ma-17	267	18	ϕ(0	ϕ(0	PRON
ma-17	267	19	)	)	PUNCT
ma-17	268	1	=	=	PUNCT
ma-17	269	1	−l2	−l2	PROPN
ma-17	269	2	and	and	CCONJ
ma-17	269	3	ϕ(1	ϕ(1	PROPN
ma-17	269	4	)	)	PUNCT
ma-17	270	1	=	=	SYM
ma-17	270	2	2l0	2l0	X
ma-17	270	3	.	.	PUNCT
ma-17	270	4	denote	denote	VERB
ma-17	270	5	by	by	ADP
ma-17	270	6	ρ	ρ	PROPN
ma-17	270	7	the	the	DET
ma-17	270	8	smallest	small	ADJ
ma-17	270	9	zero	zero	NUM
ma-17	270	10	of	of	ADP
ma-17	270	11	polynomial	polynomial	ADJ
ma-17	270	12	ϕ	ϕ	PROPN
ma-17	270	13	in	in	ADP
ma-17	270	14	(	(	PUNCT
ma-17	270	15	0	0	NUM
ma-17	270	16	,	,	PUNCT
ma-17	270	17	1)assured	1)assured	NUM
ma-17	270	18	to	to	PART
ma-17	270	19	exist	exist	VERB
ma-17	270	20	by	by	ADP
ma-17	270	21	the	the	DET
ma-17	270	22	intermediate	intermediate	ADJ
ma-17	270	23	value	value	NOUN
ma-17	270	24	theorem	theorem	VERB
ma-17	270	25	.	.	PUNCT
ma-17	271	1	lemma	lemma	PROPN
ma-17	271	2	3.4	3.4	NUM
ma-17	271	3	.	.	PUNCT
ma-17	271	4	suppose	suppose	VERB
ma-17	271	5	that	that	SCONJ
ma-17	271	6	λ0	λ0	NOUN
ma-17	271	7	≤	≤	PUNCT
ma-17	271	8	ρ	ρ	NOUN
ma-17	271	9	<	<	X
ma-17	271	10	1−	1−	NUM
ma-17	271	11	l0η	l0η	X
ma-17	271	12	.	.	PUNCT
ma-17	272	1	(	(	PUNCT
ma-17	272	2	3.14	3.14	NUM
ma-17	272	3	)	)	PUNCT
ma-17	272	4	then	then	ADV
ma-17	272	5	,	,	PUNCT
ma-17	272	6	the	the	DET
ma-17	272	7	conclusions	conclusion	NOUN
ma-17	272	8	of	of	ADP
ma-17	272	9	lemma	lemma	PROPN
ma-17	272	10	2.5	2.5	NUM
ma-17	272	11	hold	hold	NOUN
ma-17	272	12	for	for	ADP
ma-17	272	13	sequences	sequence	NOUN
ma-17	272	14	{	{	PUNCT
ma-17	272	15	sn	sn	NOUN
ma-17	272	16	}	}	PUNCT
ma-17	272	17	,	,	PUNCT
ma-17	272	18	{	{	PUNCT
ma-17	272	19	tn	tn	NOUN
ma-17	272	20	}	}	PUNCT
ma-17	272	21	with	with	ADP
ma-17	272	22	ρ	ρ	NOUN
ma-17	272	23	replacing	replace	VERB
ma-17	272	24	λ	λ	NOUN
ma-17	272	25	.	.	PUNCT
ma-17	273	1	proof	proof	NOUN
ma-17	273	2	.	.	PUNCT
ma-17	274	1	we	we	PRON
ma-17	274	2	must	must	AUX
ma-17	274	3	show	show	VERB
ma-17	274	4	this	this	DET
ma-17	274	5	time	time	NOUN
ma-17	274	6	0	0	NUM
ma-17	274	7	≤	≤	PROPN
ma-17	274	8	l(sm	l(sm	PROPN
ma-17	274	9	−	−	PROPN
ma-17	274	10	tm	tm	PROPN
ma-17	274	11	)	)	PUNCT
ma-17	274	12	2(1−	2(1−	NUM
ma-17	274	13	l0sm	l0sm	NOUN
ma-17	274	14	)	)	PUNCT
ma-17	274	15	≤	≤	NOUN
ma-17	274	16	ρ	ρ	PROPN
ma-17	274	17	,	,	PUNCT
ma-17	274	18	(	(	PUNCT
ma-17	274	19	3.15	3.15	NUM
ma-17	274	20	)	)	PUNCT
ma-17	274	21	0	0	NUM
ma-17	275	1	≤	≤	ADJ
ma-17	276	1	l(tm+1	l(tm+1	PROPN
ma-17	276	2	−	−	PROPN
ma-17	276	3	sm	sm	PROPN
ma-17	276	4	)	)	PUNCT
ma-17	276	5	2(1−	2(1−	NUM
ma-17	276	6	l0tm+1	l0tm+1	X
ma-17	276	7	)	)	PUNCT
ma-17	276	8	≤	≤	NOUN
ma-17	276	9	ρ	ρ	NOUN
ma-17	276	10	(	(	PUNCT
ma-17	276	11	3.16)and	3.16)and	NUM
ma-17	276	12	tm	tm	PROPN
ma-17	276	13	≤	≤	PROPN
ma-17	276	14	sm	sm	VERB
ma-17	276	15	≤	≤	PROPN
ma-17	276	16	tm+1	tm+1	PROPN
ma-17	276	17	.	.	PUNCT
ma-17	277	1	(	(	PUNCT
ma-17	277	2	3.17)these	3.17)these	NUM
ma-17	277	3	estimates	estimate	NOUN
ma-17	277	4	hold	hold	VERB
ma-17	277	5	for	for	ADP
ma-17	277	6	m	m	NOUN
ma-17	277	7	=	=	SYM
ma-17	277	8	0	0	NUM
ma-17	277	9	by	by	ADP
ma-17	277	10	(	(	PUNCT
ma-17	277	11	3.14	3.14	NUM
ma-17	277	12	)	)	PUNCT
ma-17	277	13	and	and	CCONJ
ma-17	277	14	the	the	DET
ma-17	277	15	definition	definition	NOUN
ma-17	277	16	of	of	ADP
ma-17	277	17	these	these	DET
ma-17	277	18	sequences	sequence	NOUN
ma-17	277	19	.	.	PUNCT
ma-17	278	1	then	then	ADV
ma-17	278	2	,	,	PUNCT
ma-17	278	3	as	as	ADP
ma-17	278	4	in	in	ADP
ma-17	278	5	lemma2.5	lemma2.5	NOUN
ma-17	278	6	we	we	PRON
ma-17	278	7	can	can	AUX
ma-17	278	8	show	show	VERB
ma-17	278	9	instead	instead	ADV
ma-17	278	10	for	for	ADP
ma-17	278	11	(	(	PUNCT
ma-17	278	12	3.15	3.15	NUM
ma-17	278	13	)	)	PUNCT
ma-17	278	14	that	that	PRON
ma-17	278	15	l	l	NOUN
ma-17	278	16	2	2	X
ma-17	278	17	ρ2mη	ρ2mη	PUNCT
ma-17	278	18	+	+	CCONJ
ma-17	278	19	ρl0(1	ρl0(1	NOUN
ma-17	278	20	+	+	CCONJ
ma-17	278	21	ρ+	ρ+	NOUN
ma-17	278	22	.	.	PUNCT
ma-17	278	23	.	.	PUNCT
ma-17	279	1	.+	.+	NOUN
ma-17	279	2	ρ2m)η	ρ2m)η	PUNCT
ma-17	280	1	−	−	NUM
ma-17	280	2	1	1	NUM
ma-17	280	3	≤	≤	NOUN
ma-17	280	4	0	0	NUM
ma-17	280	5	.	.	PUNCT
ma-17	281	1	(	(	PUNCT
ma-17	281	2	3.18	3.18	NUM
ma-17	281	3	)	)	PUNCT
ma-17	281	4	this	this	DET
ma-17	281	5	estimate	estimate	NOUN
ma-17	281	6	motivates	motivate	VERB
ma-17	281	7	us	we	PRON
ma-17	281	8	to	to	PART
ma-17	281	9	define	define	VERB
ma-17	281	10	recurrent	recurrent	ADJ
ma-17	281	11	functions	function	NOUN
ma-17	281	12	f	f	X
ma-17	281	13	(	(	PUNCT
ma-17	281	14	1)m	1)m	NUM
ma-17	281	15	by	by	ADP
ma-17	281	16	f	f	PROPN
ma-17	281	17	(	(	PUNCT
ma-17	281	18	1	1	X
ma-17	281	19	)	)	PUNCT
ma-17	281	20	m	m	PROPN
ma-17	281	21	(	(	PUNCT
ma-17	281	22	t	t	NOUN
ma-17	281	23	)	)	PUNCT
ma-17	281	24	=	=	PUNCT
ma-17	282	1	l	l	NOUN
ma-17	282	2	2	2	NUM
ma-17	282	3	t2m−1η	t2m−1η	NOUN
ma-17	282	4	+	+	CCONJ
ma-17	282	5	l0(1	l0(1	PROPN
ma-17	282	6	+	+	CCONJ
ma-17	282	7	t	t	NOUN
ma-17	282	8	+	+	X
ma-17	282	9	.	.	PUNCT
ma-17	282	10	.	.	PUNCT
ma-17	283	1	.+	.+	NOUN
ma-17	283	2	t2m)η	t2m)η	X
ma-17	284	1	−	−	NOUN
ma-17	284	2	1	1	NUM
ma-17	284	3	.	.	PUNCT
ma-17	285	1	(	(	PUNCT
ma-17	285	2	3.19	3.19	NUM
ma-17	285	3	)	)	PUNCT
ma-17	285	4	we	we	PRON
ma-17	285	5	shall	shall	AUX
ma-17	285	6	find	find	VERB
ma-17	285	7	a	a	DET
ma-17	285	8	relationship	relationship	NOUN
ma-17	285	9	between	between	ADP
ma-17	285	10	recurrent	recurrent	ADJ
ma-17	285	11	functions	function	NOUN
ma-17	285	12	f	f	X
ma-17	285	13	(	(	PUNCT
ma-17	285	14	1)m+1	1)m+1	NUM
ma-17	285	15	and	and	CCONJ
ma-17	285	16	f	f	PROPN
ma-17	285	17	(	(	PUNCT
ma-17	285	18	1)m	1)m	PROPN
ma-17	285	19	.	.	PUNCT
ma-17	286	1	by	by	ADP
ma-17	286	2	definition	definition	NOUN
ma-17	286	3	(	(	PUNCT
ma-17	286	4	3.9	3.9	NUM
ma-17	286	5	)	)	PUNCT
ma-17	286	6	,	,	PUNCT
ma-17	286	7	we	we	PRON
ma-17	286	8	havein	havein	ADV
ma-17	286	9	turn	turn	VERB
ma-17	286	10	that	that	SCONJ
ma-17	287	1	f	f	PROPN
ma-17	287	2	(	(	PUNCT
ma-17	287	3	1	1	NUM
ma-17	287	4	)	)	PUNCT
ma-17	287	5	m+1(t	m+1(t	NUM
ma-17	287	6	)	)	PUNCT
ma-17	288	1	=	=	PUNCT
ma-17	288	2	l	l	NOUN
ma-17	288	3	2	2	NUM
ma-17	288	4	t2m+1η	t2m+1η	NOUN
ma-17	288	5	+	+	CCONJ
ma-17	288	6	l0(1	l0(1	PROPN
ma-17	288	7	+	+	X
ma-17	288	8	t	t	NOUN
ma-17	288	9	+	+	X
ma-17	288	10	.	.	PUNCT
ma-17	288	11	.	.	PUNCT
ma-17	289	1	.+	.+	NOUN
ma-17	289	2	t2m+2)η	t2m+2)η	VERB
ma-17	289	3	−	−	NUM
ma-17	289	4	1	1	NUM
ma-17	289	5	−	−	PROPN
ma-17	289	6	l	l	NOUN
ma-17	289	7	2	2	NUM
ma-17	289	8	t2m−1η	t2m−1η	NOUN
ma-17	289	9	−	−	NOUN
ma-17	289	10	l0(1	l0(1	PROPN
ma-17	289	11	+	+	CCONJ
ma-17	289	12	t	t	NOUN
ma-17	289	13	+	+	X
ma-17	289	14	.	.	PUNCT
ma-17	289	15	.	.	PUNCT
ma-17	290	1	.+	.+	NOUN
ma-17	290	2	t2m)η	t2m)η	PUNCT
ma-17	291	1	+	+	CCONJ
ma-17	291	2	1	1	NUM
ma-17	291	3	+	+	NUM
ma-17	291	4	f	f	X
ma-17	291	5	(	(	PUNCT
ma-17	291	6	1	1	X
ma-17	291	7	)	)	PUNCT
ma-17	291	8	m	m	PROPN
ma-17	291	9	(	(	PUNCT
ma-17	291	10	t	t	PROPN
ma-17	291	11	)	)	PUNCT
ma-17	291	12	=	=	SYM
ma-17	291	13	f	f	PROPN
ma-17	291	14	(	(	PUNCT
ma-17	291	15	1	1	X
ma-17	291	16	)	)	PUNCT
ma-17	291	17	m	m	PROPN
ma-17	291	18	(	(	PUNCT
ma-17	291	19	t	t	PROPN
ma-17	291	20	)	)	PUNCT
ma-17	291	21	+	+	CCONJ
ma-17	291	22	(	(	PUNCT
ma-17	291	23	l	l	NOUN
ma-17	291	24	2	2	NUM
ma-17	291	25	t2	t2	NOUN
ma-17	291	26	−	−	PROPN
ma-17	291	27	l	l	NOUN
ma-17	291	28	2	2	NUM
ma-17	291	29	+	+	CCONJ
ma-17	291	30	l0(t	l0(t	PUNCT
ma-17	291	31	2	2	NUM
ma-17	291	32	+	+	CCONJ
ma-17	291	33	t3))t2m−1η	t3))t2m−1η	NOUN
ma-17	291	34	=	=	ADJ
ma-17	291	35	f	f	X
ma-17	291	36	(	(	PUNCT
ma-17	291	37	1	1	X
ma-17	291	38	)	)	PUNCT
ma-17	291	39	m	m	PROPN
ma-17	291	40	(	(	PUNCT
ma-17	291	41	t	t	PROPN
ma-17	291	42	)	)	PUNCT
ma-17	291	43	+	+	NUM
ma-17	291	44	p(t)t2m−1η	p(t)t2m−1η	NOUN
ma-17	291	45	.	.	PUNCT
ma-17	292	1	(	(	PUNCT
ma-17	292	2	3.20	3.20	NUM
ma-17	292	3	)	)	PUNCT
ma-17	292	4	in	in	ADP
ma-17	292	5	particular	particular	ADJ
ma-17	292	6	,	,	PUNCT
ma-17	292	7	we	we	PRON
ma-17	292	8	have	have	AUX
ma-17	292	9	fm+1(ρ	fm+1(ρ	VERB
ma-17	292	10	)	)	PUNCT
ma-17	292	11	=	=	SYM
ma-17	292	12	fm(ρ	fm(ρ	X
ma-17	292	13	)	)	PUNCT
ma-17	292	14	,	,	PUNCT
ma-17	292	15	(	(	PUNCT
ma-17	292	16	3.21	3.21	NUM
ma-17	292	17	)	)	PUNCT
ma-17	292	18	eur	eur	PROPN
ma-17	292	19	.	.	PUNCT
ma-17	293	1	j.	j.	PROPN
ma-17	293	2	math	math	PROPN
ma-17	293	3	.	.	PUNCT
ma-17	294	1	anal	anal	ADJ
ma-17	294	2	.	.	PUNCT
ma-17	295	1	1	1	NUM
ma-17	295	2	(	(	PUNCT
ma-17	295	3	2021	2021	NUM
ma-17	295	4	)	)	PUNCT
ma-17	295	5	78so	78so	NOUN
ma-17	295	6	evidently	evidently	ADV
ma-17	295	7	(	(	PUNCT
ma-17	295	8	3.8	3.8	NUM
ma-17	295	9	)	)	PUNCT
ma-17	295	10	holds	hold	VERB
ma-17	295	11	if	if	SCONJ
ma-17	295	12	f	f	PROPN
ma-17	295	13	(	(	PUNCT
ma-17	295	14	1	1	X
ma-17	295	15	)	)	PUNCT
ma-17	295	16	m	m	PROPN
ma-17	295	17	(	(	PUNCT
ma-17	295	18	ρ	ρ	NOUN
ma-17	295	19	)	)	PUNCT
ma-17	295	20	≤	≤	NOUN
ma-17	295	21	0	0	NUM
ma-17	295	22	.	.	PUNCT
ma-17	296	1	(	(	PUNCT
ma-17	296	2	3.22)define	3.22)define	NUM
ma-17	296	3	f	f	X
ma-17	296	4	(	(	PUNCT
ma-17	296	5	1)∞	1)∞	PROPN
ma-17	296	6	(	(	PUNCT
ma-17	296	7	t	t	NOUN
ma-17	296	8	)	)	PUNCT
ma-17	296	9	=	=	PUNCT
ma-17	297	1	limm−→∞	limm−→∞	NOUN
ma-17	297	2	f	f	PROPN
ma-17	297	3	(	(	PUNCT
ma-17	297	4	1	1	X
ma-17	297	5	)	)	PUNCT
ma-17	297	6	m	m	PROPN
ma-17	297	7	(	(	PUNCT
ma-17	297	8	t	t	PROPN
ma-17	297	9	)	)	PUNCT
ma-17	297	10	.	.	PUNCT
ma-17	298	1	then	then	ADV
ma-17	298	2	,	,	PUNCT
ma-17	298	3	we	we	PRON
ma-17	298	4	have	have	VERB
ma-17	298	5	f∞(t	f∞(t	NOUN
ma-17	298	6	)	)	PUNCT
ma-17	298	7	=	=	SYM
ma-17	299	1	l0η	l0η	X
ma-17	299	2	1−	1−	NUM
ma-17	299	3	t	t	NOUN
ma-17	299	4	−	−	NOUN
ma-17	299	5	1	1	NUM
ma-17	299	6	.	.	PUNCT
ma-17	300	1	(	(	PUNCT
ma-17	300	2	3.23	3.23	NUM
ma-17	300	3	)	)	PUNCT
ma-17	300	4	then	then	ADV
ma-17	300	5	,	,	PUNCT
ma-17	300	6	(	(	PUNCT
ma-17	300	7	3.22	3.22	NUM
ma-17	300	8	)	)	PUNCT
ma-17	300	9	holds	hold	VERB
ma-17	300	10	if	if	SCONJ
ma-17	300	11	f∞(ρ	f∞(ρ	NOUN
ma-17	300	12	)	)	PUNCT
ma-17	300	13	≤	≤	NOUN
ma-17	300	14	0	0	NUM
ma-17	300	15	,	,	PUNCT
ma-17	300	16	(	(	PUNCT
ma-17	300	17	3.24)which	3.24)which	NUM
ma-17	300	18	is	be	AUX
ma-17	300	19	true	true	ADJ
ma-17	300	20	by	by	ADP
ma-17	300	21	(	(	PUNCT
ma-17	300	22	3.14	3.14	NUM
ma-17	300	23	)	)	PUNCT
ma-17	300	24	.	.	PUNCT
ma-17	301	1	similarly	similarly	ADV
ma-17	301	2	,	,	PUNCT
ma-17	301	3	(	(	PUNCT
ma-17	301	4	3.16	3.16	NUM
ma-17	301	5	)	)	PUNCT
ma-17	301	6	holds	hold	VERB
ma-17	301	7	if	if	SCONJ
ma-17	301	8	l	l	PROPN
ma-17	301	9	2	2	NUM
ma-17	301	10	ρ2m+1η	ρ2m+1η	VERB
ma-17	301	11	+	+	CCONJ
ma-17	301	12	ρl0(1	ρl0(1	NOUN
ma-17	301	13	+	+	CCONJ
ma-17	301	14	ρ+	ρ+	NOUN
ma-17	301	15	.	.	PUNCT
ma-17	301	16	.	.	PUNCT
ma-17	302	1	.+	.+	NOUN
ma-17	302	2	ρ2m+1)η	ρ2m+1)η	NUM
ma-17	302	3	−	−	PROPN
ma-17	302	4	ρ	ρ	PROPN
ma-17	302	5	≤	≤	NUM
ma-17	302	6	0	0	NUM
ma-17	303	1	(	(	PUNCT
ma-17	304	1	3.25	3.25	NUM
ma-17	304	2	)	)	PUNCT
ma-17	304	3	or	or	CCONJ
ma-17	304	4	f	f	X
ma-17	304	5	(	(	PUNCT
ma-17	304	6	2	2	NUM
ma-17	304	7	)	)	PUNCT
ma-17	304	8	m	m	PROPN
ma-17	304	9	(	(	PUNCT
ma-17	304	10	ρ	ρ	NOUN
ma-17	304	11	)	)	PUNCT
ma-17	304	12	≤	≤	NOUN
ma-17	304	13	0	0	NUM
ma-17	304	14	.	.	PUNCT
ma-17	305	1	(	(	PUNCT
ma-17	305	2	3.26)as	3.26)as	NUM
ma-17	305	3	in	in	ADP
ma-17	305	4	(	(	PUNCT
ma-17	305	5	3.20	3.20	NUM
ma-17	305	6	)	)	PUNCT
ma-17	305	7	,	,	PUNCT
ma-17	305	8	we	we	PRON
ma-17	305	9	get	get	VERB
ma-17	305	10	in	in	ADP
ma-17	305	11	turn	turn	NOUN
ma-17	305	12	that	that	SCONJ
ma-17	306	1	f	f	X
ma-17	306	2	(	(	PUNCT
ma-17	306	3	2	2	NUM
ma-17	306	4	)	)	PUNCT
ma-17	306	5	m+1(t	m+1(t	NUM
ma-17	306	6	)	)	PUNCT
ma-17	307	1	=	=	PUNCT
ma-17	308	1	l	l	NOUN
ma-17	308	2	2	2	NUM
ma-17	309	1	t2m+2η	t2m+2η	PRON
ma-17	309	2	+	+	CCONJ
ma-17	309	3	l0(1	l0(1	PROPN
ma-17	309	4	+	+	CCONJ
ma-17	309	5	t	t	NOUN
ma-17	309	6	+	+	X
ma-17	309	7	.	.	PUNCT
ma-17	309	8	.	.	PUNCT
ma-17	310	1	.+	.+	NOUN
ma-17	310	2	t2m+3)η	t2m+3)η	NOUN
ma-17	311	1	−	−	PROPN
ma-17	311	2	1	1	NUM
ma-17	311	3	−	−	PROPN
ma-17	311	4	l	l	NOUN
ma-17	311	5	2	2	NUM
ma-17	311	6	t2mη	t2mη	NOUN
ma-17	311	7	−	−	NOUN
ma-17	311	8	l0(1	l0(1	PROPN
ma-17	311	9	+	+	CCONJ
ma-17	311	10	t	t	NOUN
ma-17	311	11	+	+	X
ma-17	311	12	.	.	PUNCT
ma-17	311	13	.	.	PUNCT
ma-17	312	1	.+	.+	NOUN
ma-17	312	2	t2m+1)η	t2m+1)η	VERB
ma-17	312	3	+	+	CCONJ
ma-17	312	4	1	1	NUM
ma-17	312	5	+	+	NUM
ma-17	312	6	f	f	X
ma-17	312	7	(	(	PUNCT
ma-17	312	8	2	2	NUM
ma-17	312	9	)	)	PUNCT
ma-17	312	10	m	m	PROPN
ma-17	312	11	(	(	PUNCT
ma-17	312	12	t	t	PROPN
ma-17	312	13	)	)	PUNCT
ma-17	312	14	=	=	SYM
ma-17	313	1	f	f	PROPN
ma-17	313	2	(	(	PUNCT
ma-17	313	3	2	2	NUM
ma-17	313	4	)	)	PUNCT
ma-17	313	5	m	m	PROPN
ma-17	313	6	(	(	PUNCT
ma-17	313	7	t	t	PROPN
ma-17	313	8	)	)	PUNCT
ma-17	313	9	+	+	NUM
ma-17	313	10	ϕ(t)t2mη	ϕ(t)t2mη	NOUN
ma-17	313	11	.	.	PUNCT
ma-17	314	1	(	(	PUNCT
ma-17	314	2	3.27	3.27	NUM
ma-17	314	3	)	)	PUNCT
ma-17	314	4	define	define	VERB
ma-17	314	5	f	f	PROPN
ma-17	314	6	(	(	PUNCT
ma-17	314	7	2)∞	2)∞	PROPN
ma-17	314	8	(	(	PUNCT
ma-17	314	9	t	t	PROPN
ma-17	314	10	)	)	PUNCT
ma-17	315	1	=	=	PROPN
ma-17	315	2	lim	lim	PROPN
ma-17	315	3	(	(	PUNCT
ma-17	315	4	2	2	NUM
ma-17	315	5	)	)	PUNCT
ma-17	315	6	m−→∞(t	m−→∞(t	NUM
ma-17	315	7	)	)	PUNCT
ma-17	315	8	.	.	PUNCT
ma-17	316	1	then	then	ADV
ma-17	316	2	,	,	PUNCT
ma-17	316	3	we	we	PRON
ma-17	316	4	get	get	VERB
ma-17	316	5	again	again	ADV
ma-17	316	6	f	f	X
ma-17	316	7	(	(	PUNCT
ma-17	316	8	2)∞	2)∞	PROPN
ma-17	316	9	(	(	PUNCT
ma-17	316	10	t	t	PROPN
ma-17	316	11	)	)	PUNCT
ma-17	317	1	=	=	SYM
ma-17	317	2	f	f	PROPN
ma-17	317	3	(	(	PUNCT
ma-17	317	4	1)∞	1)∞	PROPN
ma-17	317	5	(	(	PUNCT
ma-17	317	6	t	t	PROPN
ma-17	317	7	)	)	PUNCT
ma-17	317	8	,	,	PUNCT
ma-17	317	9	so	so	CCONJ
ma-17	317	10	f	f	X
ma-17	318	1	(	(	PUNCT
ma-17	318	2	2)∞	2)∞	PROPN
ma-17	318	3	(	(	PUNCT
ma-17	318	4	ρ	ρ	NOUN
ma-17	318	5	)	)	PUNCT
ma-17	318	6	≤	≤	NOUN
ma-17	318	7	0,can	0,can	NUM
ma-17	318	8	be	be	AUX
ma-17	318	9	shown	show	VERB
ma-17	318	10	instead	instead	ADV
ma-17	318	11	of	of	ADP
ma-17	318	12	(	(	PUNCT
ma-17	318	13	3.26	3.26	NUM
ma-17	318	14	)	)	PUNCT
ma-17	318	15	.	.	PUNCT
ma-17	319	1	but	but	CCONJ
ma-17	319	2	this	this	PRON
ma-17	319	3	is	be	AUX
ma-17	319	4	true	true	ADJ
ma-17	319	5	by	by	ADP
ma-17	319	6	(	(	PUNCT
ma-17	319	7	3.14	3.14	NUM
ma-17	319	8	)	)	PUNCT
ma-17	319	9	.	.	PUNCT
ma-17	320	1	the	the	DET
ma-17	320	2	induction	induction	NOUN
ma-17	320	3	for	for	ADP
ma-17	320	4	items	item	NOUN
ma-17	320	5	(	(	PUNCT
ma-17	320	6	3.15)-(3.17	3.15)-(3.17	NUM
ma-17	320	7	)	)	PUNCT
ma-17	320	8	iscompleted	iscomplete	VERB
ma-17	320	9	.	.	PUNCT
ma-17	321	1	the	the	DET
ma-17	321	2	rest	rest	NOUN
ma-17	321	3	of	of	ADP
ma-17	321	4	the	the	DET
ma-17	321	5	proof	proof	NOUN
ma-17	321	6	follows	follow	VERB
ma-17	321	7	as	as	ADP
ma-17	321	8	in	in	ADP
ma-17	321	9	lemma	lemma	PROPN
ma-17	321	10	2.2	2.2	NUM
ma-17	321	11	.	.	NOUN
ma-17	322	1	4	4	NUM
ma-17	322	2	.	.	X
ma-17	322	3	local	local	ADJ
ma-17	322	4	convergence	convergence	NOUN
ma-17	322	5	we	we	PRON
ma-17	322	6	shall	shall	AUX
ma-17	322	7	introduce	introduce	VERB
ma-17	322	8	real	real	ADJ
ma-17	322	9	parameters	parameter	NOUN
ma-17	322	10	and	and	CCONJ
ma-17	322	11	functions	function	NOUN
ma-17	322	12	to	to	PART
ma-17	322	13	be	be	AUX
ma-17	322	14	used	use	VERB
ma-17	322	15	in	in	ADP
ma-17	322	16	the	the	DET
ma-17	322	17	convergence	convergence	NOUN
ma-17	322	18	analysis	analysis	NOUN
ma-17	322	19	.	.	PUNCT
ma-17	323	1	set	set	VERB
ma-17	323	2	m	m	NOUN
ma-17	323	3	=	=	PUNCT
ma-17	324	1	[	[	X
ma-17	324	2	0,∞).suppose	0,∞).suppose	ADJ
ma-17	324	3	function(i	function(i	NOUN
ma-17	324	4	)	)	PUNCT
ma-17	324	5	ψ0(t)−	ψ0(t)−	PART
ma-17	324	6	1	1	NUM
ma-17	324	7	=	=	SYM
ma-17	324	8	0	0	PROPN
ma-17	324	9	has	have	VERB
ma-17	324	10	a	a	DET
ma-17	324	11	smallest	small	ADJ
ma-17	324	12	zero	zero	NUM
ma-17	324	13	r0	r0	NOUN
ma-17	324	14	∈	∈	PROPN
ma-17	324	15	m	m	VERB
ma-17	324	16	−	−	NOUN
ma-17	324	17	{	{	PUNCT
ma-17	324	18	0	0	NUM
ma-17	324	19	}	}	PUNCT
ma-17	324	20	,	,	PUNCT
ma-17	324	21	where	where	SCONJ
ma-17	324	22	function	function	NOUN
ma-17	324	23	ψ0	ψ0	ADV
ma-17	324	24	:	:	PUNCT
ma-17	324	25	m	m	AUX
ma-17	324	26	−→	−→	ADJ
ma-17	324	27	m	m	VERB
ma-17	324	28	is	be	AUX
ma-17	324	29	continuousand	continuousand	NOUN
ma-17	324	30	nondecreasing	nondecreasing	PROPN
ma-17	324	31	.	.	PUNCT
ma-17	325	1	set	set	VERB
ma-17	325	2	m0	m0	NOUN
ma-17	325	3	=	=	PUNCT
ma-17	326	1	[	[	X
ma-17	326	2	0	0	NUM
ma-17	326	3	,	,	PUNCT
ma-17	326	4	r0).(ii	r0).(ii	X
ma-17	326	5	)	)	PUNCT
ma-17	326	6	ψ1(t)−1	ψ1(t)−1	VERB
ma-17	326	7	=	=	SYM
ma-17	326	8	0	0	NUM
ma-17	326	9	,	,	PUNCT
ma-17	326	10	has	have	VERB
ma-17	326	11	a	a	DET
ma-17	326	12	smallest	small	ADJ
ma-17	326	13	zero	zero	NUM
ma-17	326	14	r1	r1	NOUN
ma-17	326	15	∈	∈	PROPN
ma-17	326	16	m0−{0	m0−{0	PROPN
ma-17	326	17	}	}	PUNCT
ma-17	326	18	,	,	PUNCT
ma-17	326	19	where	where	SCONJ
ma-17	326	20	function	function	NOUN
ma-17	326	21	ψ	ψ	X
ma-17	326	22	:	:	PUNCT
ma-17	326	23	m0	m0	PROPN
ma-17	326	24	−→	−→	NOUN
ma-17	326	25	m	m	VERB
ma-17	326	26	is	be	AUX
ma-17	326	27	continuousand	continuousand	NOUN
ma-17	326	28	nondecreasing	nondecrease	VERB
ma-17	326	29	and	and	CCONJ
ma-17	326	30	ψ1	ψ1	ADJ
ma-17	326	31	:	:	PUNCT
ma-17	326	32	m0	m0	PROPN
ma-17	326	33	−→	−→	NOUN
ma-17	326	34	m	m	VERB
ma-17	326	35	is	be	AUX
ma-17	326	36	defined	define	VERB
ma-17	326	37	by	by	ADP
ma-17	326	38	ψ1(t	ψ1(t	PUNCT
ma-17	326	39	)	)	PUNCT
ma-17	327	1	=	=	SYM
ma-17	327	2	∫	∫	PROPN
ma-17	327	3	1	1	NUM
ma-17	327	4	0	0	NUM
ma-17	327	5	ψ((1−	ψ((1−	NOUN
ma-17	327	6	θ)t)dθ	θ)t)dθ	X
ma-17	327	7	1−	1−	NUM
ma-17	327	8	ψ0(t	ψ0(t	NOUN
ma-17	327	9	)	)	PUNCT
ma-17	327	10	.	.	PUNCT
ma-17	328	1	eur	eur	PROPN
ma-17	328	2	.	.	PUNCT
ma-17	329	1	j.	j.	PROPN
ma-17	329	2	math	math	PROPN
ma-17	329	3	.	.	PUNCT
ma-17	330	1	anal	anal	ADJ
ma-17	330	2	.	.	PUNCT
ma-17	331	1	1	1	NUM
ma-17	331	2	(	(	PUNCT
ma-17	331	3	2021	2021	NUM
ma-17	331	4	)	)	PUNCT
ma-17	331	5	79(iii	79(iii	NOUN
ma-17	331	6	)	)	PUNCT
ma-17	331	7	ψ0(ψ1(t)t)−	ψ0(ψ1(t)t)−	PROPN
ma-17	331	8	1	1	NUM
ma-17	331	9	has	have	VERB
ma-17	331	10	a	a	DET
ma-17	331	11	smallest	small	ADJ
ma-17	331	12	zero	zero	NUM
ma-17	331	13	r̄1	r̄1	NOUN
ma-17	331	14	∈	∈	NOUN
ma-17	331	15	m0−{0	m0−{0	NOUN
ma-17	331	16	}	}	PUNCT
ma-17	331	17	.	.	PUNCT
ma-17	332	1	ser	ser	NOUN
ma-17	332	2	r̄2	r̄2	PUNCT
ma-17	333	1	=	=	PUNCT
ma-17	333	2	min{r0	min{r0	NOUN
ma-17	333	3	,	,	PUNCT
ma-17	333	4	r̄1	r̄1	NOUN
ma-17	333	5	}	}	PUNCT
ma-17	333	6	and	and	CCONJ
ma-17	333	7	m1	m1	PROPN
ma-17	334	1	=	=	PUNCT
ma-17	335	1	[	[	X
ma-17	335	2	0	0	NUM
ma-17	335	3	,	,	PUNCT
ma-17	335	4	r̄2).(iv	r̄2).(iv	NOUN
ma-17	335	5	)	)	PUNCT
ma-17	335	6	ψ2(t)−	ψ2(t)−	PUNCT
ma-17	335	7	1	1	NUM
ma-17	335	8	=	=	SYM
ma-17	335	9	0	0	PROPN
ma-17	335	10	has	have	VERB
ma-17	335	11	a	a	DET
ma-17	335	12	smallest	small	ADJ
ma-17	335	13	zero	zero	NUM
ma-17	335	14	r2	r2	PROPN
ma-17	335	15	∈	∈	PROPN
ma-17	335	16	m1	m1	PROPN
ma-17	335	17	−	−	PROPN
ma-17	335	18	{	{	PUNCT
ma-17	335	19	0	0	NUM
ma-17	335	20	}	}	PUNCT
ma-17	335	21	,	,	PUNCT
ma-17	335	22	where	where	SCONJ
ma-17	335	23	ψ2(t	ψ2(t	NOUN
ma-17	335	24	)	)	PUNCT
ma-17	335	25	=	=	PUNCT
ma-17	336	1	[	[	X
ma-17	336	2	ψ1(ψ1(t)t	ψ1(ψ1(t)t	NOUN
ma-17	336	3	)	)	PUNCT
ma-17	336	4	+	+	CCONJ
ma-17	336	5	(	(	PUNCT
ma-17	336	6	ψ0(t	ψ0(t	NOUN
ma-17	336	7	)	)	PUNCT
ma-17	336	8	+	+	CCONJ
ma-17	336	9	h(t	h(t	PROPN
ma-17	336	10	,	,	PUNCT
ma-17	336	11	ψ1(t)t	ψ1(t)t	NUM
ma-17	336	12	)	)	PUNCT
ma-17	336	13	)	)	PUNCT
ma-17	336	14	∫	∫	PROPN
ma-17	336	15	1	1	NUM
ma-17	336	16	0	0	NUM
ma-17	336	17	ω(θψ1(t)t)dθ	ω(θψ1(t)t)dθ	NUM
ma-17	336	18	(	(	PUNCT
ma-17	336	19	1−	1−	NUM
ma-17	336	20	ψ0(t))(1−	ψ0(t))(1−	PROPN
ma-17	336	21	ψ0(ψ1(t)t	ψ0(ψ1(t)t	NOUN
ma-17	336	22	)	)	PUNCT
ma-17	336	23	)	)	PUNCT
ma-17	336	24	]	]	PUNCT
ma-17	336	25	ψ1(t	ψ1(t	PROPN
ma-17	336	26	)	)	PUNCT
ma-17	336	27	,	,	PUNCT
ma-17	336	28	where	where	SCONJ
ma-17	336	29	ω	ω	X
ma-17	336	30	:	:	PUNCT
ma-17	336	31	m1	m1	PROPN
ma-17	336	32	−→	−→	NOUN
ma-17	336	33	m	m	PROPN
ma-17	336	34	and	and	CCONJ
ma-17	336	35	h	h	NOUN
ma-17	336	36	:	:	PUNCT
ma-17	336	37	m	m	AUX
ma-17	336	38	×m1	×m1	VERB
ma-17	336	39	−→	−→	ADJ
ma-17	336	40	m	m	NOUN
ma-17	336	41	are	be	AUX
ma-17	336	42	continuous	continuous	ADJ
ma-17	336	43	and	and	CCONJ
ma-17	336	44	nondecreasing	nondecreasing	ADJ
ma-17	336	45	.	.	PUNCT
ma-17	337	1	we	we	PRON
ma-17	337	2	shall	shall	AUX
ma-17	337	3	showthat	showthat	ADV
ma-17	337	4	r	r	NOUN
ma-17	337	5	=	=	SYM
ma-17	337	6	min{r1	min{r1	NOUN
ma-17	337	7	,	,	PUNCT
ma-17	337	8	r2	r2	PROPN
ma-17	337	9	}	}	PUNCT
ma-17	337	10	,	,	PUNCT
ma-17	337	11	(	(	PUNCT
ma-17	337	12	4.1)is	4.1)is	DET
ma-17	337	13	a	a	DET
ma-17	337	14	convergence	convergence	NOUN
ma-17	337	15	radius	radius	NOUN
ma-17	337	16	for	for	ADP
ma-17	337	17	method	method	NOUN
ma-17	337	18	(	(	PUNCT
ma-17	337	19	1.2	1.2	NUM
ma-17	337	20	)	)	PUNCT
ma-17	337	21	.	.	PUNCT
ma-17	338	1	set	set	VERB
ma-17	338	2	m2	m2	PROPN
ma-17	338	3	=	=	PUNCT
ma-17	339	1	[	[	X
ma-17	339	2	0	0	NUM
ma-17	339	3	,	,	PUNCT
ma-17	339	4	r	r	NOUN
ma-17	339	5	)	)	PUNCT
ma-17	339	6	.	.	PUNCT
ma-17	340	1	these	these	DET
ma-17	340	2	definitions	definition	NOUN
ma-17	340	3	,	,	PUNCT
ma-17	340	4	imply	imply	VERB
ma-17	340	5	that	that	SCONJ
ma-17	340	6	for	for	ADP
ma-17	340	7	each	each	DET
ma-17	340	8	t	t	NOUN
ma-17	340	9	∈	∈	PROPN
ma-17	340	10	m2	m2	PROPN
ma-17	340	11	0	0	PROPN
ma-17	340	12	≤	≤	NUM
ma-17	340	13	ψ0(t	ψ0(t	NOUN
ma-17	340	14	)	)	PUNCT
ma-17	340	15	<	<	X
ma-17	340	16	1	1	NUM
ma-17	340	17	,	,	PUNCT
ma-17	340	18	(	(	PUNCT
ma-17	340	19	4.2	4.2	NUM
ma-17	340	20	)	)	PUNCT
ma-17	340	21	0	0	NUM
ma-17	340	22	≤	≤	NUM
ma-17	340	23	ψ0(ψ1(t)t	ψ0(ψ1(t)t	NOUN
ma-17	340	24	)	)	PUNCT
ma-17	340	25	<	<	X
ma-17	340	26	1	1	NUM
ma-17	340	27	,	,	PUNCT
ma-17	340	28	(	(	PUNCT
ma-17	340	29	4.3)and	4.3)and	NOUN
ma-17	340	30	0	0	NUM
ma-17	340	31	≤	≤	NOUN
ma-17	340	32	ψi(t	ψi(t	NOUN
ma-17	340	33	)	)	PUNCT
ma-17	340	34	<	<	X
ma-17	340	35	1	1	NUM
ma-17	340	36	,	,	PUNCT
ma-17	340	37	i	i	PRON
ma-17	340	38	=	=	NOUN
ma-17	340	39	1	1	NUM
ma-17	340	40	,	,	PUNCT
ma-17	340	41	2	2	NUM
ma-17	340	42	.	.	PUNCT
ma-17	341	1	(	(	PUNCT
ma-17	341	2	4.4)the	4.4)the	DET
ma-17	341	3	conditions	condition	NOUN
ma-17	341	4	(	(	PUNCT
ma-17	341	5	h	h	NOUN
ma-17	341	6	)	)	PUNCT
ma-17	341	7	shall	shall	AUX
ma-17	341	8	be	be	AUX
ma-17	341	9	used	use	VERB
ma-17	341	10	provided	provide	VERB
ma-17	341	11	that	that	SCONJ
ma-17	341	12	x∗	x∗	PROPN
ma-17	341	13	is	be	AUX
ma-17	341	14	a	a	DET
ma-17	341	15	simple	simple	ADJ
ma-17	341	16	solution	solution	NOUN
ma-17	341	17	of	of	ADP
ma-17	341	18	equation	equation	NOUN
ma-17	341	19	f	f	X
ma-17	341	20	(	(	PUNCT
ma-17	341	21	x	x	X
ma-17	341	22	)	)	PUNCT
ma-17	341	23	=	=	SYM
ma-17	341	24	0.suppose:(h1	0.suppose:(h1	NUM
ma-17	341	25	)	)	PUNCT
ma-17	341	26	for	for	ADP
ma-17	341	27	each	each	DET
ma-17	341	28	x	x	SYM
ma-17	341	29	∈	∈	PROPN
ma-17	341	30	ω	ω	PROPN
ma-17	341	31	‖f	‖f	PRON
ma-17	341	32	′(x∗)−1(f	′(x∗)−1(f	VERB
ma-17	341	33	′(x)−	′(x)−	PROPN
ma-17	341	34	f	f	PROPN
ma-17	341	35	′(x∗))‖	′(x∗))‖	PROPN
ma-17	341	36	≤	≤	PUNCT
ma-17	341	37	ψ0(‖x	ψ0(‖x	NOUN
ma-17	341	38	−	−	PROPN
ma-17	341	39	x0‖	x0‖	PROPN
ma-17	341	40	)	)	PUNCT
ma-17	341	41	.	.	PUNCT
ma-17	342	1	set	set	VERB
ma-17	342	2	ω0	ω0	ADV
ma-17	342	3	=	=	SYM
ma-17	342	4	u(x∗	u(x∗	PROPN
ma-17	342	5	,	,	PUNCT
ma-17	342	6	r0	r0	NOUN
ma-17	342	7	)	)	PUNCT
ma-17	342	8	∩ω.(h2	∩ω.(h2	PROPN
ma-17	342	9	)	)	PUNCT
ma-17	342	10	for	for	ADP
ma-17	342	11	each	each	DET
ma-17	342	12	x	x	NOUN
ma-17	342	13	,	,	PUNCT
ma-17	342	14	y	y	PROPN
ma-17	342	15	∈	∈	PROPN
ma-17	342	16	ω0	ω0	NOUN
ma-17	342	17	‖f	‖f	ADP
ma-17	342	18	′(x∗)−1(f	′(x∗)−1(f	NOUN
ma-17	342	19	′(y)−	′(y)−	VERB
ma-17	342	20	f	f	PROPN
ma-17	342	21	′(x))‖	′(x))‖	PROPN
ma-17	342	22	≤	≤	NOUN
ma-17	342	23	ψ(‖y	ψ(‖y	SYM
ma-17	342	24	−	−	NOUN
ma-17	342	25	x‖	x‖	NUM
ma-17	342	26	)	)	PUNCT
ma-17	342	27	,	,	PUNCT
ma-17	342	28	‖f	‖f	ADP
ma-17	342	29	′(x∗)−1f	′(x∗)−1f	NOUN
ma-17	342	30	′(x)‖	′(x)‖	X
ma-17	342	31	≤	≤	ADJ
ma-17	342	32	ω(‖x	ω(‖x	NUM
ma-17	342	33	−	−	PROPN
ma-17	342	34	x∗‖),and	x∗‖),and	NOUN
ma-17	342	35	‖f	‖f	PRON
ma-17	342	36	′(x∗)−1(f	′(x∗)−1(f	NOUN
ma-17	342	37	′(x∗)−	′(x∗)−	PUNCT
ma-17	342	38	a(x	a(x	PROPN
ma-17	342	39	,	,	PUNCT
ma-17	342	40	y))‖	y))‖	VERB
ma-17	342	41	≤	≤	NOUN
ma-17	342	42	h(‖x	h(‖x	PROPN
ma-17	343	1	−	−	PROPN
ma-17	343	2	x∗‖	x∗‖	PROPN
ma-17	343	3	,	,	PUNCT
ma-17	343	4	‖y	‖y	PUNCT
ma-17	343	5	−	−	PROPN
ma-17	343	6	x∗‖).(h3	x∗‖).(h3	SYM
ma-17	343	7	)	)	PUNCT
ma-17	343	8	u[x∗	u[x∗	PROPN
ma-17	343	9	,	,	PUNCT
ma-17	343	10	r	r	X
ma-17	343	11	]	]	X
ma-17	343	12	⊂	⊂	PROPN
ma-17	343	13	ω.next	ω.next	PROPN
ma-17	343	14	,	,	PUNCT
ma-17	343	15	we	we	PRON
ma-17	343	16	show	show	VERB
ma-17	343	17	the	the	DET
ma-17	343	18	local	local	ADJ
ma-17	343	19	convergence	convergence	NOUN
ma-17	343	20	of	of	ADP
ma-17	343	21	method	method	NOUN
ma-17	343	22	(	(	PUNCT
ma-17	343	23	1.2	1.2	NUM
ma-17	343	24	)	)	PUNCT
ma-17	343	25	based	base	VERB
ma-17	343	26	on	on	ADP
ma-17	343	27	the	the	DET
ma-17	343	28	preceding	precede	VERB
ma-17	343	29	notation	notation	NOUN
ma-17	343	30	and	and	CCONJ
ma-17	343	31	conditions(h	conditions(h	NOUN
ma-17	343	32	)	)	PUNCT
ma-17	343	33	..	..	PUNCT
ma-17	343	34	theorem	theorem	VERB
ma-17	343	35	4.1	4.1	NUM
ma-17	343	36	.	.	PUNCT
ma-17	344	1	under	under	ADP
ma-17	344	2	conditions	condition	NOUN
ma-17	344	3	(	(	PUNCT
ma-17	344	4	h	h	NOUN
ma-17	344	5	)	)	PUNCT
ma-17	344	6	further	far	ADV
ma-17	344	7	suppose	suppose	VERB
ma-17	344	8	that	that	SCONJ
ma-17	344	9	x0	x0	PROPN
ma-17	344	10	∈	∈	PROPN
ma-17	344	11	u(x∗	u(x∗	PROPN
ma-17	344	12	,	,	PUNCT
ma-17	344	13	r	r	NOUN
ma-17	344	14	)	)	PUNCT
ma-17	344	15	−	−	NOUN
ma-17	344	16	{	{	PUNCT
ma-17	344	17	x∗	x∗	PROPN
ma-17	344	18	}	}	PUNCT
ma-17	344	19	.	.	PUNCT
ma-17	345	1	then	then	ADV
ma-17	345	2	,	,	PUNCT
ma-17	345	3	we	we	PRON
ma-17	345	4	conclude	conclude	VERB
ma-17	345	5	limn−→∞	limn−→∞	NOUN
ma-17	345	6	xn	xn	PUNCT
ma-17	346	1	=	=	SYM
ma-17	346	2	x∗.	x∗.	PROPN
ma-17	346	3	proof	proof	NOUN
ma-17	346	4	.	.	PUNCT
ma-17	347	1	let	let	VERB
ma-17	347	2	v	v	X
ma-17	347	3	∈	∈	PROPN
ma-17	347	4	u(x∗	u(x∗	NOUN
ma-17	347	5	,	,	PUNCT
ma-17	347	6	r)−	r)−	PROPN
ma-17	347	7	{	{	PUNCT
ma-17	347	8	x∗	x∗	PROPN
ma-17	347	9	}	}	PUNCT
ma-17	347	10	.	.	PUNCT
ma-17	348	1	using	use	VERB
ma-17	348	2	(	(	PUNCT
ma-17	348	3	4.1	4.1	NUM
ma-17	348	4	)	)	PUNCT
ma-17	348	5	,	,	PUNCT
ma-17	348	6	(	(	PUNCT
ma-17	348	7	4.2	4.2	NUM
ma-17	348	8	)	)	PUNCT
ma-17	348	9	,	,	PUNCT
ma-17	348	10	and	and	CCONJ
ma-17	348	11	(	(	PUNCT
ma-17	348	12	h1	h1	PROPN
ma-17	348	13	)	)	PUNCT
ma-17	348	14	we	we	PRON
ma-17	348	15	obtain	obtain	VERB
ma-17	348	16	in	in	ADP
ma-17	348	17	turn	turn	NOUN
ma-17	348	18	that	that	SCONJ
ma-17	348	19	‖f	‖f	DET
ma-17	348	20	′(x∗)−1(f	′(x∗)−1(f	ADJ
ma-17	348	21	′(v)−	′(v)−	ADJ
ma-17	348	22	f	f	PROPN
ma-17	348	23	′(x∗))‖	′(x∗))‖	NOUN
ma-17	348	24	≤	≤	NOUN
ma-17	348	25	ψ0(‖v	ψ0(‖v	NOUN
ma-17	348	26	−	−	PROPN
ma-17	348	27	x∗‖	x∗‖	NUM
ma-17	348	28	)	)	PUNCT
ma-17	348	29	≤	≤	PUNCT
ma-17	349	1	ψ0(r	ψ0(r	CCONJ
ma-17	349	2	)	)	PUNCT
ma-17	349	3	<	<	X
ma-17	349	4	1	1	NUM
ma-17	349	5	,	,	PUNCT
ma-17	349	6	so	so	SCONJ
ma-17	349	7	‖f	‖f	ADP
ma-17	349	8	′(v)−1f	′(v)−1f	NOUN
ma-17	349	9	′(x∗)‖	′(x∗)‖	X
ma-17	349	10	≤	≤	NUM
ma-17	349	11	1	1	NUM
ma-17	349	12	1−	1−	NUM
ma-17	349	13	ψ0(‖v	ψ0(‖v	NOUN
ma-17	349	14	−	−	PROPN
ma-17	349	15	x∗‖	x∗‖	NUM
ma-17	349	16	)	)	PUNCT
ma-17	349	17	.	.	PUNCT
ma-17	350	1	(	(	PUNCT
ma-17	350	2	4.5	4.5	NUM
ma-17	350	3	)	)	PUNCT
ma-17	350	4	eur	eur	PROPN
ma-17	350	5	.	.	PUNCT
ma-17	351	1	j.	j.	PROPN
ma-17	351	2	math	math	PROPN
ma-17	351	3	.	.	PUNCT
ma-17	352	1	anal	anal	ADJ
ma-17	352	2	.	.	PUNCT
ma-17	353	1	1	1	NUM
ma-17	353	2	(	(	PUNCT
ma-17	353	3	2021	2021	NUM
ma-17	353	4	)	)	PUNCT
ma-17	353	5	80	80	NUM
ma-17	353	6	in	in	ADP
ma-17	353	7	particular	particular	ADJ
ma-17	353	8	,	,	PUNCT
ma-17	353	9	iterate	iterate	NOUN
ma-17	353	10	is	be	AUX
ma-17	353	11	well	well	ADV
ma-17	353	12	defined	define	VERB
ma-17	353	13	for	for	ADP
ma-17	353	14	v	v	NOUN
ma-17	353	15	=	=	SYM
ma-17	353	16	x0	x0	PROPN
ma-17	353	17	and	and	CCONJ
ma-17	353	18	the	the	DET
ma-17	353	19	first	first	ADJ
ma-17	353	20	substep	substep	NOUN
ma-17	353	21	of	of	ADP
ma-17	353	22	method	method	NOUN
ma-17	353	23	(	(	PUNCT
ma-17	353	24	1.2	1.2	NUM
ma-17	353	25	)	)	PUNCT
ma-17	353	26	,	,	PUNCT
ma-17	353	27	from	from	ADP
ma-17	353	28	which	which	PRON
ma-17	353	29	wecan	wecan	VERB
ma-17	353	30	also	also	ADV
ma-17	353	31	write	write	VERB
ma-17	353	32	y0	y0	PRON
ma-17	353	33	−	−	NOUN
ma-17	353	34	x∗	x∗	PROPN
ma-17	354	1	=	=	PUNCT
ma-17	354	2	x0	x0	PROPN
ma-17	355	1	−	−	PROPN
ma-17	355	2	x∗	x∗	PROPN
ma-17	356	1	−	−	PROPN
ma-17	357	1	f	f	PROPN
ma-17	358	1	′(x0)−1f	′(x0)−1f	PROPN
ma-17	358	2	(	(	PUNCT
ma-17	358	3	x0	x0	PROPN
ma-17	358	4	)	)	PUNCT
ma-17	358	5	=	=	PUNCT
ma-17	359	1	(	(	PUNCT
ma-17	359	2	f	f	PROPN
ma-17	359	3	′(x0	′(x0	NOUN
ma-17	359	4	)	)	PUNCT
ma-17	359	5	−1f	−1f	PROPN
ma-17	359	6	′(x∗	′(x∗	PROPN
ma-17	359	7	)	)	PUNCT
ma-17	359	8	)	)	PUNCT
ma-17	360	1	×	×	NOUN
ma-17	360	2	(	(	PUNCT
ma-17	360	3	∫	∫	PROPN
ma-17	360	4	1	1	NUM
ma-17	360	5	0	0	NUM
ma-17	360	6	f	f	PROPN
ma-17	360	7	′(x∗)−1(f	′(x∗)−1(f	VERB
ma-17	360	8	′(x∗	′(x∗	PROPN
ma-17	360	9	+	+	PUNCT
ma-17	360	10	θ(x0	θ(x0	NOUN
ma-17	360	11	−	−	PROPN
ma-17	361	1	x∗))−	x∗))−	NUM
ma-17	361	2	f	f	X
ma-17	361	3	′(x0))dθ(x0	′(x0))dθ(x0	PROPN
ma-17	361	4	−	−	PROPN
ma-17	361	5	x∗	x∗	PROPN
ma-17	361	6	)	)	PUNCT
ma-17	361	7	.	.	PUNCT
ma-17	362	1	(	(	PUNCT
ma-17	362	2	4.6	4.6	NUM
ma-17	362	3	)	)	PUNCT
ma-17	362	4	by	by	ADP
ma-17	362	5	(	(	PUNCT
ma-17	362	6	4.1	4.1	NUM
ma-17	362	7	)	)	PUNCT
ma-17	362	8	,	,	PUNCT
ma-17	362	9	(	(	PUNCT
ma-17	362	10	4.4	4.4	NUM
ma-17	362	11	)	)	PUNCT
ma-17	362	12	(	(	PUNCT
ma-17	362	13	for	for	ADP
ma-17	362	14	i	i	PRON
ma-17	362	15	=	=	NOUN
ma-17	362	16	1	1	NUM
ma-17	362	17	)	)	PUNCT
ma-17	362	18	,	,	PUNCT
ma-17	362	19	(	(	PUNCT
ma-17	362	20	4.5	4.5	NUM
ma-17	362	21	)	)	PUNCT
ma-17	362	22	(	(	PUNCT
ma-17	362	23	for	for	ADP
ma-17	362	24	v	v	NOUN
ma-17	362	25	=	=	SYM
ma-17	362	26	x0	x0	PROPN
ma-17	362	27	)	)	PUNCT
ma-17	362	28	,	,	PUNCT
ma-17	362	29	(	(	PUNCT
ma-17	362	30	4.6	4.6	NUM
ma-17	362	31	)	)	PUNCT
ma-17	362	32	and	and	CCONJ
ma-17	362	33	(	(	PUNCT
ma-17	362	34	h2	h2	NOUN
ma-17	362	35	)	)	PUNCT
ma-17	362	36	,	,	PUNCT
ma-17	362	37	we	we	PRON
ma-17	362	38	get	get	VERB
ma-17	362	39	in	in	ADP
ma-17	362	40	turn	turn	NOUN
ma-17	362	41	that	that	SCONJ
ma-17	362	42	‖y0	‖y0	VERB
ma-17	362	43	−	−	PROPN
ma-17	362	44	x∗‖	x∗‖	PROPN
ma-17	362	45	≤	≤	NUM
ma-17	362	46	∫	∫	PROPN
ma-17	362	47	1	1	NUM
ma-17	362	48	0	0	NUM
ma-17	362	49	ψ̄((1−	ψ̄((1−	NOUN
ma-17	362	50	θ)‖x0	θ)‖x0	VERB
ma-17	362	51	−	−	PROPN
ma-17	362	52	x∗‖)dθ‖x0	x∗‖)dθ‖x0	NUM
ma-17	363	1	−	−	PROPN
ma-17	363	2	x∗‖	x∗‖	PROPN
ma-17	363	3	1−	1−	NUM
ma-17	364	1	ψ0(‖x0	ψ0(‖x0	INTJ
ma-17	364	2	−	−	X
ma-17	364	3	x∗‖	x∗‖	NUM
ma-17	364	4	)	)	PUNCT
ma-17	364	5	≤	≤	NUM
ma-17	364	6	‖x0	‖x0	NOUN
ma-17	365	1	−	−	PROPN
ma-17	365	2	x∗‖	x∗‖	X
ma-17	365	3	<	<	X
ma-17	365	4	r	r	NOUN
ma-17	365	5	,	,	PUNCT
ma-17	365	6	(	(	PUNCT
ma-17	365	7	4.7	4.7	NUM
ma-17	365	8	)	)	PUNCT
ma-17	365	9	so	so	ADV
ma-17	365	10	y0	y0	PROPN
ma-17	365	11	∈	∈	PROPN
ma-17	365	12	u(x∗	u(x∗	NOUN
ma-17	365	13	,	,	PUNCT
ma-17	365	14	r	r	NOUN
ma-17	365	15	)	)	PUNCT
ma-17	365	16	.	.	PUNCT
ma-17	366	1	we	we	PRON
ma-17	366	2	also	also	ADV
ma-17	366	3	have	have	VERB
ma-17	366	4	that	that	PRON
ma-17	366	5	(	(	PUNCT
ma-17	366	6	4.5	4.5	NUM
ma-17	366	7	)	)	PUNCT
ma-17	366	8	holds	hold	VERB
ma-17	366	9	for	for	ADP
ma-17	366	10	v	v	NOUN
ma-17	366	11	=	=	SYM
ma-17	366	12	y0	y0	NOUN
ma-17	366	13	,	,	PUNCT
ma-17	366	14	and	and	CCONJ
ma-17	366	15	iterate	iterate	NOUN
ma-17	366	16	x1	x1	PROPN
ma-17	366	17	is	be	AUX
ma-17	366	18	well	well	ADV
ma-17	366	19	defined	define	VERB
ma-17	366	20	fromwhich	fromwhich	NOUN
ma-17	366	21	we	we	PRON
ma-17	366	22	can	can	AUX
ma-17	366	23	write	write	VERB
ma-17	366	24	in	in	ADP
ma-17	366	25	turn	turn	NOUN
ma-17	366	26	that	that	SCONJ
ma-17	367	1	x1	x1	ADJ
ma-17	367	2	−	−	X
ma-17	367	3	x∗	x∗	PROPN
ma-17	368	1	=	=	PUNCT
ma-17	368	2	y0	y0	NOUN
ma-17	368	3	−	−	NOUN
ma-17	368	4	x∗	x∗	PROPN
ma-17	369	1	−	−	PROPN
ma-17	369	2	f	f	PROPN
ma-17	369	3	′(y0)−1f	′(y0)−1f	PROPN
ma-17	369	4	(	(	PUNCT
ma-17	369	5	x0	x0	PROPN
ma-17	369	6	)	)	PUNCT
ma-17	370	1	+	+	PROPN
ma-17	370	2	(	(	PUNCT
ma-17	370	3	f	f	NOUN
ma-17	370	4	′(y0	′(y0	NOUN
ma-17	370	5	)	)	PUNCT
ma-17	370	6	−1	−1	NOUN
ma-17	370	7	−	−	NOUN
ma-17	370	8	a0f	a0f	PUNCT
ma-17	370	9	′(x0)−1)f	′(x0)−1)f	VERB
ma-17	370	10	(	(	PUNCT
ma-17	370	11	y0	y0	NOUN
ma-17	370	12	)	)	PUNCT
ma-17	371	1	=	=	SYM
ma-17	371	2	y0	y0	NOUN
ma-17	371	3	−	−	NOUN
ma-17	371	4	x∗	x∗	PROPN
ma-17	371	5	−	−	PROPN
ma-17	372	1	f	f	PROPN
ma-17	372	2	′(y0)−1f	′(y0)−1f	PROPN
ma-17	372	3	(	(	PUNCT
ma-17	372	4	y0	y0	NOUN
ma-17	372	5	)	)	PUNCT
ma-17	372	6	+	+	NUM
ma-17	372	7	f	f	NOUN
ma-17	372	8	′(y0	′(y0	NOUN
ma-17	372	9	)	)	PUNCT
ma-17	372	10	−1(f	−1(f	PROPN
ma-17	372	11	′(x0)−	′(x0)−	PROPN
ma-17	372	12	a0)f	a0)f	PROPN
ma-17	372	13	′(x0)1f	′(x0)1f	PROPN
ma-17	372	14	(	(	PUNCT
ma-17	372	15	y0	y0	PROPN
ma-17	372	16	)	)	PUNCT
ma-17	372	17	.	.	PUNCT
ma-17	373	1	(	(	PUNCT
ma-17	373	2	4.8	4.8	NUM
ma-17	373	3	)	)	PUNCT
ma-17	373	4	in	in	ADP
ma-17	373	5	view	view	NOUN
ma-17	373	6	of	of	ADP
ma-17	373	7	(	(	PUNCT
ma-17	373	8	4.1	4.1	NUM
ma-17	373	9	)	)	PUNCT
ma-17	373	10	,	,	PUNCT
ma-17	373	11	(	(	PUNCT
ma-17	373	12	4.4	4.4	NUM
ma-17	373	13	)	)	PUNCT
ma-17	373	14	(	(	PUNCT
ma-17	373	15	for	for	ADP
ma-17	373	16	i	i	PRON
ma-17	373	17	=	=	NOUN
ma-17	373	18	2	2	NUM
ma-17	373	19	)	)	PUNCT
ma-17	373	20	,	,	PUNCT
ma-17	373	21	(	(	PUNCT
ma-17	373	22	4.5)(for	4.5)(for	NUM
ma-17	373	23	v	v	NOUN
ma-17	373	24	=	=	SYM
ma-17	373	25	x0	x0	PROPN
ma-17	373	26	,	,	PUNCT
ma-17	373	27	y0	y0	PROPN
ma-17	373	28	)	)	PUNCT
ma-17	373	29	,	,	PUNCT
ma-17	373	30	(	(	PUNCT
ma-17	373	31	4.7	4.7	NUM
ma-17	373	32	)	)	PUNCT
ma-17	373	33	,	,	PUNCT
ma-17	373	34	(	(	PUNCT
ma-17	373	35	4.8	4.8	NUM
ma-17	373	36	)	)	PUNCT
ma-17	373	37	and	and	CCONJ
ma-17	373	38	(	(	PUNCT
ma-17	373	39	h2	h2	NOUN
ma-17	373	40	)	)	PUNCT
ma-17	373	41	,	,	PUNCT
ma-17	373	42	we	we	PRON
ma-17	373	43	obtain	obtain	VERB
ma-17	373	44	in	in	ADP
ma-17	373	45	turn	turn	NOUN
ma-17	373	46	‖x1	‖x1	NOUN
ma-17	373	47	−	−	PROPN
ma-17	373	48	x∗‖	x∗‖	PROPN
ma-17	373	49	≤	≤	NOUN
ma-17	374	1	[	[	X
ma-17	374	2	ψ1(ψ1(‖x0	ψ1(ψ1(‖x0	NOUN
ma-17	374	3	−	−	PROPN
ma-17	374	4	x∗‖	x∗‖	NUM
ma-17	374	5	)	)	PUNCT
ma-17	374	6	)	)	PUNCT
ma-17	375	1	+	+	CCONJ
ma-17	375	2	(	(	PUNCT
ma-17	375	3	ψ0(‖x0	ψ0(‖x0	INTJ
ma-17	375	4	−	−	PROPN
ma-17	375	5	x∗‖	x∗‖	NUM
ma-17	375	6	)	)	PUNCT
ma-17	375	7	+	+	NUM
ma-17	375	8	h(‖x0	h(‖x0	NOUN
ma-17	375	9	−	−	PROPN
ma-17	375	10	x∗‖	x∗‖	PROPN
ma-17	375	11	,	,	PUNCT
ma-17	375	12	‖y0	‖y0	VERB
ma-17	375	13	−	−	NOUN
ma-17	375	14	x∗‖	x∗‖	NUM
ma-17	375	15	)	)	PUNCT
ma-17	375	16	)	)	PUNCT
ma-17	376	1	∫	∫	PROPN
ma-17	376	2	1	1	NUM
ma-17	376	3	0	0	NUM
ma-17	377	1	ω(θ‖y0	ω(θ‖y0	PROPN
ma-17	377	2	−	−	PROPN
ma-17	378	1	x∗‖)dθ	x∗‖)dθ	PROPN
ma-17	378	2	(	(	PUNCT
ma-17	378	3	1−	1−	NUM
ma-17	378	4	ψ0(‖y0	ψ0(‖y0	PROPN
ma-17	378	5	−	−	PROPN
ma-17	378	6	x∗‖))(1−	x∗‖))(1−	PUNCT
ma-17	379	1	ψ0(‖x0	ψ0(‖x0	DET
ma-17	379	2	−	−	PROPN
ma-17	379	3	x∗‖	x∗‖	NUM
ma-17	379	4	)	)	PUNCT
ma-17	379	5	)	)	PUNCT
ma-17	380	1	]	]	PUNCT
ma-17	380	2	‖y0	‖y0	VERB
ma-17	380	3	−	−	PROPN
ma-17	380	4	x∗‖	x∗‖	PROPN
ma-17	380	5	≤	≤	NOUN
ma-17	381	1	ψ2(‖x0	ψ2(‖x0	PRON
ma-17	381	2	−	−	PROPN
ma-17	382	1	x∗‖)‖x0	x∗‖)‖x0	NOUN
ma-17	382	2	−	−	PROPN
ma-17	382	3	x∗‖	x∗‖	PROPN
ma-17	382	4	≤	≤	NUM
ma-17	382	5	‖x0	‖x0	NOUN
ma-17	383	1	−	−	PROPN
ma-17	383	2	x∗‖	x∗‖	X
ma-17	383	3	<	<	X
ma-17	383	4	r	r	NOUN
ma-17	383	5	,	,	PUNCT
ma-17	383	6	(	(	PUNCT
ma-17	383	7	4.9	4.9	NUM
ma-17	383	8	)	)	PUNCT
ma-17	383	9	so	so	CCONJ
ma-17	383	10	x1	x1	PROPN
ma-17	383	11	∈	∈	PROPN
ma-17	383	12	u(x∗	u(x∗	NOUN
ma-17	383	13	,	,	PUNCT
ma-17	383	14	r	r	NOUN
ma-17	383	15	)	)	PUNCT
ma-17	383	16	.	.	PUNCT
ma-17	384	1	simply	simply	ADV
ma-17	384	2	,	,	PUNCT
ma-17	384	3	switch	switch	VERB
ma-17	384	4	x0	x0	PROPN
ma-17	384	5	,	,	PUNCT
ma-17	384	6	y0	y0	PROPN
ma-17	384	7	,	,	PUNCT
ma-17	384	8	x1	x1	NUM
ma-17	384	9	by	by	ADP
ma-17	384	10	xm	xm	PROPN
ma-17	384	11	,	,	PUNCT
ma-17	384	12	ym	ym	PROPN
ma-17	384	13	,	,	PUNCT
ma-17	384	14	xm+1	xm+1	PROPN
ma-17	384	15	,	,	PUNCT
ma-17	384	16	respectively	respectively	ADV
ma-17	384	17	in	in	ADP
ma-17	384	18	the	the	DET
ma-17	384	19	preceding	precede	VERB
ma-17	384	20	calcula	calcula	NOUN
ma-17	384	21	-	-	PUNCT
ma-17	384	22	tions	tion	NOUN
ma-17	384	23	to	to	PART
ma-17	384	24	get	get	VERB
ma-17	384	25	‖ym	‖ym	NUM
ma-17	384	26	−	−	PROPN
ma-17	384	27	x∗‖	x∗‖	SYM
ma-17	384	28	≤	≤	NUM
ma-17	384	29	ψ1(‖xm	ψ1(‖xm	PRON
ma-17	385	1	−	−	PROPN
ma-17	385	2	x∗‖)‖xm	x∗‖)‖xm	PUNCT
ma-17	386	1	−	−	PROPN
ma-17	386	2	x∗‖	x∗‖	PUNCT
ma-17	386	3	≤	≤	NOUN
ma-17	387	1	‖xm	‖xm	PUNCT
ma-17	387	2	−	−	PROPN
ma-17	388	1	x∗‖	x∗‖	X
ma-17	388	2	<	<	X
ma-17	388	3	r	r	X
ma-17	388	4	(	(	PUNCT
ma-17	388	5	4.10)and	4.10)and	NOUN
ma-17	388	6	‖xm+1	‖xm+1	PUNCT
ma-17	388	7	−	−	PROPN
ma-17	388	8	x∗‖	x∗‖	PROPN
ma-17	388	9	≤	≤	PROPN
ma-17	388	10	ψ2(‖xm	ψ2(‖xm	PUNCT
ma-17	388	11	−	−	PROPN
ma-17	388	12	x∗‖)‖xm	x∗‖)‖xm	PUNCT
ma-17	389	1	−	−	PROPN
ma-17	390	1	x∗‖	x∗‖	PUNCT
ma-17	390	2	≤	≤	NOUN
ma-17	391	1	‖xm	‖xm	PROPN
ma-17	391	2	−	−	PROPN
ma-17	391	3	x∗‖.	x∗‖.	PROPN
ma-17	391	4	(	(	PUNCT
ma-17	391	5	4.11)then	4.11)then	NUM
ma-17	391	6	,	,	PUNCT
ma-17	391	7	by	by	ADP
ma-17	391	8	the	the	DET
ma-17	391	9	estimation	estimation	NOUN
ma-17	391	10	‖xm+1	‖xm+1	PUNCT
ma-17	391	11	−	−	PROPN
ma-17	391	12	x∗‖	x∗‖	PROPN
ma-17	391	13	≤	≤	NOUN
ma-17	392	1	d‖xm	d‖xm	PROPN
ma-17	392	2	−	−	PROPN
ma-17	392	3	x∗‖	x∗‖	X
ma-17	392	4	<	<	X
ma-17	392	5	r	r	NOUN
ma-17	392	6	,	,	PUNCT
ma-17	392	7	(	(	PUNCT
ma-17	392	8	4.12)where	4.12)where	NUM
ma-17	392	9	d	d	X
ma-17	392	10	=	=	SYM
ma-17	392	11	ψ2(‖x0	ψ2(‖x0	PRON
ma-17	392	12	−	−	NUM
ma-17	392	13	x∗‖	x∗‖	PROPN
ma-17	392	14	)	)	PUNCT
ma-17	392	15	∈	∈	PROPN
ma-17	393	1	[	[	X
ma-17	393	2	0	0	NUM
ma-17	393	3	,	,	PUNCT
ma-17	393	4	1	1	NUM
ma-17	393	5	)	)	PUNCT
ma-17	393	6	,	,	PUNCT
ma-17	393	7	we	we	PRON
ma-17	393	8	get	get	VERB
ma-17	393	9	limm−→∞	limm−→∞	ADJ
ma-17	393	10	xm	xm	PROPN
ma-17	393	11	=	=	PUNCT
ma-17	393	12	x∗	x∗	PROPN
ma-17	393	13	and	and	CCONJ
ma-17	393	14	xm+1	xm+1	PROPN
ma-17	393	15	∈	∈	PROPN
ma-17	393	16	u(x∗	u(x∗	NOUN
ma-17	393	17	,	,	PUNCT
ma-17	393	18	r	r	NOUN
ma-17	393	19	)	)	PUNCT
ma-17	393	20	.	.	PUNCT
ma-17	394	1	�	�	PROPN
ma-17	394	2	next	next	ADV
ma-17	394	3	,	,	PUNCT
ma-17	394	4	we	we	PRON
ma-17	394	5	present	present	VERB
ma-17	394	6	a	a	DET
ma-17	394	7	uniqueness	uniqueness	NOUN
ma-17	394	8	result	result	NOUN
ma-17	394	9	.	.	PUNCT
ma-17	395	1	eur	eur	PROPN
ma-17	395	2	.	.	PUNCT
ma-17	396	1	j.	j.	PROPN
ma-17	396	2	math	math	PROPN
ma-17	396	3	.	.	PUNCT
ma-17	397	1	anal	anal	ADJ
ma-17	397	2	.	.	PUNCT
ma-17	398	1	1	1	NUM
ma-17	398	2	(	(	PUNCT
ma-17	398	3	2021	2021	NUM
ma-17	398	4	)	)	PUNCT
ma-17	398	5	81	81	NUM
ma-17	398	6	proposition	proposition	NOUN
ma-17	398	7	4.2	4.2	NUM
ma-17	398	8	.	.	PUNCT
ma-17	399	1	suppose	suppose	VERB
ma-17	399	2	:	:	PUNCT
ma-17	399	3	(	(	PUNCT
ma-17	399	4	i	i	NOUN
ma-17	399	5	)	)	PUNCT
ma-17	399	6	there	there	PRON
ma-17	399	7	exists	exist	VERB
ma-17	399	8	a	a	DET
ma-17	399	9	simple	simple	ADJ
ma-17	399	10	solution	solution	NOUN
ma-17	399	11	x∗	x∗	PROPN
ma-17	399	12	of	of	ADP
ma-17	399	13	equation	equation	NOUN
ma-17	399	14	f	f	X
ma-17	399	15	(	(	PUNCT
ma-17	399	16	x	x	X
ma-17	399	17	)	)	PUNCT
ma-17	399	18	=	=	SYM
ma-17	399	19	0	0	NUM
ma-17	399	20	(	(	PUNCT
ma-17	399	21	ii	ii	NOUN
ma-17	399	22	)	)	PUNCT
ma-17	399	23	there	there	PRON
ma-17	399	24	exists	exist	VERB
ma-17	399	25	r∗	r∗	PROPN
ma-17	399	26	≥	≥	PRON
ma-17	399	27	r	r	NOUN
ma-17	399	28	such	such	DET
ma-17	399	29	that	that	DET
ma-17	399	30	∫	∫	PROPN
ma-17	400	1	1	1	NUM
ma-17	400	2	0	0	NUM
ma-17	400	3	ψ0(θr	ψ0(θr	PROPN
ma-17	400	4	∗)dθ	∗)dθ	PROPN
ma-17	400	5	<	<	X
ma-17	400	6	1	1	NUM
ma-17	400	7	.	.	PUNCT
ma-17	401	1	(	(	PUNCT
ma-17	401	2	4.13	4.13	NUM
ma-17	401	3	)	)	PUNCT
ma-17	401	4	set	set	VERB
ma-17	401	5	ω2	ω2	PROPN
ma-17	401	6	=	=	SYM
ma-17	401	7	ω	ω	PROPN
ma-17	401	8	∩	∩	X
ma-17	401	9	u[x∗	u[x∗	PROPN
ma-17	401	10	,	,	PUNCT
ma-17	401	11	r∗	r∗	PROPN
ma-17	401	12	]	]	PUNCT
ma-17	401	13	.	.	PUNCT
ma-17	402	1	then	then	ADV
ma-17	402	2	,	,	PUNCT
ma-17	402	3	the	the	DET
ma-17	402	4	only	only	ADJ
ma-17	402	5	solution	solution	NOUN
ma-17	402	6	of	of	ADP
ma-17	402	7	equation	equation	NOUN
ma-17	402	8	f	f	X
ma-17	402	9	(	(	PUNCT
ma-17	402	10	x	x	X
ma-17	402	11	)	)	PUNCT
ma-17	402	12	=	=	SYM
ma-17	402	13	0	0	NUM
ma-17	402	14	in	in	ADP
ma-17	402	15	the	the	DET
ma-17	402	16	region	region	NOUN
ma-17	402	17	ω2	ω2	PROPN
ma-17	402	18	is	be	AUX
ma-17	402	19	x∗.	x∗.	ADJ
ma-17	402	20	proof	proof	NOUN
ma-17	402	21	.	.	PUNCT
ma-17	403	1	consider	consider	VERB
ma-17	403	2	x̃	x̃	PROPN
ma-17	403	3	∈	∈	PROPN
ma-17	403	4	ω1	ω1	PROPN
ma-17	403	5	with	with	ADP
ma-17	403	6	f	f	PROPN
ma-17	403	7	(	(	PUNCT
ma-17	403	8	x̃	x̃	PROPN
ma-17	403	9	)	)	PUNCT
ma-17	404	1	=	=	SYM
ma-17	404	2	0	0	X
ma-17	404	3	.	.	PUNCT
ma-17	405	1	set	set	VERB
ma-17	405	2	t	t	PROPN
ma-17	406	1	=	=	SYM
ma-17	406	2	∫	∫	PROPN
ma-17	406	3	1	1	NUM
ma-17	406	4	0	0	NUM
ma-17	406	5	f	f	PROPN
ma-17	406	6	′(x∗+	′(x∗+	PROPN
ma-17	406	7	θ(x̃	θ(x̃	PROPN
ma-17	407	1	−	−	PROPN
ma-17	407	2	x∗))dθ	x∗))dθ	NOUN
ma-17	407	3	.	.	PUNCT
ma-17	408	1	then	then	ADV
ma-17	408	2	,	,	PUNCT
ma-17	408	3	using	use	VERB
ma-17	408	4	(	(	PUNCT
ma-17	408	5	h1	h1	PROPN
ma-17	408	6	)	)	PUNCT
ma-17	408	7	and(4.13	and(4.13	NUM
ma-17	408	8	)	)	PUNCT
ma-17	408	9	,	,	PUNCT
ma-17	408	10	we	we	PRON
ma-17	408	11	get	get	VERB
ma-17	408	12	in	in	ADP
ma-17	408	13	turn	turn	NOUN
ma-17	408	14	that	that	SCONJ
ma-17	408	15	‖f	‖f	PRON
ma-17	408	16	′(x∗)−1(t	′(x∗)−1(t	VERB
ma-17	408	17	−	−	PROPN
ma-17	409	1	f	f	PROPN
ma-17	409	2	′(x∗))‖	′(x∗))‖	PROPN
ma-17	409	3	≤	≤	NUM
ma-17	409	4	∫	∫	PROPN
ma-17	409	5	1	1	NUM
ma-17	409	6	0	0	NUM
ma-17	409	7	ψ0(θ‖x̃	ψ0(θ‖x̃	PROPN
ma-17	409	8	−	−	PROPN
ma-17	409	9	x∗‖dθ	x∗‖dθ	PROPN
ma-17	409	10	≤	≤	NUM
ma-17	409	11	∫	∫	PROPN
ma-17	410	1	1	1	NUM
ma-17	410	2	0	0	NUM
ma-17	410	3	ψ0(θr	ψ0(θr	PROPN
ma-17	410	4	∗)dθ	∗)dθ	PROPN
ma-17	410	5	<	<	X
ma-17	410	6	1	1	NUM
ma-17	410	7	,	,	PUNCT
ma-17	410	8	so	so	ADV
ma-17	410	9	x̃	x̃	PROPN
ma-17	410	10	=	=	SYM
ma-17	410	11	x∗	x∗	PROPN
ma-17	410	12	,	,	PUNCT
ma-17	410	13	follows	follow	VERB
ma-17	410	14	by	by	ADP
ma-17	410	15	t−1	t−1	PROPN
ma-17	410	16	∈	∈	PROPN
ma-17	410	17	l(b1	l(b1	NOUN
ma-17	410	18	,	,	PUNCT
ma-17	410	19	b	b	NOUN
ma-17	410	20	)	)	PUNCT
ma-17	410	21	and	and	CCONJ
ma-17	410	22	t	t	PROPN
ma-17	410	23	(	(	PUNCT
ma-17	410	24	x̃	x̃	PROPN
ma-17	410	25	−	−	PROPN
ma-17	410	26	x∗	x∗	PROPN
ma-17	410	27	)	)	PUNCT
ma-17	411	1	=	=	SYM
ma-17	411	2	f	f	PROPN
ma-17	411	3	(	(	PUNCT
ma-17	411	4	x̃)−	x̃)−	PROPN
ma-17	411	5	f	f	PROPN
ma-17	411	6	(	(	PUNCT
ma-17	411	7	x∗	x∗	PROPN
ma-17	411	8	)	)	PUNCT
ma-17	411	9	=	=	PUNCT
ma-17	412	1	0−	0−	NUM
ma-17	412	2	0	0	NUM
ma-17	413	1	=	=	SYM
ma-17	413	2	0	0	X
ma-17	413	3	.	.	PUNCT
ma-17	413	4	�	�	PROPN
ma-17	413	5	5	5	NUM
ma-17	413	6	.	.	PUNCT
ma-17	413	7	numerical	numerical	ADJ
ma-17	413	8	experiments	experiment	NOUN
ma-17	413	9	we	we	PRON
ma-17	413	10	provide	provide	VERB
ma-17	413	11	some	some	DET
ma-17	413	12	examples	example	NOUN
ma-17	413	13	in	in	ADP
ma-17	413	14	this	this	DET
ma-17	413	15	section	section	NOUN
ma-17	413	16	.	.	PUNCT
ma-17	414	1	example	example	NOUN
ma-17	415	1	5.1	5.1	NUM
ma-17	415	2	.	.	PUNCT
ma-17	416	1	define	define	VERB
ma-17	416	2	function	function	NOUN
ma-17	416	3	q(t	q(t	PROPN
ma-17	416	4	)	)	PUNCT
ma-17	417	1	=	=	SYM
ma-17	417	2	ξ0	ξ0	PROPN
ma-17	417	3	t	t	NOUN
ma-17	417	4	+	+	CCONJ
ma-17	417	5	ξ1	ξ1	NOUN
ma-17	417	6	+	+	CCONJ
ma-17	417	7	ξ2	ξ2	ADJ
ma-17	417	8	sin	sin	NOUN
ma-17	417	9	ξ3	ξ3	PROPN
ma-17	417	10	t	t	PROPN
ma-17	417	11	,	,	PUNCT
ma-17	417	12	x0	x0	PROPN
ma-17	417	13	=	=	PUNCT
ma-17	417	14	0	0	PROPN
ma-17	417	15	,	,	PUNCT
ma-17	417	16	where	where	SCONJ
ma-17	417	17	ξj	ξj	NOUN
ma-17	417	18	,	,	PUNCT
ma-17	417	19	j	j	PROPN
ma-17	417	20	=	=	SYM
ma-17	417	21	0	0	NUM
ma-17	417	22	,	,	PUNCT
ma-17	417	23	1	1	NUM
ma-17	417	24	,	,	PUNCT
ma-17	417	25	2	2	NUM
ma-17	417	26	,	,	PUNCT
ma-17	417	27	3	3	NUM
ma-17	417	28	are	be	AUX
ma-17	417	29	parameters	parameter	NOUN
ma-17	417	30	.	.	PUNCT
ma-17	418	1	choose	choose	VERB
ma-17	418	2	p0(t	p0(t	NOUN
ma-17	418	3	)	)	PUNCT
ma-17	418	4	=	=	SYM
ma-17	418	5	l0	l0	PROPN
ma-17	418	6	t	t	PROPN
ma-17	418	7	and	and	CCONJ
ma-17	418	8	p	p	PROPN
ma-17	418	9	(	(	PUNCT
ma-17	418	10	t	t	PROPN
ma-17	418	11	)	)	PUNCT
ma-17	418	12	=	=	SYM
ma-17	419	1	lt	lt	PROPN
ma-17	419	2	.	.	PROPN
ma-17	419	3	notice	notice	VERB
ma-17	419	4	that	that	SCONJ
ma-17	419	5	l0	l0	PROPN
ma-17	419	6	and	and	CCONJ
ma-17	419	7	l	l	NOUN
ma-17	419	8	are	be	AUX
ma-17	419	9	the	the	DET
ma-17	419	10	center	center	ADJ
ma-17	419	11	lipschitz	lipschitz	NOUN
ma-17	419	12	and	and	CCONJ
ma-17	419	13	lipschitz	lipschitz	NOUN
ma-17	419	14	constants	constant	NOUN
ma-17	419	15	,	,	PUNCT
ma-17	419	16	respectively	respectively	ADV
ma-17	419	17	.	.	PUNCT
ma-17	420	1	then	then	ADV
ma-17	420	2	,	,	PUNCT
ma-17	420	3	from	from	ADP
ma-17	420	4	the	the	DET
ma-17	420	5	graph	graph	NOUN
ma-17	420	6	of	of	ADP
ma-17	420	7	q(t	q(t	NOUN
ma-17	420	8	)	)	PUNCT
ma-17	420	9	clearly	clearly	ADV
ma-17	420	10	for	for	ADP
ma-17	420	11	ξ3	ξ3	PROPN
ma-17	420	12	large	large	ADJ
ma-17	420	13	and	and	CCONJ
ma-17	420	14	ξ2	ξ2	ADJ
ma-17	420	15	small	small	ADJ
ma-17	420	16	,	,	PUNCT
ma-17	420	17	l0l	l0l	PROPN
ma-17	420	18	can	can	AUX
ma-17	420	19	be	be	AUX
ma-17	420	20	small	small	ADJ
ma-17	420	21	(	(	PUNCT
ma-17	420	22	arbitrarily	arbitrarily	ADV
ma-17	420	23	)	)	PUNCT
ma-17	420	24	.	.	PUNCT
ma-17	421	1	notice	notice	VERB
ma-17	421	2	that	that	SCONJ
ma-17	421	3	l0	l0	NOUN
ma-17	422	1	l	l	NOUN
ma-17	422	2	−→	−→	NOUN
ma-17	422	3	0	0	NUM
ma-17	422	4	.	.	PUNCT
ma-17	422	5	example	example	NOUN
ma-17	422	6	5.2	5.2	NUM
ma-17	422	7	.	.	PUNCT
ma-17	423	1	let	let	VERB
ma-17	423	2	b	b	NOUN
ma-17	423	3	=	=	SYM
ma-17	423	4	b1	b1	PROPN
ma-17	423	5	=	=	SYM
ma-17	423	6	c[0	c[0	PROPN
ma-17	423	7	,	,	PUNCT
ma-17	423	8	1	1	NUM
ma-17	423	9	]	]	PUNCT
ma-17	423	10	and	and	CCONJ
ma-17	423	11	ω	ω	NUM
ma-17	423	12	=	=	SYM
ma-17	423	13	u[0	u[0	PROPN
ma-17	423	14	,	,	PUNCT
ma-17	423	15	1	1	NUM
ma-17	423	16	]	]	PUNCT
ma-17	423	17	.	.	PUNCT
ma-17	424	1	it	it	PRON
ma-17	424	2	is	be	AUX
ma-17	424	3	well	well	ADV
ma-17	424	4	known	know	VERB
ma-17	424	5	that	that	SCONJ
ma-17	424	6	the	the	DET
ma-17	424	7	boundary	boundary	ADJ
ma-17	424	8	value	value	NOUN
ma-17	424	9	problem	problem	NOUN
ma-17	424	10	[	[	X
ma-17	424	11	16	16	NUM
ma-17	424	12	]	]	PUNCT
ma-17	424	13	.	.	PUNCT
ma-17	425	1	ς(0	ς(0	PROPN
ma-17	425	2	)	)	PUNCT
ma-17	425	3	=	=	SYM
ma-17	425	4	0	0	NUM
ma-17	425	5	,	,	PUNCT
ma-17	425	6	(	(	PUNCT
ma-17	425	7	1	1	X
ma-17	425	8	)	)	PUNCT
ma-17	425	9	=	=	SYM
ma-17	425	10	1	1	NUM
ma-17	425	11	,	,	PUNCT
ma-17	425	12	ς	ς	PROPN
ma-17	425	13	′′	′′	PROPN
ma-17	425	14	=	=	PUNCT
ma-17	425	15	−ς	−ς	PROPN
ma-17	425	16	−	−	PROPN
ma-17	425	17	σς2	σς2	NOUN
ma-17	425	18	can	can	AUX
ma-17	425	19	be	be	AUX
ma-17	425	20	given	give	VERB
ma-17	425	21	as	as	ADP
ma-17	425	22	a	a	DET
ma-17	425	23	hammerstein	hammerstein	NOUN
ma-17	425	24	-	-	PUNCT
ma-17	425	25	like	like	ADJ
ma-17	425	26	nonlinear	nonlinear	ADJ
ma-17	425	27	integral	integral	ADJ
ma-17	425	28	equation	equation	NOUN
ma-17	425	29	ς(s	ς(s	PROPN
ma-17	425	30	)	)	PUNCT
ma-17	426	1	=	=	SYM
ma-17	426	2	s	s	PART
ma-17	427	1	+	+	NUM
ma-17	427	2	∫	∫	PROPN
ma-17	427	3	1	1	NUM
ma-17	427	4	0	0	NUM
ma-17	427	5	q(s	q(s	X
ma-17	427	6	,	,	PUNCT
ma-17	427	7	t)(ς3(t	t)(ς3(t	PRON
ma-17	427	8	)	)	PUNCT
ma-17	427	9	+	+	NUM
ma-17	427	10	σς2(t))dt	σς2(t))dt	NOUN
ma-17	427	11	where	where	SCONJ
ma-17	427	12	σ	σ	PROPN
ma-17	427	13	is	be	AUX
ma-17	427	14	a	a	DET
ma-17	427	15	parameter	parameter	NOUN
ma-17	427	16	.	.	PUNCT
ma-17	428	1	then	then	ADV
ma-17	428	2	,	,	PUNCT
ma-17	428	3	define	define	VERB
ma-17	428	4	f	f	X
ma-17	428	5	:	:	PUNCT
ma-17	428	6	ω	ω	NUM
ma-17	428	7	−→	−→	NOUN
ma-17	428	8	b1	b1	NOUN
ma-17	428	9	by	by	ADP
ma-17	428	10	[	[	X
ma-17	428	11	f	f	X
ma-17	428	12	(	(	PUNCT
ma-17	428	13	x)](s	x)](s	PROPN
ma-17	428	14	)	)	PUNCT
ma-17	429	1	=	=	PUNCT
ma-17	430	1	x(s)−	x(s)−	PROPN
ma-17	430	2	s	s	PART
ma-17	430	3	−	−	NOUN
ma-17	430	4	∫	∫	PROPN
ma-17	430	5	1	1	NUM
ma-17	430	6	0	0	NUM
ma-17	430	7	q(s	q(s	PROPN
ma-17	430	8	,	,	PUNCT
ma-17	430	9	t)(x3(t	t)(x3(t	NOUN
ma-17	430	10	)	)	PUNCT
ma-17	430	11	+	+	NUM
ma-17	430	12	σx2(t))dt	σx2(t))dt	NOUN
ma-17	430	13	.	.	PUNCT
ma-17	431	1	eur	eur	PROPN
ma-17	431	2	.	.	PUNCT
ma-17	432	1	j.	j.	PROPN
ma-17	432	2	math	math	PROPN
ma-17	432	3	.	.	PUNCT
ma-17	433	1	anal	anal	ADJ
ma-17	433	2	.	.	PUNCT
ma-17	434	1	1	1	NUM
ma-17	434	2	(	(	PUNCT
ma-17	434	3	2021	2021	NUM
ma-17	434	4	)	)	PUNCT
ma-17	434	5	82	82	NUM
ma-17	434	6	choose	choose	VERB
ma-17	434	7	ς0(s	ς0(s	NOUN
ma-17	434	8	)	)	PUNCT
ma-17	434	9	=	=	SYM
ma-17	434	10	s	s	PROPN
ma-17	434	11	and	and	CCONJ
ma-17	434	12	ω	ω	NUM
ma-17	434	13	=	=	SYM
ma-17	434	14	u(ς0	u(ς0	NOUN
ma-17	434	15	,	,	PUNCT
ma-17	434	16	ρ0	ρ0	PROPN
ma-17	434	17	)	)	PUNCT
ma-17	434	18	.	.	PUNCT
ma-17	435	1	then	then	ADV
ma-17	435	2	,	,	PUNCT
ma-17	435	3	clearly	clearly	ADV
ma-17	435	4	u(ς0	u(ς0	ADJ
ma-17	435	5	,	,	PUNCT
ma-17	435	6	ρ0	ρ0	PROPN
ma-17	435	7	)	)	PUNCT
ma-17	435	8	⊂	⊂	PROPN
ma-17	436	1	u(0	u(0	PROPN
ma-17	436	2	,	,	PUNCT
ma-17	436	3	ρ0	ρ0	PROPN
ma-17	436	4	+	+	PROPN
ma-17	436	5	1	1	NUM
ma-17	436	6	)	)	PUNCT
ma-17	436	7	,	,	PUNCT
ma-17	436	8	since	since	SCONJ
ma-17	436	9	‖ς0‖	‖ς0‖	NOUN
ma-17	436	10	=	=	SYM
ma-17	436	11	1	1	X
ma-17	436	12	.	.	PUNCT
ma-17	436	13	suppose	suppose	VERB
ma-17	436	14	2σ	2σ	PRON
ma-17	436	15	<	<	X
ma-17	436	16	5	5	X
ma-17	436	17	.	.	PUNCT
ma-17	437	1	then	then	ADV
ma-17	437	2	,	,	PUNCT
ma-17	437	3	conditions	condition	NOUN
ma-17	437	4	(	(	PUNCT
ma-17	437	5	a	a	X
ma-17	437	6	)	)	PUNCT
ma-17	437	7	are	be	AUX
ma-17	437	8	satisfied	satisfied	ADJ
ma-17	437	9	for	for	ADP
ma-17	437	10	l0	l0	NOUN
ma-17	437	11	=	=	PUNCT
ma-17	437	12	2σ	2σ	NOUN
ma-17	438	1	+	+	CCONJ
ma-17	438	2	3ρ0	3ρ0	NUM
ma-17	438	3	+	+	CCONJ
ma-17	438	4	6	6	NUM
ma-17	438	5	8	8	NUM
ma-17	438	6	,	,	PUNCT
ma-17	438	7	l	l	NOUN
ma-17	438	8	=	=	PUNCT
ma-17	438	9	σ	σ	NOUN
ma-17	439	1	+	+	NUM
ma-17	439	2	6ρ0	6ρ0	NUM
ma-17	439	3	+	+	CCONJ
ma-17	439	4	3	3	NUM
ma-17	439	5	4	4	NUM
ma-17	439	6	,	,	PUNCT
ma-17	439	7	and	and	CCONJ
ma-17	439	8	η	η	PROPN
ma-17	439	9	=	=	SYM
ma-17	439	10	1+σ	1+σ	NUM
ma-17	439	11	5−2σ	5−2σ	NUM
ma-17	439	12	.	.	PUNCT
ma-17	440	1	notice	notice	VERB
ma-17	440	2	that	that	SCONJ
ma-17	440	3	l0	l0	PROPN
ma-17	440	4	<	<	X
ma-17	440	5	l.	l.	PROPN
ma-17	440	6	in	in	ADP
ma-17	440	7	the	the	DET
ma-17	440	8	last	last	ADJ
ma-17	440	9	two	two	NUM
ma-17	440	10	examples	example	NOUN
ma-17	440	11	we	we	PRON
ma-17	440	12	consider	consider	VERB
ma-17	440	13	traub	traub	PROPN
ma-17	440	14	’s	’s	PART
ma-17	440	15	method	method	NOUN
ma-17	440	16	(	(	PUNCT
ma-17	440	17	1.3	1.3	NUM
ma-17	440	18	)	)	PUNCT
ma-17	440	19	.	.	PUNCT
ma-17	441	1	so	so	ADV
ma-17	441	2	,	,	PUNCT
ma-17	441	3	we	we	PRON
ma-17	441	4	take	take	VERB
ma-17	441	5	a(x	a(x	NOUN
ma-17	441	6	,	,	PUNCT
ma-17	441	7	y	y	NOUN
ma-17	441	8	)	)	PUNCT
ma-17	441	9	=	=	VERB
ma-17	442	1	i	i	PROPN
ma-17	442	2	and	and	CCONJ
ma-17	442	3	h(s	h(s	PROPN
ma-17	442	4	,	,	PUNCT
ma-17	442	5	t	t	PROPN
ma-17	442	6	)	)	PUNCT
ma-17	442	7	=	=	SYM
ma-17	442	8	0	0	X
ma-17	442	9	.	.	PUNCT
ma-17	442	10	example	example	NOUN
ma-17	442	11	5.3	5.3	NUM
ma-17	442	12	.	.	PUNCT
ma-17	443	1	consider	consider	VERB
ma-17	443	2	the	the	DET
ma-17	443	3	motion	motion	NOUN
ma-17	443	4	system	system	NOUN
ma-17	443	5	g′1(v1	g′1(v1	NOUN
ma-17	443	6	)	)	PUNCT
ma-17	443	7	=	=	SYM
ma-17	443	8	ev1	ev1	PROPN
ma-17	443	9	,	,	PUNCT
ma-17	443	10	g′2(y	g′2(y	PROPN
ma-17	443	11	)	)	PUNCT
ma-17	443	12	=	=	PUNCT
ma-17	443	13	(	(	PUNCT
ma-17	443	14	e	e	X
ma-17	443	15	−	−	PROPN
ma-17	443	16	1)v2	1)v2	PROPN
ma-17	443	17	+	+	CCONJ
ma-17	443	18	1	1	NUM
ma-17	443	19	,	,	PUNCT
ma-17	443	20	g′3(v3	g′3(v3	NOUN
ma-17	443	21	)	)	PUNCT
ma-17	443	22	=	=	SYM
ma-17	443	23	1	1	NUM
ma-17	443	24	with	with	ADP
ma-17	443	25	g1(0	g1(0	NOUN
ma-17	443	26	)	)	PUNCT
ma-17	443	27	=	=	SYM
ma-17	443	28	g2(0	g2(0	NOUN
ma-17	443	29	)	)	PUNCT
ma-17	443	30	=	=	SYM
ma-17	443	31	g3(0	g3(0	PROPN
ma-17	443	32	)	)	PUNCT
ma-17	443	33	=	=	SYM
ma-17	444	1	0	0	X
ma-17	444	2	.	.	PUNCT
ma-17	445	1	let	let	VERB
ma-17	445	2	g	g	PROPN
ma-17	445	3	=	=	SYM
ma-17	445	4	(	(	PUNCT
ma-17	445	5	g1	g1	PROPN
ma-17	445	6	,	,	PUNCT
ma-17	445	7	g2	g2	PROPN
ma-17	445	8	,	,	PUNCT
ma-17	445	9	g3	g3	PROPN
ma-17	445	10	)	)	PUNCT
ma-17	445	11	.	.	PUNCT
ma-17	446	1	let	let	VERB
ma-17	446	2	b	b	NOUN
ma-17	446	3	=	=	SYM
ma-17	446	4	b1	b1	PROPN
ma-17	446	5	=	=	SYM
ma-17	446	6	r3,ω	r3,ω	PROPN
ma-17	446	7	=	=	PROPN
ma-17	446	8	ū(0	ū(0	PROPN
ma-17	446	9	,	,	PUNCT
ma-17	446	10	1	1	NUM
ma-17	446	11	)	)	PUNCT
ma-17	446	12	,	,	PUNCT
ma-17	446	13	x∗	x∗	PROPN
ma-17	446	14	=	=	SYM
ma-17	446	15	(	(	PUNCT
ma-17	446	16	0	0	NUM
ma-17	446	17	,	,	PUNCT
ma-17	446	18	0	0	NUM
ma-17	446	19	,	,	PUNCT
ma-17	446	20	0)t	0)t	INTJ
ma-17	446	21	.	.	PUNCT
ma-17	447	1	define	define	VERB
ma-17	447	2	function	function	NOUN
ma-17	447	3	g	g	NOUN
ma-17	447	4	on	on	ADP
ma-17	447	5	ω	ω	PROPN
ma-17	447	6	for	for	ADP
ma-17	447	7	v	v	NOUN
ma-17	447	8	=	=	SYM
ma-17	447	9	(	(	PUNCT
ma-17	447	10	v1	v1	PROPN
ma-17	447	11	,	,	PUNCT
ma-17	447	12	v2	v2	PROPN
ma-17	447	13	,	,	PUNCT
ma-17	447	14	v3	v3	PROPN
ma-17	447	15	)	)	PUNCT
ma-17	447	16	t	t	PROPN
ma-17	447	17	by	by	ADP
ma-17	447	18	g(v	g(v	NOUN
ma-17	447	19	)	)	PUNCT
ma-17	447	20	=	=	SYM
ma-17	447	21	(	(	PUNCT
ma-17	447	22	ev1	ev1	PROPN
ma-17	448	1	−	−	PROPN
ma-17	448	2	1	1	NUM
ma-17	448	3	,	,	PUNCT
ma-17	448	4	e	e	NOUN
ma-17	448	5	−	−	PROPN
ma-17	448	6	1	1	NUM
ma-17	448	7	2	2	NUM
ma-17	448	8	v22	v22	NOUN
ma-17	448	9	+	+	CCONJ
ma-17	448	10	v2	v2	PROPN
ma-17	448	11	,	,	PUNCT
ma-17	448	12	v3	v3	PROPN
ma-17	448	13	)	)	PUNCT
ma-17	448	14	t	t	PROPN
ma-17	448	15	.	.	PUNCT
ma-17	449	1	then	then	ADV
ma-17	449	2	,	,	PUNCT
ma-17	449	3	we	we	PRON
ma-17	449	4	get	get	VERB
ma-17	449	5	g′(v	g′(v	PROPN
ma-17	449	6	)	)	PUNCT
ma-17	450	1	=	=	SYM
ma-17	450	2			NOUN
ma-17	450	3	ex	ex	X
ma-17	450	4	0	0	NUM
ma-17	450	5	0	0	NUM
ma-17	450	6	0	0	NUM
ma-17	451	1	(	(	PUNCT
ma-17	451	2	e	e	X
ma-17	451	3	−	−	PROPN
ma-17	451	4	1)v2	1)v2	PROPN
ma-17	451	5	+	+	CCONJ
ma-17	451	6	1	1	NUM
ma-17	451	7	0	0	NUM
ma-17	451	8	0	0	NUM
ma-17	451	9	0	0	NUM
ma-17	451	10	1	1	NUM
ma-17	451	11			NOUN
ma-17	451	12	,	,	PUNCT
ma-17	451	13	so	so	CCONJ
ma-17	451	14	ψ0(t	ψ0(t	NOUN
ma-17	451	15	)	)	PUNCT
ma-17	452	1	=	=	SYM
ma-17	452	2	(	(	PUNCT
ma-17	452	3	e−	e−	PROPN
ma-17	452	4	1)t	1)t	NOUN
ma-17	452	5	,	,	PUNCT
ma-17	452	6	ψ(t	ψ(t	PROPN
ma-17	452	7	)	)	PUNCT
ma-17	452	8	=	=	PUNCT
ma-17	453	1	e	e	X
ma-17	453	2	1	1	NUM
ma-17	453	3	e−1	e−1	PROPN
ma-17	453	4	t	t	PROPN
ma-17	453	5	,	,	PUNCT
ma-17	453	6	ω(t	ω(t	NOUN
ma-17	453	7	)	)	PUNCT
ma-17	453	8	=	=	PUNCT
ma-17	453	9	e	e	X
ma-17	453	10	1	1	NUM
ma-17	453	11	e−1	e−1	PROPN
ma-17	453	12	and	and	CCONJ
ma-17	453	13	k	k	PROPN
ma-17	453	14	=	=	PUNCT
ma-17	453	15	e	e	PROPN
ma-17	453	16	is	be	AUX
ma-17	453	17	the	the	DET
ma-17	453	18	lipschitz	lipschitz	NOUN
ma-17	453	19	constant	constant	ADJ
ma-17	453	20	on	on	ADP
ma-17	453	21	ω	ω	NUM
ma-17	453	22	and	and	CCONJ
ma-17	453	23	ρt	ρt	PROPN
ma-17	453	24	is	be	AUX
ma-17	453	25	given	give	VERB
ma-17	453	26	in	in	ADP
ma-17	453	27	[	[	X
ma-17	453	28	29,35	29,35	NOUN
ma-17	453	29	]	]	X
ma-17	453	30	.	.	PUNCT
ma-17	454	1	then	then	ADV
ma-17	454	2	,	,	PUNCT
ma-17	454	3	the	the	DET
ma-17	454	4	radii	radius	NOUN
ma-17	454	5	:	:	PUNCT
ma-17	454	6	r1	r1	PROPN
ma-17	454	7	=	=	PUNCT
ma-17	454	8	0.3827	0.3827	NUM
ma-17	454	9	=	=	PUNCT
ma-17	454	10	ρa	ρa	NOUN
ma-17	455	1	=	=	SYM
ma-17	455	2	2	2	NUM
ma-17	455	3	2(e	2(e	NUM
ma-17	455	4	−	−	NOUN
ma-17	455	5	1	1	NUM
ma-17	455	6	)	)	PUNCT
ma-17	455	7	+	+	CCONJ
ma-17	455	8	e	e	NOUN
ma-17	455	9	1	1	NUM
ma-17	455	10	e−1	e−1	PROPN
ma-17	455	11	,	,	PUNCT
ma-17	455	12	r2	r2	PROPN
ma-17	455	13	=	=	PUNCT
ma-17	456	1	0.3061	0.3061	NUM
ma-17	457	1	=	=	SYM
ma-17	457	2	r	r	NOUN
ma-17	457	3	,	,	PUNCT
ma-17	457	4	ρt	ρt	NOUN
ma-17	457	5	=	=	SYM
ma-17	457	6	2	2	NUM
ma-17	457	7	3k	3k	NOUN
ma-17	457	8	=	=	SYM
ma-17	457	9	0.2453	0.2453	NUM
ma-17	457	10	.	.	PUNCT
ma-17	457	11	example	example	NOUN
ma-17	457	12	5.4	5.4	NUM
ma-17	457	13	.	.	PUNCT
ma-17	458	1	consider	consider	VERB
ma-17	458	2	b	b	NOUN
ma-17	458	3	=	=	SYM
ma-17	458	4	b1	b1	NOUN
ma-17	458	5	=	=	SYM
ma-17	458	6	c[0	c[0	PROPN
ma-17	458	7	,	,	PUNCT
ma-17	458	8	1	1	NUM
ma-17	458	9	]	]	PUNCT
ma-17	458	10	,	,	PUNCT
ma-17	458	11	ω	ω	PROPN
ma-17	458	12	=	=	SYM
ma-17	458	13	u(0	u(0	PROPN
ma-17	458	14	,	,	PUNCT
ma-17	458	15	1	1	NUM
ma-17	458	16	)	)	PUNCT
ma-17	458	17	and	and	CCONJ
ma-17	458	18	q	q	NOUN
ma-17	458	19	:	:	PUNCT
ma-17	458	20	ω	ω	NUM
ma-17	458	21	−→	−→	NOUN
ma-17	458	22	b1	b1	NOUN
ma-17	458	23	defined	define	VERB
ma-17	458	24	by	by	ADP
ma-17	458	25	q(ς)(x	q(ς)(x	NOUN
ma-17	458	26	)	)	PUNCT
ma-17	458	27	=	=	SYM
ma-17	459	1	%	%	NOUN
ma-17	459	2	(	(	PUNCT
ma-17	459	3	x)−	x)−	PROPN
ma-17	459	4	5	5	NUM
ma-17	459	5	∫	∫	PROPN
ma-17	459	6	1	1	NUM
ma-17	459	7	0	0	NUM
ma-17	459	8	xθς(θ)3dθ	xθς(θ)3dθ	X
ma-17	459	9	.	.	PUNCT
ma-17	460	1	(	(	PUNCT
ma-17	460	2	5.1	5.1	NUM
ma-17	460	3	)	)	PUNCT
ma-17	460	4	we	we	PRON
ma-17	460	5	obtain	obtain	VERB
ma-17	460	6	q′(ς(ξ))(x	q′(ς(ξ))(x	NOUN
ma-17	460	7	)	)	PUNCT
ma-17	460	8	=	=	PUNCT
ma-17	460	9	ξ(x)−	ξ(x)−	PROPN
ma-17	460	10	15	15	NUM
ma-17	460	11	∫	∫	NOUN
ma-17	460	12	1	1	NUM
ma-17	460	13	0	0	NUM
ma-17	461	1	xθς(θ)2ξ(θ)dθ	xθς(θ)2ξ(θ)dθ	PROPN
ma-17	461	2	,	,	PUNCT
ma-17	461	3	for	for	ADP
ma-17	461	4	each	each	DET
ma-17	461	5	ξ	ξ	PROPN
ma-17	461	6	∈	∈	PROPN
ma-17	461	7	d.	d.	NOUN
ma-17	461	8	then	then	ADV
ma-17	461	9	,	,	PUNCT
ma-17	461	10	since	since	SCONJ
ma-17	461	11	x∗	x∗	PROPN
ma-17	461	12	=	=	SYM
ma-17	461	13	0	0	NUM
ma-17	461	14	,	,	PUNCT
ma-17	461	15	we	we	PRON
ma-17	461	16	set	set	VERB
ma-17	461	17	ψ0(t	ψ0(t	NOUN
ma-17	461	18	)	)	PUNCT
ma-17	461	19	=	=	NOUN
ma-17	461	20	7.5	7.5	NUM
ma-17	461	21	t	t	NOUN
ma-17	461	22	,	,	PUNCT
ma-17	461	23	ψ(t	ψ(t	PROPN
ma-17	461	24	)	)	PUNCT
ma-17	461	25	=	=	SYM
ma-17	461	26	15	15	NUM
ma-17	461	27	t	t	NOUN
ma-17	461	28	,	,	PUNCT
ma-17	461	29	ω(t	ω(t	NOUN
ma-17	461	30	)	)	PUNCT
ma-17	461	31	=	=	SYM
ma-17	461	32	15	15	NUM
ma-17	461	33	and	and	CCONJ
ma-17	461	34	k	k	NOUN
ma-17	462	1	=	=	NOUN
ma-17	462	2	15	15	NUM
ma-17	462	3	.	.	PUNCT
ma-17	463	1	then	then	ADV
ma-17	463	2	,	,	PUNCT
ma-17	463	3	the	the	DET
ma-17	463	4	radii	radius	NOUN
ma-17	463	5	:	:	PUNCT
ma-17	463	6	r1	r1	NOUN
ma-17	463	7	=	=	SYM
ma-17	463	8	0.0667	0.0667	NUM
ma-17	463	9	=	=	SYM
ma-17	463	10	ρa	ρa	NOUN
ma-17	463	11	=	=	SYM
ma-17	463	12	2	2	NUM
ma-17	463	13	2(7.5	2(7.5	NUM
ma-17	463	14	)	)	PUNCT
ma-17	464	1	+	+	CCONJ
ma-17	464	2	15	15	NUM
ma-17	464	3	,	,	PUNCT
ma-17	464	4	r2	r2	NOUN
ma-17	464	5	=	=	NOUN
ma-17	464	6	0.0290	0.0290	NUM
ma-17	464	7	=	=	SYM
ma-17	464	8	r	r	NOUN
ma-17	464	9	,	,	PUNCT
ma-17	464	10	ρt	ρt	NOUN
ma-17	464	11	=	=	SYM
ma-17	464	12	2	2	NUM
ma-17	464	13	3k	3k	NOUN
ma-17	464	14	=	=	SYM
ma-17	464	15	0.0444	0.0444	NUM
ma-17	464	16	.	.	PUNCT
ma-17	464	17	notice	notice	VERB
ma-17	464	18	that	that	SCONJ
ma-17	464	19	in	in	ADP
ma-17	464	20	the	the	DET
ma-17	464	21	last	last	ADJ
ma-17	464	22	two	two	NUM
ma-17	464	23	examples	example	NOUN
ma-17	464	24	ρa	ρa	PRON
ma-17	464	25	is	be	AUX
ma-17	464	26	the	the	DET
ma-17	464	27	radius	radius	NOUN
ma-17	464	28	given	give	VERB
ma-17	464	29	by	by	ADP
ma-17	464	30	us	we	PRON
ma-17	464	31	in	in	ADP
ma-17	464	32	[	[	X
ma-17	464	33	1–7	1–7	X
ma-17	464	34	]	]	PUNCT
ma-17	464	35	and	and	CCONJ
ma-17	464	36	is	be	AUX
ma-17	464	37	the	the	DET
ma-17	464	38	largest	large	ADJ
ma-17	464	39	.	.	PUNCT
ma-17	465	1	eur	eur	PROPN
ma-17	465	2	.	.	PUNCT
ma-17	466	1	j.	j.	PROPN
ma-17	466	2	math	math	PROPN
ma-17	466	3	.	.	PUNCT
ma-17	467	1	anal	anal	ADJ
ma-17	467	2	.	.	PUNCT
ma-17	468	1	1	1	NUM
ma-17	468	2	(	(	PUNCT
ma-17	468	3	2021	2021	NUM
ma-17	468	4	)	)	PUNCT
ma-17	468	5	836	836	NUM
ma-17	468	6	.	.	PUNCT
ma-17	469	1	conclusion	conclusion	NOUN
ma-17	469	2	we	we	PRON
ma-17	469	3	have	have	AUX
ma-17	469	4	provided	provide	VERB
ma-17	469	5	sufficient	sufficient	ADJ
ma-17	469	6	convergence	convergence	NOUN
ma-17	469	7	criterion	criterion	NOUN
ma-17	469	8	for	for	ADP
ma-17	469	9	the	the	DET
ma-17	469	10	semi	semi	ADJ
ma-17	469	11	-	-	ADJ
ma-17	469	12	local	local	ADJ
ma-17	469	13	and	and	CCONJ
ma-17	469	14	local	local	ADJ
ma-17	469	15	convergence	convergence	NOUN
ma-17	469	16	oftwo	oftwo	VERB
ma-17	469	17	-	-	PUNCT
ma-17	469	18	step	step	NOUN
ma-17	469	19	methods	method	NOUN
ma-17	469	20	.	.	PUNCT
ma-17	470	1	upon	upon	SCONJ
ma-17	470	2	specializing	specialize	VERB
ma-17	470	3	the	the	DET
ma-17	470	4	parameters	parameter	NOUN
ma-17	470	5	involved	involve	VERB
ma-17	470	6	we	we	PRON
ma-17	470	7	show	show	VERB
ma-17	470	8	that	that	SCONJ
ma-17	470	9	although	although	SCONJ
ma-17	470	10	our	our	PRON
ma-17	470	11	majorizingsequence	majorizingsequence	NOUN
ma-17	470	12	is	be	AUX
ma-17	470	13	more	more	ADV
ma-17	470	14	general	general	ADJ
ma-17	470	15	than	than	ADP
ma-17	470	16	earlier	early	ADJ
ma-17	470	17	ones	one	NOUN
ma-17	470	18	:	:	PUNCT
ma-17	470	19	convergence	convergence	NOUN
ma-17	470	20	criteria	criterion	NOUN
ma-17	470	21	are	be	AUX
ma-17	470	22	weaker	weak	ADJ
ma-17	470	23	(	(	PUNCT
ma-17	470	24	i.e.	i.e.	X
ma-17	470	25	,	,	PUNCT
ma-17	470	26	the	the	DET
ma-17	470	27	utility	utility	NOUN
ma-17	470	28	of	of	ADP
ma-17	470	29	themethods	themethod	NOUN
ma-17	470	30	is	be	AUX
ma-17	470	31	extended	extend	VERB
ma-17	470	32	)	)	PUNCT
ma-17	470	33	;	;	PUNCT
ma-17	470	34	the	the	DET
ma-17	470	35	upper	upper	ADJ
ma-17	470	36	error	error	NOUN
ma-17	470	37	estimates	estimate	NOUN
ma-17	470	38	are	be	AUX
ma-17	470	39	more	more	ADV
ma-17	470	40	accurate	accurate	ADJ
ma-17	470	41	(	(	PUNCT
ma-17	470	42	i.e.	i.e.	X
ma-17	470	43	at	at	ADV
ma-17	470	44	least	least	ADJ
ma-17	470	45	as	as	ADP
ma-17	470	46	few	few	ADJ
ma-17	470	47	iterates	iterate	NOUN
ma-17	470	48	arerequired	arerequire	VERB
ma-17	470	49	to	to	PART
ma-17	470	50	achieve	achieve	VERB
ma-17	470	51	a	a	DET
ma-17	470	52	predecided	predecided	ADJ
ma-17	470	53	error	error	NOUN
ma-17	470	54	tolerance	tolerance	NOUN
ma-17	470	55	)	)	PUNCT
ma-17	470	56	and	and	CCONJ
ma-17	470	57	we	we	PRON
ma-17	470	58	have	have	VERB
ma-17	470	59	an	an	DET
ma-17	470	60	at	at	ADV
ma-17	470	61	least	least	ADJ
ma-17	470	62	as	as	ADP
ma-17	470	63	large	large	ADJ
ma-17	470	64	ball	ball	NOUN
ma-17	470	65	containingthe	containingthe	NOUN
ma-17	470	66	solution	solution	NOUN
ma-17	470	67	.	.	PUNCT
ma-17	471	1	these	these	DET
ma-17	471	2	benefits	benefit	NOUN
ma-17	471	3	are	be	AUX
ma-17	471	4	obtained	obtain	VERB
ma-17	471	5	without	without	ADP
ma-17	471	6	additional	additional	ADJ
ma-17	471	7	hypotheses	hypothesis	NOUN
ma-17	471	8	.	.	PUNCT
ma-17	472	1	according	accord	VERB
ma-17	472	2	to	to	ADP
ma-17	472	3	our	our	PRON
ma-17	472	4	newtechnique	newtechnique	NOUN
ma-17	472	5	we	we	PRON
ma-17	472	6	locate	locate	VERB
ma-17	472	7	a	a	DET
ma-17	472	8	more	more	ADV
ma-17	472	9	accurate	accurate	ADJ
ma-17	472	10	domain	domain	NOUN
ma-17	472	11	than	than	SCONJ
ma-17	472	12	before	before	ADP
ma-17	472	13	containing	contain	VERB
ma-17	472	14	the	the	DET
ma-17	472	15	iterates	iterate	NOUN
ma-17	472	16	resulting	result	VERB
ma-17	472	17	to	to	ADP
ma-17	472	18	moreaccurate	moreaccurate	NOUN
ma-17	472	19	(	(	PUNCT
ma-17	472	20	at	at	ADV
ma-17	472	21	least	least	ADJ
ma-17	472	22	as	as	ADP
ma-17	472	23	small	small	ADJ
ma-17	472	24	)	)	PUNCT
ma-17	472	25	lipschitz	lipschitz	NOUN
ma-17	472	26	condition.our	condition.our	NOUN
ma-17	472	27	theoretical	theoretical	ADJ
ma-17	472	28	results	result	NOUN
ma-17	472	29	are	be	AUX
ma-17	472	30	further	far	ADV
ma-17	472	31	justified	justify	VERB
ma-17	472	32	using	use	VERB
ma-17	472	33	numerical	numerical	ADJ
ma-17	472	34	experiments	experiment	NOUN
ma-17	472	35	.	.	PUNCT
ma-17	473	1	references	reference	NOUN
ma-17	473	2	[	[	X
ma-17	473	3	1	1	NUM
ma-17	473	4	]	]	X
ma-17	473	5	i.k	i.k	PROPN
ma-17	473	6	.	.	PROPN
ma-17	473	7	argyros	argyros	PROPN
ma-17	473	8	,	,	PUNCT
ma-17	473	9	on	on	ADP
ma-17	473	10	the	the	DET
ma-17	473	11	newton	newton	PROPN
ma-17	473	12	kantorovich	kantorovich	PROPN
ma-17	473	13	hypothesis	hypothesis	NOUN
ma-17	473	14	for	for	ADP
ma-17	473	15	solving	solve	VERB
ma-17	473	16	equations	equation	NOUN
ma-17	473	17	,	,	PUNCT
ma-17	473	18	j.	j.	PROPN
ma-17	473	19	comput	comput	PROPN
ma-17	473	20	.	.	PUNCT
ma-17	474	1	math	math	NOUN
ma-17	474	2	.	.	PUNCT
ma-17	475	1	169	169	NUM
ma-17	475	2	(	(	PUNCT
ma-17	475	3	2004	2004	NUM
ma-17	475	4	)	)	PUNCT
ma-17	475	5	,	,	PUNCT
ma-17	475	6	315	315	NUM
ma-17	475	7	-	-	SYM
ma-17	475	8	332	332	NUM
ma-17	475	9	,	,	PUNCT
ma-17	475	10	https://doi.org/10.1016/j.cam.2004.01.029[2	https://doi.org/10.1016/j.cam.2004.01.029[2	PROPN
ma-17	475	11	]	]	X
ma-17	475	12	i.k	i.k	PROPN
ma-17	475	13	.	.	PROPN
ma-17	475	14	argyros	argyros	PROPN
ma-17	475	15	,	,	PUNCT
ma-17	475	16	computational	computational	ADJ
ma-17	475	17	theory	theory	NOUN
ma-17	475	18	of	of	ADP
ma-17	475	19	iterative	iterative	ADJ
ma-17	475	20	methods	method	NOUN
ma-17	475	21	.	.	PUNCT
ma-17	476	1	series	series	NOUN
ma-17	476	2	:	:	PUNCT
ma-17	476	3	studies	study	NOUN
ma-17	476	4	in	in	ADP
ma-17	476	5	computational	computational	ADJ
ma-17	476	6	mathematics	mathematic	NOUN
ma-17	476	7	,	,	PUNCT
ma-17	476	8	15	15	NUM
ma-17	476	9	,	,	PUNCT
ma-17	476	10	editors	editor	NOUN
ma-17	476	11	:	:	PUNCT
ma-17	476	12	c.k	c.k	PROPN
ma-17	476	13	.	.	PROPN
ma-17	476	14	chui	chui	PROPN
ma-17	476	15	and	and	CCONJ
ma-17	476	16	l.	l.	PROPN
ma-17	476	17	wuytack	wuytack	PROPN
ma-17	476	18	,	,	PUNCT
ma-17	476	19	elsevier	elsevier	PROPN
ma-17	476	20	publ	publ	PROPN
ma-17	476	21	.	.	PUNCT
ma-17	477	1	co.	co.	PROPN
ma-17	477	2	new	new	PROPN
ma-17	477	3	york	york	PROPN
ma-17	477	4	,	,	PUNCT
ma-17	477	5	u.s.a	u.s.a	PROPN
ma-17	477	6	,	,	PUNCT
ma-17	477	7	2007.[3	2007.[3	NUM
ma-17	477	8	]	]	X
ma-17	477	9	i.k	i.k	PROPN
ma-17	477	10	.	.	PROPN
ma-17	477	11	argyros	argyros	PROPN
ma-17	477	12	,	,	PUNCT
ma-17	477	13	convergence	convergence	NOUN
ma-17	477	14	and	and	CCONJ
ma-17	477	15	applications	application	NOUN
ma-17	477	16	of	of	ADP
ma-17	477	17	newton	newton	NOUN
ma-17	477	18	-	-	PUNCT
ma-17	477	19	type	type	NOUN
ma-17	477	20	iterations	iteration	NOUN
ma-17	477	21	,	,	PUNCT
ma-17	477	22	springer	springer	NOUN
ma-17	477	23	verlag	verlag	PROPN
ma-17	477	24	,	,	PUNCT
ma-17	477	25	berlin	berlin	PROPN
ma-17	477	26	,	,	PUNCT
ma-17	477	27	germany	germany	PROPN
ma-17	477	28	,	,	PUNCT
ma-17	477	29	(	(	PUNCT
ma-17	477	30	2008	2008	NUM
ma-17	477	31	)	)	PUNCT
ma-17	477	32	,	,	PUNCT
ma-17	477	33	https://doi.org/10.1007/978-0-387-72743-1.[4	https://doi.org/10.1007/978-0-387-72743-1.[4	PROPN
ma-17	477	34	]	]	X
ma-17	477	35	i.k	i.k	PROPN
ma-17	477	36	.	.	PROPN
ma-17	477	37	argyros	argyros	PROPN
ma-17	477	38	,	,	PUNCT
ma-17	477	39	s.	s.	PROPN
ma-17	477	40	hilout	hilout	PROPN
ma-17	477	41	,	,	PUNCT
ma-17	477	42	weaker	weak	ADJ
ma-17	477	43	conditions	condition	NOUN
ma-17	477	44	for	for	ADP
ma-17	477	45	the	the	DET
ma-17	477	46	convergence	convergence	NOUN
ma-17	477	47	of	of	ADP
ma-17	477	48	newton	newton	PROPN
ma-17	477	49	’s	’s	PART
ma-17	477	50	method	method	NOUN
ma-17	477	51	.	.	PUNCT
ma-17	478	1	j.	j.	PROPN
ma-17	478	2	complex	complex	PROPN
ma-17	478	3	.	.	PUNCT
ma-17	479	1	28	28	NUM
ma-17	479	2	(	(	PUNCT
ma-17	479	3	2012	2012	NUM
ma-17	479	4	)	)	PUNCT
ma-17	479	5	,	,	PUNCT
ma-17	479	6	364–387	364–387	NUM
ma-17	479	7	,	,	PUNCT
ma-17	479	8	https://doi.org/10.1016/j.jco.2011.12.003.[5	https://doi.org/10.1016/j.jco.2011.12.003.[5	ADV
ma-17	479	9	]	]	X
ma-17	479	10	i.k	i.k	PROPN
ma-17	479	11	.	.	PROPN
ma-17	479	12	argyros	argyros	PROPN
ma-17	479	13	,	,	PUNCT
ma-17	479	14	s.	s.	PROPN
ma-17	479	15	hilout	hilout	PROPN
ma-17	479	16	,	,	PUNCT
ma-17	479	17	on	on	ADP
ma-17	479	18	an	an	DET
ma-17	479	19	improved	improved	ADJ
ma-17	479	20	convergence	convergence	NOUN
ma-17	479	21	analysis	analysis	NOUN
ma-17	479	22	of	of	ADP
ma-17	479	23	newton	newton	PROPN
ma-17	479	24	’s	’s	PART
ma-17	479	25	method	method	NOUN
ma-17	479	26	,	,	PUNCT
ma-17	479	27	appl	appl	PROPN
ma-17	479	28	.	.	PROPN
ma-17	479	29	math	math	NOUN
ma-17	479	30	.	.	PUNCT
ma-17	480	1	comput	comput	NOUN
ma-17	480	2	.	.	PUNCT
ma-17	481	1	225	225	NUM
ma-17	481	2	(	(	PUNCT
ma-17	481	3	2013),372	2013),372	NUM
ma-17	481	4	-	-	SYM
ma-17	481	5	386	386	NUM
ma-17	481	6	,	,	PUNCT
ma-17	481	7	https://doi.org/10.1016/j.amc.2013.09.049.[6	https://doi.org/10.1016/j.amc.2013.09.049.[6	PRON
ma-17	481	8	]	]	X
ma-17	481	9	i.k	i.k	PROPN
ma-17	481	10	.	.	PROPN
ma-17	481	11	argyros	argyros	PROPN
ma-17	481	12	,	,	PUNCT
ma-17	481	13	a.a	a.a	PROPN
ma-17	481	14	.	.	PROPN
ma-17	481	15	magréñan	magréñan	PROPN
ma-17	481	16	,	,	PUNCT
ma-17	481	17	iterative	iterative	NOUN
ma-17	481	18	methods	method	NOUN
ma-17	481	19	and	and	CCONJ
ma-17	481	20	their	their	PRON
ma-17	481	21	dynamics	dynamic	NOUN
ma-17	481	22	with	with	ADP
ma-17	481	23	applications	application	NOUN
ma-17	481	24	,	,	PUNCT
ma-17	481	25	crc	crc	NOUN
ma-17	481	26	press	press	NOUN
ma-17	481	27	,	,	PUNCT
ma-17	481	28	new	new	PROPN
ma-17	481	29	york	york	PROPN
ma-17	481	30	,	,	PUNCT
ma-17	481	31	usa,2017.[7	usa,2017.[7	NOUN
ma-17	481	32	]	]	X
ma-17	481	33	i.k	i.k	PROPN
ma-17	481	34	.	.	PROPN
ma-17	481	35	argyros	argyros	PROPN
ma-17	481	36	,	,	PUNCT
ma-17	481	37	a.a	a.a	PROPN
ma-17	481	38	.	.	PROPN
ma-17	481	39	magréñan	magréñan	PROPN
ma-17	481	40	,	,	PUNCT
ma-17	481	41	a	a	DET
ma-17	481	42	contemporary	contemporary	ADJ
ma-17	481	43	study	study	NOUN
ma-17	481	44	of	of	ADP
ma-17	481	45	iterative	iterative	ADJ
ma-17	481	46	methods	method	NOUN
ma-17	481	47	,	,	PUNCT
ma-17	481	48	elsevier	elsevier	NOUN
ma-17	481	49	(	(	PUNCT
ma-17	481	50	academic	academic	ADJ
ma-17	481	51	press),new	press),new	PROPN
ma-17	481	52	york	york	PROPN
ma-17	481	53	,	,	PUNCT
ma-17	481	54	2018	2018	NUM
ma-17	481	55	,	,	PUNCT
ma-17	481	56	https://www.elsevier.com/books/a-contemporary-study-of-iterative-methods/	https://www.elsevier.com/books/a-contemporary-study-of-iterative-methods/	NOUN
ma-17	481	57	magrenan/978	magrenan/978	PROPN
ma-17	481	58	-	-	PUNCT
ma-17	481	59	0	0	NUM
ma-17	481	60	-	-	PUNCT
ma-17	481	61	12	12	NUM
ma-17	481	62	-	-	PUNCT
ma-17	481	63	809214	809214	NUM
ma-17	481	64	-	-	SYM
ma-17	481	65	9.[8	9.[8	NUM
ma-17	481	66	]	]	X
ma-17	481	67	r.	r.	PROPN
ma-17	481	68	behl	behl	PROPN
ma-17	481	69	,	,	PUNCT
ma-17	481	70	p.	p.	PROPN
ma-17	481	71	maroju	maroju	PROPN
ma-17	481	72	,	,	PUNCT
ma-17	481	73	e.	e.	PROPN
ma-17	481	74	martinez	martinez	PROPN
ma-17	481	75	,	,	PUNCT
ma-17	481	76	s.	s.	PROPN
ma-17	481	77	singh	singh	PROPN
ma-17	481	78	,	,	PUNCT
ma-17	481	79	a	a	DET
ma-17	481	80	study	study	NOUN
ma-17	481	81	of	of	ADP
ma-17	481	82	the	the	DET
ma-17	481	83	local	local	ADJ
ma-17	481	84	convergence	convergence	NOUN
ma-17	481	85	of	of	ADP
ma-17	481	86	a	a	DET
ma-17	481	87	fifth	fifth	ADJ
ma-17	481	88	order	order	NOUN
ma-17	481	89	iterative	iterative	NOUN
ma-17	481	90	method	method	NOUN
ma-17	481	91	,	,	PUNCT
ma-17	481	92	indianj	indianj	ADJ
ma-17	481	93	.	.	PUNCT
ma-17	482	1	pure	pure	ADJ
ma-17	482	2	appl	appl	PROPN
ma-17	482	3	.	.	PUNCT
ma-17	482	4	math	math	NOUN
ma-17	482	5	.	.	PUNCT
ma-17	483	1	51	51	NUM
ma-17	483	2	(	(	PUNCT
ma-17	483	3	2020	2020	NUM
ma-17	483	4	)	)	PUNCT
ma-17	483	5	,	,	PUNCT
ma-17	483	6	439	439	NUM
ma-17	483	7	-	-	SYM
ma-17	483	8	455	455	NUM
ma-17	483	9	,	,	PUNCT
ma-17	483	10	https://doi.org/10.1007/s13226-020-0409-5.[9	https://doi.org/10.1007/s13226-020-0409-5.[9	PROPN
ma-17	483	11	]	]	X
ma-17	483	12	e.	e.	PROPN
ma-17	483	13	cătinaş	cătinaş	PROPN
ma-17	483	14	,	,	PUNCT
ma-17	483	15	the	the	DET
ma-17	483	16	inexact	inexact	ADJ
ma-17	483	17	,	,	PUNCT
ma-17	483	18	inexact	inexact	ADJ
ma-17	483	19	perturbed	perturb	VERB
ma-17	483	20	,	,	PUNCT
ma-17	483	21	and	and	CCONJ
ma-17	483	22	quasi	quasi	ADJ
ma-17	483	23	-	-	ADJ
ma-17	483	24	newton	newton	PROPN
ma-17	483	25	methods	method	NOUN
ma-17	483	26	are	be	AUX
ma-17	483	27	equivalent	equivalent	ADJ
ma-17	483	28	models	model	NOUN
ma-17	483	29	,	,	PUNCT
ma-17	483	30	math	math	NOUN
ma-17	483	31	.	.	PUNCT
ma-17	484	1	comp.74	comp.74	PROPN
ma-17	484	2	(	(	PUNCT
ma-17	484	3	2005	2005	NUM
ma-17	484	4	)	)	PUNCT
ma-17	484	5	,	,	PUNCT
ma-17	484	6	291	291	NUM
ma-17	484	7	-	-	SYM
ma-17	484	8	301	301	NUM
ma-17	484	9	,	,	PUNCT
ma-17	484	10	https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.96.1713&rep=rep1	https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.96.1713&rep=rep1	NOUN
ma-17	484	11	&	&	CCONJ
ma-17	484	12	type	type	NOUN
ma-17	484	13	=	=	NOUN
ma-17	484	14	pdf.[10	pdf.[10	NOUN
ma-17	484	15	]	]	PUNCT
ma-17	484	16	x.	x.	NOUN
ma-17	484	17	chen	chen	PROPN
ma-17	484	18	,	,	PUNCT
ma-17	484	19	t.	t.	PROPN
ma-17	484	20	yamamoto	yamamoto	PROPN
ma-17	484	21	,	,	PUNCT
ma-17	484	22	convergence	convergence	NOUN
ma-17	484	23	domains	domain	NOUN
ma-17	484	24	of	of	ADP
ma-17	484	25	certain	certain	ADJ
ma-17	484	26	iterative	iterative	NOUN
ma-17	484	27	methods	method	NOUN
ma-17	484	28	for	for	ADP
ma-17	484	29	solving	solve	VERB
ma-17	484	30	nonlinear	nonlinear	ADJ
ma-17	484	31	equations	equation	NOUN
ma-17	484	32	,	,	PUNCT
ma-17	484	33	numer.funct	numer.funct	PROPN
ma-17	484	34	.	.	PROPN
ma-17	484	35	anal	anal	PROPN
ma-17	484	36	.	.	PUNCT
ma-17	485	1	optim	optim	PROPN
ma-17	485	2	.	.	PUNCT
ma-17	486	1	10	10	NUM
ma-17	486	2	(	(	PUNCT
ma-17	486	3	1989	1989	NUM
ma-17	486	4	)	)	PUNCT
ma-17	486	5	,	,	PUNCT
ma-17	486	6	37	37	NUM
ma-17	486	7	-	-	SYM
ma-17	486	8	48	48	NUM
ma-17	486	9	,	,	PUNCT
ma-17	486	10	https://doi.org/10.1080/01630568908816289.[11	https://doi.org/10.1080/01630568908816289.[11	PROPN
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ma-17	486	17	,	,	PUNCT
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ma-17	487	4	.	.	PUNCT
ma-17	488	1	11	11	NUM
ma-17	488	2	(	(	PUNCT
ma-17	488	3	1968	1968	NUM
ma-17	488	4	)	)	PUNCT
ma-17	488	5	,	,	PUNCT
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ma-17	488	7	,	,	PUNCT
ma-17	488	8	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
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ma-17	488	10	]	]	PUNCT
ma-17	488	11	j.e	j.e	PROPN
ma-17	488	12	.	.	PROPN
ma-17	488	13	dennis	dennis	PROPN
ma-17	488	14	jr	jr	PROPN
ma-17	488	15	.	.	PROPN
ma-17	488	16	,	,	PUNCT
ma-17	488	17	r.b	r.b	PROPN
ma-17	488	18	.	.	PROPN
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ma-17	488	20	,	,	PUNCT
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ma-17	488	22	methods	method	NOUN
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ma-17	488	27	nonlinear	nonlinear	ADJ
ma-17	488	28	equations	equation	NOUN
ma-17	488	29	,	,	PUNCT
ma-17	488	30	siam	siam	PROPN
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ma-17	488	33	,	,	PUNCT
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ma-17	488	35	.	.	PUNCT
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ma-17	489	3	by	by	ADP
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ma-17	489	5	-	-	PUNCT
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ma-17	489	7	,	,	PUNCT
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ma-17	489	10	,	,	PUNCT
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ma-17	489	13	,	,	PUNCT
ma-17	489	14	(	(	PUNCT
ma-17	489	15	1983	1983	NUM
ma-17	489	16	)	)	PUNCT
ma-17	489	17	,	,	PUNCT
ma-17	489	18	https://epubs	https://epubs	PROPN
ma-17	489	19	.	.	NOUN
ma-17	489	20	siam.org/doi/pdf/10.1137/1.9781611971200.fm.[13	siam.org/doi/pdf/10.1137/1.9781611971200.fm.[13	NOUN
ma-17	489	21	]	]	PUNCT
ma-17	489	22	p.	p.	NOUN
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ma-17	489	24	,	,	PUNCT
ma-17	489	25	g.	g.	PROPN
ma-17	489	26	heindl	heindl	PROPN
ma-17	489	27	,	,	PUNCT
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ma-17	489	29	invariant	invariant	ADJ
ma-17	489	30	convergence	convergence	NOUN
ma-17	489	31	theorems	theorem	NOUN
ma-17	489	32	for	for	ADP
ma-17	489	33	newton	newton	PROPN
ma-17	489	34	’s	’s	PART
ma-17	489	35	method	method	NOUN
ma-17	489	36	and	and	CCONJ
ma-17	489	37	extensions	extension	NOUN
ma-17	489	38	to	to	ADP
ma-17	489	39	relatedmethods	relatedmethod	NOUN
ma-17	489	40	.	.	PUNCT
ma-17	490	1	siam	siam	PROPN
ma-17	490	2	j.	j.	PROPN
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ma-17	490	4	.	.	PUNCT
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ma-17	491	2	.	.	PUNCT
ma-17	492	1	16	16	NUM
ma-17	492	2	(	(	PUNCT
ma-17	492	3	1979	1979	NUM
ma-17	492	4	)	)	PUNCT
ma-17	492	5	,	,	PUNCT
ma-17	492	6	1	1	NUM
ma-17	492	7	-	-	SYM
ma-17	492	8	10	10	NUM
ma-17	492	9	,	,	PUNCT
ma-17	492	10	https://doi.org/10.1137/0716001	https://doi.org/10.1137/0716001	NOUN
ma-17	492	11	.	.	PUNCT
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ma-17	493	2	https://doi.org/10.1007/978-0-387-72743-1	https://doi.org/10.1007/978-0-387-72743-1	PROPN
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ma-17	494	9	https://doi.org/10.1007/bf02166685	https://doi.org/10.1007/bf02166685	PROPN
ma-17	494	10	https://doi.org/10.1007/bf02166685	https://doi.org/10.1007/bf02166685	PROPN
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ma-17	494	12	https://epubs.siam.org/doi/pdf/10.1137/1.9781611971200.fm	https://epubs.siam.org/doi/pdf/10.1137/1.9781611971200.fm	PROPN
ma-17	494	13	https://doi.org/10.1137/0716001	https://doi.org/10.1137/0716001	ADJ
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ma-17	494	15	.	.	PUNCT
ma-17	495	1	j.	j.	PROPN
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ma-17	495	3	.	.	PUNCT
ma-17	496	1	anal	anal	ADJ
ma-17	496	2	.	.	PUNCT
ma-17	497	1	1	1	NUM
ma-17	497	2	(	(	PUNCT
ma-17	497	3	2021	2021	NUM
ma-17	497	4	)	)	PUNCT
ma-17	498	1	84	84	NUM
ma-17	499	1	[	[	X
ma-17	499	2	14	14	NUM
ma-17	499	3	]	]	X
ma-17	499	4	p.	p.	NOUN
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ma-17	499	11	problems	problem	NOUN
ma-17	499	12	.	.	PUNCT
ma-17	500	1	affine	affine	PROPN
ma-17	500	2	invariance	invariance	NOUN
ma-17	500	3	and	and	CCONJ
ma-17	500	4	adaptive	adaptive	ADJ
ma-17	500	5	algorithms	algorithm	NOUN
ma-17	500	6	,	,	PUNCT
ma-17	500	7	springer	springer	NOUN
ma-17	500	8	seriesin	seriesin	PROPN
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ma-17	500	10	mathematics	mathematic	NOUN
ma-17	500	11	,	,	PUNCT
ma-17	500	12	35	35	NUM
ma-17	500	13	,	,	PUNCT
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ma-17	500	16	,	,	PUNCT
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ma-17	501	1	(	(	PUNCT
ma-17	501	2	2004	2004	NUM
ma-17	501	3	)	)	PUNCT
ma-17	501	4	,	,	PUNCT
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ma-17	501	8	s.	s.	PROPN
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ma-17	501	10	,	,	PUNCT
ma-17	501	11	h.	h.	PROPN
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ma-17	501	13	,	,	PUNCT
ma-17	501	14	m.z	m.z	PROPN
ma-17	501	15	.	.	PROPN
ma-17	501	16	sarikaya	sarikaya	PROPN
ma-17	501	17	,	,	PUNCT
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ma-17	501	22	for	for	ADP
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ma-17	501	31	math	math	NOUN
ma-17	501	32	.	.	PUNCT
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ma-17	502	3	(	(	PUNCT
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ma-17	502	5	)	)	PUNCT
ma-17	502	6	,	,	PUNCT
ma-17	502	7	171	171	NUM
ma-17	502	8	-	-	SYM
ma-17	502	9	188	188	NUM
ma-17	502	10	.	.	PUNCT
ma-17	503	1	https://doi.org/10.18514/mmn.2020.3076.[16	https://doi.org/10.18514/mmn.2020.3076.[16	PROPN
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ma-17	503	4	a.	a.	PROPN
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ma-17	503	6	,	,	PUNCT
ma-17	503	7	m.	m.	NOUN
ma-17	503	8	a.	a.	PROPN
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ma-17	503	10	,	,	PUNCT
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ma-17	503	12	’s	’s	PART
ma-17	503	13	method	method	NOUN
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ma-17	503	16	updated	update	VERB
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ma-17	503	18	of	of	ADP
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ma-17	503	27	,	,	PUNCT
ma-17	503	28	(	(	PUNCT
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ma-17	503	30	)	)	PUNCT
ma-17	503	31	,	,	PUNCT
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ma-17	503	40	.	.	PUNCT
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ma-17	503	44	noguera	noguera	PROPN
ma-17	503	45	,	,	PUNCT
ma-17	503	46	ostrowski	ostrowski	ADJ
ma-17	503	47	type	type	NOUN
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ma-17	503	51	systems	system	NOUN
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ma-17	504	2	.	.	PUNCT
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ma-17	504	4	.	.	PUNCT
ma-17	505	1	281	281	NUM
ma-17	505	2	(	(	PUNCT
ma-17	505	3	2011	2011	NUM
ma-17	505	4	)	)	PUNCT
ma-17	505	5	,	,	PUNCT
ma-17	505	6	2377	2377	NUM
ma-17	505	7	-	-	SYM
ma-17	505	8	2385	2385	NUM
ma-17	505	9	,	,	PUNCT
ma-17	505	10	https://doi.org/10.1016/j.amc.2011.08.011.[18	https://doi.org/10.1016/j.amc.2011.08.011.[18	PROPN
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ma-17	505	13	.	.	PROPN
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ma-17	505	15	,	,	PUNCT
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ma-17	505	17	.	.	PROPN
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ma-17	505	27	of	of	ADP
ma-17	505	28	newton	newton	PROPN
ma-17	505	29	-	-	PUNCT
ma-17	505	30	kantorovich	kantorovich	PROPN
ma-17	505	31	method	method	NOUN
ma-17	505	32	undercenter	undercenter	ADJ
ma-17	505	33	-	-	PUNCT
ma-17	505	34	lipschitz	lipschitz	NOUN
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ma-17	505	36	,	,	PUNCT
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ma-17	505	38	.	.	PROPN
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ma-17	505	40	.	.	PUNCT
ma-17	506	1	comput	comput	NOUN
ma-17	506	2	.	.	PUNCT
ma-17	507	1	221	221	NUM
ma-17	507	2	(	(	PUNCT
ma-17	507	3	2013	2013	NUM
ma-17	507	4	)	)	PUNCT
ma-17	507	5	,	,	PUNCT
ma-17	507	6	79	79	NUM
ma-17	507	7	-	-	SYM
ma-17	507	8	88	88	NUM
ma-17	507	9	,	,	PUNCT
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ma-17	507	11	.	.	PUNCT
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ma-17	508	2	]	]	X
ma-17	508	3	m.a	m.a	PROPN
ma-17	508	4	.	.	PROPN
ma-17	508	5	hernandez	hernandez	PROPN
ma-17	508	6	,	,	PUNCT
ma-17	508	7	n.	n.	PROPN
ma-17	508	8	romero	romero	PROPN
ma-17	508	9	,	,	PUNCT
ma-17	508	10	on	on	ADP
ma-17	508	11	a	a	DET
ma-17	508	12	characterization	characterization	NOUN
ma-17	508	13	of	of	ADP
ma-17	508	14	some	some	DET
ma-17	508	15	newton	newton	NOUN
ma-17	508	16	-	-	PUNCT
ma-17	508	17	like	like	ADJ
ma-17	508	18	methods	method	NOUN
ma-17	508	19	of	of	ADP
ma-17	508	20	r−	r−	NOUN
ma-17	508	21	order	order	NOUN
ma-17	508	22	at	at	ADV
ma-17	508	23	least	least	ADV
ma-17	508	24	three	three	NUM
ma-17	508	25	,	,	PUNCT
ma-17	508	26	j.comput	j.comput	NOUN
ma-17	508	27	.	.	PUNCT
ma-17	509	1	appl	appl	PROPN
ma-17	509	2	.	.	PROPN
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ma-17	509	4	.	.	PUNCT
ma-17	510	1	183	183	NUM
ma-17	510	2	(	(	PUNCT
ma-17	510	3	2005	2005	NUM
ma-17	510	4	)	)	PUNCT
ma-17	510	5	,	,	PUNCT
ma-17	510	6	53	53	NUM
ma-17	510	7	-	-	SYM
ma-17	510	8	66	66	NUM
ma-17	510	9	,	,	PUNCT
ma-17	510	10	https://doi.org/10.1016/j.cam.2005.01.001.[20	https://doi.org/10.1016/j.cam.2005.01.001.[20	PROPN
ma-17	510	11	]	]	PUNCT
ma-17	510	12	l.v	l.v	PROPN
ma-17	510	13	.	.	PROPN
ma-17	510	14	kantorovich	kantorovich	PROPN
ma-17	510	15	,	,	PUNCT
ma-17	510	16	g.p	g.p	PROPN
ma-17	510	17	.	.	PROPN
ma-17	510	18	akilov	akilov	PROPN
ma-17	510	19	,	,	PUNCT
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ma-17	510	28	(	(	PUNCT
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ma-17	510	35	i.k	i.k	PROPN
ma-17	510	36	.	.	PROPN
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ma-17	510	38	,	,	PUNCT
ma-17	510	39	j.j	j.j	PROPN
ma-17	510	40	.	.	PROPN
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ma-17	510	43	j.a	j.a	PROPN
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ma-17	510	46	,	,	PUNCT
ma-17	510	47	ball	ball	NOUN
ma-17	510	48	convergence	convergence	NOUN
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ma-17	510	52	-	-	PUNCT
ma-17	510	53	order	order	NOUN
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ma-17	510	62	conditions	condition	NOUN
ma-17	510	63	,	,	PUNCT
ma-17	510	64	j.	j.	PROPN
ma-17	510	65	math	math	PROPN
ma-17	510	66	.	.	PUNCT
ma-17	511	1	chem	chem	PROPN
ma-17	511	2	.	.	PUNCT
ma-17	512	1	56	56	NUM
ma-17	512	2	(	(	PUNCT
ma-17	512	3	2018	2018	NUM
ma-17	512	4	)	)	PUNCT
ma-17	512	5	,	,	PUNCT
ma-17	512	6	2117	2117	NUM
ma-17	512	7	-	-	SYM
ma-17	512	8	2131	2131	NUM
ma-17	512	9	,	,	PUNCT
ma-17	512	10	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-17	512	11	s10910	s10910	PROPN
ma-17	512	12	-	-	PUNCT
ma-17	512	13	018	018	NUM
ma-17	512	14	-	-	PUNCT
ma-17	512	15	0856	0856	NUM
ma-17	512	16	-	-	PUNCT
ma-17	512	17	y.[22	y.[22	PROPN
ma-17	512	18	]	]	X
ma-17	512	19	a.a	a.a	PROPN
ma-17	512	20	.	.	PROPN
ma-17	512	21	magréñan	magréñan	PROPN
ma-17	512	22	,	,	PUNCT
ma-17	512	23	j.m	j.m	PROPN
ma-17	512	24	.	.	PROPN
ma-17	512	25	gutiérrez	gutiérrez	PROPN
ma-17	512	26	,	,	PUNCT
ma-17	512	27	real	real	ADJ
ma-17	512	28	dynamics	dynamic	NOUN
ma-17	512	29	for	for	ADP
ma-17	512	30	damped	damped	PROPN
ma-17	512	31	newton	newton	PROPN
ma-17	512	32	’s	’s	PART
ma-17	512	33	method	method	NOUN
ma-17	512	34	applied	apply	VERB
ma-17	512	35	to	to	ADP
ma-17	512	36	cubic	cubic	ADJ
ma-17	512	37	polynomials	polynomial	NOUN
ma-17	512	38	,	,	PUNCT
ma-17	512	39	j.	j.	PROPN
ma-17	512	40	comput.appl	comput.appl	PROPN
ma-17	512	41	.	.	PUNCT
ma-17	512	42	math	math	NOUN
ma-17	512	43	.	.	PUNCT
ma-17	513	1	275	275	NUM
ma-17	513	2	(	(	PUNCT
ma-17	513	3	2015	2015	NUM
ma-17	513	4	)	)	PUNCT
ma-17	513	5	,	,	PUNCT
ma-17	513	6	527–538	527–538	NUM
ma-17	513	7	,	,	PUNCT
ma-17	513	8	https://dl.acm.org/doi/abs/10.5555/2946148.2946231.[23	https://dl.acm.org/doi/abs/10.5555/2946148.2946231.[23	NOUN
ma-17	513	9	]	]	PUNCT
ma-17	513	10	m.z	m.z	PROPN
ma-17	513	11	.	.	PROPN
ma-17	513	12	nashed	nashe	VERB
ma-17	513	13	,	,	PUNCT
ma-17	513	14	x.	x.	PROPN
ma-17	513	15	chen	chen	PROPN
ma-17	513	16	,	,	PUNCT
ma-17	513	17	convergence	convergence	NOUN
ma-17	513	18	of	of	ADP
ma-17	513	19	newton	newton	PROPN
ma-17	513	20	-	-	PUNCT
ma-17	513	21	like	like	ADJ
ma-17	513	22	methods	method	NOUN
ma-17	513	23	for	for	ADP
ma-17	513	24	singular	singular	ADJ
ma-17	513	25	operator	operator	NOUN
ma-17	513	26	equations	equation	NOUN
ma-17	513	27	using	use	VERB
ma-17	513	28	outer	outer	ADJ
ma-17	513	29	inverses	inverse	NOUN
ma-17	513	30	,	,	PUNCT
ma-17	513	31	numer	numer	PROPN
ma-17	513	32	.	.	PROPN
ma-17	513	33	math	math	NOUN
ma-17	513	34	.	.	PUNCT
ma-17	514	1	66	66	NUM
ma-17	514	2	(	(	PUNCT
ma-17	514	3	1993	1993	NUM
ma-17	514	4	)	)	PUNCT
ma-17	514	5	,	,	PUNCT
ma-17	514	6	235	235	NUM
ma-17	514	7	-	-	SYM
ma-17	514	8	257	257	NUM
ma-17	514	9	,	,	PUNCT
ma-17	514	10	https://doi.org/10.1007/bf01385696.[24	https://doi.org/10.1007/bf01385696.[24	NOUN
ma-17	514	11	]	]	PUNCT
ma-17	515	1	l.m	l.m	PROPN
ma-17	515	2	.	.	PROPN
ma-17	515	3	ortega	ortega	PROPN
ma-17	515	4	,	,	PUNCT
ma-17	515	5	w.c	w.c	PROPN
ma-17	515	6	.	.	PROPN
ma-17	515	7	rheinboldt	rheinboldt	ADJ
ma-17	515	8	„	„	PUNCT
ma-17	515	9	iterative	iterative	NOUN
ma-17	515	10	solution	solution	NOUN
ma-17	515	11	of	of	ADP
ma-17	515	12	nonlinear	nonlinear	ADJ
ma-17	515	13	equations	equation	NOUN
ma-17	515	14	in	in	ADP
ma-17	515	15	sev	sev	NOUN
ma-17	515	16	-	-	ADJ
ma-17	515	17	eral	eral	ADJ
ma-17	515	18	variables	variable	NOUN
ma-17	515	19	,	,	PUNCT
ma-17	515	20	academic	academic	ADJ
ma-17	515	21	press	press	NOUN
ma-17	515	22	,	,	PUNCT
ma-17	515	23	new	new	PROPN
ma-17	515	24	york	york	PROPN
ma-17	515	25	,	,	PUNCT
ma-17	515	26	(	(	PUNCT
ma-17	515	27	1970	1970	NUM
ma-17	515	28	)	)	PUNCT
ma-17	515	29	,	,	PUNCT
ma-17	515	30	https://www.elsevier.com/books/	https://www.elsevier.com/books/	NOUN
ma-17	515	31	iterative	iterative	NOUN
ma-17	515	32	-	-	PUNCT
ma-17	515	33	solution	solution	NOUN
ma-17	515	34	-	-	PUNCT
ma-17	515	35	of	of	ADP
ma-17	515	36	-	-	PUNCT
ma-17	515	37	nonlinear	nonlinear	ADJ
ma-17	515	38	-	-	PUNCT
ma-17	515	39	equations	equation	NOUN
ma-17	515	40	-	-	PUNCT
ma-17	515	41	in	in	ADP
ma-17	515	42	-	-	PUNCT
ma-17	515	43	several	several	ADJ
ma-17	515	44	-	-	PUNCT
ma-17	515	45	variables	variable	NOUN
ma-17	515	46	/	/	SYM
ma-17	515	47	ortega/978	ortega/978	PROPN
ma-17	515	48	-	-	PUNCT
ma-17	515	49	0	0	NUM
ma-17	515	50	-	-	PUNCT
ma-17	515	51	12	12	NUM
ma-17	515	52	-	-	PUNCT
ma-17	515	53	528550	528550	NUM
ma-17	515	54	-	-	PUNCT
ma-17	515	55	6.[25	6.[25	NUM
ma-17	515	56	]	]	X
ma-17	515	57	a.	a.	NOUN
ma-17	515	58	m.	m.	PROPN
ma-17	515	59	ostrowski	ostrowski	PROPN
ma-17	515	60	,	,	PUNCT
ma-17	515	61	solution	solution	NOUN
ma-17	515	62	of	of	ADP
ma-17	515	63	equations	equation	NOUN
ma-17	515	64	in	in	ADP
ma-17	515	65	euclidean	euclidean	NOUN
ma-17	515	66	and	and	CCONJ
ma-17	515	67	banach	banach	NOUN
ma-17	515	68	spaces	space	NOUN
ma-17	515	69	,	,	PUNCT
ma-17	515	70	elsevier	elsevier	NOUN
ma-17	515	71	,	,	PUNCT
ma-17	515	72	1973.[26	1973.[26	NUM
ma-17	515	73	]	]	X
ma-17	515	74	f.a	f.a	PROPN
ma-17	515	75	.	.	PROPN
ma-17	515	76	potra	potra	PROPN
ma-17	515	77	,	,	PUNCT
ma-17	515	78	v.	v.	ADP
ma-17	515	79	pták	pták	ADJ
ma-17	515	80	,	,	PUNCT
ma-17	515	81	nondiscrete	nondiscrete	ADJ
ma-17	515	82	induction	induction	NOUN
ma-17	515	83	and	and	CCONJ
ma-17	515	84	iterative	iterative	NOUN
ma-17	515	85	processes	process	NOUN
ma-17	515	86	.	.	PUNCT
ma-17	516	1	research	research	NOUN
ma-17	516	2	notes	note	NOUN
ma-17	516	3	in	in	ADP
ma-17	516	4	mathematics	mathematic	NOUN
ma-17	516	5	,	,	PUNCT
ma-17	516	6	103	103	NUM
ma-17	516	7	.	.	PUNCT
ma-17	517	1	pit	pit	NOUN
ma-17	517	2	-	-	PUNCT
ma-17	517	3	man(advanced	man(advance	VERB
ma-17	517	4	publishing	publishing	NOUN
ma-17	517	5	program	program	NOUN
ma-17	517	6	)	)	PUNCT
ma-17	517	7	,	,	PUNCT
ma-17	517	8	boston	boston	PROPN
ma-17	517	9	,	,	PUNCT
ma-17	517	10	ma	ma	PROPN
ma-17	517	11	.	.	PROPN
ma-17	517	12	(	(	PUNCT
ma-17	517	13	1984	1984	NUM
ma-17	517	14	)	)	PUNCT
ma-17	517	15	,	,	PUNCT
ma-17	517	16	http://www.sciepub.com/reference/50811.[27	http://www.sciepub.com/reference/50811.[27	NOUN
ma-17	517	17	]	]	PUNCT
ma-17	518	1	p.d	p.d	PROPN
ma-17	518	2	.	.	PROPN
ma-17	518	3	proinov	proinov	PROPN
ma-17	518	4	,	,	PUNCT
ma-17	518	5	general	general	ADJ
ma-17	518	6	local	local	ADJ
ma-17	518	7	convergence	convergence	NOUN
ma-17	518	8	theory	theory	NOUN
ma-17	518	9	for	for	ADP
ma-17	518	10	a	a	DET
ma-17	518	11	class	class	NOUN
ma-17	518	12	of	of	ADP
ma-17	518	13	iterative	iterative	NOUN
ma-17	518	14	processes	process	NOUN
ma-17	518	15	and	and	CCONJ
ma-17	518	16	its	its	PRON
ma-17	518	17	applications	application	NOUN
ma-17	518	18	to	to	PART
ma-17	518	19	newton’smethod	newton’smethod	VERB
ma-17	518	20	,	,	PUNCT
ma-17	518	21	j.	j.	PROPN
ma-17	518	22	complex	complex	PROPN
ma-17	518	23	.	.	PUNCT
ma-17	519	1	25	25	NUM
ma-17	519	2	(	(	PUNCT
ma-17	519	3	2009	2009	NUM
ma-17	519	4	)	)	PUNCT
ma-17	519	5	,	,	PUNCT
ma-17	519	6	38	38	NUM
ma-17	519	7	-	-	SYM
ma-17	519	8	62	62	NUM
ma-17	519	9	,	,	PUNCT
ma-17	519	10	https://doi.org/10.1016/j.jco.2008.05.006.[28	https://doi.org/10.1016/j.jco.2008.05.006.[28	PROPN
ma-17	519	11	]	]	X
ma-17	519	12	m.a	m.a	PROPN
ma-17	519	13	.	.	PROPN
ma-17	519	14	ragusa	ragusa	PROPN
ma-17	519	15	,	,	PUNCT
ma-17	519	16	parabolic	parabolic	PROPN
ma-17	519	17	herz	herz	PROPN
ma-17	519	18	spaces	space	NOUN
ma-17	519	19	and	and	CCONJ
ma-17	519	20	their	their	PRON
ma-17	519	21	applications	application	NOUN
ma-17	519	22	,	,	PUNCT
ma-17	519	23	appl	appl	PROPN
ma-17	519	24	.	.	PROPN
ma-17	519	25	math	math	PROPN
ma-17	519	26	.	.	PUNCT
ma-17	520	1	lett	lett	PROPN
ma-17	520	2	.	.	PUNCT
ma-17	521	1	25	25	NUM
ma-17	521	2	(	(	PUNCT
ma-17	521	3	2012	2012	NUM
ma-17	521	4	)	)	PUNCT
ma-17	521	5	,	,	PUNCT
ma-17	521	6	1270	1270	NUM
ma-17	521	7	-	-	SYM
ma-17	521	8	1273	1273	NUM
ma-17	521	9	,	,	PUNCT
ma-17	521	10	https	https	NOUN
ma-17	521	11	:	:	PUNCT
ma-17	521	12	//doi.org/10.1063/1.3498444[29	//doi.org/10.1063/1.3498444[29	SYM
ma-17	521	13	]	]	X
ma-17	521	14	w.c	w.c	PROPN
ma-17	521	15	.	.	PROPN
ma-17	521	16	rheinboldt	rheinboldt	PROPN
ma-17	521	17	,	,	PUNCT
ma-17	521	18	an	an	DET
ma-17	521	19	adaptive	adaptive	ADJ
ma-17	521	20	continuation	continuation	NOUN
ma-17	521	21	process	process	NOUN
ma-17	521	22	of	of	ADP
ma-17	521	23	solving	solve	VERB
ma-17	521	24	systems	system	NOUN
ma-17	521	25	of	of	ADP
ma-17	521	26	nonlinear	nonlinear	ADJ
ma-17	521	27	equations	equation	NOUN
ma-17	521	28	.	.	PUNCT
ma-17	522	1	polish	polish	PROPN
ma-17	522	2	academy	academy	PROPN
ma-17	522	3	ofscience	ofscience	PROPN
ma-17	522	4	,	,	PUNCT
ma-17	522	5	banach	banach	PROPN
ma-17	522	6	ctr	ctr	PROPN
ma-17	522	7	.	.	PUNCT
ma-17	522	8	publ	publ	PROPN
ma-17	522	9	.	.	PUNCT
ma-17	523	1	3	3	NUM
ma-17	523	2	(	(	PUNCT
ma-17	523	3	1978	1978	NUM
ma-17	523	4	)	)	PUNCT
ma-17	523	5	,	,	PUNCT
ma-17	523	6	129	129	NUM
ma-17	523	7	-	-	SYM
ma-17	523	8	142	142	NUM
ma-17	523	9	,	,	PUNCT
ma-17	523	10	https://eudml.org/doc/208686.[30	https://eudml.org/doc/208686.[30	PROPN
ma-17	523	11	]	]	X
ma-17	523	12	s.m	s.m	PROPN
ma-17	523	13	.	.	PROPN
ma-17	523	14	shakhno	shakhno	PROPN
ma-17	523	15	,	,	PUNCT
ma-17	523	16	o.p	o.p	PROPN
ma-17	523	17	.	.	PROPN
ma-17	523	18	gnatyshyn	gnatyshyn	PROPN
ma-17	523	19	,	,	PUNCT
ma-17	523	20	,	,	PUNCT
ma-17	523	21	on	on	ADP
ma-17	523	22	an	an	DET
ma-17	523	23	iterative	iterative	ADJ
ma-17	523	24	algorithm	algorithm	NOUN
ma-17	523	25	of	of	ADP
ma-17	523	26	order	order	NOUN
ma-17	523	27	1.839	1.839	NUM
ma-17	523	28	...	...	PUNCT
ma-17	524	1	for	for	ADP
ma-17	524	2	solving	solve	VERB
ma-17	524	3	nonlinear	nonlinear	NOUN
ma-17	524	4	least	least	ADJ
ma-17	524	5	squaresproblems	squaresproblem	NOUN
ma-17	524	6	,	,	PUNCT
ma-17	524	7	appl	appl	PROPN
ma-17	524	8	.	.	PROPN
ma-17	524	9	math	math	PROPN
ma-17	524	10	.	.	PUNCT
ma-17	524	11	appl	appl	PROPN
ma-17	524	12	.	.	PROPN
ma-17	524	13	161	161	NUM
ma-17	524	14	(	(	PUNCT
ma-17	524	15	2005	2005	NUM
ma-17	524	16	)	)	PUNCT
ma-17	524	17	,	,	PUNCT
ma-17	524	18	253	253	NUM
ma-17	524	19	-	-	SYM
ma-17	524	20	264	264	NUM
ma-17	524	21	,	,	PUNCT
ma-17	524	22	https://doi.org/10.1016/j.amc.2003.12.025.[31	https://doi.org/10.1016/j.amc.2003.12.025.[31	PROPN
ma-17	524	23	]	]	PUNCT
ma-17	524	24	s.m	s.m	PROPN
ma-17	524	25	.	.	PROPN
ma-17	524	26	shakhno	shakhno	PROPN
ma-17	524	27	,	,	PUNCT
ma-17	524	28	r.p	r.p	PROPN
ma-17	524	29	.	.	PROPN
ma-17	524	30	iakymchuk	iakymchuk	PROPN
ma-17	524	31	,	,	PUNCT
ma-17	524	32	h.p	h.p	PROPN
ma-17	524	33	.	.	PROPN
ma-17	524	34	yarmola	yarmola	PROPN
ma-17	524	35	,	,	PUNCT
ma-17	524	36	convergence	convergence	NOUN
ma-17	524	37	analysis	analysis	NOUN
ma-17	524	38	of	of	ADP
ma-17	524	39	a	a	DET
ma-17	524	40	two	two	NUM
ma-17	524	41	step	step	NOUN
ma-17	524	42	method	method	NOUN
ma-17	524	43	for	for	ADP
ma-17	524	44	the	the	DET
ma-17	524	45	nonlin	nonlin	NOUN
ma-17	524	46	-	-	PUNCT
ma-17	524	47	ear	ear	NOUN
ma-17	524	48	squares	square	NOUN
ma-17	524	49	problem	problem	NOUN
ma-17	524	50	with	with	ADP
ma-17	524	51	decomposition	decomposition	NOUN
ma-17	524	52	of	of	ADP
ma-17	524	53	operator	operator	NOUN
ma-17	524	54	,	,	PUNCT
ma-17	524	55	j.	j.	PROPN
ma-17	524	56	numer	numer	PROPN
ma-17	524	57	.	.	PUNCT
ma-17	524	58	appl	appl	PROPN
ma-17	524	59	.	.	PROPN
ma-17	524	60	math	math	PROPN
ma-17	524	61	.	.	PUNCT
ma-17	525	1	128	128	NUM
ma-17	525	2	(	(	PUNCT
ma-17	525	3	2018	2018	NUM
ma-17	525	4	)	)	PUNCT
ma-17	525	5	,	,	PUNCT
ma-17	525	6	82	82	NUM
ma-17	525	7	-	-	SYM
ma-17	525	8	95	95	NUM
ma-17	525	9	,	,	PUNCT
ma-17	525	10	https://hal	https://hal	PROPN
ma-17	525	11	.	.	PUNCT
ma-17	525	12	archives-ouvertes.fr/hal-01857847/document.[32	archives-ouvertes.fr/hal-01857847/document.[32	PROPN
ma-17	525	13	]	]	X
ma-17	526	1	j.r	j.r	PROPN
ma-17	526	2	.	.	PROPN
ma-17	526	3	sharma	sharma	PROPN
ma-17	526	4	,	,	PUNCT
ma-17	526	5	r.k	r.k	PROPN
ma-17	526	6	.	.	PROPN
ma-17	526	7	guha	guha	PROPN
ma-17	526	8	,	,	PUNCT
ma-17	526	9	r.	r.	PROPN
ma-17	526	10	sharma	sharma	PROPN
ma-17	526	11	,	,	PUNCT
ma-17	526	12	an	an	DET
ma-17	526	13	efficient	efficient	ADJ
ma-17	526	14	fourth	fourth	ADJ
ma-17	526	15	order	order	NOUN
ma-17	526	16	weighted	weight	VERB
ma-17	526	17	newton	newton	PROPN
ma-17	526	18	method	method	NOUN
ma-17	526	19	for	for	ADP
ma-17	526	20	systems	system	NOUN
ma-17	526	21	of	of	ADP
ma-17	526	22	nonlinearequations	nonlinearequation	NOUN
ma-17	526	23	.	.	PUNCT
ma-17	527	1	numer	numer	PROPN
ma-17	527	2	.	.	PUNCT
ma-17	528	1	algorithms	algorithms	PROPN
ma-17	528	2	,	,	PUNCT
ma-17	528	3	62	62	NUM
ma-17	528	4	(	(	PUNCT
ma-17	528	5	2013	2013	NUM
ma-17	528	6	)	)	PUNCT
ma-17	528	7	,	,	PUNCT
ma-17	528	8	307	307	NUM
ma-17	528	9	-	-	SYM
ma-17	528	10	323	323	NUM
ma-17	528	11	,	,	PUNCT
ma-17	528	12	https://doi.org/10.1007/s11075-012-9585-7.[33	https://doi.org/10.1007/s11075-012-9585-7.[33	PROPN
ma-17	528	13	]	]	X
ma-17	528	14	f.	f.	PROPN
ma-17	528	15	soleymani	soleymani	PROPN
ma-17	528	16	,	,	PUNCT
ma-17	528	17	t.	t.	PROPN
ma-17	528	18	lotfi	lotfi	PROPN
ma-17	528	19	,	,	PUNCT
ma-17	528	20	p.	p.	NOUN
ma-17	528	21	bakhtiari	bakhtiari	PROPN
ma-17	528	22	,	,	PUNCT
ma-17	528	23	a	a	DET
ma-17	528	24	multi	multi	ADJ
ma-17	528	25	-	-	ADJ
ma-17	528	26	step	step	ADJ
ma-17	528	27	class	class	NOUN
ma-17	528	28	of	of	ADP
ma-17	528	29	iterative	iterative	ADJ
ma-17	528	30	methods	method	NOUN
ma-17	528	31	for	for	ADP
ma-17	528	32	nonlinear	nonlinear	ADJ
ma-17	528	33	systems	system	NOUN
ma-17	528	34	.	.	PUNCT
ma-17	529	1	optim	optim	ADJ
ma-17	529	2	.	.	PUNCT
ma-17	530	1	lett	lett	PROPN
ma-17	530	2	.	.	PUNCT
ma-17	531	1	8(2014	8(2014	NUM
ma-17	531	2	)	)	PUNCT
ma-17	531	3	,	,	PUNCT
ma-17	531	4	1001	1001	NUM
ma-17	531	5	-	-	SYM
ma-17	531	6	1015	1015	NUM
ma-17	531	7	,	,	PUNCT
ma-17	531	8	https://doi.org/10.1007/s11590-013-0617-6	https://doi.org/10.1007/s11590-013-0617-6	NUM
ma-17	531	9	.	.	PUNCT
ma-17	532	1	https://www.springer.com/gp/book/9783540210993	https://www.springer.com/gp/book/9783540210993	PROPN
ma-17	532	2	https://www.springer.com/gp/book/9783540210993	https://www.springer.com/gp/book/9783540210993	PROPN
ma-17	532	3	https://doi.org/10.18514/mmn.2020.3076	https://doi.org/10.18514/mmn.2020.3076	NOUN
ma-17	532	4	https://www.springer.com/gp/book/9783319559759	https://www.springer.com/gp/book/9783319559759	PROPN
ma-17	532	5	https://doi.org/10.1016/j.amc.2011.08.011	https://doi.org/10.1016/j.amc.2011.08.011	PROPN
ma-17	532	6	https://doi.org/10.1016/j.amc.2013.05.078	https://doi.org/10.1016/j.amc.2013.05.078	PROPN
ma-17	532	7	https://doi.org/10.1016/j.amc.2013.05.078	https://doi.org/10.1016/j.amc.2013.05.078	PROPN
ma-17	532	8	https://doi.org/10.1016/j.cam.2005.01.001	https://doi.org/10.1016/j.cam.2005.01.001	PROPN
ma-17	532	9	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-17	532	10	s10910	s10910	PROPN
ma-17	532	11	-	-	PUNCT
ma-17	532	12	018	018	NUM
ma-17	532	13	-	-	PUNCT
ma-17	532	14	0856	0856	NUM
ma-17	532	15	-	-	PUNCT
ma-17	532	16	y	y	PROPN
ma-17	532	17	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-17	532	18	s10910	s10910	PROPN
ma-17	532	19	-	-	PUNCT
ma-17	532	20	018	018	NUM
ma-17	532	21	-	-	PUNCT
ma-17	532	22	0856	0856	NUM
ma-17	532	23	-	-	PUNCT
ma-17	532	24	y	y	PROPN
ma-17	532	25	https://dl.acm.org/doi/abs/10.5555/2946148.2946231	https://dl.acm.org/doi/abs/10.5555/2946148.2946231	PROPN
ma-17	532	26	https://doi.org/10.1007/bf01385696	https://doi.org/10.1007/bf01385696	PROPN
ma-17	532	27	https://www.elsevier.com/books/iterative-solution-of-nonlinear-equations-in-several-variables/ortega/978-0-12-528550-6	https://www.elsevier.com/books/iterative-solution-of-nonlinear-equations-in-several-variables/ortega/978-0-12-528550-6	PROPN
ma-17	532	28	https://www.elsevier.com/books/iterative-solution-of-nonlinear-equations-in-several-variables/ortega/978-0-12-528550-6	https://www.elsevier.com/books/iterative-solution-of-nonlinear-equations-in-several-variables/ortega/978-0-12-528550-6	PROPN
ma-17	532	29	http://www.sciepub.com/reference/50811	http://www.sciepub.com/reference/50811	PROPN
ma-17	532	30	https://doi.org/10.1016/j.jco.2008.05.006	https://doi.org/10.1016/j.jco.2008.05.006	ADJ
ma-17	532	31	https://doi.org/10.1063/1.3498444	https://doi.org/10.1063/1.3498444	PROPN
ma-17	532	32	https://doi.org/10.1063/1.3498444	https://doi.org/10.1063/1.3498444	PROPN
ma-17	532	33	https://eudml.org/doc/208686	https://eudml.org/doc/208686	CCONJ
ma-17	532	34	https://doi.org/10.1016/j.amc.2003.12.025	https://doi.org/10.1016/j.amc.2003.12.025	PROPN
ma-17	532	35	https://hal.archives-ouvertes.fr/hal-01857847/document	https://hal.archives-ouvertes.fr/hal-01857847/document	PROPN
ma-17	532	36	https://hal.archives-ouvertes.fr/hal-01857847/document	https://hal.archives-ouvertes.fr/hal-01857847/document	PROPN
ma-17	532	37	https://doi.org/10.1007/s11075-012-9585-7	https://doi.org/10.1007/s11075-012-9585-7	NUM
ma-17	532	38	https://doi.org/10.1007/s11590-013-0617-6	https://doi.org/10.1007/s11590-013-0617-6	NUM
ma-17	532	39	eur	eur	NOUN
ma-17	532	40	.	.	PUNCT
ma-17	533	1	j.	j.	PROPN
ma-17	533	2	math	math	PROPN
ma-17	533	3	.	.	PUNCT
ma-17	534	1	anal	anal	ADJ
ma-17	534	2	.	.	PUNCT
ma-17	535	1	1	1	NUM
ma-17	535	2	(	(	PUNCT
ma-17	535	3	2021	2021	NUM
ma-17	535	4	)	)	PUNCT
ma-17	535	5	85	85	NUM
ma-17	536	1	[	[	SYM
ma-17	536	2	34	34	NUM
ma-17	536	3	]	]	X
ma-17	536	4	j.f	j.f	PROPN
ma-17	536	5	.	.	PROPN
ma-17	536	6	steffensen	steffensen	PROPN
ma-17	536	7	,	,	PUNCT
ma-17	536	8	remarks	remark	VERB
ma-17	536	9	on	on	ADP
ma-17	536	10	iteration	iteration	NOUN
ma-17	536	11	.	.	PUNCT
ma-17	537	1	skand	skand	PROPN
ma-17	537	2	aktuar	aktuar	PROPN
ma-17	537	3	tidsr	tidsr	PROPN
ma-17	537	4	.	.	PUNCT
ma-17	538	1	16	16	NUM
ma-17	538	2	(	(	PUNCT
ma-17	538	3	1993	1993	NUM
ma-17	538	4	)	)	PUNCT
ma-17	538	5	,	,	PUNCT
ma-17	538	6	64	64	NUM
ma-17	538	7	-	-	SYM
ma-17	538	8	72	72	NUM
ma-17	538	9	,	,	PUNCT
ma-17	538	10	https://doi.org/10.1080/	https://doi.org/10.1080/	PROPN
ma-17	538	11	03461238.1933.10419209.[35	03461238.1933.10419209.[35	PROPN
ma-17	538	12	]	]	X
ma-17	538	13	j.f	j.f	PROPN
ma-17	538	14	.	.	PROPN
ma-17	538	15	traub	traub	PROPN
ma-17	538	16	,	,	PUNCT
ma-17	538	17	iterative	iterative	NOUN
ma-17	538	18	methods	method	NOUN
ma-17	538	19	for	for	ADP
ma-17	538	20	the	the	DET
ma-17	538	21	solution	solution	NOUN
ma-17	538	22	of	of	ADP
ma-17	538	23	equations	equation	NOUN
ma-17	538	24	prentice	prentice	PROPN
ma-17	538	25	hall	hall	PROPN
ma-17	538	26	,	,	PUNCT
ma-17	538	27	new	new	PROPN
ma-17	538	28	jersey	jersey	PROPN
ma-17	538	29	,	,	PUNCT
ma-17	538	30	u.s.a	u.s.a	PROPN
ma-17	538	31	,	,	PUNCT
ma-17	538	32	(	(	PUNCT
ma-17	538	33	1964	1964	NUM
ma-17	538	34	)	)	PUNCT
ma-17	538	35	,	,	PUNCT
ma-17	538	36	https://doi	https://doi	PROPN
ma-17	538	37	.	.	PUNCT
ma-17	538	38	org/10.1017	org/10.1017	SYM
ma-17	538	39	/	/	SYM
ma-17	538	40	s0008439500028125.[36	s0008439500028125.[36	PROPN
ma-17	538	41	]	]	X
ma-17	538	42	j.f	j.f	PROPN
ma-17	538	43	.	.	PROPN
ma-17	538	44	traub	traub	PROPN
ma-17	538	45	,	,	PUNCT
ma-17	538	46	a.g	a.g	PROPN
ma-17	538	47	.	.	PROPN
ma-17	538	48	werschulz	werschulz	PROPN
ma-17	538	49	,	,	PUNCT
ma-17	538	50	complexity	complexity	NOUN
ma-17	538	51	and	and	CCONJ
ma-17	538	52	information	information	NOUN
ma-17	538	53	,	,	PUNCT
ma-17	538	54	lezioni	lezioni	NOUN
ma-17	538	55	lince.[lincei	lince.[lincei	NOUN
ma-17	538	56	lectures	lecture	NOUN
ma-17	538	57	]	]	PUNCT
ma-17	538	58	cambridge	cambridge	PROPN
ma-17	538	59	university	university	PROPN
ma-17	538	60	press	press	PROPN
ma-17	538	61	,	,	PUNCT
ma-17	538	62	cambridge	cambridge	PROPN
ma-17	538	63	,	,	PUNCT
ma-17	538	64	1998	1998	NUM
ma-17	538	65	,	,	PUNCT
ma-17	538	66	xii+139	xii+139	PROPN
ma-17	538	67	pp.[37	pp.[37	PROPN
ma-17	538	68	]	]	X
ma-17	538	69	j.f	j.f	PROPN
ma-17	538	70	.	.	PROPN
ma-17	538	71	traub	traub	PROPN
ma-17	538	72	,	,	PUNCT
ma-17	538	73	wozniakowski	wozniakowski	ADJ
ma-17	538	74	,	,	PUNCT
ma-17	538	75	h	h	NOUN
ma-17	538	76	,	,	PUNCT
ma-17	538	77	path	path	NOUN
ma-17	538	78	integration	integration	NOUN
ma-17	538	79	on	on	ADP
ma-17	538	80	a	a	DET
ma-17	538	81	quantum	quantum	ADJ
ma-17	538	82	computer	computer	NOUN
ma-17	538	83	,	,	PUNCT
ma-17	539	1	quant	quant	NOUN
ma-17	539	2	.	.	PUNCT
ma-17	539	3	inf	inf	PROPN
ma-17	539	4	.	.	PUNCT
ma-17	539	5	process	process	NOUN
ma-17	539	6	.	.	PUNCT
ma-17	540	1	1	1	NUM
ma-17	540	2	(	(	PUNCT
ma-17	540	3	2002	2002	NUM
ma-17	540	4	)	)	PUNCT
ma-17	540	5	,	,	PUNCT
ma-17	540	6	356	356	NUM
ma-17	540	7	-	-	SYM
ma-17	540	8	388	388	NUM
ma-17	540	9	,	,	PUNCT
ma-17	540	10	https://arxiv.org/abs/quant-ph/0109113.[38	https://arxiv.org/abs/quant-ph/0109113.[38	NOUN
ma-17	540	11	]	]	PUNCT
ma-17	540	12	t.	t.	PROPN
ma-17	540	13	yamamoto	yamamoto	PROPN
ma-17	540	14	,	,	PUNCT
ma-17	540	15	a	a	DET
ma-17	540	16	convergence	convergence	NOUN
ma-17	540	17	theorem	theorem	NOUN
ma-17	540	18	for	for	ADP
ma-17	540	19	newton	newton	PROPN
ma-17	540	20	-	-	PUNCT
ma-17	540	21	like	like	ADJ
ma-17	540	22	methods	method	NOUN
ma-17	540	23	in	in	ADP
ma-17	540	24	banach	banach	NOUN
ma-17	540	25	spaces	space	NOUN
ma-17	540	26	.	.	PUNCT
ma-17	541	1	numer	numer	PROPN
ma-17	541	2	.	.	PUNCT
ma-17	541	3	math	math	NOUN
ma-17	541	4	.	.	PUNCT
ma-17	542	1	51	51	NUM
ma-17	542	2	(	(	PUNCT
ma-17	542	3	1987	1987	NUM
ma-17	542	4	)	)	PUNCT
ma-17	542	5	,	,	PUNCT
ma-17	542	6	545	545	NUM
ma-17	542	7	-	-	SYM
ma-17	542	8	557	557	NUM
ma-17	542	9	,	,	PUNCT
ma-17	542	10	https://eudml.org/doc/133212.[39	https://eudml.org/doc/133212.[39	PROPN
ma-17	542	11	]	]	X
ma-17	542	12	r.	r.	PROPN
ma-17	542	13	verma	verma	PROPN
ma-17	542	14	,	,	PUNCT
ma-17	542	15	new	new	ADJ
ma-17	542	16	trends	trend	NOUN
ma-17	542	17	in	in	ADP
ma-17	542	18	fractional	fractional	ADJ
ma-17	542	19	programming	programming	NOUN
ma-17	542	20	,	,	PUNCT
ma-17	542	21	nova	nova	PROPN
ma-17	542	22	science	science	NOUN
ma-17	542	23	publisher	publisher	NOUN
ma-17	542	24	,	,	PUNCT
ma-17	542	25	new	new	PROPN
ma-17	542	26	york	york	PROPN
ma-17	542	27	,	,	PUNCT
ma-17	542	28	usa	usa	PROPN
ma-17	542	29	,	,	PUNCT
ma-17	542	30	(	(	PUNCT
ma-17	542	31	2019).[40	2019).[40	NUM
ma-17	542	32	]	]	PUNCT
ma-17	542	33	l.	l.	PROPN
ma-17	542	34	xu	xu	PROPN
ma-17	542	35	,	,	PUNCT
ma-17	542	36	y.-m	y.-m	PROPN
ma-17	542	37	.	.	PUNCT
ma-17	543	1	chu	chu	PROPN
ma-17	543	2	,	,	PUNCT
ma-17	543	3	s.	s.	PROPN
ma-17	543	4	rashid	rashid	PROPN
ma-17	543	5	,	,	PUNCT
ma-17	543	6	a.a	a.a	PROPN
ma-17	543	7	.	.	PROPN
ma-17	543	8	el	el	PROPN
ma-17	543	9	-	-	PUNCT
ma-17	543	10	deeb	deeb	PROPN
ma-17	543	11	,	,	PUNCT
ma-17	543	12	k.s	k.s	PROPN
ma-17	543	13	.	.	PROPN
ma-17	543	14	nisar	nisar	PROPN
ma-17	543	15	,	,	PUNCT
ma-17	543	16	on	on	ADP
ma-17	543	17	new	new	ADJ
ma-17	543	18	unifed	unifed	ADJ
ma-17	543	19	bounds	bound	NOUN
ma-17	543	20	for	for	ADP
ma-17	543	21	a	a	DET
ma-17	543	22	family	family	NOUN
ma-17	543	23	of	of	ADP
ma-17	543	24	functions	function	NOUN
ma-17	543	25	via	via	ADP
ma-17	543	26	fractionalq	fractionalq	ADJ
ma-17	543	27	-	-	PUNCT
ma-17	543	28	calculus	calculus	NOUN
ma-17	543	29	theory	theory	NOUN
ma-17	543	30	,	,	PUNCT
ma-17	543	31	j.	j.	PROPN
ma-17	543	32	funct	funct	PROPN
ma-17	543	33	.	.	PUNCT
ma-17	544	1	space	space	NOUN
ma-17	544	2	2020	2020	NUM
ma-17	544	3	(	(	PUNCT
ma-17	544	4	2020	2020	NUM
ma-17	544	5	)	)	PUNCT
ma-17	544	6	,	,	PUNCT
ma-17	544	7	4984612	4984612	NUM
ma-17	544	8	,	,	PUNCT
ma-17	544	9	https://doi.org/10.1155/2020/4984612.[41	https://doi.org/10.1155/2020/4984612.[41	PROPN
ma-17	544	10	]	]	X
ma-17	544	11	p.p	p.p	PROPN
ma-17	544	12	.	.	PROPN
ma-17	544	13	zabrejko	zabrejko	PROPN
ma-17	544	14	,	,	PUNCT
ma-17	544	15	d.f	d.f	PROPN
ma-17	544	16	.	.	PROPN
ma-17	544	17	nguen	nguen	PROPN
ma-17	544	18	,	,	PUNCT
ma-17	544	19	the	the	DET
ma-17	544	20	majorant	majorant	NOUN
ma-17	544	21	method	method	NOUN
ma-17	544	22	in	in	ADP
ma-17	544	23	the	the	DET
ma-17	544	24	theory	theory	NOUN
ma-17	544	25	of	of	ADP
ma-17	544	26	newton	newton	PROPN
ma-17	544	27	-	-	PUNCT
ma-17	544	28	kantorovich	kantorovich	PROPN
ma-17	544	29	approximations	approximation	NOUN
ma-17	544	30	and	and	CCONJ
ma-17	544	31	the	the	DET
ma-17	544	32	ptákerror	ptákerror	NOUN
ma-17	544	33	estimates	estimate	NOUN
ma-17	544	34	,	,	PUNCT
ma-17	544	35	numer	numer	PROPN
ma-17	544	36	.	.	PUNCT
ma-17	544	37	funct	funct	PROPN
ma-17	544	38	.	.	PUNCT
ma-17	545	1	anal	anal	PROPN
ma-17	545	2	.	.	PUNCT
ma-17	546	1	optim	optim	PROPN
ma-17	546	2	.	.	PUNCT
ma-17	547	1	9	9	NUM
ma-17	547	2	(	(	PUNCT
ma-17	547	3	1987	1987	NUM
ma-17	547	4	)	)	PUNCT
ma-17	547	5	,	,	PUNCT
ma-17	547	6	671	671	NUM
ma-17	547	7	-	-	SYM
ma-17	547	8	684	684	NUM
ma-17	547	9	,	,	PUNCT
ma-17	547	10	https://doi.org/10.1080/01630568708816254	https://doi.org/10.1080/01630568708816254	ADV
ma-17	547	11	.	.	PUNCT
ma-17	548	1	https://doi.org/10.1080/03461238.1933.10419209	https://doi.org/10.1080/03461238.1933.10419209	AUX
ma-17	548	2	https://doi.org/10.1080/03461238.1933.10419209	https://doi.org/10.1080/03461238.1933.10419209	VERB
ma-17	549	1	https://doi.org/10.1017/s0008439500028125	https://doi.org/10.1017/s0008439500028125	PRON
ma-17	549	2	https://doi.org/10.1017/s0008439500028125	https://doi.org/10.1017/s0008439500028125	NUM
ma-17	549	3	https://arxiv.org/abs/quant-ph/0109113	https://arxiv.org/abs/quant-ph/0109113	PROPN
ma-17	549	4	https://eudml.org/doc/133212	https://eudml.org/doc/133212	ADV
ma-17	549	5	https://doi.org/10.1155/2020/4984612	https://doi.org/10.1155/2020/4984612	ADJ
ma-17	549	6	https://doi.org/10.1080/01630568708816254	https://doi.org/10.1080/01630568708816254	ADJ
ma-17	549	7	1	1	NUM
ma-17	549	8	.	.	PUNCT
ma-17	549	9	introduction	introduction	NOUN
ma-17	549	10	2	2	NUM
ma-17	549	11	.	.	PUNCT
ma-17	549	12	results	result	NOUN
ma-17	549	13	on	on	ADP
ma-17	549	14	majorizing	majorize	VERB
ma-17	549	15	sequences	sequence	NOUN
ma-17	549	16	3	3	NUM
ma-17	549	17	.	.	PUNCT
ma-17	549	18	semi	semi	ADJ
ma-17	549	19	-	-	ADJ
ma-17	549	20	local	local	ADJ
ma-17	549	21	convergence	convergence	NOUN
ma-17	549	22	4	4	NUM
ma-17	549	23	.	.	PUNCT
ma-17	549	24	local	local	ADJ
ma-17	549	25	convergence	convergence	NOUN
ma-17	549	26	5	5	NUM
ma-17	549	27	.	.	PUNCT
ma-17	550	1	numerical	numerical	ADJ
ma-17	550	2	experiments	experiment	NOUN
ma-17	550	3	6	6	NUM
ma-17	550	4	.	.	PUNCT
ma-17	551	1	conclusion	conclusion	NOUN
ma-17	551	2	references	reference	NOUN