id	sid	tid	token	lemma	pos
ma-170	1	1	2023	2023	NUM
ma-170	1	2	ada	ada	PROPN
ma-170	1	3	academica	academica	PROPN
ma-170	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-170	1	5	.	.	PUNCT
ma-170	2	1	j.	j.	PROPN
ma-170	2	2	math	math	PROPN
ma-170	2	3	.	.	PUNCT
ma-170	3	1	anal	anal	ADJ
ma-170	3	2	.	.	PUNCT
ma-170	4	1	3	3	NUM
ma-170	4	2	(	(	PUNCT
ma-170	4	3	2023	2023	NUM
ma-170	4	4	)	)	PUNCT
ma-170	4	5	24doi	24doi	NOUN
ma-170	4	6	:	:	PUNCT
ma-170	4	7	10.28924	10.28924	NUM
ma-170	4	8	/	/	SYM
ma-170	4	9	ada	ada	NOUN
ma-170	4	10	/	/	SYM
ma-170	4	11	ma.3.24	ma.3.24	ADJ
ma-170	4	12	seventh	seventh	ADJ
ma-170	4	13	order	order	NOUN
ma-170	4	14	derivative	derivative	ADJ
ma-170	4	15	-	-	PUNCT
ma-170	4	16	free	free	ADJ
ma-170	4	17	methods	method	NOUN
ma-170	4	18	for	for	ADP
ma-170	4	19	non	non	ADJ
ma-170	4	20	-	-	ADJ
ma-170	4	21	differentiable	differentiable	ADJ
ma-170	4	22	operator	operator	NOUN
ma-170	4	23	equations	equation	NOUN
ma-170	4	24	sunil	sunil	PROPN
ma-170	4	25	kumar1	kumar1	PROPN
ma-170	4	26	,	,	PUNCT
ma-170	4	27	janak	janak	PROPN
ma-170	4	28	raj	raj	PROPN
ma-170	4	29	sharma2	sharma2	PROPN
ma-170	4	30	,	,	PUNCT
ma-170	4	31	ioannis	ioannis	PROPN
ma-170	4	32	k.	k.	PROPN
ma-170	4	33	argyros3,∗	argyros3,∗	PROPN
ma-170	4	34	,	,	PUNCT
ma-170	4	35	samundra	samundra	NOUN
ma-170	4	36	regmi4	regmi4	PROPN
ma-170	4	37	1department	1department	NUM
ma-170	4	38	of	of	ADP
ma-170	4	39	mathematics	mathematic	NOUN
ma-170	4	40	,	,	PUNCT
ma-170	4	41	university	university	NOUN
ma-170	4	42	centre	centre	NOUN
ma-170	4	43	for	for	ADP
ma-170	4	44	research	research	NOUN
ma-170	4	45	and	and	CCONJ
ma-170	4	46	development	development	NOUN
ma-170	4	47	,	,	PUNCT
ma-170	4	48	chandigarh	chandigarh	PROPN
ma-170	4	49	university	university	NOUN
ma-170	4	50	,	,	PUNCT
ma-170	4	51	mohali-140413	mohali-140413	PROPN
ma-170	4	52	,	,	PUNCT
ma-170	4	53	india	india	PROPN
ma-170	4	54	sfageria1988@gmail.com	sfageria1988@gmail.com	X
ma-170	5	1	2department	2department	NUM
ma-170	5	2	of	of	ADP
ma-170	5	3	mathematics	mathematic	NOUN
ma-170	5	4	,	,	PUNCT
ma-170	5	5	sant	sant	PROPN
ma-170	5	6	longowal	longowal	PROPN
ma-170	5	7	institute	institute	PROPN
ma-170	5	8	of	of	ADP
ma-170	5	9	engineering	engineering	PROPN
ma-170	5	10	&	&	CCONJ
ma-170	5	11	technology	technology	PROPN
ma-170	5	12	,	,	PUNCT
ma-170	5	13	longowal	longowal	NOUN
ma-170	5	14	,	,	PUNCT
ma-170	5	15	punjab	punjab	PROPN
ma-170	5	16	148106	148106	NUM
ma-170	5	17	,	,	PUNCT
ma-170	5	18	india	india	PROPN
ma-170	5	19	jrshira@yahoo.co.in	jrshira@yahoo.co.in	PROPN
ma-170	5	20	3department	3department	PROPN
ma-170	5	21	of	of	ADP
ma-170	5	22	computing	computing	NOUN
ma-170	5	23	and	and	CCONJ
ma-170	5	24	mathematical	mathematical	ADJ
ma-170	5	25	sciences	sciences	PROPN
ma-170	5	26	,	,	PUNCT
ma-170	5	27	cameron	cameron	PROPN
ma-170	5	28	university	university	PROPN
ma-170	5	29	,	,	PUNCT
ma-170	5	30	lawton	lawton	PROPN
ma-170	5	31	,	,	PUNCT
ma-170	5	32	ok	ok	PROPN
ma-170	5	33	73505	73505	NUM
ma-170	5	34	,	,	PUNCT
ma-170	5	35	usa	usa	PROPN
ma-170	5	36	iargyros@cameron.edu	iargyros@cameron.edu	PROPN
ma-170	6	1	4department	4department	NUM
ma-170	6	2	of	of	ADP
ma-170	6	3	mathematics	mathematic	NOUN
ma-170	6	4	,	,	PUNCT
ma-170	6	5	university	university	PROPN
ma-170	6	6	of	of	ADP
ma-170	6	7	houston	houston	PROPN
ma-170	6	8	,	,	PUNCT
ma-170	6	9	houston	houston	PROPN
ma-170	6	10	,	,	PUNCT
ma-170	6	11	tx	tx	PROPN
ma-170	6	12	,	,	PUNCT
ma-170	6	13	77024	77024	NUM
ma-170	6	14	,	,	PUNCT
ma-170	6	15	usa	usa	PROPN
ma-170	6	16	sregmi5@uh.edu	sregmi5@uh.edu	PROPN
ma-170	6	17	∗correspondence	∗correspondence	NOUN
ma-170	6	18	:	:	PUNCT
ma-170	6	19	iargyros@cameron.edu	iargyros@cameron.edu	X
ma-170	7	1	abstract	abstract	ADJ
ma-170	7	2	.	.	PUNCT
ma-170	8	1	in	in	ADP
ma-170	8	2	nonlinear	nonlinear	ADJ
ma-170	8	3	problems	problem	NOUN
ma-170	8	4	where	where	SCONJ
ma-170	8	5	function	function	NOUN
ma-170	8	6	’s	’s	PART
ma-170	8	7	derivatives	derivative	NOUN
ma-170	8	8	are	be	AUX
ma-170	8	9	difficult	difficult	ADJ
ma-170	8	10	or	or	CCONJ
ma-170	8	11	expensive	expensive	ADJ
ma-170	8	12	to	to	PART
ma-170	8	13	compute	compute	VERB
ma-170	8	14	,	,	PUNCT
ma-170	8	15	derivative	derivative	ADJ
ma-170	8	16	-	-	PUNCT
ma-170	8	17	free	free	ADJ
ma-170	8	18	iterative	iterative	NOUN
ma-170	8	19	methods	method	NOUN
ma-170	8	20	are	be	AUX
ma-170	8	21	good	good	ADJ
ma-170	8	22	options	option	NOUN
ma-170	8	23	to	to	PART
ma-170	8	24	find	find	VERB
ma-170	8	25	the	the	DET
ma-170	8	26	numerical	numerical	ADJ
ma-170	8	27	solution	solution	NOUN
ma-170	8	28	.	.	PUNCT
ma-170	9	1	one	one	NUM
ma-170	9	2	of	of	ADP
ma-170	9	3	the	the	DET
ma-170	9	4	importantparts	importantpart	NOUN
ma-170	9	5	in	in	ADP
ma-170	9	6	the	the	DET
ma-170	9	7	development	development	NOUN
ma-170	9	8	of	of	ADP
ma-170	9	9	such	such	ADJ
ma-170	9	10	methods	method	NOUN
ma-170	9	11	is	be	AUX
ma-170	9	12	to	to	PART
ma-170	9	13	study	study	VERB
ma-170	9	14	their	their	PRON
ma-170	9	15	convergence	convergence	NOUN
ma-170	9	16	properties	property	NOUN
ma-170	9	17	.	.	PUNCT
ma-170	10	1	in	in	ADP
ma-170	10	2	this	this	DET
ma-170	10	3	paper	paper	NOUN
ma-170	10	4	,	,	PUNCT
ma-170	10	5	wereview	wereview	VERB
ma-170	10	6	the	the	DET
ma-170	10	7	concepts	concept	NOUN
ma-170	10	8	of	of	ADP
ma-170	10	9	local	local	ADJ
ma-170	10	10	and	and	CCONJ
ma-170	10	11	semi	semi	ADJ
ma-170	10	12	-	-	ADJ
ma-170	10	13	local	local	ADJ
ma-170	10	14	convergence	convergence	NOUN
ma-170	10	15	for	for	ADP
ma-170	10	16	a	a	DET
ma-170	10	17	derivative	derivative	ADJ
ma-170	10	18	-	-	PUNCT
ma-170	10	19	free	free	ADJ
ma-170	10	20	method	method	NOUN
ma-170	10	21	for	for	ADP
ma-170	10	22	nonlinearequations	nonlinearequation	NOUN
ma-170	10	23	.	.	PUNCT
ma-170	11	1	in	in	ADP
ma-170	11	2	the	the	DET
ma-170	11	3	earlier	early	ADJ
ma-170	11	4	study	study	NOUN
ma-170	11	5	of	of	ADP
ma-170	11	6	the	the	DET
ma-170	11	7	considered	consider	VERB
ma-170	11	8	method	method	NOUN
ma-170	11	9	,	,	PUNCT
ma-170	11	10	the	the	DET
ma-170	11	11	convergence	convergence	NOUN
ma-170	11	12	analysis	analysis	NOUN
ma-170	11	13	was	be	AUX
ma-170	11	14	carried	carry	VERB
ma-170	11	15	outassuming	outassume	VERB
ma-170	11	16	the	the	DET
ma-170	11	17	existence	existence	NOUN
ma-170	11	18	of	of	ADP
ma-170	11	19	higher	high	ADJ
ma-170	11	20	order	order	NOUN
ma-170	11	21	derivatives	derivative	NOUN
ma-170	11	22	while	while	SCONJ
ma-170	11	23	no	no	DET
ma-170	11	24	derivative	derivative	NOUN
ma-170	11	25	is	be	AUX
ma-170	11	26	used	use	VERB
ma-170	11	27	in	in	ADP
ma-170	11	28	the	the	DET
ma-170	11	29	method	method	NOUN
ma-170	11	30	.	.	PUNCT
ma-170	12	1	suchassumptions	suchassumption	NOUN
ma-170	12	2	certainly	certainly	ADV
ma-170	12	3	restrict	restrict	VERB
ma-170	12	4	its	its	PRON
ma-170	12	5	applicability	applicability	NOUN
ma-170	12	6	.	.	PUNCT
ma-170	13	1	the	the	DET
ma-170	13	2	present	present	ADJ
ma-170	13	3	study	study	NOUN
ma-170	13	4	further	far	ADV
ma-170	13	5	provides	provide	VERB
ma-170	13	6	the	the	DET
ma-170	13	7	estimate	estimate	NOUN
ma-170	13	8	ofconvergence	ofconvergence	NOUN
ma-170	13	9	radius	radius	NOUN
ma-170	13	10	and	and	CCONJ
ma-170	13	11	bounds	bound	NOUN
ma-170	13	12	on	on	ADP
ma-170	13	13	the	the	DET
ma-170	13	14	error	error	NOUN
ma-170	13	15	for	for	ADP
ma-170	13	16	the	the	DET
ma-170	13	17	given	give	VERB
ma-170	13	18	method	method	NOUN
ma-170	13	19	.	.	PUNCT
ma-170	14	1	thus	thus	ADV
ma-170	14	2	,	,	PUNCT
ma-170	14	3	the	the	DET
ma-170	14	4	applicability	applicability	NOUN
ma-170	14	5	of	of	ADP
ma-170	14	6	themethod	themethod	NOUN
ma-170	14	7	clearly	clearly	ADV
ma-170	14	8	seems	seem	VERB
ma-170	14	9	to	to	PART
ma-170	14	10	be	be	AUX
ma-170	14	11	extended	extend	VERB
ma-170	14	12	over	over	ADP
ma-170	14	13	the	the	DET
ma-170	14	14	wider	wide	ADJ
ma-170	14	15	class	class	NOUN
ma-170	14	16	of	of	ADP
ma-170	14	17	problems	problem	NOUN
ma-170	14	18	.	.	PUNCT
ma-170	15	1	we	we	PRON
ma-170	15	2	also	also	ADV
ma-170	15	3	review	review	VERB
ma-170	15	4	some	some	PRON
ma-170	15	5	of	of	ADP
ma-170	15	6	therecent	therecent	NOUN
ma-170	15	7	developments	development	NOUN
ma-170	15	8	in	in	ADP
ma-170	15	9	this	this	DET
ma-170	15	10	area	area	NOUN
ma-170	15	11	.	.	PUNCT
ma-170	16	1	the	the	DET
ma-170	16	2	results	result	NOUN
ma-170	16	3	presented	present	VERB
ma-170	16	4	in	in	ADP
ma-170	16	5	this	this	DET
ma-170	16	6	paper	paper	NOUN
ma-170	16	7	can	can	AUX
ma-170	16	8	be	be	AUX
ma-170	16	9	useful	useful	ADJ
ma-170	16	10	for	for	ADP
ma-170	16	11	practitionersand	practitionersand	NOUN
ma-170	16	12	researchers	researcher	NOUN
ma-170	16	13	in	in	ADP
ma-170	16	14	developing	develop	VERB
ma-170	16	15	and	and	CCONJ
ma-170	16	16	analyzing	analyze	VERB
ma-170	16	17	derivative	derivative	ADJ
ma-170	16	18	-	-	PUNCT
ma-170	16	19	free	free	ADJ
ma-170	16	20	numerical	numerical	ADJ
ma-170	16	21	algorithms	algorithm	NOUN
ma-170	16	22	.	.	PUNCT
ma-170	17	1	1	1	X
ma-170	17	2	.	.	X
ma-170	17	3	introduction	introduction	NOUN
ma-170	17	4	there	there	PRON
ma-170	17	5	are	be	VERB
ma-170	17	6	several	several	ADJ
ma-170	17	7	numerical	numerical	ADJ
ma-170	17	8	methods	method	NOUN
ma-170	17	9	such	such	ADJ
ma-170	17	10	as	as	ADP
ma-170	17	11	newton	newton	PROPN
ma-170	17	12	’s	’s	PART
ma-170	17	13	method	method	NOUN
ma-170	17	14	,	,	PUNCT
ma-170	17	15	broyden	broyden	NOUN
ma-170	17	16	’s	’s	PART
ma-170	17	17	method	method	NOUN
ma-170	17	18	,	,	PUNCT
ma-170	17	19	secant	secant	ADJ
ma-170	17	20	methodand	methodand	PROPN
ma-170	17	21	steffensen	steffensen	PROPN
ma-170	17	22	’s	’s	PART
ma-170	17	23	method	method	NOUN
ma-170	17	24	[	[	X
ma-170	17	25	3–11,13,14,17	3–11,13,14,17	NUM
ma-170	17	26	]	]	PUNCT
ma-170	17	27	that	that	PRON
ma-170	17	28	can	can	AUX
ma-170	17	29	be	be	AUX
ma-170	17	30	used	use	VERB
ma-170	17	31	to	to	PART
ma-170	17	32	approximate	approximate	VERB
ma-170	17	33	x∗	x∗	PROPN
ma-170	17	34	of	of	ADP
ma-170	17	35	the	the	DET
ma-170	17	36	equation	equation	NOUN
ma-170	18	1	f	f	X
ma-170	18	2	(	(	PUNCT
ma-170	18	3	x	x	X
ma-170	18	4	)	)	PUNCT
ma-170	18	5	=	=	SYM
ma-170	18	6	0	0	NUM
ma-170	18	7	,	,	PUNCT
ma-170	18	8	(	(	PUNCT
ma-170	18	9	1.1	1.1	NUM
ma-170	18	10	)	)	PUNCT
ma-170	18	11	for	for	ADP
ma-170	18	12	f	f	PROPN
ma-170	18	13	:	:	PUNCT
ma-170	19	1	ω	ω	PROPN
ma-170	19	2	⊂	⊂	PROPN
ma-170	19	3	z	z	X
ma-170	19	4	→	→	SYM
ma-170	19	5	z	z	X
ma-170	19	6	,	,	PUNCT
ma-170	19	7	f	f	PROPN
ma-170	19	8	is	be	AUX
ma-170	19	9	a	a	DET
ma-170	19	10	continuous	continuous	ADJ
ma-170	19	11	operator	operator	NOUN
ma-170	19	12	,	,	PUNCT
ma-170	19	13	acting	act	VERB
ma-170	19	14	between	between	ADP
ma-170	19	15	banach	banach	NOUN
ma-170	19	16	space	space	NOUN
ma-170	19	17	z	z	PROPN
ma-170	19	18	and	and	CCONJ
ma-170	19	19	itself.newton	itself.newton	PROPN
ma-170	19	20	’s	’s	PART
ma-170	19	21	method	method	NOUN
ma-170	19	22	is	be	AUX
ma-170	19	23	a	a	DET
ma-170	19	24	popular	popular	ADJ
ma-170	19	25	iterative	iterative	NOUN
ma-170	19	26	method	method	NOUN
ma-170	19	27	used	use	VERB
ma-170	19	28	to	to	PART
ma-170	19	29	find	find	VERB
ma-170	19	30	the	the	DET
ma-170	19	31	roots	root	NOUN
ma-170	19	32	of	of	ADP
ma-170	19	33	a	a	DET
ma-170	19	34	nonlinear	nonlinear	ADJ
ma-170	19	35	equation	equation	NOUN
ma-170	19	36	.	.	PUNCT
ma-170	20	1	received	receive	VERB
ma-170	20	2	:	:	PUNCT
ma-170	20	3	30	30	NUM
ma-170	20	4	apr	apr	NOUN
ma-170	20	5	2023	2023	NUM
ma-170	20	6	.	.	PUNCT
ma-170	21	1	key	key	ADJ
ma-170	21	2	words	word	NOUN
ma-170	21	3	and	and	CCONJ
ma-170	21	4	phrases	phrase	NOUN
ma-170	21	5	.	.	PUNCT
ma-170	22	1	divided	divide	VERB
ma-170	22	2	difference	difference	NOUN
ma-170	22	3	;	;	PUNCT
ma-170	22	4	banach	banach	NOUN
ma-170	22	5	space	space	NOUN
ma-170	22	6	;	;	PUNCT
ma-170	22	7	convergence	convergence	NOUN
ma-170	22	8	;	;	PUNCT
ma-170	22	9	order	order	NOUN
ma-170	22	10	of	of	ADP
ma-170	22	11	convergence.1	convergence.1	PROPN
ma-170	22	12	https://adac.ee	https://adac.ee	PROPN
ma-170	22	13	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	PUNCT
ma-170	22	14	eur	eur	PROPN
ma-170	22	15	.	.	PUNCT
ma-170	23	1	j.	j.	PROPN
ma-170	23	2	math	math	PROPN
ma-170	23	3	.	.	PUNCT
ma-170	24	1	anal	anal	PROPN
ma-170	24	2	.	.	PUNCT
ma-170	25	1	10.28924	10.28924	NUM
ma-170	25	2	/	/	SYM
ma-170	25	3	ada	ada	PROPN
ma-170	25	4	/	/	SYM
ma-170	25	5	ma.3.24	ma.3.24	ADJ
ma-170	25	6	2iterative	2iterative	NUM
ma-170	25	7	solution	solution	NOUN
ma-170	25	8	methods	method	NOUN
ma-170	25	9	are	be	AUX
ma-170	25	10	commonly	commonly	ADV
ma-170	25	11	used	use	VERB
ma-170	25	12	when	when	SCONJ
ma-170	25	13	it	it	PRON
ma-170	25	14	is	be	AUX
ma-170	25	15	not	not	PART
ma-170	25	16	possible	possible	ADJ
ma-170	25	17	to	to	PART
ma-170	25	18	obtain	obtain	VERB
ma-170	25	19	the	the	DET
ma-170	25	20	solution	solution	NOUN
ma-170	25	21	x∗	x∗	PROPN
ma-170	25	22	inclosed	inclose	VERB
ma-170	25	23	or	or	CCONJ
ma-170	25	24	analytical	analytical	ADJ
ma-170	25	25	form	form	NOUN
ma-170	25	26	.	.	PUNCT
ma-170	26	1	instead	instead	ADV
ma-170	26	2	,	,	PUNCT
ma-170	26	3	these	these	DET
ma-170	26	4	methods	method	NOUN
ma-170	26	5	generate	generate	VERB
ma-170	26	6	a	a	DET
ma-170	26	7	sequence	sequence	NOUN
ma-170	26	8	of	of	ADP
ma-170	26	9	approximate	approximate	ADJ
ma-170	26	10	solutionsthat	solutionsthat	ADJ
ma-170	26	11	converge	converge	NOUN
ma-170	26	12	towards	towards	ADP
ma-170	26	13	the	the	DET
ma-170	26	14	true	true	ADJ
ma-170	26	15	solution	solution	NOUN
ma-170	26	16	x∗.steffensen	x∗.steffensen	PROPN
ma-170	26	17	’s	’s	PART
ma-170	26	18	method	method	NOUN
ma-170	26	19	[	[	X
ma-170	26	20	5	5	NUM
ma-170	26	21	,	,	PUNCT
ma-170	26	22	9	9	NUM
ma-170	26	23	]	]	PUNCT
ma-170	26	24	defined	define	VERB
ma-170	26	25	for	for	ADP
ma-170	26	26	each	each	DET
ma-170	26	27	n	n	NOUN
ma-170	26	28	=	=	SYM
ma-170	26	29	0	0	NUM
ma-170	26	30	,	,	PUNCT
ma-170	26	31	1	1	NUM
ma-170	26	32	,	,	PUNCT
ma-170	26	33	2	2	NUM
ma-170	26	34	,	,	PUNCT
ma-170	26	35	.	.	PUNCT
ma-170	26	36	.	.	PUNCT
ma-170	26	37	.	.	PUNCT
ma-170	27	1	by	by	ADP
ma-170	27	2	xn+1	xn+1	PROPN
ma-170	27	3	=	=	SYM
ma-170	27	4	xn	xn	PROPN
ma-170	27	5	−	−	PROPN
ma-170	27	6	b−1f	b−1f	X
ma-170	27	7	(	(	PUNCT
ma-170	27	8	xn	xn	PROPN
ma-170	27	9	)	)	PUNCT
ma-170	27	10	,	,	PUNCT
ma-170	27	11	(	(	PUNCT
ma-170	27	12	1.2	1.2	NUM
ma-170	27	13	)	)	PUNCT
ma-170	27	14	where	where	SCONJ
ma-170	27	15	b	b	NOUN
ma-170	27	16	=	=	SYM
ma-170	27	17	bn	bn	NOUN
ma-170	27	18	=	=	SYM
ma-170	28	1	[	[	X
ma-170	28	2	un	un	PROPN
ma-170	28	3	,	,	PUNCT
ma-170	28	4	xn;f	xn;f	PUNCT
ma-170	28	5	]	]	PUNCT
ma-170	28	6	and	and	CCONJ
ma-170	28	7	un	un	PROPN
ma-170	29	1	=	=	PROPN
ma-170	29	2	xn	xn	PROPN
ma-170	30	1	+	+	NUM
ma-170	30	2	f	f	X
ma-170	30	3	(	(	PUNCT
ma-170	30	4	xn	xn	PROPN
ma-170	30	5	)	)	PUNCT
ma-170	30	6	,	,	PUNCT
ma-170	30	7	has	have	AUX
ma-170	30	8	been	be	AUX
ma-170	30	9	used	use	VERB
ma-170	30	10	extensively	extensively	ADV
ma-170	30	11	to	to	PART
ma-170	30	12	generate	generate	VERB
ma-170	30	13	such	such	ADJ
ma-170	30	14	asequence	asequence	NOUN
ma-170	30	15	converging	converge	VERB
ma-170	30	16	quadratically	quadratically	ADV
ma-170	30	17	to	to	ADP
ma-170	30	18	x∗.many	x∗.many	PROPN
ma-170	30	19	iterative	iterative	NOUN
ma-170	30	20	approaches	approach	NOUN
ma-170	30	21	have	have	AUX
ma-170	30	22	been	be	AUX
ma-170	30	23	developed	develop	VERB
ma-170	30	24	to	to	PART
ma-170	30	25	improve	improve	VERB
ma-170	30	26	efficiency	efficiency	NOUN
ma-170	30	27	and	and	CCONJ
ma-170	30	28	order	order	NOUN
ma-170	30	29	convergence(see	convergence(see	VERB
ma-170	31	1	[	[	X
ma-170	31	2	1	1	NUM
ma-170	31	3	,	,	PUNCT
ma-170	31	4	2	2	NUM
ma-170	31	5	,	,	PUNCT
ma-170	31	6	15,16	15,16	NUM
ma-170	31	7	]	]	PUNCT
ma-170	31	8	)	)	PUNCT
ma-170	31	9	.	.	PUNCT
ma-170	32	1	an	an	DET
ma-170	32	2	approach	approach	NOUN
ma-170	32	3	established	establish	VERB
ma-170	32	4	in	in	ADP
ma-170	32	5	[	[	X
ma-170	32	6	16	16	NUM
ma-170	32	7	]	]	PUNCT
ma-170	32	8	that	that	PRON
ma-170	32	9	is	be	AUX
ma-170	32	10	defined	define	VERB
ma-170	32	11	for	for	ADP
ma-170	32	12	x0	x0	PROPN
ma-170	32	13	∈	∈	PROPN
ma-170	32	14	ω	ω	PROPN
ma-170	32	15	by	by	ADP
ma-170	32	16	un	un	PROPN
ma-170	33	1	=	=	PROPN
ma-170	33	2	xn	xn	PROPN
ma-170	34	1	+	+	NUM
ma-170	34	2	f	f	X
ma-170	34	3	(	(	PUNCT
ma-170	34	4	xn	xn	PROPN
ma-170	34	5	)	)	PUNCT
ma-170	34	6	,	,	PUNCT
ma-170	34	7	vn	vn	PROPN
ma-170	34	8	=	=	SYM
ma-170	34	9	xn	xn	PROPN
ma-170	35	1	−	−	PROPN
ma-170	35	2	f	f	PROPN
ma-170	35	3	(	(	PUNCT
ma-170	35	4	xn	xn	PROPN
ma-170	35	5	)	)	PUNCT
ma-170	35	6	,	,	PUNCT
ma-170	36	1	d	d	NOUN
ma-170	36	2	=	=	PUNCT
ma-170	36	3	dn	dn	PROPN
ma-170	36	4	=	=	PUNCT
ma-170	37	1	[	[	X
ma-170	37	2	un	un	X
ma-170	37	3	,	,	PUNCT
ma-170	37	4	vn;f	vn;f	PUNCT
ma-170	37	5	]	]	X
ma-170	37	6	,	,	PUNCT
ma-170	37	7	yn	yn	X
ma-170	37	8	=	=	PUNCT
ma-170	37	9	xn	xn	PROPN
ma-170	37	10	−d−1f	−d−1f	PROPN
ma-170	37	11	(	(	PUNCT
ma-170	37	12	xn	xn	PROPN
ma-170	37	13	)	)	PUNCT
ma-170	37	14	,	,	PUNCT
ma-170	38	1	zn	zn	PROPN
ma-170	38	2	=	=	SYM
ma-170	38	3	yn	yn	PROPN
ma-170	38	4	−	−	PROPN
ma-170	39	1	(	(	PUNCT
ma-170	39	2	3i	3i	NOUN
ma-170	39	3	−	−	PROPN
ma-170	39	4	2d−1[yn	2d−1[yn	NUM
ma-170	39	5	,	,	PUNCT
ma-170	39	6	xn;f	xn;f	PUNCT
ma-170	39	7	]	]	X
ma-170	39	8	)	)	PUNCT
ma-170	39	9	d−1f	d−1f	NOUN
ma-170	39	10	(	(	PUNCT
ma-170	39	11	yn	yn	PROPN
ma-170	39	12	)	)	PUNCT
ma-170	39	13	,	,	PUNCT
ma-170	39	14	xn+1	xn+1	PROPN
ma-170	39	15	=	=	SYM
ma-170	39	16	zn	zn	PROPN
ma-170	39	17	−	−	PROPN
ma-170	39	18	(	(	PUNCT
ma-170	39	19	13	13	NUM
ma-170	39	20	4	4	NUM
ma-170	39	21	i	i	PRON
ma-170	39	22	−d−1[zn	−d−1[zn	NOUN
ma-170	39	23	,	,	PUNCT
ma-170	39	24	yn;f	yn;f	PUNCT
ma-170	39	25	]	]	PUNCT
ma-170	39	26	(	(	PUNCT
ma-170	39	27	7	7	NUM
ma-170	39	28	2	2	NUM
ma-170	40	1	i	i	PRON
ma-170	40	2	−	−	NUM
ma-170	40	3	5	5	NUM
ma-170	40	4	4	4	NUM
ma-170	40	5	d−1[zn	d−1[zn	NOUN
ma-170	40	6	,	,	PUNCT
ma-170	40	7	yn;f	yn;f	NOUN
ma-170	40	8	]	]	PUNCT
ma-170	40	9	)	)	PUNCT
ma-170	40	10	)	)	PUNCT
ma-170	40	11	d−1f	d−1f	NOUN
ma-170	40	12	(	(	PUNCT
ma-170	40	13	zn	zn	NOUN
ma-170	40	14	)	)	PUNCT
ma-170	40	15	,	,	PUNCT
ma-170	40	16	(	(	PUNCT
ma-170	40	17	1.3	1.3	NUM
ma-170	40	18	)	)	PUNCT
ma-170	40	19	has	have	AUX
ma-170	40	20	received	receive	VERB
ma-170	40	21	significant	significant	ADJ
ma-170	40	22	attention	attention	NOUN
ma-170	40	23	in	in	ADP
ma-170	40	24	this	this	DET
ma-170	40	25	paper	paper	NOUN
ma-170	40	26	.	.	PUNCT
ma-170	41	1	the	the	DET
ma-170	41	2	convergence	convergence	NOUN
ma-170	41	3	order	order	NOUN
ma-170	41	4	seven	seven	NUM
ma-170	41	5	is	be	AUX
ma-170	41	6	shown	show	VERB
ma-170	41	7	in	in	ADP
ma-170	41	8	[	[	X
ma-170	41	9	16],when	16],when	NOUN
ma-170	41	10	z	z	NOUN
ma-170	41	11	=	=	SYM
ma-170	41	12	rm	rm	PROPN
ma-170	41	13	etc	etc	X
ma-170	41	14	.	.	PUNCT
ma-170	41	15	using	use	VERB
ma-170	41	16	assumption	assumption	NOUN
ma-170	41	17	on	on	ADP
ma-170	41	18	f	f	PROPN
ma-170	41	19	i	i	PRON
ma-170	41	20	,	,	PUNCT
ma-170	41	21	i	i	PRON
ma-170	41	22	=	=	NOUN
ma-170	41	23	1	1	NUM
ma-170	41	24	,	,	PUNCT
ma-170	41	25	2	2	NUM
ma-170	41	26	,	,	PUNCT
ma-170	41	27	.	.	PUNCT
ma-170	41	28	.	.	PUNCT
ma-170	41	29	.	.	PUNCT
ma-170	42	1	,	,	PUNCT
ma-170	42	2	8	8	NUM
ma-170	42	3	not	not	PART
ma-170	42	4	present	present	ADJ
ma-170	42	5	in	in	ADP
ma-170	42	6	the	the	DET
ma-170	42	7	method	method	NOUN
ma-170	42	8	,	,	PUNCT
ma-170	42	9	significantlyreducing	significantlyreduce	VERB
ma-170	42	10	its	its	PRON
ma-170	42	11	applicability	applicability	NOUN
ma-170	42	12	although	although	SCONJ
ma-170	42	13	it	it	PRON
ma-170	42	14	may	may	AUX
ma-170	42	15	converge.consider	converge.consider	VERB
ma-170	42	16	the	the	DET
ma-170	42	17	function	function	NOUN
ma-170	42	18	f	f	PROPN
ma-170	42	19	(	(	PUNCT
ma-170	42	20	t	t	PROPN
ma-170	42	21	)	)	PUNCT
ma-170	42	22	=	=	PRON
ma-170	43	1	{	{	PUNCT
ma-170	43	2	7t3	7t3	NUM
ma-170	43	3	log(t	log(t	NOUN
ma-170	43	4	)	)	PUNCT
ma-170	44	1	+	+	CCONJ
ma-170	44	2	5t5	5t5	NUM
ma-170	44	3	−	−	PROPN
ma-170	44	4	5t4	5t4	NUM
ma-170	44	5	,	,	PUNCT
ma-170	44	6	t	t	PROPN
ma-170	44	7	6=	6=	NUM
ma-170	44	8	0	0	NUM
ma-170	44	9	0	0	NUM
ma-170	44	10	,	,	PUNCT
ma-170	44	11	t	t	NOUN
ma-170	44	12	=	=	SYM
ma-170	44	13	0	0	NUM
ma-170	44	14	(	(	PUNCT
ma-170	44	15	1.4	1.4	NUM
ma-170	44	16	)	)	PUNCT
ma-170	44	17	then	then	ADV
ma-170	44	18	,	,	PUNCT
ma-170	44	19	in	in	ADP
ma-170	44	20	any	any	DET
ma-170	44	21	neighborhood	neighborhood	NOUN
ma-170	44	22	of	of	ADP
ma-170	44	23	0	0	NUM
ma-170	44	24	and	and	CCONJ
ma-170	44	25	1	1	NUM
ma-170	44	26	,	,	PUNCT
ma-170	44	27	say	say	VERB
ma-170	44	28	f	f	PROPN
ma-170	44	29	′′′	′′′	PROPN
ma-170	44	30	is	be	AUX
ma-170	44	31	unbounded	unbounded	ADJ
ma-170	44	32	.	.	PUNCT
ma-170	45	1	hence	hence	ADV
ma-170	45	2	,	,	PUNCT
ma-170	45	3	the	the	DET
ma-170	45	4	results	result	NOUN
ma-170	45	5	in	in	ADP
ma-170	45	6	[	[	X
ma-170	45	7	16	16	NUM
ma-170	45	8	]	]	X
ma-170	45	9	cannotassure	cannotassure	NOUN
ma-170	45	10	convergence	convergence	NOUN
ma-170	45	11	to	to	ADP
ma-170	45	12	t∗	t∗	NOUN
ma-170	45	13	=	=	NOUN
ma-170	45	14	1	1	NUM
ma-170	45	15	.	.	PUNCT
ma-170	46	1	but	but	CCONJ
ma-170	46	2	the	the	DET
ma-170	46	3	method	method	NOUN
ma-170	46	4	converges.in	converges.in	PRON
ma-170	46	5	this	this	DET
ma-170	46	6	article	article	NOUN
ma-170	46	7	we	we	PRON
ma-170	46	8	study	study	VERB
ma-170	46	9	convergence	convergence	NOUN
ma-170	46	10	of	of	ADP
ma-170	46	11	the	the	DET
ma-170	46	12	method	method	NOUN
ma-170	46	13	(	(	PUNCT
ma-170	46	14	1.3	1.3	NUM
ma-170	46	15	)	)	PUNCT
ma-170	46	16	that	that	PRON
ma-170	46	17	includes	include	VERB
ma-170	46	18	mainly	mainly	ADV
ma-170	46	19	the	the	DET
ma-170	46	20	local	local	ADJ
ma-170	46	21	andsemi	andsemi	NOUN
ma-170	46	22	-	-	ADJ
ma-170	46	23	local	local	ADJ
ma-170	46	24	convergence	convergence	NOUN
ma-170	46	25	(	(	PUNCT
ma-170	46	26	not	not	PART
ma-170	46	27	provided	provide	VERB
ma-170	46	28	in	in	ADP
ma-170	46	29	[	[	PUNCT
ma-170	46	30	16]).local	16]).local	ADJ
ma-170	46	31	convergence	convergence	NOUN
ma-170	46	32	analysis	analysis	NOUN
ma-170	46	33	uses	use	VERB
ma-170	46	34	information	information	NOUN
ma-170	46	35	about	about	ADP
ma-170	46	36	the	the	DET
ma-170	46	37	actual	actual	ADJ
ma-170	46	38	solution	solution	NOUN
ma-170	46	39	to	to	PART
ma-170	46	40	determine	determine	VERB
ma-170	46	41	the	the	DET
ma-170	46	42	rateand	rateand	NOUN
ma-170	46	43	radius	radius	NOUN
ma-170	46	44	of	of	ADP
ma-170	46	45	convergence	convergence	NOUN
ma-170	46	46	of	of	ADP
ma-170	46	47	the	the	DET
ma-170	46	48	method	method	NOUN
ma-170	46	49	.	.	PUNCT
ma-170	47	1	this	this	PRON
ma-170	47	2	typically	typically	ADV
ma-170	47	3	involves	involve	VERB
ma-170	47	4	estimating	estimate	VERB
ma-170	47	5	the	the	DET
ma-170	47	6	size	size	NOUN
ma-170	47	7	of	of	ADP
ma-170	47	8	the	the	DET
ma-170	47	9	regionaround	regionaround	NOUN
ma-170	47	10	the	the	DET
ma-170	47	11	true	true	ADJ
ma-170	47	12	solution	solution	NOUN
ma-170	47	13	where	where	SCONJ
ma-170	47	14	the	the	DET
ma-170	47	15	method	method	NOUN
ma-170	47	16	is	be	AUX
ma-170	47	17	guaranteed	guarantee	VERB
ma-170	47	18	to	to	PART
ma-170	47	19	converge	converge	VERB
ma-170	47	20	.	.	PUNCT
ma-170	48	1	this	this	DET
ma-170	48	2	type	type	NOUN
ma-170	48	3	of	of	ADP
ma-170	48	4	analysis	analysis	NOUN
ma-170	48	5	alsousually	alsousually	ADV
ma-170	48	6	involves	involve	VERB
ma-170	48	7	deriving	derive	VERB
ma-170	48	8	upper	upper	ADJ
ma-170	48	9	bounds	bound	NOUN
ma-170	48	10	on	on	ADP
ma-170	48	11	the	the	DET
ma-170	48	12	error	error	NOUN
ma-170	48	13	norms	norm	NOUN
ma-170	48	14	,	,	PUNCT
ma-170	48	15	which	which	PRON
ma-170	48	16	provide	provide	VERB
ma-170	48	17	an	an	DET
ma-170	48	18	estimate	estimate	NOUN
ma-170	48	19	of	of	ADP
ma-170	48	20	how	how	SCONJ
ma-170	48	21	closethe	closethe	ADJ
ma-170	48	22	iterates	iterate	NOUN
ma-170	48	23	of	of	ADP
ma-170	48	24	the	the	DET
ma-170	48	25	method	method	NOUN
ma-170	48	26	are	be	AUX
ma-170	48	27	to	to	ADP
ma-170	48	28	the	the	DET
ma-170	48	29	true	true	ADJ
ma-170	48	30	solution.in	solution.in	PROPN
ma-170	48	31	contrast	contrast	NOUN
ma-170	48	32	,	,	PUNCT
ma-170	48	33	in	in	ADP
ma-170	48	34	semi	semi	ADJ
ma-170	48	35	-	-	ADJ
ma-170	48	36	local	local	ADJ
ma-170	48	37	convergence	convergence	NOUN
ma-170	48	38	analysis	analysis	NOUN
ma-170	48	39	,	,	PUNCT
ma-170	48	40	the	the	DET
ma-170	48	41	convergence	convergence	NOUN
ma-170	48	42	behavior	behavior	NOUN
ma-170	48	43	of	of	ADP
ma-170	48	44	the	the	DET
ma-170	48	45	method	method	NOUN
ma-170	48	46	is	be	AUX
ma-170	48	47	studiedusing	studieduse	VERB
ma-170	48	48	information	information	NOUN
ma-170	48	49	from	from	ADP
ma-170	48	50	the	the	DET
ma-170	48	51	initial	initial	ADJ
ma-170	48	52	point	point	NOUN
ma-170	48	53	,	,	PUNCT
ma-170	48	54	typically	typically	ADV
ma-170	48	55	by	by	ADP
ma-170	48	56	deriving	derive	VERB
ma-170	48	57	sufficient	sufficient	ADJ
ma-170	48	58	conditions	condition	NOUN
ma-170	48	59	that	that	PRON
ma-170	48	60	guaranteeconvergence	guaranteeconvergence	NOUN
ma-170	48	61	of	of	ADP
ma-170	48	62	the	the	DET
ma-170	48	63	method	method	NOUN
ma-170	48	64	.	.	PUNCT
ma-170	49	1	this	this	DET
ma-170	49	2	analysis	analysis	NOUN
ma-170	49	3	is	be	AUX
ma-170	49	4	usually	usually	ADV
ma-170	49	5	carried	carry	VERB
ma-170	49	6	out	out	ADP
ma-170	49	7	without	without	ADP
ma-170	49	8	any	any	DET
ma-170	49	9	knowledge	knowledge	NOUN
ma-170	49	10	of	of	ADP
ma-170	49	11	theactual	theactual	ADJ
ma-170	49	12	solution	solution	NOUN
ma-170	49	13	of	of	ADP
ma-170	49	14	the	the	DET
ma-170	49	15	problem.generalized	problem.generalize	VERB
ma-170	49	16	lipschitz	lipschitz	NOUN
ma-170	49	17	-	-	PUNCT
ma-170	49	18	type	type	NOUN
ma-170	49	19	conditions	condition	NOUN
ma-170	49	20	are	be	AUX
ma-170	49	21	often	often	ADV
ma-170	49	22	used	use	VERB
ma-170	49	23	in	in	ADP
ma-170	49	24	both	both	DET
ma-170	49	25	semi	semi	ADJ
ma-170	49	26	-	-	ADJ
ma-170	49	27	local	local	ADJ
ma-170	49	28	and	and	CCONJ
ma-170	49	29	local	local	ADJ
ma-170	49	30	convergenceanalysis	convergenceanalysis	NOUN
ma-170	49	31	.	.	PUNCT
ma-170	50	1	these	these	DET
ma-170	50	2	conditions	condition	NOUN
ma-170	50	3	involve	involve	VERB
ma-170	50	4	bounding	bound	VERB
ma-170	50	5	the	the	DET
ma-170	50	6	difference	difference	NOUN
ma-170	50	7	between	between	ADP
ma-170	50	8	the	the	DET
ma-170	50	9	iterates	iterate	NOUN
ma-170	50	10	of	of	ADP
ma-170	50	11	the	the	DET
ma-170	50	12	method	method	NOUN
ma-170	50	13	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	PROPN
ma-170	50	14	eur	eur	PROPN
ma-170	50	15	.	.	PUNCT
ma-170	51	1	j.	j.	PROPN
ma-170	51	2	math	math	PROPN
ma-170	51	3	.	.	PUNCT
ma-170	52	1	anal	anal	PROPN
ma-170	52	2	.	.	PUNCT
ma-170	53	1	10.28924	10.28924	NUM
ma-170	53	2	/	/	SYM
ma-170	53	3	ada	ada	PROPN
ma-170	53	4	/	/	SYM
ma-170	53	5	ma.3.24	ma.3.24	PROPN
ma-170	53	6	3and	3and	NUM
ma-170	53	7	the	the	DET
ma-170	53	8	true	true	ADJ
ma-170	53	9	solution	solution	NOUN
ma-170	53	10	using	use	VERB
ma-170	53	11	a	a	DET
ma-170	53	12	lipschitz	lipschitz	NOUN
ma-170	53	13	constant	constant	ADJ
ma-170	53	14	or	or	CCONJ
ma-170	53	15	a	a	DET
ma-170	53	16	related	related	ADJ
ma-170	53	17	quantity	quantity	NOUN
ma-170	53	18	.	.	PUNCT
ma-170	54	1	these	these	DET
ma-170	54	2	conditions	condition	NOUN
ma-170	54	3	can	can	AUX
ma-170	54	4	beused	beuse	VERB
ma-170	54	5	to	to	PART
ma-170	54	6	derive	derive	VERB
ma-170	54	7	sufficient	sufficient	ADJ
ma-170	54	8	conditions	condition	NOUN
ma-170	54	9	for	for	ADP
ma-170	54	10	convergence	convergence	NOUN
ma-170	54	11	,	,	PUNCT
ma-170	54	12	as	as	ADV
ma-170	54	13	well	well	ADV
ma-170	54	14	as	as	ADP
ma-170	54	15	to	to	PART
ma-170	54	16	estimate	estimate	VERB
ma-170	54	17	the	the	DET
ma-170	54	18	rate	rate	NOUN
ma-170	54	19	and	and	CCONJ
ma-170	54	20	radius	radius	NOUN
ma-170	54	21	ofconvergence	ofconvergence	NOUN
ma-170	54	22	of	of	ADP
ma-170	54	23	the	the	DET
ma-170	54	24	method.it	method.it	PROPN
ma-170	54	25	is	be	AUX
ma-170	54	26	crucial	crucial	ADJ
ma-170	54	27	to	to	PART
ma-170	54	28	examine	examine	VERB
ma-170	54	29	how	how	SCONJ
ma-170	54	30	technique	technique	NOUN
ma-170	54	31	(	(	PUNCT
ma-170	54	32	1.3	1.3	NUM
ma-170	54	33	)	)	PUNCT
ma-170	54	34	converges	converge	NOUN
ma-170	54	35	in	in	ADP
ma-170	54	36	both	both	CCONJ
ma-170	54	37	the	the	DET
ma-170	54	38	local	local	ADJ
ma-170	54	39	(	(	PUNCT
ma-170	54	40	section	section	NOUN
ma-170	54	41	2	2	NUM
ma-170	54	42	)	)	PUNCT
ma-170	54	43	and	and	CCONJ
ma-170	54	44	thesemi	thesemi	NOUN
ma-170	54	45	-	-	ADJ
ma-170	54	46	local	local	ADJ
ma-170	54	47	(	(	PUNCT
ma-170	54	48	section	section	NOUN
ma-170	54	49	3	3	NUM
ma-170	54	50	)	)	PUNCT
ma-170	54	51	cases	case	NOUN
ma-170	54	52	.	.	PUNCT
ma-170	55	1	moreover	moreover	ADV
ma-170	55	2	,	,	PUNCT
ma-170	55	3	our	our	PRON
ma-170	55	4	approach	approach	NOUN
ma-170	55	5	gives	give	VERB
ma-170	55	6	a	a	DET
ma-170	55	7	prior	prior	ADJ
ma-170	55	8	error	error	NOUN
ma-170	55	9	estimates	estimate	NOUN
ma-170	55	10	and	and	CCONJ
ma-170	55	11	isolationof	isolationof	VERB
ma-170	55	12	the	the	DET
ma-170	55	13	solution	solution	NOUN
ma-170	55	14	results	result	NOUN
ma-170	55	15	not	not	PART
ma-170	55	16	provided	provide	VERB
ma-170	55	17	before	before	ADV
ma-170	55	18	and	and	CCONJ
ma-170	55	19	in	in	ADP
ma-170	55	20	banach	banach	NOUN
ma-170	55	21	space	space	NOUN
ma-170	55	22	.	.	PUNCT
ma-170	56	1	this	this	DET
ma-170	56	2	approach	approach	NOUN
ma-170	56	3	also	also	ADV
ma-170	56	4	enables	enable	VERB
ma-170	56	5	acomparison	acomparison	NOUN
ma-170	56	6	of	of	ADP
ma-170	56	7	the	the	DET
ma-170	56	8	convergence	convergence	NOUN
ma-170	56	9	criteria	criterion	NOUN
ma-170	56	10	of	of	ADP
ma-170	56	11	method	method	NOUN
ma-170	56	12	.	.	PUNCT
ma-170	57	1	if	if	SCONJ
ma-170	57	2	the	the	DET
ma-170	57	3	approach	approach	NOUN
ma-170	57	4	is	be	AUX
ma-170	57	5	examined	examine	VERB
ma-170	57	6	separately	separately	ADV
ma-170	57	7	,	,	PUNCT
ma-170	57	8	the	the	DET
ma-170	57	9	newconvergence	newconvergence	ADJ
ma-170	57	10	criteria	criterion	NOUN
ma-170	57	11	may	may	AUX
ma-170	57	12	be	be	AUX
ma-170	57	13	weaker	weak	ADJ
ma-170	57	14	than	than	ADP
ma-170	57	15	those	those	PRON
ma-170	57	16	that	that	PRON
ma-170	57	17	have	have	AUX
ma-170	57	18	been	be	AUX
ma-170	57	19	provided	provide	VERB
ma-170	57	20	.	.	PUNCT
ma-170	58	1	the	the	DET
ma-170	58	2	numerical	numerical	PROPN
ma-170	58	3	examplesare	examplesare	NOUN
ma-170	58	4	included	include	VERB
ma-170	58	5	in	in	ADP
ma-170	58	6	section	section	NOUN
ma-170	58	7	4	4	NUM
ma-170	58	8	,	,	PUNCT
ma-170	58	9	and	and	CCONJ
ma-170	58	10	the	the	DET
ma-170	58	11	conclusions	conclusion	NOUN
ma-170	58	12	are	be	AUX
ma-170	58	13	discussed	discuss	VERB
ma-170	58	14	in	in	ADP
ma-170	58	15	section	section	NOUN
ma-170	58	16	5	5	NUM
ma-170	58	17	.	.	NOUN
ma-170	59	1	2	2	NUM
ma-170	59	2	.	.	X
ma-170	59	3	local	local	ADJ
ma-170	59	4	convergence	convergence	NOUN
ma-170	59	5	some	some	DET
ma-170	59	6	real	real	ADJ
ma-170	59	7	functions	function	NOUN
ma-170	59	8	assist	assist	VERB
ma-170	59	9	in	in	ADP
ma-170	59	10	the	the	DET
ma-170	59	11	local	local	ADJ
ma-170	59	12	analysis	analysis	NOUN
ma-170	59	13	of	of	ADP
ma-170	59	14	the	the	DET
ma-170	59	15	method	method	NOUN
ma-170	59	16	.	.	PUNCT
ma-170	60	1	set	set	VERB
ma-170	60	2	t	t	PROPN
ma-170	60	3	=	=	PUNCT
ma-170	61	1	[	[	X
ma-170	61	2	0,+∞	0,+∞	NUM
ma-170	61	3	)	)	PUNCT
ma-170	61	4	.	.	PUNCT
ma-170	62	1	assume	assume	VERB
ma-170	62	2	:	:	PUNCT
ma-170	62	3	(	(	PUNCT
ma-170	62	4	h1	h1	PROPN
ma-170	62	5	)	)	PUNCT
ma-170	62	6	there	there	PRON
ma-170	62	7	exist	exist	VERB
ma-170	62	8	continuous	continuous	ADJ
ma-170	62	9	as	as	ADV
ma-170	62	10	well	well	ADV
ma-170	62	11	as	as	ADP
ma-170	62	12	nondecreasing	nondecreasing	ADJ
ma-170	62	13	functions	function	NOUN
ma-170	62	14	(	(	PUNCT
ma-170	62	15	cn	cn	NOUN
ma-170	62	16	)	)	PUNCT
ma-170	62	17	f1	f1	NOUN
ma-170	62	18	:	:	PUNCT
ma-170	62	19	t	t	PROPN
ma-170	62	20	→	→	SYM
ma-170	62	21	t	t	PROPN
ma-170	62	22	,	,	PUNCT
ma-170	62	23	f2	f2	PROPN
ma-170	62	24	:	:	PUNCT
ma-170	62	25	t	t	PROPN
ma-170	62	26	→	→	SYM
ma-170	62	27	t	t	PROPN
ma-170	62	28	,	,	PUNCT
ma-170	62	29	and	and	CCONJ
ma-170	62	30	w0	w0	PROPN
ma-170	62	31	:	:	PUNCT
ma-170	62	32	t	t	PROPN
ma-170	62	33	×	×	PROPN
ma-170	62	34	t	t	PROPN
ma-170	62	35	→	→	SYM
ma-170	62	36	r	r	NOUN
ma-170	62	37	so	so	SCONJ
ma-170	62	38	that	that	SCONJ
ma-170	62	39	the	the	DET
ma-170	62	40	equation	equation	NOUN
ma-170	62	41	w0(f1(t	w0(f1(t	VERB
ma-170	62	42	)	)	PUNCT
ma-170	62	43	,	,	PUNCT
ma-170	62	44	f2(t))−	f2(t))−	NOUN
ma-170	62	45	1	1	NUM
ma-170	62	46	=	=	SYM
ma-170	62	47	0	0	NUM
ma-170	62	48	admits	admit	VERB
ma-170	62	49	a	a	DET
ma-170	62	50	smallest	small	ADJ
ma-170	62	51	solution	solution	NOUN
ma-170	62	52	(	(	PUNCT
ma-170	62	53	ss	ss	NOUN
ma-170	62	54	)	)	PUNCT
ma-170	62	55	denoted	denote	VERB
ma-170	62	56	by	by	ADP
ma-170	62	57	δ	δ	PROPN
ma-170	62	58	∈	∈	PROPN
ma-170	62	59	t	t	PROPN
ma-170	62	60	−	−	PROPN
ma-170	62	61	{	{	PUNCT
ma-170	62	62	0	0	NUM
ma-170	62	63	}	}	PUNCT
ma-170	62	64	.	.	PUNCT
ma-170	63	1	let	let	VERB
ma-170	63	2	t0	t0	NOUN
ma-170	63	3	=	=	PUNCT
ma-170	64	1	[	[	X
ma-170	64	2	0	0	NUM
ma-170	64	3	,	,	PUNCT
ma-170	64	4	δ	δ	PROPN
ma-170	64	5	)	)	PUNCT
ma-170	64	6	.	.	PUNCT
ma-170	65	1	(	(	PUNCT
ma-170	65	2	h2	h2	NOUN
ma-170	65	3	)	)	PUNCT
ma-170	65	4	there	there	PRON
ma-170	65	5	exist	exist	VERB
ma-170	65	6	(	(	PUNCT
ma-170	65	7	cn	cn	NOUN
ma-170	65	8	)	)	PUNCT
ma-170	65	9	functions	function	NOUN
ma-170	65	10	w	w	NOUN
ma-170	65	11	:	:	PUNCT
ma-170	65	12	t0	t0	PROPN
ma-170	65	13	→	→	SYM
ma-170	65	14	t	t	PROPN
ma-170	65	15	,	,	PUNCT
ma-170	65	16	w1	w1	NOUN
ma-170	65	17	:	:	PUNCT
ma-170	65	18	t0×t0×t0	t0×t0×t0	PROPN
ma-170	65	19	→	→	SYM
ma-170	65	20	t	t	PROPN
ma-170	65	21	,	,	PUNCT
ma-170	65	22	and	and	CCONJ
ma-170	65	23	w2	w2	NOUN
ma-170	65	24	:	:	PUNCT
ma-170	65	25	t0×t0×t0	t0×t0×t0	PROPN
ma-170	65	26	→	→	PUNCT
ma-170	65	27	tsuch	tsuch	ADP
ma-170	65	28	that	that	SCONJ
ma-170	65	29	the	the	DET
ma-170	65	30	equations	equation	NOUN
ma-170	65	31	hi(t)−	hi(t)−	PROPN
ma-170	65	32	1	1	NUM
ma-170	65	33	=	=	SYM
ma-170	65	34	0	0	NUM
ma-170	65	35	,	,	PUNCT
ma-170	65	36	i	i	PRON
ma-170	65	37	=	=	NOUN
ma-170	65	38	1	1	NUM
ma-170	65	39	,	,	PUNCT
ma-170	65	40	2	2	NUM
ma-170	65	41	,	,	PUNCT
ma-170	65	42	3have	3have	NUM
ma-170	65	43	(	(	PUNCT
ma-170	65	44	ss	ss	NOUN
ma-170	65	45	)	)	PUNCT
ma-170	65	46	solutions	solution	NOUN
ma-170	65	47	denoted	denote	VERB
ma-170	65	48	by	by	ADP
ma-170	65	49	δi	δi	PROPN
ma-170	65	50	∈	∈	PROPN
ma-170	65	51	t0	t0	PROPN
ma-170	65	52	−	−	PROPN
ma-170	65	53	{	{	PUNCT
ma-170	65	54	0	0	NUM
ma-170	65	55	}	}	PUNCT
ma-170	65	56	,	,	PUNCT
ma-170	65	57	provided	provide	VERB
ma-170	65	58	that	that	SCONJ
ma-170	65	59	h1(t	h1(t	NOUN
ma-170	65	60	)	)	PUNCT
ma-170	65	61	=	=	SYM
ma-170	65	62	w1(f1(t	w1(f1(t	X
ma-170	65	63	)	)	PUNCT
ma-170	65	64	,	,	PUNCT
ma-170	65	65	f2(t	f2(t	PROPN
ma-170	65	66	)	)	PUNCT
ma-170	65	67	,	,	PUNCT
ma-170	65	68	t	t	PROPN
ma-170	65	69	)	)	PUNCT
ma-170	65	70	1−	1−	NUM
ma-170	66	1	w0(f1(t	w0(f1(t	X
ma-170	66	2	)	)	PUNCT
ma-170	66	3	,	,	PUNCT
ma-170	66	4	f2(t	f2(t	PROPN
ma-170	66	5	)	)	PUNCT
ma-170	66	6	)	)	PUNCT
ma-170	66	7	,	,	PUNCT
ma-170	67	1	h2(t	h2(t	X
ma-170	67	2	)	)	PUNCT
ma-170	67	3	=	=	PUNCT
ma-170	68	1	[	[	X
ma-170	68	2	w1(h1(t)t	w1(h1(t)t	X
ma-170	68	3	,	,	PUNCT
ma-170	68	4	f1(t	f1(t	PROPN
ma-170	68	5	)	)	PUNCT
ma-170	68	6	,	,	PUNCT
ma-170	68	7	f2(t	f2(t	PROPN
ma-170	68	8	)	)	PUNCT
ma-170	68	9	)	)	PUNCT
ma-170	68	10	1−	1−	NUM
ma-170	68	11	w0(f1(t	w0(f1(t	X
ma-170	68	12	)	)	PUNCT
ma-170	68	13	,	,	PUNCT
ma-170	68	14	f2(t	f2(t	PROPN
ma-170	68	15	)	)	PUNCT
ma-170	68	16	)	)	PUNCT
ma-170	69	1	+	+	CCONJ
ma-170	69	2	2w2(t	2w2(t	NUM
ma-170	69	3	,	,	PUNCT
ma-170	69	4	h1(t)t	h1(t)t	NUM
ma-170	69	5	,	,	PUNCT
ma-170	69	6	f1(t	f1(t	NUM
ma-170	69	7	)	)	PUNCT
ma-170	69	8	,	,	PUNCT
ma-170	69	9	f2(t))(1	f2(t))(1	NOUN
ma-170	70	1	+	+	CCONJ
ma-170	70	2	w(t	w(t	PROPN
ma-170	70	3	)	)	PUNCT
ma-170	70	4	)	)	PUNCT
ma-170	71	1	(	(	PUNCT
ma-170	71	2	1−	1−	NUM
ma-170	71	3	w0(f1(t	w0(f1(t	X
ma-170	71	4	)	)	PUNCT
ma-170	71	5	,	,	PUNCT
ma-170	71	6	f2(t)))2	f2(t)))2	NOUN
ma-170	71	7	]	]	PUNCT
ma-170	71	8	h1(t	h1(t	X
ma-170	71	9	)	)	PUNCT
ma-170	71	10	,	,	PUNCT
ma-170	71	11	h0(t	h0(t	X
ma-170	71	12	)	)	PUNCT
ma-170	71	13	=	=	SYM
ma-170	71	14	1	1	NUM
ma-170	71	15	4	4	NUM
ma-170	71	16	[	[	PUNCT
ma-170	71	17	5	5	NUM
ma-170	71	18	(	(	PUNCT
ma-170	71	19	w2(h1(t)t	w2(h1(t)t	NUM
ma-170	71	20	,	,	PUNCT
ma-170	71	21	h2(t)t	h2(t)t	X
ma-170	71	22	,	,	PUNCT
ma-170	71	23	f1(t	f1(t	PROPN
ma-170	71	24	)	)	PUNCT
ma-170	71	25	,	,	PUNCT
ma-170	71	26	f2(t	f2(t	PROPN
ma-170	71	27	)	)	PUNCT
ma-170	71	28	)	)	PUNCT
ma-170	71	29	1−	1−	NUM
ma-170	72	1	w0(f1(t	w0(f1(t	X
ma-170	72	2	)	)	PUNCT
ma-170	72	3	,	,	PUNCT
ma-170	72	4	f2(t	f2(t	PROPN
ma-170	72	5	)	)	PUNCT
ma-170	72	6	)	)	PUNCT
ma-170	72	7	)	)	PUNCT
ma-170	73	1	2	2	NUM
ma-170	73	2	+	+	CCONJ
ma-170	73	3	4	4	NUM
ma-170	73	4	w2(h1(t)t	w2(h1(t)t	NOUN
ma-170	73	5	,	,	PUNCT
ma-170	73	6	h2(t)t	h2(t)t	X
ma-170	73	7	,	,	PUNCT
ma-170	73	8	f1(t	f1(t	PROPN
ma-170	73	9	)	)	PUNCT
ma-170	73	10	,	,	PUNCT
ma-170	73	11	f2(t	f2(t	PROPN
ma-170	73	12	)	)	PUNCT
ma-170	73	13	)	)	PUNCT
ma-170	73	14	1−	1−	NUM
ma-170	74	1	w0(f1(t	w0(f1(t	X
ma-170	74	2	)	)	PUNCT
ma-170	74	3	,	,	PUNCT
ma-170	74	4	f2(t	f2(t	PROPN
ma-170	74	5	)	)	PUNCT
ma-170	74	6	)	)	PUNCT
ma-170	74	7	]	]	PUNCT
ma-170	74	8	,	,	PUNCT
ma-170	74	9	h3(t	h3(t	X
ma-170	74	10	)	)	PUNCT
ma-170	74	11	=	=	PUNCT
ma-170	75	1	[	[	X
ma-170	75	2	w1(f1(t	w1(f1(t	NOUN
ma-170	75	3	)	)	PUNCT
ma-170	75	4	,	,	PUNCT
ma-170	75	5	f2(t	f2(t	PROPN
ma-170	75	6	)	)	PUNCT
ma-170	75	7	,	,	PUNCT
ma-170	75	8	h2(t)t	h2(t)t	X
ma-170	75	9	)	)	PUNCT
ma-170	75	10	1−	1−	NUM
ma-170	75	11	w0(f1(t	w0(f1(t	X
ma-170	75	12	)	)	PUNCT
ma-170	75	13	,	,	PUNCT
ma-170	75	14	f2(t	f2(t	PROPN
ma-170	75	15	)	)	PUNCT
ma-170	75	16	)	)	PUNCT
ma-170	76	1	+	+	CCONJ
ma-170	76	2	h0(t)(1	h0(t)(1	ADP
ma-170	76	3	+	+	ADJ
ma-170	76	4	w(h2(t)t	w(h2(t)t	PROPN
ma-170	76	5	)	)	PUNCT
ma-170	76	6	)	)	PUNCT
ma-170	76	7	1−	1−	NUM
ma-170	77	1	w0(f1(t	w0(f1(t	X
ma-170	77	2	)	)	PUNCT
ma-170	77	3	,	,	PUNCT
ma-170	77	4	f2(t	f2(t	PROPN
ma-170	77	5	)	)	PUNCT
ma-170	77	6	)	)	PUNCT
ma-170	77	7	]	]	PUNCT
ma-170	78	1	h2(t	h2(t	X
ma-170	78	2	)	)	PUNCT
ma-170	78	3	.	.	PUNCT
ma-170	79	1	consider	consider	VERB
ma-170	79	2	,	,	PUNCT
ma-170	79	3	the	the	DET
ma-170	79	4	parameter	parameter	NOUN
ma-170	79	5	δ∗	δ∗	PROPN
ma-170	79	6	given	give	VERB
ma-170	79	7	as	as	ADP
ma-170	79	8	δ∗	δ∗	NOUN
ma-170	79	9	=	=	PUNCT
ma-170	79	10	min{δi	min{δi	X
ma-170	79	11	}	}	PUNCT
ma-170	79	12	.	.	PUNCT
ma-170	80	1	(	(	PUNCT
ma-170	80	2	2.5	2.5	NUM
ma-170	80	3	)	)	PUNCT
ma-170	80	4	let	let	VERB
ma-170	80	5	t1	t1	NOUN
ma-170	80	6	=	=	PUNCT
ma-170	81	1	[	[	X
ma-170	81	2	0	0	NUM
ma-170	81	3	,	,	PUNCT
ma-170	81	4	δ∗	δ∗	PROPN
ma-170	81	5	)	)	PUNCT
ma-170	81	6	.	.	PUNCT
ma-170	82	1	these	these	DET
ma-170	82	2	definitions	definition	NOUN
ma-170	82	3	imply	imply	VERB
ma-170	82	4	0	0	NUM
ma-170	82	5	≤	≤	NUM
ma-170	82	6	w0(f1(t	w0(f1(t	PROPN
ma-170	82	7	)	)	PUNCT
ma-170	82	8	,	,	PUNCT
ma-170	82	9	f2(t	f2(t	PROPN
ma-170	82	10	)	)	PUNCT
ma-170	82	11	)	)	PUNCT
ma-170	82	12	<	<	X
ma-170	82	13	1	1	NUM
ma-170	82	14	(	(	PUNCT
ma-170	82	15	2.6	2.6	NUM
ma-170	82	16	)	)	PUNCT
ma-170	82	17	and	and	CCONJ
ma-170	82	18	0	0	NUM
ma-170	82	19	≤	≤	NUM
ma-170	82	20	hi(t	hi(t	NOUN
ma-170	82	21	)	)	PUNCT
ma-170	82	22	<	<	X
ma-170	82	23	1	1	NUM
ma-170	82	24	,	,	PUNCT
ma-170	82	25	(	(	PUNCT
ma-170	82	26	2.7	2.7	NUM
ma-170	82	27	)	)	PUNCT
ma-170	82	28	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	NOUN
ma-170	82	29	eur	eur	ADJ
ma-170	82	30	.	.	PUNCT
ma-170	83	1	j.	j.	PROPN
ma-170	83	2	math	math	PROPN
ma-170	83	3	.	.	PUNCT
ma-170	84	1	anal	anal	PROPN
ma-170	84	2	.	.	PUNCT
ma-170	85	1	10.28924	10.28924	NUM
ma-170	85	2	/	/	SYM
ma-170	85	3	ada	ada	PROPN
ma-170	85	4	/	/	SYM
ma-170	85	5	ma.3.24	ma.3.24	PROPN
ma-170	85	6	4for	4for	PROPN
ma-170	85	7	all	all	DET
ma-170	85	8	t	t	PROPN
ma-170	85	9	∈	∈	PROPN
ma-170	85	10	t1.let	t1.let	NOUN
ma-170	85	11	b(x̄	b(x̄	PROPN
ma-170	85	12	,	,	PUNCT
ma-170	85	13	r	r	NOUN
ma-170	85	14	)	)	PUNCT
ma-170	85	15	,	,	PUNCT
ma-170	85	16	b̄[x̄	b̄[x̄	NOUN
ma-170	85	17	,	,	PUNCT
ma-170	85	18	r	r	NOUN
ma-170	85	19	]	]	PUNCT
ma-170	85	20	abbreviate	abbreviate	VERB
ma-170	85	21	open	open	ADJ
ma-170	85	22	and	and	CCONJ
ma-170	85	23	closed	closed	ADJ
ma-170	85	24	balls	ball	NOUN
ma-170	85	25	in	in	ADP
ma-170	85	26	s1	s1	NOUN
ma-170	85	27	,	,	PUNCT
ma-170	85	28	respectively	respectively	ADV
ma-170	85	29	so	so	SCONJ
ma-170	85	30	that	that	SCONJ
ma-170	85	31	thecenter	thecenter	NOUN
ma-170	85	32	is	be	AUX
ma-170	85	33	x̄	x̄	NUM
ma-170	85	34	and	and	CCONJ
ma-170	85	35	the	the	DET
ma-170	85	36	radius	radius	NOUN
ma-170	85	37	is	be	AUX
ma-170	85	38	some	some	DET
ma-170	85	39	r	r	NOUN
ma-170	85	40	>	>	X
ma-170	85	41	0	0	NUM
ma-170	85	42	.	.	PUNCT
ma-170	86	1	the	the	DET
ma-170	86	2	preceding	precede	VERB
ma-170	86	3	real	real	ADJ
ma-170	86	4	functions	function	NOUN
ma-170	86	5	are	be	AUX
ma-170	86	6	associated	associate	VERB
ma-170	86	7	tothe	tothe	ADP
ma-170	86	8	divided	divide	VERB
ma-170	86	9	difference	difference	NOUN
ma-170	87	1	[	[	X
ma-170	87	2	.	.	PUNCT
ma-170	87	3	,	,	PUNCT
ma-170	87	4	.;f	.;f	PUNCT
ma-170	87	5	]	]	PUNCT
ma-170	88	1	as	as	ADP
ma-170	88	2	:	:	PUNCT
ma-170	88	3	(	(	PUNCT
ma-170	88	4	h3	h3	NOUN
ma-170	88	5	)	)	PUNCT
ma-170	88	6	there	there	PRON
ma-170	88	7	exists	exist	VERB
ma-170	88	8	an	an	DET
ma-170	88	9	invertible	invertible	ADJ
ma-170	88	10	operator	operator	NOUN
ma-170	88	11	l	l	NOUN
ma-170	88	12	∈	∈	PROPN
ma-170	88	13	l(z	l(z	PROPN
ma-170	88	14	)	)	PUNCT
ma-170	88	15	so	so	SCONJ
ma-170	88	16	that	that	SCONJ
ma-170	88	17	for	for	ADP
ma-170	88	18	each	each	DET
ma-170	88	19	x	x	SYM
ma-170	88	20	∈	∈	PROPN
ma-170	88	21	ω	ω	PROPN
ma-170	88	22	,	,	PUNCT
ma-170	88	23	u	u	NOUN
ma-170	88	24	=	=	PUNCT
ma-170	88	25	x	x	PROPN
ma-170	88	26	+	+	NUM
ma-170	88	27	f	f	X
ma-170	88	28	(	(	PUNCT
ma-170	88	29	x	x	NOUN
ma-170	88	30	)	)	PUNCT
ma-170	88	31	,	,	PUNCT
ma-170	88	32	v	v	X
ma-170	88	33	=	=	SYM
ma-170	88	34	x	x	SYM
ma-170	89	1	−	−	PROPN
ma-170	89	2	f	f	X
ma-170	89	3	(	(	PUNCT
ma-170	89	4	x	x	X
ma-170	89	5	)	)	PUNCT
ma-170	89	6	||l−1([u	||l−1([u	PROPN
ma-170	89	7	,	,	PUNCT
ma-170	89	8	v	v	NOUN
ma-170	89	9	;	;	PUNCT
ma-170	89	10	f	f	X
ma-170	89	11	]	]	X
ma-170	89	12	−	−	PROPN
ma-170	89	13	l)||	l)||	NOUN
ma-170	89	14	≤	≤	PROPN
ma-170	89	15	w0(||u	w0(||u	PROPN
ma-170	89	16	−	−	PROPN
ma-170	89	17	x∗||	x∗||	NUM
ma-170	89	18	,	,	PUNCT
ma-170	89	19	||v	||v	NOUN
ma-170	89	20	−	−	PROPN
ma-170	89	21	x∗||	x∗||	NUM
ma-170	89	22	)	)	PUNCT
ma-170	89	23	,	,	PUNCT
ma-170	89	24	||u	||u	NUM
ma-170	89	25	−	−	PROPN
ma-170	89	26	x∗||	x∗||	PUNCT
ma-170	90	1	≤	≤	NUM
ma-170	90	2	f1(||x	f1(||x	PROPN
ma-170	90	3	−	−	PROPN
ma-170	90	4	x∗||	x∗||	NUM
ma-170	90	5	)	)	PUNCT
ma-170	90	6	,	,	PUNCT
ma-170	90	7	||v	||v	NOUN
ma-170	90	8	−	−	NOUN
ma-170	90	9	x∗||	x∗||	PUNCT
ma-170	90	10	≤	≤	NOUN
ma-170	90	11	f2(||x	f2(||x	NOUN
ma-170	90	12	−	−	PROPN
ma-170	90	13	x∗||	x∗||	NUM
ma-170	90	14	)	)	PUNCT
ma-170	90	15	.	.	PUNCT
ma-170	91	1	let	let	VERB
ma-170	91	2	b0	b0	NOUN
ma-170	91	3	=	=	PUNCT
ma-170	91	4	b(x∗	b(x∗	PROPN
ma-170	91	5	,	,	PUNCT
ma-170	91	6	δ	δ	PROPN
ma-170	91	7	)	)	PUNCT
ma-170	91	8	.	.	PUNCT
ma-170	92	1	(	(	PUNCT
ma-170	92	2	h4	h4	PROPN
ma-170	92	3	)	)	PUNCT
ma-170	92	4	||l−1([x	||l−1([x	PROPN
ma-170	92	5	,	,	PUNCT
ma-170	92	6	x∗;f	x∗;f	PUNCT
ma-170	93	1	]	]	X
ma-170	93	2	−	−	PROPN
ma-170	93	3	l)||	l)||	NOUN
ma-170	93	4	≤	≤	X
ma-170	93	5	w(||x	w(||x	NOUN
ma-170	93	6	−	−	PROPN
ma-170	93	7	x∗||	x∗||	NUM
ma-170	93	8	)	)	PUNCT
ma-170	93	9	,	,	PUNCT
ma-170	93	10	||l−1([x	||l−1([x	SYM
ma-170	93	11	,	,	PUNCT
ma-170	93	12	y	y	PROPN
ma-170	93	13	;	;	PUNCT
ma-170	93	14	f	f	X
ma-170	93	15	]	]	X
ma-170	93	16	−	−	PROPN
ma-170	94	1	[	[	X
ma-170	94	2	z	z	X
ma-170	94	3	,	,	PUNCT
ma-170	94	4	x∗;f	x∗;f	PUNCT
ma-170	94	5	]	]	PUNCT
ma-170	94	6	)	)	PUNCT
ma-170	94	7	||	||	X
ma-170	95	1	≤	≤	NUM
ma-170	95	2	w1(||x	w1(||x	NOUN
ma-170	95	3	−	−	PROPN
ma-170	95	4	x∗||	x∗||	NUM
ma-170	95	5	,	,	PUNCT
ma-170	95	6	||y	||y	PROPN
ma-170	95	7	−	−	PROPN
ma-170	95	8	x∗||	x∗||	NUM
ma-170	95	9	,	,	PUNCT
ma-170	95	10	||z	||z	VERB
ma-170	95	11	−	−	PROPN
ma-170	95	12	x∗||	x∗||	NUM
ma-170	95	13	)	)	PUNCT
ma-170	95	14	and	and	CCONJ
ma-170	95	15	||l−1([u	||l−1([u	PROPN
ma-170	95	16	,	,	PUNCT
ma-170	95	17	v	v	NOUN
ma-170	95	18	;	;	PUNCT
ma-170	95	19	f	f	X
ma-170	95	20	]	]	X
ma-170	95	21	−	−	PROPN
ma-170	96	1	[	[	X
ma-170	96	2	y	y	PROPN
ma-170	96	3	,	,	PUNCT
ma-170	96	4	x	x	PROPN
ma-170	96	5	;	;	PUNCT
ma-170	96	6	f	f	PROPN
ma-170	96	7	]	]	PUNCT
ma-170	96	8	)	)	PUNCT
ma-170	96	9	||	||	PROPN
ma-170	96	10	≤	≤	NUM
ma-170	96	11	w2(||x	w2(||x	NOUN
ma-170	96	12	−	−	PROPN
ma-170	96	13	x∗||	x∗||	NUM
ma-170	96	14	,	,	PUNCT
ma-170	96	15	||y	||y	PROPN
ma-170	96	16	−	−	PROPN
ma-170	96	17	x∗||	x∗||	NUM
ma-170	96	18	,	,	PUNCT
ma-170	96	19	||u	||u	NUM
ma-170	96	20	−	−	PROPN
ma-170	96	21	x∗||	x∗||	NUM
ma-170	96	22	,	,	PUNCT
ma-170	96	23	||v	||v	NOUN
ma-170	96	24	−	−	PROPN
ma-170	96	25	x∗||	x∗||	NUM
ma-170	96	26	)	)	PUNCT
ma-170	96	27	,	,	PUNCT
ma-170	96	28	for	for	ADP
ma-170	96	29	each	each	DET
ma-170	96	30	x	x	PROPN
ma-170	96	31	,	,	PUNCT
ma-170	96	32	y	y	PROPN
ma-170	96	33	,	,	PUNCT
ma-170	96	34	z	z	PROPN
ma-170	96	35	,	,	PUNCT
ma-170	96	36	u	u	NOUN
ma-170	96	37	,	,	PUNCT
ma-170	96	38	v	v	PROPN
ma-170	96	39	∈	∈	PROPN
ma-170	96	40	b0	b0	NOUN
ma-170	96	41	.	.	PUNCT
ma-170	97	1	(	(	PUNCT
ma-170	97	2	h5	h5	PROPN
ma-170	97	3	)	)	PUNCT
ma-170	97	4	b[x∗	b[x∗	PROPN
ma-170	97	5	,	,	PUNCT
ma-170	97	6	δ∗	δ∗	PROPN
ma-170	97	7	]	]	PUNCT
ma-170	98	1	⊂	⊂	PROPN
ma-170	98	2	ω.the	ω.the	DET
ma-170	98	3	local	local	ADJ
ma-170	98	4	analysis	analysis	NOUN
ma-170	98	5	is	be	AUX
ma-170	98	6	based	base	VERB
ma-170	98	7	on	on	ADP
ma-170	98	8	the	the	DET
ma-170	98	9	conditions	condition	NOUN
ma-170	98	10	(	(	PUNCT
ma-170	98	11	h1)−	h1)−	PROPN
ma-170	98	12	(	(	PUNCT
ma-170	98	13	h5	h5	PROPN
ma-170	98	14	)	)	PUNCT
ma-170	98	15	under	under	ADP
ma-170	98	16	the	the	DET
ma-170	98	17	preceding	precede	VERB
ma-170	98	18	notations	notation	NOUN
ma-170	98	19	.	.	PUNCT
ma-170	99	1	theorem	theorem	VERB
ma-170	99	2	2.1	2.1	NUM
ma-170	99	3	assume	assume	VERB
ma-170	99	4	the	the	DET
ma-170	99	5	conditions	condition	NOUN
ma-170	99	6	(	(	PUNCT
ma-170	99	7	h1)−	h1)−	PROPN
ma-170	99	8	(	(	PUNCT
ma-170	99	9	h5	h5	PROPN
ma-170	99	10	)	)	PUNCT
ma-170	99	11	are	be	AUX
ma-170	99	12	validated	validate	VERB
ma-170	99	13	.	.	PUNCT
ma-170	100	1	if	if	SCONJ
ma-170	100	2	x0	x0	PROPN
ma-170	100	3	∈	∈	PROPN
ma-170	100	4	b(x∗	b(x∗	PROPN
ma-170	100	5	,	,	PUNCT
ma-170	100	6	δ∗)−	δ∗)−	PROPN
ma-170	100	7	{	{	PUNCT
ma-170	100	8	x∗	x∗	PROPN
ma-170	100	9	}	}	PUNCT
ma-170	100	10	,	,	PUNCT
ma-170	100	11	then	then	ADV
ma-170	100	12	the	the	DET
ma-170	100	13	following	follow	VERB
ma-170	100	14	items	item	NOUN
ma-170	100	15	are	be	AUX
ma-170	100	16	valid	valid	ADJ
ma-170	100	17	{	{	PUNCT
ma-170	100	18	xn	xn	NOUN
ma-170	100	19	}	}	PUNCT
ma-170	100	20	⊂	⊂	PROPN
ma-170	100	21	b(x∗	b(x∗	PROPN
ma-170	100	22	,	,	PUNCT
ma-170	100	23	δ∗	δ∗	PROPN
ma-170	100	24	)	)	PUNCT
ma-170	100	25	,	,	PUNCT
ma-170	100	26	(	(	PUNCT
ma-170	100	27	2.8	2.8	NUM
ma-170	100	28	)	)	PUNCT
ma-170	100	29	‖yn	‖yn	PROPN
ma-170	100	30	−	−	PROPN
ma-170	100	31	x∗‖	x∗‖	PROPN
ma-170	100	32	≤	≤	NUM
ma-170	100	33	h1(‖xn	h1(‖xn	PUNCT
ma-170	100	34	−	−	PROPN
ma-170	100	35	x∗‖)‖xn	x∗‖)‖xn	PUNCT
ma-170	101	1	−	−	PROPN
ma-170	101	2	x∗‖	x∗‖	PROPN
ma-170	101	3	≤	≤	PROPN
ma-170	101	4	‖‖xn	‖‖xn	PROPN
ma-170	101	5	−	−	PROPN
ma-170	101	6	x∗‖	x∗‖	PROPN
ma-170	101	7	<	<	X
ma-170	101	8	δ∗	δ∗	PROPN
ma-170	101	9	,	,	PUNCT
ma-170	101	10	(	(	PUNCT
ma-170	101	11	2.9	2.9	NUM
ma-170	101	12	)	)	PUNCT
ma-170	102	1	‖zn	‖zn	NUM
ma-170	102	2	−	−	NUM
ma-170	102	3	x∗‖	x∗‖	PROPN
ma-170	102	4	≤	≤	NUM
ma-170	102	5	h2(‖xn	h2(‖xn	PUNCT
ma-170	102	6	−	−	PROPN
ma-170	102	7	x∗‖)‖xn	x∗‖)‖xn	PUNCT
ma-170	103	1	−	−	PROPN
ma-170	103	2	x∗‖	x∗‖	PROPN
ma-170	103	3	≤	≤	PROPN
ma-170	103	4	‖‖xn	‖‖xn	PROPN
ma-170	104	1	−	−	PROPN
ma-170	104	2	x∗‖	x∗‖	PROPN
ma-170	104	3	,	,	PUNCT
ma-170	104	4	(	(	PUNCT
ma-170	104	5	2.10	2.10	NUM
ma-170	104	6	)	)	PUNCT
ma-170	104	7	‖xn+1	‖xn+1	PUNCT
ma-170	104	8	−	−	PROPN
ma-170	104	9	x∗‖	x∗‖	PROPN
ma-170	104	10	≤	≤	NUM
ma-170	104	11	h3(‖xn	h3(‖xn	PROPN
ma-170	104	12	−	−	PROPN
ma-170	104	13	x∗‖)‖xn	x∗‖)‖xn	PUNCT
ma-170	105	1	−	−	PROPN
ma-170	105	2	x∗‖	x∗‖	PROPN
ma-170	105	3	≤	≤	PROPN
ma-170	105	4	‖‖xn	‖‖xn	PROPN
ma-170	105	5	−	−	PROPN
ma-170	105	6	x∗‖	x∗‖	PROPN
ma-170	105	7	(	(	PUNCT
ma-170	105	8	2.11	2.11	NUM
ma-170	105	9	)	)	PUNCT
ma-170	105	10	and	and	CCONJ
ma-170	105	11	the	the	DET
ma-170	105	12	sequence	sequence	NOUN
ma-170	105	13	{	{	PUNCT
ma-170	105	14	xn	xn	NOUN
ma-170	105	15	}	}	PUNCT
ma-170	105	16	is	be	AUX
ma-170	105	17	convergent	convergent	ADJ
ma-170	105	18	to	to	ADP
ma-170	105	19	x∗.	x∗.	DET
ma-170	105	20	proof	proof	NOUN
ma-170	105	21	.	.	PUNCT
ma-170	106	1	these	these	DET
ma-170	106	2	items	item	NOUN
ma-170	106	3	are	be	AUX
ma-170	106	4	shown	show	VERB
ma-170	106	5	by	by	ADP
ma-170	106	6	mathematical	mathematical	ADJ
ma-170	106	7	induction	induction	NOUN
ma-170	106	8	.	.	PUNCT
ma-170	107	1	by	by	ADP
ma-170	107	2	the	the	DET
ma-170	107	3	condition	condition	NOUN
ma-170	107	4	(	(	PUNCT
ma-170	107	5	h3	h3	NOUN
ma-170	107	6	)	)	PUNCT
ma-170	107	7	,	,	PUNCT
ma-170	107	8	estimate	estimate	INTJ
ma-170	107	9	(	(	PUNCT
ma-170	107	10	2.7)for	2.7)for	NUM
ma-170	107	11	u0	u0	ADJ
ma-170	107	12	=	=	NOUN
ma-170	107	13	x0	x0	PROPN
ma-170	108	1	+	+	CCONJ
ma-170	108	2	f	f	X
ma-170	108	3	(	(	PUNCT
ma-170	108	4	x0	x0	PROPN
ma-170	108	5	)	)	PUNCT
ma-170	108	6	,	,	PUNCT
ma-170	108	7	v0	v0	NOUN
ma-170	108	8	=	=	PUNCT
ma-170	108	9	x0	x0	PROPN
ma-170	109	1	−	−	PROPN
ma-170	109	2	f	f	X
ma-170	109	3	(	(	PUNCT
ma-170	109	4	x0	x0	PROPN
ma-170	109	5	)	)	PUNCT
ma-170	110	1	it	it	PRON
ma-170	110	2	follows	follow	VERB
ma-170	110	3	‖l−1([u0	‖l−1([u0	NOUN
ma-170	110	4	,	,	PUNCT
ma-170	110	5	v0;f	v0;f	ADJ
ma-170	110	6	]	]	SYM
ma-170	110	7	−	−	NOUN
ma-170	110	8	l)‖	l)‖	NOUN
ma-170	110	9	≤	≤	NUM
ma-170	111	1	w0(‖u0	w0(‖u0	PRON
ma-170	111	2	−	−	PROPN
ma-170	111	3	x∗‖	x∗‖	PROPN
ma-170	111	4	,	,	PUNCT
ma-170	111	5	‖v0	‖v0	PROPN
ma-170	111	6	−	−	NOUN
ma-170	111	7	x∗‖	x∗‖	NUM
ma-170	111	8	)	)	PUNCT
ma-170	111	9	≤	≤	NOUN
ma-170	111	10	w0(f1(‖x0	w0(f1(‖x0	NOUN
ma-170	111	11	−	−	PROPN
ma-170	111	12	x∗‖	x∗‖	NUM
ma-170	111	13	)	)	PUNCT
ma-170	111	14	,	,	PUNCT
ma-170	111	15	f2(‖x0	f2(‖x0	PROPN
ma-170	111	16	−	−	PROPN
ma-170	111	17	x∗‖	x∗‖	PROPN
ma-170	111	18	)	)	PUNCT
ma-170	111	19	)	)	PUNCT
ma-170	111	20	≤	≤	NUM
ma-170	111	21	w0(f1(u	w0(f1(u	NOUN
ma-170	111	22	)	)	PUNCT
ma-170	111	23	,	,	PUNCT
ma-170	111	24	f2(v	f2(v	PROPN
ma-170	111	25	)	)	PUNCT
ma-170	111	26	)	)	PUNCT
ma-170	112	1	<	<	X
ma-170	113	1	1	1	X
ma-170	113	2	.	.	PUNCT
ma-170	113	3	(	(	PUNCT
ma-170	113	4	2.12	2.12	NUM
ma-170	113	5	)	)	PUNCT
ma-170	113	6	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	PROPN
ma-170	113	7	eur	eur	PROPN
ma-170	113	8	.	.	PUNCT
ma-170	114	1	j.	j.	PROPN
ma-170	114	2	math	math	PROPN
ma-170	114	3	.	.	PUNCT
ma-170	115	1	anal	anal	PROPN
ma-170	115	2	.	.	PUNCT
ma-170	116	1	10.28924	10.28924	NUM
ma-170	116	2	/	/	SYM
ma-170	116	3	ada	ada	PROPN
ma-170	116	4	/	/	SYM
ma-170	116	5	ma.3.24	ma.3.24	PROPN
ma-170	116	6	5then	5then	NUM
ma-170	116	7	,	,	PUNCT
ma-170	116	8	the	the	DET
ma-170	116	9	existence	existence	NOUN
ma-170	116	10	of	of	ADP
ma-170	116	11	[	[	X
ma-170	116	12	u0	u0	ADJ
ma-170	116	13	,	,	PUNCT
ma-170	116	14	v0;f	v0;f	ADJ
ma-170	116	15	]	]	SYM
ma-170	116	16	−1	−1	NOUN
ma-170	116	17	is	be	AUX
ma-170	116	18	assured	assure	VERB
ma-170	116	19	by	by	ADP
ma-170	116	20	the	the	DET
ma-170	116	21	estimate	estimate	NOUN
ma-170	116	22	(	(	PUNCT
ma-170	116	23	2.12	2.12	NUM
ma-170	116	24	)	)	PUNCT
ma-170	116	25	and	and	CCONJ
ma-170	116	26	the	the	DET
ma-170	116	27	perturbation	perturbation	NOUN
ma-170	116	28	lemmaon	lemmaon	PROPN
ma-170	116	29	linear	linear	PROPN
ma-170	116	30	operators	operator	NOUN
ma-170	116	31	with	with	ADP
ma-170	116	32	inverses	inverse	NOUN
ma-170	116	33	attributed	attribute	VERB
ma-170	116	34	to	to	ADP
ma-170	116	35	banach	banach	NOUN
ma-170	116	36	[	[	X
ma-170	116	37	6	6	NUM
ma-170	116	38	]	]	PUNCT
ma-170	116	39	.	.	PUNCT
ma-170	117	1	we	we	PRON
ma-170	117	2	also	also	ADV
ma-170	117	3	have	have	VERB
ma-170	117	4	‖[u0	‖[u0	NOUN
ma-170	117	5	,	,	PUNCT
ma-170	117	6	v0;f	v0;f	ADJ
ma-170	117	7	]	]	SYM
ma-170	117	8	−1l‖	−1l‖	PROPN
ma-170	117	9	≤	≤	NUM
ma-170	117	10	1	1	NUM
ma-170	117	11	1−	1−	NUM
ma-170	117	12	w0(f1(‖u0	w0(f1(‖u0	NOUN
ma-170	117	13	−	−	PROPN
ma-170	117	14	x∗‖	x∗‖	PROPN
ma-170	117	15	)	)	PUNCT
ma-170	117	16	,	,	PUNCT
ma-170	117	17	f2(‖u0	f2(‖u0	PROPN
ma-170	118	1	−	−	PROPN
ma-170	118	2	x∗‖	x∗‖	NUM
ma-170	118	3	)	)	PUNCT
ma-170	118	4	.	.	PUNCT
ma-170	119	1	(	(	PUNCT
ma-170	119	2	2.13	2.13	NUM
ma-170	119	3	)	)	PUNCT
ma-170	119	4	thus	thus	ADV
ma-170	119	5	,	,	PUNCT
ma-170	119	6	the	the	DET
ma-170	119	7	iterate	iterate	NOUN
ma-170	119	8	y0	y0	NOUN
ma-170	119	9	is	be	AUX
ma-170	119	10	well	well	ADV
ma-170	119	11	defined	define	VERB
ma-170	119	12	and	and	CCONJ
ma-170	119	13	y0	y0	NOUN
ma-170	119	14	−	−	NOUN
ma-170	119	15	x∗	x∗	PROPN
ma-170	120	1	=	=	PUNCT
ma-170	120	2	x0	x0	PROPN
ma-170	121	1	−	−	PROPN
ma-170	121	2	x∗	x∗	PROPN
ma-170	121	3	−	−	PROPN
ma-170	122	1	[	[	X
ma-170	122	2	u0	u0	X
ma-170	122	3	,	,	PUNCT
ma-170	122	4	v0;f	v0;f	PROPN
ma-170	122	5	]	]	SYM
ma-170	122	6	−1f	−1f	PROPN
ma-170	122	7	(	(	PUNCT
ma-170	122	8	x0	x0	PROPN
ma-170	122	9	)	)	PUNCT
ma-170	122	10	.	.	PUNCT
ma-170	123	1	[	[	X
ma-170	123	2	u0	u0	X
ma-170	123	3	,	,	PUNCT
ma-170	123	4	v0;f	v0;f	ADJ
ma-170	123	5	]	]	SYM
ma-170	123	6	−1([u0	−1([u0	NOUN
ma-170	123	7	,	,	PUNCT
ma-170	123	8	v0;f	v0;f	ADJ
ma-170	123	9	]	]	PUNCT
ma-170	123	10	−	−	PROPN
ma-170	124	1	[	[	X
ma-170	124	2	x0	x0	PROPN
ma-170	124	3	,	,	PUNCT
ma-170	124	4	x	x	X
ma-170	124	5	∗;f	∗;f	NUM
ma-170	124	6	]	]	X
ma-170	124	7	)	)	PUNCT
ma-170	124	8	(	(	PUNCT
ma-170	124	9	x0	x0	PROPN
ma-170	124	10	−	−	PROPN
ma-170	124	11	x∗	x∗	PROPN
ma-170	124	12	)	)	PUNCT
ma-170	124	13	.	.	PUNCT
ma-170	125	1	(	(	PUNCT
ma-170	125	2	2.14	2.14	NUM
ma-170	125	3	)	)	PUNCT
ma-170	125	4	then	then	ADV
ma-170	125	5	,	,	PUNCT
ma-170	125	6	the	the	DET
ma-170	125	7	conditions	condition	NOUN
ma-170	125	8	(	(	PUNCT
ma-170	125	9	h3	h3	NOUN
ma-170	125	10	)	)	PUNCT
ma-170	125	11	,	,	PUNCT
ma-170	125	12	(	(	PUNCT
ma-170	125	13	h4	h4	PROPN
ma-170	125	14	)	)	PUNCT
ma-170	125	15	,	,	PUNCT
ma-170	125	16	(	(	PUNCT
ma-170	125	17	2.5	2.5	NUM
ma-170	125	18	)	)	PUNCT
ma-170	125	19	,	,	PUNCT
ma-170	125	20	(	(	PUNCT
ma-170	125	21	2.7	2.7	NUM
ma-170	125	22	)	)	PUNCT
ma-170	125	23	(	(	PUNCT
ma-170	125	24	for	for	ADP
ma-170	125	25	i	i	PRON
ma-170	125	26	=	=	NOUN
ma-170	125	27	1	1	NUM
ma-170	125	28	)	)	PUNCT
ma-170	125	29	,	,	PUNCT
ma-170	125	30	(	(	PUNCT
ma-170	125	31	2.13	2.13	NUM
ma-170	125	32	)	)	PUNCT
ma-170	125	33	and	and	CCONJ
ma-170	125	34	(	(	PUNCT
ma-170	125	35	2.14	2.14	NUM
ma-170	125	36	)	)	PUNCT
ma-170	125	37	give	give	VERB
ma-170	125	38	in	in	ADP
ma-170	125	39	turn	turn	NOUN
ma-170	125	40	‖y0	‖y0	PUNCT
ma-170	125	41	−	−	PROPN
ma-170	125	42	x∗‖	x∗‖	PROPN
ma-170	125	43	≤	≤	NOUN
ma-170	125	44	w1(‖u0	w1(‖u0	ADP
ma-170	125	45	−	−	PROPN
ma-170	125	46	x∗‖	x∗‖	PROPN
ma-170	125	47	,	,	PUNCT
ma-170	125	48	‖v0	‖v0	PROPN
ma-170	125	49	−	−	PROPN
ma-170	125	50	x∗‖	x∗‖	PROPN
ma-170	125	51	,	,	PUNCT
ma-170	125	52	‖x0	‖x0	NOUN
ma-170	125	53	−	−	PROPN
ma-170	126	1	x∗‖)‖x0	x∗‖)‖x0	NOUN
ma-170	126	2	−	−	PROPN
ma-170	126	3	x∗‖	x∗‖	PROPN
ma-170	126	4	1−	1−	NUM
ma-170	126	5	w0(f1(‖x0	w0(f1(‖x0	NOUN
ma-170	126	6	−	−	PROPN
ma-170	126	7	x∗‖	x∗‖	NUM
ma-170	126	8	)	)	PUNCT
ma-170	126	9	,	,	PUNCT
ma-170	126	10	f2(‖x0	f2(‖x0	PROPN
ma-170	126	11	−	−	PROPN
ma-170	126	12	x∗‖	x∗‖	PROPN
ma-170	126	13	)	)	PUNCT
ma-170	126	14	)	)	PUNCT
ma-170	126	15	≤h1(‖x0	≤h1(‖x0	VERB
ma-170	126	16	−	−	PROPN
ma-170	127	1	x∗‖)‖x0	x∗‖)‖x0	NOUN
ma-170	128	1	−	−	PROPN
ma-170	129	1	x∗‖	x∗‖	PROPN
ma-170	129	2	≤	≤	NUM
ma-170	129	3	‖x0	‖x0	NOUN
ma-170	130	1	−	−	PROPN
ma-170	130	2	x∗‖	x∗‖	X
ma-170	130	3	<	<	X
ma-170	130	4	δ∗.	δ∗.	X
ma-170	130	5	(	(	PUNCT
ma-170	130	6	2.15	2.15	NUM
ma-170	130	7	)	)	PUNCT
ma-170	130	8	hence	hence	ADV
ma-170	130	9	,	,	PUNCT
ma-170	130	10	the	the	DET
ma-170	130	11	iterate	iterate	NOUN
ma-170	130	12	y0	y0	PROPN
ma-170	130	13	∈	∈	PROPN
ma-170	130	14	b(x∗	b(x∗	NOUN
ma-170	130	15	,	,	PUNCT
ma-170	130	16	δ∗	δ∗	PROPN
ma-170	130	17	)	)	PUNCT
ma-170	130	18	and	and	CCONJ
ma-170	130	19	the	the	DET
ma-170	130	20	item	item	NOUN
ma-170	130	21	(	(	PUNCT
ma-170	130	22	2.9	2.9	NUM
ma-170	130	23	)	)	PUNCT
ma-170	130	24	is	be	AUX
ma-170	130	25	validated	validate	VERB
ma-170	130	26	for	for	ADP
ma-170	130	27	n	n	NOUN
ma-170	130	28	=	=	SYM
ma-170	130	29	0.notice	0.notice	NUM
ma-170	130	30	that	that	SCONJ
ma-170	130	31	the	the	DET
ma-170	130	32	iterates	iterate	NOUN
ma-170	130	33	z0	z0	PROPN
ma-170	130	34	and	and	CCONJ
ma-170	130	35	x1	x1	PROPN
ma-170	130	36	are	be	AUX
ma-170	130	37	also	also	ADV
ma-170	130	38	well	well	ADV
ma-170	130	39	defined	define	VERB
ma-170	130	40	by	by	ADP
ma-170	130	41	the	the	DET
ma-170	130	42	second	second	ADJ
ma-170	130	43	and	and	CCONJ
ma-170	130	44	the	the	DET
ma-170	130	45	third	third	ADJ
ma-170	130	46	substep	substep	NOUN
ma-170	130	47	ofthe	ofthe	NOUN
ma-170	130	48	method	method	NOUN
ma-170	130	49	(	(	PUNCT
ma-170	130	50	1.3	1.3	NUM
ma-170	130	51	)	)	PUNCT
ma-170	130	52	.	.	PUNCT
ma-170	131	1	in	in	ADP
ma-170	131	2	particular	particular	ADJ
ma-170	131	3	,	,	PUNCT
ma-170	131	4	we	we	PRON
ma-170	131	5	get	get	VERB
ma-170	131	6	z0	z0	NOUN
ma-170	131	7	−	−	NOUN
ma-170	131	8	x∗	x∗	NOUN
ma-170	132	1	=	=	PUNCT
ma-170	132	2	y0	y0	NOUN
ma-170	132	3	−	−	NOUN
ma-170	132	4	x∗	x∗	PROPN
ma-170	133	1	−d−1f	−d−1f	PROPN
ma-170	133	2	(	(	PUNCT
ma-170	133	3	y0	y0	NOUN
ma-170	133	4	)	)	PUNCT
ma-170	133	5	+	+	NOUN
ma-170	134	1	2d−1(d	2d−1(d	NUM
ma-170	134	2	−	−	NOUN
ma-170	135	1	[	[	X
ma-170	135	2	yn	yn	X
ma-170	135	3	,	,	PUNCT
ma-170	135	4	xn;f	xn;f	PUNCT
ma-170	135	5	]	]	X
ma-170	135	6	)	)	PUNCT
ma-170	135	7	d−1f	d−1f	NOUN
ma-170	135	8	(	(	PUNCT
ma-170	135	9	yn	yn	NOUN
ma-170	135	10	)	)	PUNCT
ma-170	135	11	=	=	X
ma-170	135	12	d−1(d	d−1(d	NOUN
ma-170	135	13	−	−	PROPN
ma-170	136	1	[	[	X
ma-170	136	2	yn	yn	X
ma-170	136	3	,	,	PUNCT
ma-170	136	4	x	x	X
ma-170	136	5	∗;f	∗;f	NUM
ma-170	136	6	]	]	X
ma-170	136	7	)	)	PUNCT
ma-170	136	8	(	(	PUNCT
ma-170	136	9	yn	yn	PRON
ma-170	136	10	−	−	NOUN
ma-170	136	11	x∗	x∗	PROPN
ma-170	136	12	)	)	PUNCT
ma-170	137	1	+	+	CCONJ
ma-170	138	1	2d−1([u0	2d−1([u0	NOUN
ma-170	138	2	,	,	PUNCT
ma-170	138	3	v0;f	v0;f	PROPN
ma-170	138	4	]	]	PUNCT
ma-170	138	5	−	−	PROPN
ma-170	139	1	[	[	X
ma-170	139	2	y0	y0	NOUN
ma-170	139	3	,	,	PUNCT
ma-170	139	4	x0;f	x0;f	PROPN
ma-170	139	5	]	]	PUNCT
ma-170	139	6	)	)	PUNCT
ma-170	139	7	d−1f	d−1f	NOUN
ma-170	139	8	(	(	PUNCT
ma-170	139	9	y0	y0	NOUN
ma-170	139	10	)	)	PUNCT
ma-170	139	11	.	.	PUNCT
ma-170	140	1	(	(	PUNCT
ma-170	140	2	2.16	2.16	NUM
ma-170	140	3	)	)	PUNCT
ma-170	141	1	but	but	CCONJ
ma-170	141	2	we	we	PRON
ma-170	141	3	can	can	AUX
ma-170	141	4	write	write	VERB
ma-170	141	5	by	by	ADP
ma-170	141	6	the	the	DET
ma-170	141	7	first	first	ADJ
ma-170	141	8	substep	substep	NOUN
ma-170	141	9	that	that	PRON
ma-170	142	1	f	f	PROPN
ma-170	142	2	(	(	PUNCT
ma-170	142	3	y0	y0	NOUN
ma-170	142	4	)	)	PUNCT
ma-170	142	5	=	=	SYM
ma-170	142	6	f	f	X
ma-170	142	7	(	(	PUNCT
ma-170	142	8	y0)−	y0)−	PROPN
ma-170	142	9	f	f	X
ma-170	142	10	(	(	PUNCT
ma-170	142	11	x∗	x∗	PROPN
ma-170	142	12	)	)	PUNCT
ma-170	142	13	=	=	PUNCT
ma-170	143	1	[	[	X
ma-170	143	2	y0	y0	NOUN
ma-170	143	3	,	,	PUNCT
ma-170	143	4	x	x	X
ma-170	143	5	∗;f	∗;f	NUM
ma-170	143	6	]	]	X
ma-170	143	7	(	(	PUNCT
ma-170	143	8	y0	y0	NOUN
ma-170	143	9	−	−	NOUN
ma-170	143	10	x∗	x∗	NOUN
ma-170	143	11	)	)	PUNCT
ma-170	143	12	,	,	PUNCT
ma-170	143	13	so	so	CCONJ
ma-170	143	14	by	by	ADP
ma-170	143	15	(	(	PUNCT
ma-170	143	16	h4	h4	PROPN
ma-170	143	17	)	)	PUNCT
ma-170	143	18	‖l−1f	‖l−1f	NOUN
ma-170	143	19	(	(	PUNCT
ma-170	143	20	y0)‖	y0)‖	NOUN
ma-170	143	21	=	=	SYM
ma-170	143	22	‖l−1([y0	‖l−1([y0	PROPN
ma-170	143	23	,	,	PUNCT
ma-170	143	24	x	x	X
ma-170	144	1	∗;f	∗;f	NUM
ma-170	144	2	]	]	X
ma-170	144	3	−	−	NOUN
ma-170	144	4	l+	l+	X
ma-170	144	5	l)(y0	l)(y0	NOUN
ma-170	144	6	−	−	PROPN
ma-170	144	7	x∗)‖	x∗)‖	SYM
ma-170	144	8	≤	≤	NUM
ma-170	144	9	(	(	PUNCT
ma-170	144	10	1	1	NUM
ma-170	144	11	+	+	CCONJ
ma-170	144	12	w(‖y0	w(‖y0	ADJ
ma-170	144	13	−	−	ADP
ma-170	144	14	x∗‖))‖y0	x∗‖))‖y0	PROPN
ma-170	144	15	−	−	PROPN
ma-170	144	16	x∗‖.	x∗‖.	PROPN
ma-170	144	17	(	(	PUNCT
ma-170	144	18	2.17	2.17	NUM
ma-170	144	19	)	)	PUNCT
ma-170	144	20	consequently	consequently	ADV
ma-170	144	21	,	,	PUNCT
ma-170	144	22	(	(	PUNCT
ma-170	144	23	2.5	2.5	NUM
ma-170	144	24	)	)	PUNCT
ma-170	144	25	,	,	PUNCT
ma-170	144	26	(	(	PUNCT
ma-170	144	27	2.7	2.7	NUM
ma-170	144	28	)	)	PUNCT
ma-170	144	29	(	(	PUNCT
ma-170	144	30	for	for	ADP
ma-170	144	31	i	i	PRON
ma-170	144	32	=	=	NOUN
ma-170	144	33	2	2	NUM
ma-170	144	34	)	)	PUNCT
ma-170	144	35	,	,	PUNCT
ma-170	144	36	(	(	PUNCT
ma-170	144	37	h4	h4	PROPN
ma-170	144	38	)	)	PUNCT
ma-170	144	39	,	,	PUNCT
ma-170	144	40	(	(	PUNCT
ma-170	144	41	2.13	2.13	NUM
ma-170	144	42	)	)	PUNCT
ma-170	144	43	,	,	PUNCT
ma-170	144	44	(	(	PUNCT
ma-170	144	45	2.16	2.16	NUM
ma-170	144	46	)	)	PUNCT
ma-170	144	47	and	and	CCONJ
ma-170	144	48	(	(	PUNCT
ma-170	144	49	2.17	2.17	NUM
ma-170	144	50	)	)	PUNCT
ma-170	144	51	imply	imply	ADV
ma-170	144	52	‖z0	‖z0	VERB
ma-170	144	53	−	−	PROPN
ma-170	144	54	x∗‖	x∗‖	PROPN
ma-170	144	55	≤	≤	PROPN
ma-170	144	56	[	[	PUNCT
ma-170	144	57	w1(‖y0	w1(‖y0	PROPN
ma-170	144	58	−	−	PROPN
ma-170	144	59	x∗‖	x∗‖	PROPN
ma-170	144	60	,	,	PUNCT
ma-170	144	61	‖u0	‖u0	NOUN
ma-170	144	62	−	−	PROPN
ma-170	144	63	x∗‖	x∗‖	PROPN
ma-170	144	64	,	,	PUNCT
ma-170	144	65	‖v0	‖v0	PROPN
ma-170	144	66	−	−	NOUN
ma-170	144	67	x∗‖	x∗‖	NUM
ma-170	144	68	)	)	PUNCT
ma-170	144	69	1−	1−	NUM
ma-170	144	70	w0(f1(‖x0	w0(f1(‖x0	NOUN
ma-170	144	71	−	−	PROPN
ma-170	144	72	x∗‖	x∗‖	NUM
ma-170	144	73	)	)	PUNCT
ma-170	144	74	,	,	PUNCT
ma-170	144	75	f2(‖x0	f2(‖x0	PROPN
ma-170	144	76	−	−	PROPN
ma-170	144	77	x∗‖	x∗‖	PROPN
ma-170	144	78	)	)	PUNCT
ma-170	144	79	)	)	PUNCT
ma-170	145	1	+	+	CCONJ
ma-170	145	2	2w2(‖x0	2w2(‖x0	NUM
ma-170	145	3	−	−	PROPN
ma-170	145	4	x∗‖	x∗‖	NUM
ma-170	145	5	,	,	PUNCT
ma-170	145	6	‖y0	‖y0	VERB
ma-170	145	7	−	−	PROPN
ma-170	145	8	x∗‖	x∗‖	PROPN
ma-170	145	9	,	,	PUNCT
ma-170	145	10	‖u0	‖u0	NOUN
ma-170	145	11	−	−	PROPN
ma-170	145	12	x∗‖	x∗‖	PROPN
ma-170	145	13	,	,	PUNCT
ma-170	145	14	‖v0	‖v0	PRON
ma-170	145	15	−	−	NOUN
ma-170	145	16	x∗‖)(1	x∗‖)(1	PUNCT
ma-170	146	1	+	+	CCONJ
ma-170	146	2	w(‖y0	w(‖y0	ADJ
ma-170	146	3	−	−	PROPN
ma-170	146	4	x∗‖	x∗‖	NUM
ma-170	146	5	)	)	PUNCT
ma-170	146	6	)	)	PUNCT
ma-170	146	7	(	(	PUNCT
ma-170	146	8	1−	1−	NUM
ma-170	146	9	w0(f1(‖x0	w0(f1(‖x0	NOUN
ma-170	146	10	−	−	PROPN
ma-170	146	11	x∗‖	x∗‖	NUM
ma-170	146	12	)	)	PUNCT
ma-170	146	13	,	,	PUNCT
ma-170	146	14	f2(‖x0	f2(‖x0	PROPN
ma-170	146	15	−	−	PROPN
ma-170	147	1	x∗‖)))2	x∗‖)))2	X
ma-170	147	2	]	]	PUNCT
ma-170	148	1	‖y0	‖y0	X
ma-170	148	2	−	−	PROPN
ma-170	148	3	x∗‖	x∗‖	PROPN
ma-170	148	4	,	,	PUNCT
ma-170	148	5	≤	≤	PUNCT
ma-170	149	1	h2(‖x0	h2(‖x0	PROPN
ma-170	149	2	−	−	PROPN
ma-170	149	3	x∗‖)‖x0	x∗‖)‖x0	NOUN
ma-170	149	4	−	−	PROPN
ma-170	149	5	x∗‖	x∗‖	PROPN
ma-170	149	6	≤	≤	PROPN
ma-170	150	1	‖x0	‖x0	NOUN
ma-170	150	2	−	−	PROPN
ma-170	150	3	x∗‖.	x∗‖.	PROPN
ma-170	150	4	(	(	PUNCT
ma-170	150	5	2.18	2.18	NUM
ma-170	150	6	)	)	PUNCT
ma-170	150	7	thus	thus	ADV
ma-170	150	8	,	,	PUNCT
ma-170	150	9	the	the	DET
ma-170	150	10	iterate	iterate	NOUN
ma-170	150	11	z0	z0	PROPN
ma-170	150	12	∈	∈	PROPN
ma-170	150	13	b(x∗	b(x∗	PROPN
ma-170	150	14	,	,	PUNCT
ma-170	150	15	δ∗	δ∗	PROPN
ma-170	150	16	)	)	PUNCT
ma-170	150	17	and	and	CCONJ
ma-170	150	18	the	the	DET
ma-170	150	19	item	item	NOUN
ma-170	150	20	(	(	PUNCT
ma-170	150	21	2.10	2.10	NUM
ma-170	150	22	)	)	PUNCT
ma-170	150	23	is	be	AUX
ma-170	150	24	validated	validate	VERB
ma-170	150	25	for	for	ADP
ma-170	150	26	n	n	NOUN
ma-170	150	27	=	=	SYM
ma-170	150	28	0	0	NUM
ma-170	150	29	.	.	PUNCT
ma-170	151	1	moreover	moreover	ADV
ma-170	151	2	,	,	PUNCT
ma-170	151	3	the	the	DET
ma-170	151	4	thirdsubstep	thirdsubstep	NOUN
ma-170	151	5	gives	give	VERB
ma-170	151	6	x1	x1	PROPN
ma-170	151	7	−	−	PROPN
ma-170	151	8	x∗	x∗	PROPN
ma-170	151	9	=	=	SYM
ma-170	151	10	z0	z0	PROPN
ma-170	151	11	−	−	PROPN
ma-170	151	12	x∗	x∗	PROPN
ma-170	152	1	−d−1f	−d−1f	PROPN
ma-170	153	1	(	(	PUNCT
ma-170	153	2	z0)−	z0)−	X
ma-170	153	3	ad−1f	ad−1f	PROPN
ma-170	153	4	(	(	PUNCT
ma-170	153	5	z0	z0	PROPN
ma-170	153	6	)	)	PUNCT
ma-170	153	7	=	=	SYM
ma-170	153	8	d−1(d	d−1(d	NOUN
ma-170	153	9	−	−	PROPN
ma-170	154	1	[	[	X
ma-170	154	2	z0	z0	X
ma-170	154	3	,	,	PUNCT
ma-170	154	4	x	x	X
ma-170	154	5	∗;f	∗;f	NUM
ma-170	154	6	]	]	X
ma-170	154	7	)	)	PUNCT
ma-170	154	8	(	(	PUNCT
ma-170	154	9	z0	z0	PROPN
ma-170	154	10	−	−	PROPN
ma-170	154	11	x∗)−	x∗)−	PRON
ma-170	155	1	ad−1f	ad−1f	PROPN
ma-170	155	2	(	(	PUNCT
ma-170	155	3	z0	z0	PROPN
ma-170	155	4	)	)	PUNCT
ma-170	155	5	,	,	PUNCT
ma-170	155	6	(	(	PUNCT
ma-170	155	7	2.19	2.19	NUM
ma-170	155	8	)	)	PUNCT
ma-170	155	9	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	NOUN
ma-170	155	10	eur	eur	PROPN
ma-170	155	11	.	.	PUNCT
ma-170	156	1	j.	j.	PROPN
ma-170	156	2	math	math	PROPN
ma-170	156	3	.	.	PUNCT
ma-170	157	1	anal	anal	PROPN
ma-170	157	2	.	.	PUNCT
ma-170	158	1	10.28924	10.28924	NUM
ma-170	158	2	/	/	SYM
ma-170	158	3	ada	ada	PROPN
ma-170	158	4	/	/	SYM
ma-170	158	5	ma.3.24	ma.3.24	PROPN
ma-170	158	6	6where	6where	NUM
ma-170	158	7	a	a	PRON
ma-170	158	8	=	=	NOUN
ma-170	159	1	−	−	PROPN
ma-170	160	1	[	[	X
ma-170	160	2	9	9	NUM
ma-170	160	3	4	4	NUM
ma-170	160	4	i	i	NOUN
ma-170	160	5	−	−	NUM
ma-170	160	6	7	7	NUM
ma-170	160	7	2	2	NUM
ma-170	160	8	d−1[zn	d−1[zn	NOUN
ma-170	160	9	,	,	PUNCT
ma-170	160	10	yn;f	yn;f	ADJ
ma-170	160	11	]	]	PUNCT
ma-170	161	1	+	+	CCONJ
ma-170	161	2	5	5	NUM
ma-170	161	3	4	4	NUM
ma-170	161	4	(	(	PUNCT
ma-170	161	5	d−1[zn	d−1[zn	NOUN
ma-170	161	6	,	,	PUNCT
ma-170	161	7	yn;f	yn;f	NOUN
ma-170	161	8	]	]	PUNCT
ma-170	161	9	)	)	PUNCT
ma-170	161	10	2	2	NUM
ma-170	161	11	]	]	PUNCT
ma-170	161	12	=	=	PUNCT
ma-170	162	1	−	−	PROPN
ma-170	162	2	1	1	NUM
ma-170	162	3	4	4	NUM
ma-170	162	4	(	(	PUNCT
ma-170	162	5	5(d−1([zn	5(d−1([zn	NUM
ma-170	162	6	,	,	PUNCT
ma-170	162	7	yn;f	yn;f	NOUN
ma-170	162	8	]	]	PUNCT
ma-170	162	9	−	−	PROPN
ma-170	163	1	[	[	X
ma-170	163	2	un	un	X
ma-170	163	3	,	,	PUNCT
ma-170	163	4	vn;f	vn;f	PUNCT
ma-170	163	5	]	]	X
ma-170	163	6	)	)	PUNCT
ma-170	163	7	)	)	PUNCT
ma-170	163	8	2	2	NUM
ma-170	163	9	−	−	PROPN
ma-170	163	10	4d−1([zn	4d−1([zn	NUM
ma-170	163	11	,	,	PUNCT
ma-170	163	12	yn;f	yn;f	NOUN
ma-170	163	13	]	]	PUNCT
ma-170	163	14	−	−	PROPN
ma-170	164	1	[	[	X
ma-170	164	2	un	un	X
ma-170	164	3	,	,	PUNCT
ma-170	164	4	vn;f	vn;f	PUNCT
ma-170	164	5	]	]	X
ma-170	164	6	)	)	PUNCT
ma-170	164	7	)	)	PUNCT
ma-170	164	8	.	.	PUNCT
ma-170	165	1	therefore	therefore	ADV
ma-170	165	2	,	,	PUNCT
ma-170	165	3	‖a‖	‖a‖	PROPN
ma-170	165	4	≤	≤	NUM
ma-170	165	5	1	1	NUM
ma-170	165	6	4	4	NUM
ma-170	165	7	[	[	PUNCT
ma-170	165	8	5	5	NUM
ma-170	165	9	(	(	PUNCT
ma-170	165	10	w2(‖y0	w2(‖y0	PROPN
ma-170	165	11	−	−	PROPN
ma-170	165	12	x∗‖	x∗‖	PROPN
ma-170	165	13	,	,	PUNCT
ma-170	165	14	‖z0	‖z0	NOUN
ma-170	165	15	−	−	PROPN
ma-170	165	16	x∗‖	x∗‖	PROPN
ma-170	165	17	,	,	PUNCT
ma-170	165	18	‖u0	‖u0	NOUN
ma-170	165	19	−	−	PROPN
ma-170	166	1	x∗‖	x∗‖	PROPN
ma-170	166	2	,	,	PUNCT
ma-170	166	3	‖v0	‖v0	PROPN
ma-170	166	4	−	−	NOUN
ma-170	166	5	x∗‖	x∗‖	NUM
ma-170	166	6	)	)	PUNCT
ma-170	166	7	1−	1−	NUM
ma-170	166	8	w0(f1(‖x0	w0(f1(‖x0	NOUN
ma-170	166	9	−	−	PROPN
ma-170	166	10	x∗‖	x∗‖	NUM
ma-170	166	11	)	)	PUNCT
ma-170	166	12	,	,	PUNCT
ma-170	166	13	f2(‖x0	f2(‖x0	PROPN
ma-170	166	14	−	−	PROPN
ma-170	166	15	x∗‖	x∗‖	PROPN
ma-170	166	16	)	)	PUNCT
ma-170	166	17	)	)	PUNCT
ma-170	166	18	)	)	PUNCT
ma-170	167	1	2	2	NUM
ma-170	167	2	+	+	CCONJ
ma-170	167	3	4	4	NUM
ma-170	167	4	w2(‖y0	w2(‖y0	PROPN
ma-170	167	5	−	−	PROPN
ma-170	167	6	x∗‖	x∗‖	PROPN
ma-170	167	7	,	,	PUNCT
ma-170	167	8	‖z0	‖z0	NOUN
ma-170	167	9	−	−	PROPN
ma-170	167	10	x∗‖	x∗‖	PROPN
ma-170	167	11	,	,	PUNCT
ma-170	167	12	‖u0	‖u0	NOUN
ma-170	167	13	−	−	PROPN
ma-170	168	1	x∗‖	x∗‖	PROPN
ma-170	168	2	,	,	PUNCT
ma-170	168	3	‖v0	‖v0	PROPN
ma-170	168	4	−	−	NOUN
ma-170	168	5	x∗‖	x∗‖	NUM
ma-170	168	6	)	)	PUNCT
ma-170	168	7	1−	1−	NUM
ma-170	168	8	w0(f1(‖x0	w0(f1(‖x0	NOUN
ma-170	168	9	−	−	PROPN
ma-170	168	10	x∗‖	x∗‖	NUM
ma-170	168	11	)	)	PUNCT
ma-170	168	12	,	,	PUNCT
ma-170	168	13	f2(‖x0	f2(‖x0	PROPN
ma-170	168	14	−	−	PROPN
ma-170	168	15	x∗‖	x∗‖	PROPN
ma-170	168	16	)	)	PUNCT
ma-170	168	17	)	)	PUNCT
ma-170	168	18	]	]	PUNCT
ma-170	169	1	=	=	PUNCT
ma-170	169	2	h0	h0	PROPN
ma-170	169	3	.	.	PUNCT
ma-170	170	1	(	(	PUNCT
ma-170	170	2	2.20	2.20	NUM
ma-170	170	3	)	)	PUNCT
ma-170	170	4	then	then	ADV
ma-170	170	5	,	,	PUNCT
ma-170	170	6	by	by	ADP
ma-170	170	7	(	(	PUNCT
ma-170	170	8	2.5	2.5	NUM
ma-170	170	9	)	)	PUNCT
ma-170	170	10	,	,	PUNCT
ma-170	170	11	(	(	PUNCT
ma-170	170	12	2.7	2.7	NUM
ma-170	170	13	)	)	PUNCT
ma-170	170	14	(	(	PUNCT
ma-170	170	15	for	for	ADP
ma-170	170	16	i	i	PRON
ma-170	170	17	=	=	NOUN
ma-170	170	18	3	3	NUM
ma-170	170	19	)	)	PUNCT
ma-170	170	20	,	,	PUNCT
ma-170	170	21	(	(	PUNCT
ma-170	170	22	h4	h4	PROPN
ma-170	170	23	)	)	PUNCT
ma-170	170	24	,	,	PUNCT
ma-170	170	25	(	(	PUNCT
ma-170	170	26	2.13	2.13	NUM
ma-170	170	27	)	)	PUNCT
ma-170	170	28	and	and	CCONJ
ma-170	170	29	(	(	PUNCT
ma-170	170	30	2.18)-(2.20	2.18)-(2.20	NUM
ma-170	170	31	)	)	PUNCT
ma-170	170	32	‖x1	‖x1	NOUN
ma-170	170	33	−	−	PROPN
ma-170	170	34	x∗‖	x∗‖	SYM
ma-170	170	35	≤	≤	NOUN
ma-170	170	36	[	[	PUNCT
ma-170	170	37	w1(‖u0	w1(‖u0	PROPN
ma-170	170	38	−	−	PROPN
ma-170	170	39	x∗‖	x∗‖	PROPN
ma-170	170	40	,	,	PUNCT
ma-170	170	41	‖v0	‖v0	PROPN
ma-170	170	42	−	−	PROPN
ma-170	170	43	x∗‖	x∗‖	PROPN
ma-170	170	44	,	,	PUNCT
ma-170	170	45	‖z0	‖z0	NOUN
ma-170	170	46	−	−	PROPN
ma-170	170	47	x∗‖	x∗‖	PROPN
ma-170	170	48	)	)	PUNCT
ma-170	170	49	1−	1−	NUM
ma-170	170	50	w0(f1(‖x0	w0(f1(‖x0	NOUN
ma-170	170	51	−	−	PROPN
ma-170	170	52	x∗‖	x∗‖	NUM
ma-170	170	53	)	)	PUNCT
ma-170	170	54	,	,	PUNCT
ma-170	170	55	f2(‖x0	f2(‖x0	PROPN
ma-170	170	56	−	−	PROPN
ma-170	170	57	x∗‖	x∗‖	PROPN
ma-170	170	58	)	)	PUNCT
ma-170	170	59	)	)	PUNCT
ma-170	171	1	+	+	CCONJ
ma-170	171	2	h0(1	h0(1	PROPN
ma-170	171	3	+	+	CCONJ
ma-170	171	4	w(‖z0	w(‖z0	NOUN
ma-170	171	5	−	−	NOUN
ma-170	171	6	x∗‖	x∗‖	NUM
ma-170	171	7	)	)	PUNCT
ma-170	171	8	)	)	PUNCT
ma-170	172	1	1−	1−	NUM
ma-170	172	2	w0(f1(‖x0	w0(f1(‖x0	NOUN
ma-170	172	3	−	−	PROPN
ma-170	172	4	x∗‖	x∗‖	NUM
ma-170	172	5	)	)	PUNCT
ma-170	172	6	,	,	PUNCT
ma-170	172	7	f2(‖x0	f2(‖x0	PROPN
ma-170	172	8	−	−	PROPN
ma-170	172	9	x∗‖	x∗‖	PROPN
ma-170	172	10	)	)	PUNCT
ma-170	172	11	)	)	PUNCT
ma-170	172	12	]	]	PUNCT
ma-170	172	13	‖z0	‖z0	PUNCT
ma-170	172	14	−	−	PROPN
ma-170	172	15	x∗‖	x∗‖	PROPN
ma-170	172	16	≤	≤	NOUN
ma-170	173	1	h3(‖x0	h3(‖x0	PRON
ma-170	173	2	−	−	PROPN
ma-170	173	3	x∗‖)‖x0	x∗‖)‖x0	PROPN
ma-170	173	4	−	−	PROPN
ma-170	173	5	x∗‖	x∗‖	PROPN
ma-170	173	6	≤	≤	PROPN
ma-170	174	1	‖x0	‖x0	NOUN
ma-170	174	2	−	−	PROPN
ma-170	174	3	x∗‖.	x∗‖.	PROPN
ma-170	174	4	(	(	PUNCT
ma-170	174	5	2.21	2.21	NUM
ma-170	174	6	)	)	PUNCT
ma-170	174	7	hence	hence	ADV
ma-170	174	8	,	,	PUNCT
ma-170	174	9	the	the	DET
ma-170	174	10	items	item	NOUN
ma-170	174	11	(	(	PUNCT
ma-170	174	12	2.8	2.8	NUM
ma-170	174	13	)	)	PUNCT
ma-170	174	14	and	and	CCONJ
ma-170	174	15	(	(	PUNCT
ma-170	174	16	2.11	2.11	NUM
ma-170	174	17	)	)	PUNCT
ma-170	174	18	are	be	AUX
ma-170	174	19	validated	validate	VERB
ma-170	174	20	for	for	ADP
ma-170	174	21	n	n	NOUN
ma-170	174	22	=	=	SYM
ma-170	174	23	0	0	NUM
ma-170	174	24	and	and	CCONJ
ma-170	174	25	the	the	DET
ma-170	174	26	iterate	iterate	NOUN
ma-170	174	27	x1	x1	PROPN
ma-170	174	28	∈	∈	PROPN
ma-170	174	29	b(x∗	b(x∗	PROPN
ma-170	174	30	,	,	PUNCT
ma-170	174	31	δ∗	δ∗	PROPN
ma-170	174	32	)	)	PUNCT
ma-170	174	33	.	.	PUNCT
ma-170	175	1	if	if	SCONJ
ma-170	175	2	thepreceding	thepreceding	NOUN
ma-170	175	3	calculations	calculation	NOUN
ma-170	175	4	are	be	AUX
ma-170	175	5	repeated	repeat	VERB
ma-170	175	6	with	with	ADP
ma-170	175	7	xm	xm	PROPN
ma-170	175	8	,	,	PUNCT
ma-170	175	9	ym	ym	PROPN
ma-170	175	10	,	,	PUNCT
ma-170	175	11	xm+1	xm+1	PROPN
ma-170	175	12	,	,	PUNCT
ma-170	175	13	replacing	replace	VERB
ma-170	175	14	x0	x0	PRON
ma-170	175	15	,	,	PUNCT
ma-170	175	16	y0	y0	PROPN
ma-170	175	17	,	,	PUNCT
ma-170	175	18	x1	x1	PROPN
ma-170	175	19	,	,	PUNCT
ma-170	175	20	respectively	respectively	ADV
ma-170	175	21	,	,	PUNCT
ma-170	175	22	theinduction	theinduction	NOUN
ma-170	175	23	for	for	ADP
ma-170	175	24	the	the	DET
ma-170	175	25	items	item	NOUN
ma-170	175	26	(	(	PUNCT
ma-170	175	27	2.8)-(2.11	2.8)-(2.11	NUM
ma-170	175	28	)	)	PUNCT
ma-170	175	29	is	be	AUX
ma-170	175	30	terminated	terminate	VERB
ma-170	175	31	.	.	PUNCT
ma-170	176	1	furthermore	furthermore	ADV
ma-170	176	2	,	,	PUNCT
ma-170	176	3	from	from	ADP
ma-170	176	4	estimation	estimation	NOUN
ma-170	176	5	‖xm+1	‖xm+1	NUM
ma-170	176	6	−	−	PROPN
ma-170	176	7	x∗‖	x∗‖	PROPN
ma-170	176	8	≤	≤	NOUN
ma-170	177	1	µ‖xm	µ‖xm	PROPN
ma-170	177	2	−	−	PROPN
ma-170	177	3	x∗‖	x∗‖	X
ma-170	177	4	<	<	X
ma-170	177	5	‖xm	‖xm	PROPN
ma-170	177	6	−	−	PROPN
ma-170	177	7	x∗‖	x∗‖	PROPN
ma-170	177	8	,	,	PUNCT
ma-170	177	9	(	(	PUNCT
ma-170	177	10	2.22	2.22	NUM
ma-170	177	11	)	)	PUNCT
ma-170	177	12	where	where	SCONJ
ma-170	177	13	µ	µ	X
ma-170	177	14	=	=	SYM
ma-170	177	15	h3(‖x0	h3(‖x0	PROPN
ma-170	177	16	−	−	PROPN
ma-170	177	17	x∗‖	x∗‖	PROPN
ma-170	177	18	)	)	PUNCT
ma-170	177	19	∈	∈	PROPN
ma-170	178	1	[	[	X
ma-170	178	2	0	0	NUM
ma-170	178	3	,	,	PUNCT
ma-170	178	4	1	1	NUM
ma-170	178	5	)	)	PUNCT
ma-170	178	6	,	,	PUNCT
ma-170	178	7	we	we	PRON
ma-170	178	8	conclude	conclude	VERB
ma-170	178	9	that	that	SCONJ
ma-170	178	10	limm→∞	limm→∞	PROPN
ma-170	178	11	xm	xm	PROPN
ma-170	179	1	=	=	PUNCT
ma-170	179	2	x∗	x∗	PROPN
ma-170	179	3	and	and	CCONJ
ma-170	179	4	the	the	DET
ma-170	179	5	iterate	iterate	NOUN
ma-170	179	6	xm+1	xm+1	PROPN
ma-170	179	7	∈	∈	PROPN
ma-170	179	8	b(x∗	b(x∗	PROPN
ma-170	179	9	,	,	PUNCT
ma-170	179	10	δ∗	δ∗	PROPN
ma-170	179	11	)	)	PUNCT
ma-170	179	12	.	.	PUNCT
ma-170	180	1	�	�	PROPN
ma-170	180	2	remark	remark	VERB
ma-170	180	3	2.2	2.2	NUM
ma-170	180	4	the	the	DET
ma-170	180	5	second	second	ADJ
ma-170	180	6	and	and	CCONJ
ma-170	180	7	third	third	ADJ
ma-170	180	8	hypotheses	hypothesis	NOUN
ma-170	180	9	in	in	ADP
ma-170	180	10	(	(	PUNCT
ma-170	180	11	h3	h3	NOUN
ma-170	180	12	)	)	PUNCT
ma-170	180	13	are	be	AUX
ma-170	180	14	left	leave	VERB
ma-170	180	15	as	as	ADV
ma-170	180	16	uncluttered	uncluttered	ADJ
ma-170	180	17	as	as	ADP
ma-170	180	18	possible	possible	ADJ
ma-170	180	19	.	.	PUNCT
ma-170	181	1	somepossible	somepossible	ADJ
ma-170	181	2	choices	choice	NOUN
ma-170	181	3	for	for	ADP
ma-170	181	4	the	the	DET
ma-170	181	5	functions	function	NOUN
ma-170	181	6	f1	f1	NOUN
ma-170	181	7	and	and	CCONJ
ma-170	181	8	f2	f2	PROPN
ma-170	181	9	are	be	AUX
ma-170	181	10	specified	specify	VERB
ma-170	181	11	.	.	PUNCT
ma-170	182	1	un	un	PROPN
ma-170	182	2	−	−	PROPN
ma-170	182	3	x∗	x∗	PROPN
ma-170	183	1	=	=	PUNCT
ma-170	183	2	xn	xn	PROPN
ma-170	184	1	−	−	NOUN
ma-170	184	2	x∗	x∗	PROPN
ma-170	184	3	+	+	CCONJ
ma-170	184	4	f	f	X
ma-170	184	5	(	(	PUNCT
ma-170	184	6	xn	xn	PROPN
ma-170	184	7	)	)	PUNCT
ma-170	184	8	=	=	PUNCT
ma-170	185	1	(	(	PUNCT
ma-170	185	2	i	i	PRON
ma-170	185	3	+	+	X
ma-170	186	1	[	[	X
ma-170	186	2	xn	xn	X
ma-170	186	3	,	,	PUNCT
ma-170	186	4	x	x	X
ma-170	186	5	∗;f	∗;f	NUM
ma-170	186	6	]	]	X
ma-170	186	7	)	)	PUNCT
ma-170	186	8	(	(	PUNCT
ma-170	187	1	xn	xn	NOUN
ma-170	187	2	−	−	PROPN
ma-170	187	3	x∗	x∗	PROPN
ma-170	187	4	)	)	PUNCT
ma-170	187	5	=	=	SYM
ma-170	188	1	(	(	PUNCT
ma-170	188	2	i	i	PRON
ma-170	188	3	+	+	CCONJ
ma-170	188	4	l+	l+	NOUN
ma-170	188	5	ll−1([xn	ll−1([xn	NOUN
ma-170	188	6	,	,	PUNCT
ma-170	188	7	x	x	X
ma-170	189	1	∗;f	∗;f	NUM
ma-170	190	1	]	]	X
ma-170	190	2	−	−	PROPN
ma-170	190	3	l))(xn	l))(xn	NOUN
ma-170	190	4	−	−	NOUN
ma-170	190	5	x∗	x∗	PROPN
ma-170	190	6	)	)	PUNCT
ma-170	190	7	,	,	PUNCT
ma-170	190	8	so	so	ADV
ma-170	190	9	‖un	‖un	PROPN
ma-170	190	10	−	−	PROPN
ma-170	190	11	x∗‖	x∗‖	SYM
ma-170	190	12	≤	≤	NOUN
ma-170	190	13	(	(	PUNCT
ma-170	190	14	‖i	‖i	NOUN
ma-170	190	15	+	+	CCONJ
ma-170	190	16	l‖+	l‖+	ADJ
ma-170	190	17	(	(	PUNCT
ma-170	190	18	‖l‖w(‖(xn	‖l‖w(‖(xn	NOUN
ma-170	190	19	−	−	NOUN
ma-170	190	20	x∗)‖	x∗)‖	PROPN
ma-170	190	21	)	)	PUNCT
ma-170	190	22	)	)	PUNCT
ma-170	190	23	)	)	PUNCT
ma-170	191	1	‖(xn	‖(xn	ADP
ma-170	191	2	−	−	NOUN
ma-170	191	3	x∗)‖.thus	x∗)‖.thus	ADV
ma-170	191	4	,	,	PUNCT
ma-170	191	5	we	we	PRON
ma-170	191	6	can	can	AUX
ma-170	191	7	choose	choose	VERB
ma-170	191	8	f1(t	f1(t	PART
ma-170	191	9	)	)	PUNCT
ma-170	191	10	=	=	SYM
ma-170	191	11	(	(	PUNCT
ma-170	191	12	‖i	‖i	NOUN
ma-170	191	13	+	+	CCONJ
ma-170	191	14	l‖+	l‖+	ADJ
ma-170	191	15	‖l‖w(t	‖l‖w(t	NOUN
ma-170	191	16	)	)	PUNCT
ma-170	191	17	)	)	PUNCT
ma-170	191	18	t.notice	t.notice	NOUN
ma-170	191	19	also	also	ADV
ma-170	191	20	that	that	SCONJ
ma-170	191	21	we	we	PRON
ma-170	191	22	can	can	AUX
ma-170	191	23	set	set	VERB
ma-170	191	24	w(t	w(t	PROPN
ma-170	191	25	)	)	PUNCT
ma-170	192	1	=	=	SYM
ma-170	192	2	w0(0	w0(0	PROPN
ma-170	192	3	,	,	PUNCT
ma-170	192	4	t).similarly	t).similarly	ADV
ma-170	192	5	,	,	PUNCT
ma-170	192	6	we	we	PRON
ma-170	192	7	define	define	VERB
ma-170	192	8	f2(t	f2(t	PRON
ma-170	192	9	)	)	PUNCT
ma-170	192	10	=	=	SYM
ma-170	192	11	(	(	PUNCT
ma-170	192	12	‖i	‖i	NOUN
ma-170	192	13	−	−	NOUN
ma-170	192	14	l‖+	l‖+	ADJ
ma-170	192	15	‖l‖w(t	‖l‖w(t	NOUN
ma-170	192	16	)	)	PUNCT
ma-170	192	17	)	)	PUNCT
ma-170	193	1	t.in	t.in	NOUN
ma-170	193	2	view	view	NOUN
ma-170	193	3	of	of	ADP
ma-170	193	4	the	the	DET
ma-170	193	5	above	above	ADP
ma-170	193	6	the	the	DET
ma-170	193	7	second	second	ADJ
ma-170	193	8	and	and	CCONJ
ma-170	193	9	third	third	ADJ
ma-170	193	10	conditions	condition	NOUN
ma-170	193	11	in	in	ADP
ma-170	193	12	(	(	PUNCT
ma-170	193	13	h3	h3	NOUN
ma-170	193	14	)	)	PUNCT
ma-170	193	15	can	can	AUX
ma-170	193	16	be	be	AUX
ma-170	193	17	dropped	drop	VERB
ma-170	193	18	if	if	SCONJ
ma-170	193	19	(	(	PUNCT
ma-170	193	20	h5	h5	PROPN
ma-170	193	21	)	)	PUNCT
ma-170	193	22	is	be	AUX
ma-170	193	23	replaced	replace	VERB
ma-170	193	24	by	by	ADP
ma-170	193	25	(	(	PUNCT
ma-170	193	26	h5	h5	PROPN
ma-170	193	27	)	)	PUNCT
ma-170	194	1	′	′	NUM
ma-170	195	1	b[x∗	b[x∗	NOUN
ma-170	195	2	,	,	PUNCT
ma-170	195	3	δ̄	δ̄	NOUN
ma-170	195	4	]	]	PUNCT
ma-170	195	5	⊂	⊂	PROPN
ma-170	195	6	ω	ω	PROPN
ma-170	195	7	,	,	PUNCT
ma-170	195	8	where	where	SCONJ
ma-170	195	9	δ̄	δ̄	NOUN
ma-170	195	10	=	=	SYM
ma-170	195	11	max{δ∗	max{δ∗	NOUN
ma-170	195	12	,	,	PUNCT
ma-170	195	13	f1(δ∗)δ∗	f1(δ∗)δ∗	PROPN
ma-170	195	14	,	,	PUNCT
ma-170	195	15	f2(δ∗)δ∗	f2(δ∗)δ∗	PROPN
ma-170	195	16	}	}	PUNCT
ma-170	195	17	.	.	PUNCT
ma-170	196	1	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	PROPN
ma-170	196	2	eur	eur	PROPN
ma-170	196	3	.	.	PUNCT
ma-170	197	1	j.	j.	PROPN
ma-170	197	2	math	math	PROPN
ma-170	197	3	.	.	PUNCT
ma-170	198	1	anal	anal	PROPN
ma-170	198	2	.	.	PUNCT
ma-170	199	1	10.28924	10.28924	NUM
ma-170	199	2	/	/	SYM
ma-170	199	3	ada	ada	PROPN
ma-170	199	4	/	/	SYM
ma-170	199	5	ma.3.24	ma.3.24	ADJ
ma-170	199	6	7possible	7possible	NUM
ma-170	199	7	choices	choice	NOUN
ma-170	199	8	for	for	ADP
ma-170	199	9	l	l	NOUN
ma-170	199	10	are	be	AUX
ma-170	199	11	l	l	NOUN
ma-170	199	12	=	=	PUNCT
ma-170	199	13	f	f	PROPN
ma-170	199	14	′(x∗	′(x∗	NOUN
ma-170	199	15	)	)	PUNCT
ma-170	199	16	(	(	PUNCT
ma-170	199	17	the	the	DET
ma-170	199	18	differentiable	differentiable	ADJ
ma-170	199	19	case	case	NOUN
ma-170	199	20	)	)	PUNCT
ma-170	199	21	or	or	CCONJ
ma-170	199	22	l	l	NOUN
ma-170	199	23	=	=	PUNCT
ma-170	200	1	[	[	X
ma-170	200	2	.	.	X
ma-170	200	3	,	,	PUNCT
ma-170	200	4	.;f	.;f	PUNCT
ma-170	200	5	]	]	PUNCT
ma-170	200	6	(	(	PUNCT
ma-170	200	7	the	the	DET
ma-170	200	8	non	non	ADJ
ma-170	200	9	-	-	ADJ
ma-170	200	10	differentiable	differentiable	ADJ
ma-170	200	11	case	case	NOUN
ma-170	200	12	)	)	PUNCT
ma-170	200	13	.	.	PUNCT
ma-170	201	1	in	in	ADP
ma-170	201	2	practice	practice	NOUN
ma-170	201	3	l	l	NOUN
ma-170	201	4	should	should	AUX
ma-170	201	5	be	be	AUX
ma-170	201	6	chosen	choose	VERB
ma-170	201	7	to	to	PART
ma-170	201	8	optimize	optimize	VERB
ma-170	201	9	the	the	DET
ma-170	201	10	results.next	results.next	NOUN
ma-170	201	11	,	,	PUNCT
ma-170	201	12	the	the	DET
ma-170	201	13	point	point	NOUN
ma-170	201	14	x∗	x∗	PROPN
ma-170	201	15	is	be	AUX
ma-170	201	16	shown	show	VERB
ma-170	201	17	to	to	PART
ma-170	201	18	be	be	AUX
ma-170	201	19	the	the	DET
ma-170	201	20	only	only	ADJ
ma-170	201	21	solution	solution	NOUN
ma-170	201	22	of	of	ADP
ma-170	201	23	the	the	DET
ma-170	201	24	equation	equation	NOUN
ma-170	202	1	f	f	X
ma-170	202	2	(	(	PUNCT
ma-170	202	3	x	x	X
ma-170	202	4	)	)	PUNCT
ma-170	202	5	=	=	SYM
ma-170	202	6	0	0	NUM
ma-170	203	1	in	in	ADP
ma-170	203	2	a	a	DET
ma-170	203	3	certain	certain	ADJ
ma-170	203	4	set	set	NOUN
ma-170	203	5	.	.	PUNCT
ma-170	204	1	preposition	preposition	NOUN
ma-170	204	2	2.3	2.3	NUM
ma-170	204	3	assume	assume	VERB
ma-170	204	4	:	:	PUNCT
ma-170	204	5	there	there	PRON
ma-170	204	6	exists	exist	VERB
ma-170	204	7	a	a	DET
ma-170	204	8	solution	solution	NOUN
ma-170	204	9	x∗1	x∗1	VERB
ma-170	204	10	∈	∈	PROPN
ma-170	204	11	b(x∗	b(x∗	NOUN
ma-170	204	12	,	,	PUNCT
ma-170	204	13	δ4	δ4	NOUN
ma-170	204	14	)	)	PUNCT
ma-170	204	15	of	of	ADP
ma-170	204	16	the	the	DET
ma-170	204	17	equation	equation	NOUN
ma-170	204	18	f	f	X
ma-170	204	19	(	(	PUNCT
ma-170	204	20	x	x	X
ma-170	204	21	)	)	PUNCT
ma-170	204	22	=	=	SYM
ma-170	204	23	0	0	NUM
ma-170	204	24	for	for	ADP
ma-170	204	25	some	some	DET
ma-170	204	26	δ4	δ4	NOUN
ma-170	204	27	>	>	X
ma-170	204	28	0	0	NUM
ma-170	204	29	;	;	PUNCT
ma-170	204	30	the	the	DET
ma-170	204	31	first	first	ADJ
ma-170	204	32	assumption	assumption	NOUN
ma-170	204	33	in	in	ADP
ma-170	204	34	(	(	PUNCT
ma-170	204	35	h3	h3	NOUN
ma-170	204	36	)	)	PUNCT
ma-170	204	37	is	be	AUX
ma-170	204	38	validated	validate	VERB
ma-170	204	39	on	on	ADP
ma-170	204	40	the	the	DET
ma-170	204	41	ball	ball	NOUN
ma-170	204	42	b(x∗	b(x∗	NOUN
ma-170	204	43	,	,	PUNCT
ma-170	204	44	δ4	δ4	PROPN
ma-170	204	45	)	)	PUNCT
ma-170	204	46	and	and	CCONJ
ma-170	204	47	there	there	PRON
ma-170	204	48	exists	exist	VERB
ma-170	204	49	δ5	δ5	NOUN
ma-170	204	50	≥	≥	NOUN
ma-170	204	51	δ4	δ4	NOUN
ma-170	204	52	so	so	SCONJ
ma-170	204	53	that	that	DET
ma-170	204	54	w(δ5	w(δ5	NOUN
ma-170	204	55	)	)	PUNCT
ma-170	204	56	<	<	X
ma-170	205	1	1	1	X
ma-170	205	2	.	.	PUNCT
ma-170	205	3	let	let	VERB
ma-170	205	4	b1	b1	NOUN
ma-170	205	5	=	=	SYM
ma-170	205	6	ω	ω	PROPN
ma-170	205	7	∩	∩	ADJ
ma-170	205	8	b[x∗	b[x∗	PROPN
ma-170	205	9	,	,	PUNCT
ma-170	205	10	δ5	δ5	NOUN
ma-170	205	11	]	]	PUNCT
ma-170	205	12	.	.	PUNCT
ma-170	206	1	then	then	ADV
ma-170	206	2	,	,	PUNCT
ma-170	206	3	the	the	DET
ma-170	206	4	only	only	ADJ
ma-170	206	5	solution	solution	NOUN
ma-170	206	6	of	of	ADP
ma-170	206	7	the	the	DET
ma-170	206	8	equation	equation	NOUN
ma-170	206	9	f	f	X
ma-170	206	10	(	(	PUNCT
ma-170	206	11	x	x	X
ma-170	206	12	)	)	PUNCT
ma-170	207	1	=	=	SYM
ma-170	207	2	0	0	NUM
ma-170	207	3	in	in	ADP
ma-170	207	4	the	the	DET
ma-170	207	5	set	set	NOUN
ma-170	207	6	b1	b1	NOUN
ma-170	207	7	is	be	AUX
ma-170	207	8	x∗.	x∗.	ADJ
ma-170	207	9	proof	proof	NOUN
ma-170	207	10	.	.	PUNCT
ma-170	208	1	let	let	VERB
ma-170	208	2	q	q	NOUN
ma-170	209	1	=	=	PUNCT
ma-170	210	1	[	[	X
ma-170	210	2	x∗	x∗	NOUN
ma-170	210	3	,	,	PUNCT
ma-170	210	4	x∗1	x∗1	VERB
ma-170	210	5	]	]	PUNCT
ma-170	210	6	.	.	PUNCT
ma-170	211	1	by	by	ADP
ma-170	211	2	the	the	DET
ma-170	211	3	assumption	assumption	NOUN
ma-170	211	4	it	it	PRON
ma-170	211	5	follows	follow	VERB
ma-170	211	6	‖l−1(q−	‖l−1(q−	PROPN
ma-170	211	7	l)‖	l)‖	NOUN
ma-170	211	8	≤	≤	NUM
ma-170	211	9	w(‖x∗1	w(‖x∗1	X
ma-170	211	10	−	−	PROPN
ma-170	211	11	x∗‖	x∗‖	NUM
ma-170	211	12	)	)	PUNCT
ma-170	211	13	≤	≤	NOUN
ma-170	211	14	w(δ5	w(δ5	NOUN
ma-170	211	15	)	)	PUNCT
ma-170	211	16	<	<	X
ma-170	212	1	1	1	NUM
ma-170	212	2	,	,	PUNCT
ma-170	212	3	thus	thus	ADV
ma-170	212	4	q−1	q−1	PROPN
ma-170	212	5	∈	∈	PROPN
ma-170	212	6	l(z	l(z	PROPN
ma-170	212	7	)	)	PUNCT
ma-170	212	8	and	and	CCONJ
ma-170	212	9	consequently	consequently	ADV
ma-170	212	10	from	from	ADP
ma-170	212	11	the	the	DET
ma-170	212	12	approximation	approximation	NOUN
ma-170	212	13	x∗1	x∗1	VERB
ma-170	212	14	−	−	PUNCT
ma-170	213	1	x∗	x∗	PROPN
ma-170	214	1	=	=	SYM
ma-170	214	2	q−1(f	q−1(f	PROPN
ma-170	214	3	(	(	PUNCT
ma-170	214	4	x∗1	x∗1	ADJ
ma-170	214	5	)	)	PUNCT
ma-170	215	1	−	−	PROPN
ma-170	215	2	f	f	PROPN
ma-170	215	3	(	(	PUNCT
ma-170	215	4	x∗	x∗	PROPN
ma-170	215	5	)	)	PUNCT
ma-170	215	6	)	)	PUNCT
ma-170	216	1	=	=	SYM
ma-170	216	2	q−1(0	q−1(0	PROPN
ma-170	216	3	)	)	PUNCT
ma-170	216	4	=	=	SYM
ma-170	217	1	0	0	NUM
ma-170	217	2	,	,	PUNCT
ma-170	217	3	it	it	PRON
ma-170	217	4	is	be	AUX
ma-170	217	5	concluded	conclude	VERB
ma-170	217	6	that	that	SCONJ
ma-170	217	7	x∗1	x∗1	VERB
ma-170	217	8	=	=	SYM
ma-170	217	9	x∗.	x∗.	PROPN
ma-170	217	10	�	�	PROPN
ma-170	217	11	clearly	clearly	ADV
ma-170	217	12	,	,	PUNCT
ma-170	217	13	we	we	PRON
ma-170	217	14	can	can	AUX
ma-170	217	15	choose	choose	VERB
ma-170	217	16	δ4	δ4	NOUN
ma-170	217	17	=	=	SYM
ma-170	217	18	δ∗.	δ∗.	PART
ma-170	217	19	3	3	NUM
ma-170	217	20	.	.	PUNCT
ma-170	217	21	semi	semi	ADJ
ma-170	217	22	-	-	ADJ
ma-170	217	23	local	local	ADJ
ma-170	217	24	analysis	analysis	NOUN
ma-170	217	25	the	the	DET
ma-170	217	26	role	role	NOUN
ma-170	217	27	of	of	ADP
ma-170	217	28	x∗	x∗	PROPN
ma-170	217	29	is	be	AUX
ma-170	217	30	exchanged	exchange	VERB
ma-170	217	31	by	by	ADP
ma-170	217	32	x0	x0	PROPN
ma-170	217	33	.	.	PUNCT
ma-170	218	1	but	but	CCONJ
ma-170	218	2	there	there	PRON
ma-170	218	3	are	be	VERB
ma-170	218	4	some	some	PRON
ma-170	218	5	more	more	ADV
ma-170	218	6	differences.assume	differences.assume	ADJ
ma-170	218	7	:	:	PUNCT
ma-170	218	8	(	(	PUNCT
ma-170	218	9	c1	c1	NOUN
ma-170	218	10	)	)	PUNCT
ma-170	218	11	there	there	PRON
ma-170	218	12	exist	exist	VERB
ma-170	218	13	(	(	PUNCT
ma-170	218	14	cn	cn	ADJ
ma-170	218	15	)	)	PUNCT
ma-170	218	16	functions	function	NOUN
ma-170	218	17	g1	g1	NOUN
ma-170	218	18	:	:	PUNCT
ma-170	218	19	t0	t0	PROPN
ma-170	218	20	→	→	SYM
ma-170	218	21	t	t	PROPN
ma-170	218	22	,	,	PUNCT
ma-170	218	23	g2	g2	PROPN
ma-170	218	24	:	:	PUNCT
ma-170	218	25	t0	t0	PROPN
ma-170	218	26	→	→	SYM
ma-170	218	27	t	t	PROPN
ma-170	218	28	and	and	CCONJ
ma-170	218	29	w0	w0	PROPN
ma-170	218	30	:	:	PUNCT
ma-170	219	1	t0	t0	PROPN
ma-170	219	2	×	×	PROPN
ma-170	219	3	t0	t0	PROPN
ma-170	219	4	→	→	SYM
ma-170	219	5	t	t	PROPN
ma-170	219	6	so	so	SCONJ
ma-170	219	7	that	that	SCONJ
ma-170	219	8	theequation	theequation	NOUN
ma-170	219	9	w0(g1(t	w0(g1(t	ADV
ma-170	219	10	)	)	PUNCT
ma-170	219	11	,	,	PUNCT
ma-170	219	12	g2(t))−	g2(t))−	NOUN
ma-170	219	13	1	1	NUM
ma-170	219	14	=	=	SYM
ma-170	219	15	0	0	PROPN
ma-170	219	16	has	have	VERB
ma-170	219	17	a	a	DET
ma-170	219	18	(	(	PUNCT
ma-170	219	19	ss	ss	NOUN
ma-170	219	20	)	)	PUNCT
ma-170	219	21	denoted	denote	VERB
ma-170	219	22	by	by	ADP
ma-170	219	23	r0	r0	PROPN
ma-170	219	24	∈	∈	PROPN
ma-170	219	25	t0	t0	PROPN
ma-170	219	26	−	−	PROPN
ma-170	219	27	{	{	PUNCT
ma-170	219	28	0	0	NUM
ma-170	219	29	}	}	PUNCT
ma-170	219	30	.	.	PUNCT
ma-170	220	1	set	set	VERB
ma-170	220	2	t3	t3	NOUN
ma-170	220	3	=	=	PUNCT
ma-170	221	1	[	[	X
ma-170	221	2	0	0	NUM
ma-170	221	3	,	,	PUNCT
ma-170	221	4	r0).define	r0).define	VERB
ma-170	221	5	the	the	DET
ma-170	221	6	scaler	scaler	NOUN
ma-170	221	7	sequence	sequence	NOUN
ma-170	221	8	{	{	PUNCT
ma-170	221	9	an	an	NOUN
ma-170	221	10	}	}	PUNCT
ma-170	221	11	for	for	ADP
ma-170	221	12	a0	a0	NOUN
ma-170	221	13	=	=	SYM
ma-170	221	14	0	0	NUM
ma-170	221	15	,	,	PUNCT
ma-170	221	16	b0	b0	VERB
ma-170	221	17	∈	∈	PROPN
ma-170	222	1	[	[	X
ma-170	222	2	0	0	NUM
ma-170	222	3	,	,	PUNCT
ma-170	222	4	r0	r0	NOUN
ma-170	222	5	)	)	PUNCT
ma-170	222	6	and	and	CCONJ
ma-170	222	7	some	some	DET
ma-170	222	8	(	(	PUNCT
ma-170	222	9	cn	cn	NOUN
ma-170	222	10	)	)	PUNCT
ma-170	222	11	functions	function	NOUN
ma-170	222	12	g1	g1	NOUN
ma-170	222	13	:	:	PUNCT
ma-170	222	14	t3	t3	PROPN
ma-170	222	15	→	→	SYM
ma-170	222	16	t	t	PROPN
ma-170	222	17	,	,	PUNCT
ma-170	222	18	g2	g2	PROPN
ma-170	222	19	:	:	PUNCT
ma-170	222	20	t3	t3	PROPN
ma-170	222	21	→	→	SYM
ma-170	222	22	t	t	PROPN
ma-170	222	23	,	,	PUNCT
ma-170	222	24	w2	w2	NOUN
ma-170	222	25	:	:	PUNCT
ma-170	222	26	t3	t3	PROPN
ma-170	222	27	×	×	PROPN
ma-170	222	28	t3	t3	PROPN
ma-170	222	29	×	×	PROPN
ma-170	222	30	t3	t3	PROPN
ma-170	222	31	×	×	PROPN
ma-170	222	32	t3	t3	PROPN
ma-170	222	33	→	→	PROPN
ma-170	222	34	t	t	PROPN
ma-170	222	35	by	by	ADP
ma-170	222	36	cn	cn	PROPN
ma-170	222	37	=	=	PROPN
ma-170	222	38	bn	bn	PROPN
ma-170	223	1	+	+	X
ma-170	224	1	[	[	X
ma-170	224	2	w2(an	w2(an	PROPN
ma-170	224	3	,	,	PUNCT
ma-170	224	4	bn	bn	NOUN
ma-170	224	5	,	,	PUNCT
ma-170	224	6	f1(an	f1(an	PROPN
ma-170	224	7	)	)	PUNCT
ma-170	224	8	,	,	PUNCT
ma-170	224	9	f2(an	f2(an	PROPN
ma-170	224	10	)	)	PUNCT
ma-170	224	11	)	)	PUNCT
ma-170	224	12	1−	1−	NUM
ma-170	224	13	w0(g1(an	w0(g1(an	NOUN
ma-170	224	14	)	)	PUNCT
ma-170	224	15	,	,	PUNCT
ma-170	224	16	g2(an	g2(an	PROPN
ma-170	224	17	)	)	PUNCT
ma-170	224	18	)	)	PUNCT
ma-170	225	1	+	+	CCONJ
ma-170	226	1	2w2(an	2w2(an	NUM
ma-170	226	2	,	,	PUNCT
ma-170	226	3	bn	bn	NOUN
ma-170	226	4	,	,	PUNCT
ma-170	226	5	f1(an	f1(an	PROPN
ma-170	226	6	)	)	PUNCT
ma-170	226	7	,	,	PUNCT
ma-170	226	8	f2(an	f2(an	PROPN
ma-170	226	9	)	)	PUNCT
ma-170	226	10	)	)	PUNCT
ma-170	227	1	(	(	PUNCT
ma-170	227	2	1−	1−	NUM
ma-170	227	3	w0(g1(an	w0(g1(an	X
ma-170	227	4	)	)	PUNCT
ma-170	228	1	,	,	PUNCT
ma-170	228	2	g2(an)))2	g2(an)))2	X
ma-170	228	3	]	]	PUNCT
ma-170	228	4	(	(	PUNCT
ma-170	228	5	βn	βn	ADP
ma-170	228	6	−	−	PROPN
ma-170	228	7	an	an	NOUN
ma-170	228	8	)	)	PUNCT
ma-170	228	9	,	,	PUNCT
ma-170	228	10	(	(	PUNCT
ma-170	228	11	3.23	3.23	NUM
ma-170	228	12	)	)	PUNCT
ma-170	228	13	βn	βn	NOUN
ma-170	229	1	=	=	NOUN
ma-170	229	2	1	1	NUM
ma-170	229	3	4	4	NUM
ma-170	229	4	[	[	PUNCT
ma-170	229	5	5	5	NUM
ma-170	229	6	(	(	PUNCT
ma-170	229	7	w2(an	w2(an	PROPN
ma-170	229	8	,	,	PUNCT
ma-170	229	9	bn	bn	NOUN
ma-170	229	10	,	,	PUNCT
ma-170	229	11	f1(an	f1(an	PROPN
ma-170	229	12	)	)	PUNCT
ma-170	229	13	,	,	PUNCT
ma-170	229	14	f2(an	f2(an	PROPN
ma-170	229	15	)	)	PUNCT
ma-170	229	16	)	)	PUNCT
ma-170	229	17	1−	1−	NUM
ma-170	229	18	w0(g1(an	w0(g1(an	NOUN
ma-170	229	19	)	)	PUNCT
ma-170	229	20	,	,	PUNCT
ma-170	229	21	g2(an	g2(an	PROPN
ma-170	229	22	)	)	PUNCT
ma-170	229	23	)	)	PUNCT
ma-170	229	24	)	)	PUNCT
ma-170	230	1	2	2	NUM
ma-170	230	2	+	+	NUM
ma-170	230	3	4	4	NUM
ma-170	230	4	(	(	PUNCT
ma-170	230	5	w2(an	w2(an	PROPN
ma-170	230	6	,	,	PUNCT
ma-170	230	7	bn	bn	NOUN
ma-170	230	8	,	,	PUNCT
ma-170	230	9	f1(an	f1(an	PROPN
ma-170	230	10	)	)	PUNCT
ma-170	230	11	,	,	PUNCT
ma-170	230	12	f2(an	f2(an	PROPN
ma-170	230	13	)	)	PUNCT
ma-170	230	14	)	)	PUNCT
ma-170	230	15	1−	1−	NUM
ma-170	230	16	w0(g1(an	w0(g1(an	NOUN
ma-170	230	17	)	)	PUNCT
ma-170	230	18	,	,	PUNCT
ma-170	230	19	g2(an	g2(an	PROPN
ma-170	230	20	)	)	PUNCT
ma-170	230	21	)	)	PUNCT
ma-170	230	22	)	)	PUNCT
ma-170	231	1	2	2	X
ma-170	231	2	]	]	PUNCT
ma-170	231	3	,	,	PUNCT
ma-170	231	4	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	PUNCT
ma-170	231	5	eur	eur	ADJ
ma-170	231	6	.	.	PUNCT
ma-170	232	1	j.	j.	PROPN
ma-170	232	2	math	math	PROPN
ma-170	232	3	.	.	PUNCT
ma-170	233	1	anal	anal	PROPN
ma-170	233	2	.	.	PUNCT
ma-170	234	1	10.28924	10.28924	NUM
ma-170	234	2	/	/	SYM
ma-170	234	3	ada	ada	PROPN
ma-170	234	4	/	/	SYM
ma-170	234	5	ma.3.24	ma.3.24	ADJ
ma-170	234	6	8	8	NUM
ma-170	234	7	γn	γn	NOUN
ma-170	234	8	=	=	SYM
ma-170	234	9	w2(an	w2(an	PROPN
ma-170	234	10	,	,	PUNCT
ma-170	234	11	bn	bn	NOUN
ma-170	234	12	,	,	PUNCT
ma-170	234	13	g1(an	g1(an	PROPN
ma-170	234	14	)	)	PUNCT
ma-170	234	15	,	,	PUNCT
ma-170	234	16	g2(an))(bn	g2(an))(bn	PROPN
ma-170	234	17	−	−	PROPN
ma-170	234	18	an	an	PROPN
ma-170	234	19	)	)	PUNCT
ma-170	234	20	,	,	PUNCT
ma-170	234	21	an+1	an+1	X
ma-170	234	22	=	=	SYM
ma-170	234	23	cn	cn	PROPN
ma-170	235	1	+	+	CCONJ
ma-170	235	2	(	(	PUNCT
ma-170	235	3	1	1	NUM
ma-170	235	4	+	+	CCONJ
ma-170	235	5	w0(bn	w0(bn	PROPN
ma-170	235	6	,	,	PUNCT
ma-170	235	7	cn))(cn	cn))(cn	NOUN
ma-170	235	8	−	−	NOUN
ma-170	235	9	bn)βn	bn)βn	SYM
ma-170	235	10	+	+	NUM
ma-170	235	11	γn	γn	ADP
ma-170	235	12	1−	1−	NUM
ma-170	235	13	w0(g1(an	w0(g1(an	NOUN
ma-170	235	14	)	)	PUNCT
ma-170	235	15	,	,	PUNCT
ma-170	235	16	g2(an	g2(an	PROPN
ma-170	235	17	)	)	PUNCT
ma-170	235	18	)	)	PUNCT
ma-170	235	19	,	,	PUNCT
ma-170	235	20	δn+1	δn+1	PROPN
ma-170	235	21	=	=	SYM
ma-170	235	22	(	(	PUNCT
ma-170	235	23	1	1	NUM
ma-170	235	24	+	+	NUM
ma-170	235	25	v0(an	v0(an	PROPN
ma-170	235	26	,	,	PUNCT
ma-170	235	27	bn))(an+1	bn))(an+1	PROPN
ma-170	235	28	−	−	PROPN
ma-170	235	29	an	an	X
ma-170	235	30	)	)	PUNCT
ma-170	235	31	+	+	CCONJ
ma-170	235	32	(	(	PUNCT
ma-170	235	33	1	1	NUM
ma-170	235	34	+	+	CCONJ
ma-170	235	35	w0(g1(an	w0(g1(an	X
ma-170	235	36	)	)	PUNCT
ma-170	235	37	,	,	PUNCT
ma-170	235	38	g2(an)))(bn	g2(an)))(bn	PROPN
ma-170	235	39	−	−	PROPN
ma-170	235	40	an	an	PROPN
ma-170	235	41	)	)	PUNCT
ma-170	235	42	and	and	CCONJ
ma-170	235	43	bn+1	bn+1	NUM
ma-170	235	44	=	=	SYM
ma-170	235	45	an+1	an+1	X
ma-170	235	46	+	+	CCONJ
ma-170	235	47	δn+1	δn+1	PROPN
ma-170	235	48	1−	1−	NUM
ma-170	235	49	w0(g1(an+1	w0(g1(an+1	NOUN
ma-170	235	50	)	)	PUNCT
ma-170	235	51	,	,	PUNCT
ma-170	235	52	g2(an+1	g2(an+1	NOUN
ma-170	235	53	)	)	PUNCT
ma-170	235	54	)	)	PUNCT
ma-170	235	55	.	.	PUNCT
ma-170	236	1	next	next	ADV
ma-170	236	2	,	,	PUNCT
ma-170	236	3	general	general	ADJ
ma-170	236	4	convergence	convergence	NOUN
ma-170	236	5	conditions	condition	NOUN
ma-170	236	6	are	be	AUX
ma-170	236	7	developed	develop	VERB
ma-170	236	8	.	.	PUNCT
ma-170	237	1	lemma	lemma	PROPN
ma-170	237	2	3.1	3.1	NUM
ma-170	237	3	assume	assume	VERB
ma-170	237	4	there	there	PRON
ma-170	237	5	exists	exist	VERB
ma-170	237	6	µ1	µ1	PROPN
ma-170	237	7	∈	∈	PROPN
ma-170	238	1	[	[	X
ma-170	238	2	0	0	NUM
ma-170	238	3	,	,	PUNCT
ma-170	238	4	r0	r0	NOUN
ma-170	238	5	)	)	PUNCT
ma-170	238	6	such	such	ADJ
ma-170	238	7	that	that	PRON
ma-170	238	8	for	for	ADP
ma-170	238	9	each	each	DET
ma-170	238	10	n	n	NOUN
ma-170	238	11	=	=	SYM
ma-170	238	12	0	0	NUM
ma-170	238	13	,	,	PUNCT
ma-170	238	14	1	1	NUM
ma-170	238	15	,	,	PUNCT
ma-170	238	16	2	2	NUM
ma-170	238	17	,	,	PUNCT
ma-170	238	18	.	.	PUNCT
ma-170	238	19	.	.	PUNCT
ma-170	239	1	.	.	PUNCT
ma-170	240	1	,	,	PUNCT
ma-170	240	2	(	(	PUNCT
ma-170	240	3	c2	c2	PROPN
ma-170	240	4	)	)	PUNCT
ma-170	240	5	w0(g1(an	w0(g1(an	PROPN
ma-170	240	6	)	)	PUNCT
ma-170	240	7	,	,	PUNCT
ma-170	240	8	g2(an	g2(an	PROPN
ma-170	240	9	)	)	PUNCT
ma-170	240	10	)	)	PUNCT
ma-170	241	1	<	<	X
ma-170	241	2	1	1	NUM
ma-170	241	3	and	and	CCONJ
ma-170	241	4	an	an	DET
ma-170	241	5	≤	≤	NUM
ma-170	241	6	µ1	µ1	PROPN
ma-170	241	7	.	.	PUNCT
ma-170	242	1	then	then	ADV
ma-170	242	2	,	,	PUNCT
ma-170	242	3	the	the	DET
ma-170	242	4	following	follow	VERB
ma-170	242	5	items	item	NOUN
ma-170	242	6	hold	hold	VERB
ma-170	242	7	0	0	NUM
ma-170	242	8	≤	≤	NUM
ma-170	242	9	an	an	DET
ma-170	242	10	≤	≤	NUM
ma-170	242	11	bn	bn	NOUN
ma-170	242	12	≤	≤	NUM
ma-170	242	13	cn	cn	PROPN
ma-170	242	14	≤	≤	PROPN
ma-170	242	15	an+1	an+1	VERB
ma-170	242	16	≤	≤	PROPN
ma-170	242	17	µ1	µ1	PROPN
ma-170	242	18	and	and	CCONJ
ma-170	242	19	there	there	PRON
ma-170	242	20	exists	exist	VERB
ma-170	242	21	a∗	a∗	PROPN
ma-170	242	22	∈	∈	PROPN
ma-170	242	23	(	(	PUNCT
ma-170	242	24	0	0	NUM
ma-170	242	25	,	,	PUNCT
ma-170	242	26	µ1	µ1	PROPN
ma-170	242	27	]	]	PUNCT
ma-170	242	28	such	such	ADJ
ma-170	242	29	that	that	SCONJ
ma-170	242	30	limn→∞	limn→∞	PROPN
ma-170	242	31	an	an	DET
ma-170	242	32	=	=	NOUN
ma-170	242	33	a∗.	a∗.	NOUN
ma-170	242	34	proof	proof	NOUN
ma-170	242	35	.	.	PUNCT
ma-170	243	1	the	the	DET
ma-170	243	2	conclusions	conclusion	NOUN
ma-170	243	3	follow	follow	VERB
ma-170	243	4	immediately	immediately	ADV
ma-170	243	5	by	by	ADP
ma-170	243	6	the	the	DET
ma-170	243	7	formula	formula	NOUN
ma-170	243	8	(	(	PUNCT
ma-170	243	9	3.23	3.23	NUM
ma-170	243	10	)	)	PUNCT
ma-170	243	11	and	and	CCONJ
ma-170	243	12	the	the	DET
ma-170	243	13	condition	condition	NOUN
ma-170	243	14	(	(	PUNCT
ma-170	243	15	c2	c2	PROPN
ma-170	243	16	)	)	PUNCT
ma-170	243	17	.	.	PUNCT
ma-170	244	1	�	�	PROPN
ma-170	244	2	notice	notice	VERB
ma-170	244	3	that	that	SCONJ
ma-170	244	4	the	the	DET
ma-170	244	5	limit	limit	NOUN
ma-170	244	6	a∗	a∗	NOUN
ma-170	244	7	is	be	AUX
ma-170	244	8	unique	unique	ADJ
ma-170	244	9	,	,	PUNCT
ma-170	244	10	since	since	SCONJ
ma-170	244	11	it	it	PRON
ma-170	244	12	is	be	AUX
ma-170	244	13	the	the	DET
ma-170	244	14	unique	unique	ADJ
ma-170	244	15	least	least	ADV
ma-170	244	16	upper	upper	ADJ
ma-170	244	17	bound	bind	VERB
ma-170	244	18	of	of	ADP
ma-170	244	19	the	the	DET
ma-170	244	20	sequence	sequence	NOUN
ma-170	244	21	{	{	PUNCT
ma-170	244	22	an	an	X
ma-170	244	23	}	}	PUNCT
ma-170	244	24	.	.	PUNCT
ma-170	245	1	(	(	PUNCT
ma-170	245	2	c3	c3	NOUN
ma-170	245	3	)	)	PUNCT
ma-170	245	4	there	there	PRON
ma-170	245	5	exist	exist	VERB
ma-170	245	6	an	an	DET
ma-170	245	7	invertible	invertible	ADJ
ma-170	245	8	operator	operator	NOUN
ma-170	245	9	l	l	NOUN
ma-170	245	10	and	and	CCONJ
ma-170	245	11	a	a	DET
ma-170	245	12	point	point	NOUN
ma-170	245	13	x0	x0	PROPN
ma-170	245	14	∈	∈	PROPN
ma-170	245	15	ω	ω	NUM
ma-170	245	16	such	such	ADJ
ma-170	245	17	that	that	PRON
ma-170	245	18	for	for	ADP
ma-170	245	19	each	each	DET
ma-170	245	20	x	x	NOUN
ma-170	245	21	,	,	PUNCT
ma-170	245	22	y	y	PROPN
ma-170	245	23	∈	∈	PROPN
ma-170	245	24	ω	ω	PROPN
ma-170	245	25	,	,	PUNCT
ma-170	245	26	u	u	NOUN
ma-170	245	27	=	=	PUNCT
ma-170	245	28	x	x	PROPN
ma-170	246	1	+	+	NUM
ma-170	246	2	f	f	X
ma-170	246	3	(	(	PUNCT
ma-170	246	4	x	x	NOUN
ma-170	246	5	)	)	PUNCT
ma-170	246	6	,	,	PUNCT
ma-170	246	7	v	v	X
ma-170	246	8	=	=	SYM
ma-170	246	9	x	x	SYM
ma-170	246	10	−	−	PROPN
ma-170	246	11	f	f	X
ma-170	246	12	(	(	PUNCT
ma-170	246	13	x	x	NOUN
ma-170	246	14	)	)	PUNCT
ma-170	246	15	‖l−1([u	‖l−1([u	NOUN
ma-170	246	16	,	,	PUNCT
ma-170	246	17	v	v	NOUN
ma-170	246	18	;	;	PUNCT
ma-170	246	19	f	f	X
ma-170	247	1	]	]	PUNCT
ma-170	247	2	−	−	PROPN
ma-170	247	3	l)‖	l)‖	VERB
ma-170	247	4	≤	≤	NUM
ma-170	247	5	w0(‖u	w0(‖u	PROPN
ma-170	247	6	−	−	PROPN
ma-170	247	7	x0‖	x0‖	PROPN
ma-170	247	8	,	,	PUNCT
ma-170	247	9	‖v	‖v	NOUN
ma-170	247	10	−	−	PROPN
ma-170	247	11	x0‖	x0‖	PROPN
ma-170	247	12	)	)	PUNCT
ma-170	247	13	,	,	PUNCT
ma-170	247	14	‖u	‖u	PROPN
ma-170	247	15	−	−	PROPN
ma-170	247	16	x0‖	x0‖	PROPN
ma-170	247	17	≤	≤	PROPN
ma-170	248	1	g1(‖x	g1(‖x	NOUN
ma-170	248	2	−	−	PROPN
ma-170	248	3	x0‖	x0‖	PROPN
ma-170	248	4	)	)	PUNCT
ma-170	248	5	,	,	PUNCT
ma-170	248	6	‖v	‖v	NOUN
ma-170	248	7	−	−	PROPN
ma-170	248	8	x0‖	x0‖	PROPN
ma-170	248	9	≤	≤	PROPN
ma-170	248	10	g2(‖x	g2(‖x	PROPN
ma-170	248	11	−	−	PROPN
ma-170	248	12	x0‖	x0‖	PROPN
ma-170	248	13	)	)	PUNCT
ma-170	248	14	and	and	CCONJ
ma-170	248	15	w0(g1(‖f	w0(g1(‖f	PRON
ma-170	248	16	(	(	PUNCT
ma-170	248	17	x0)‖	x0)‖	PROPN
ma-170	248	18	)	)	PUNCT
ma-170	248	19	,	,	PUNCT
ma-170	248	20	g2(‖f	g2(‖f	X
ma-170	248	21	(	(	PUNCT
ma-170	248	22	x0)‖	x0)‖	PROPN
ma-170	248	23	)	)	PUNCT
ma-170	248	24	)	)	PUNCT
ma-170	249	1	<	<	X
ma-170	249	2	1.the	1.the	DET
ma-170	249	3	existence	existence	NOUN
ma-170	249	4	of	of	ADP
ma-170	249	5	[	[	X
ma-170	249	6	u0	u0	ADJ
ma-170	249	7	,	,	PUNCT
ma-170	249	8	v0;f	v0;f	ADJ
ma-170	249	9	]	]	SYM
ma-170	249	10	−1	−1	NOUN
ma-170	249	11	is	be	AUX
ma-170	249	12	guaranteed	guarantee	VERB
ma-170	249	13	,	,	PUNCT
ma-170	249	14	by	by	ADP
ma-170	249	15	the	the	DET
ma-170	249	16	banach	banach	NOUN
ma-170	249	17	lemma	lemma	PROPN
ma-170	249	18	and	and	CCONJ
ma-170	249	19	since	since	SCONJ
ma-170	249	20	l−1‖[u0	l−1‖[u0	NOUN
ma-170	249	21	,	,	PUNCT
ma-170	249	22	v0;f	v0;f	ADJ
ma-170	249	23	]	]	SYM
ma-170	249	24	−	−	PROPN
ma-170	249	25	l‖	l‖	PROPN
ma-170	249	26	≤	≤	NUM
ma-170	250	1	w0(‖u0	w0(‖u0	PRON
ma-170	250	2	−	−	PROPN
ma-170	250	3	x0‖	x0‖	PROPN
ma-170	250	4	,	,	PUNCT
ma-170	250	5	‖v0	‖v0	PRON
ma-170	250	6	−	−	PROPN
ma-170	250	7	x0‖	x0‖	PROPN
ma-170	250	8	)	)	PUNCT
ma-170	250	9	<	<	X
ma-170	250	10	1	1	X
ma-170	250	11	.	.	PUNCT
ma-170	250	12	(	(	PUNCT
ma-170	250	13	c4	c4	NOUN
ma-170	250	14	)	)	PUNCT
ma-170	250	15	‖[u0	‖[u0	NOUN
ma-170	250	16	,	,	PUNCT
ma-170	250	17	v0;f	v0;f	PROPN
ma-170	250	18	]	]	SYM
ma-170	250	19	−1f	−1f	PROPN
ma-170	250	20	(	(	PUNCT
ma-170	250	21	x0)‖	x0)‖	PROPN
ma-170	250	22	≤	≤	NUM
ma-170	250	23	b0	b0	NOUN
ma-170	250	24	.	.	PUNCT
ma-170	251	1	let	let	VERB
ma-170	251	2	b2	b2	NOUN
ma-170	251	3	=	=	PUNCT
ma-170	251	4	b(x0	b(x0	NOUN
ma-170	251	5	,	,	PUNCT
ma-170	251	6	µ0	µ0	PROPN
ma-170	251	7	)	)	PUNCT
ma-170	251	8	.	.	PUNCT
ma-170	252	1	(	(	PUNCT
ma-170	252	2	c5	c5	PROPN
ma-170	252	3	)	)	PUNCT
ma-170	252	4	‖l−1([x	‖l−1([x	VERB
ma-170	252	5	,	,	PUNCT
ma-170	252	6	y	y	PROPN
ma-170	252	7	;	;	PUNCT
ma-170	252	8	f	f	X
ma-170	253	1	]	]	X
ma-170	253	2	−	−	X
ma-170	254	1	[	[	X
ma-170	254	2	u	u	NOUN
ma-170	254	3	,	,	PUNCT
ma-170	254	4	v	v	NOUN
ma-170	254	5	;	;	PUNCT
ma-170	254	6	f	f	PROPN
ma-170	254	7	]	]	X
ma-170	254	8	)	)	PUNCT
ma-170	254	9	‖	‖	PROPN
ma-170	254	10	≤	≤	PROPN
ma-170	254	11	w2(‖x−x0‖	w2(‖x−x0‖	PROPN
ma-170	254	12	,	,	PUNCT
ma-170	254	13	‖y−x0‖	‖y−x0‖	PROPN
ma-170	254	14	,	,	PUNCT
ma-170	254	15	‖u−x0‖	‖u−x0‖	PROPN
ma-170	254	16	,	,	PUNCT
ma-170	254	17	‖v−x0‖	‖v−x0‖	PROPN
ma-170	254	18	)	)	PUNCT
ma-170	254	19	for	for	ADP
ma-170	254	20	each	each	DET
ma-170	254	21	x	x	PROPN
ma-170	254	22	,	,	PUNCT
ma-170	254	23	y	y	PROPN
ma-170	254	24	,	,	PUNCT
ma-170	254	25	u	u	PROPN
ma-170	254	26	,	,	PUNCT
ma-170	254	27	v	v	PROPN
ma-170	254	28	∈	∈	PROPN
ma-170	254	29	b2	b2	NOUN
ma-170	254	30	.	.	PUNCT
ma-170	255	1	(	(	PUNCT
ma-170	255	2	c6	c6	PROPN
ma-170	255	3	)	)	PUNCT
ma-170	255	4	b[x0	b[x0	PROPN
ma-170	255	5	,	,	PUNCT
ma-170	255	6	a	a	DET
ma-170	255	7	∗	∗	NOUN
ma-170	255	8	]	]	PUNCT
ma-170	255	9	⊂	⊂	PROPN
ma-170	255	10	ω	ω	PROPN
ma-170	255	11	.	.	PUNCT
ma-170	256	1	next	next	ADV
ma-170	256	2	,	,	PUNCT
ma-170	256	3	the	the	DET
ma-170	256	4	semi	semi	ADJ
ma-170	256	5	-	-	ADJ
ma-170	256	6	local	local	ADJ
ma-170	256	7	convergence	convergence	NOUN
ma-170	256	8	is	be	AUX
ma-170	256	9	provided	provide	VERB
ma-170	256	10	for	for	ADP
ma-170	256	11	the	the	DET
ma-170	256	12	method	method	NOUN
ma-170	256	13	(	(	PUNCT
ma-170	256	14	1.3	1.3	NUM
ma-170	256	15	)	)	PUNCT
ma-170	256	16	.	.	PUNCT
ma-170	257	1	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	PROPN
ma-170	257	2	eur	eur	PROPN
ma-170	257	3	.	.	PUNCT
ma-170	258	1	j.	j.	PROPN
ma-170	258	2	math	math	PROPN
ma-170	258	3	.	.	PUNCT
ma-170	259	1	anal	anal	PROPN
ma-170	259	2	.	.	PUNCT
ma-170	260	1	10.28924	10.28924	NUM
ma-170	260	2	/	/	SYM
ma-170	260	3	ada	ada	PROPN
ma-170	260	4	/	/	SYM
ma-170	260	5	ma.3.24	ma.3.24	ADJ
ma-170	260	6	9	9	NUM
ma-170	260	7	theorem	theorem	ADJ
ma-170	260	8	3.2	3.2	NUM
ma-170	260	9	assume	assume	VERB
ma-170	260	10	the	the	DET
ma-170	260	11	conditions	condition	NOUN
ma-170	260	12	(	(	PUNCT
ma-170	260	13	c1)−	c1)−	NOUN
ma-170	260	14	(	(	PUNCT
ma-170	260	15	c6	c6	PROPN
ma-170	260	16	)	)	PUNCT
ma-170	260	17	hold	hold	VERB
ma-170	260	18	.	.	PUNCT
ma-170	261	1	then	then	ADV
ma-170	261	2	,	,	PUNCT
ma-170	261	3	the	the	DET
ma-170	261	4	following	follow	VERB
ma-170	261	5	items	item	NOUN
ma-170	261	6	hold	hold	VERB
ma-170	261	7	{	{	PUNCT
ma-170	261	8	xn	xn	NOUN
ma-170	261	9	}	}	PUNCT
ma-170	261	10	⊂	⊂	PROPN
ma-170	261	11	b(x0	b(x0	NOUN
ma-170	261	12	,	,	PUNCT
ma-170	261	13	a	a	DET
ma-170	261	14	∗	∗	NOUN
ma-170	261	15	)	)	PUNCT
ma-170	261	16	,	,	PUNCT
ma-170	261	17	(	(	PUNCT
ma-170	261	18	3.24	3.24	NUM
ma-170	261	19	)	)	PUNCT
ma-170	261	20	‖yn	‖yn	NUM
ma-170	261	21	−	−	NOUN
ma-170	261	22	xn‖	xn‖	PROPN
ma-170	261	23	≤	≤	PROPN
ma-170	261	24	bn	bn	ADP
ma-170	261	25	−	−	PROPN
ma-170	261	26	an	an	PROPN
ma-170	261	27	,	,	PUNCT
ma-170	261	28	(	(	PUNCT
ma-170	261	29	3.25	3.25	NUM
ma-170	261	30	)	)	PUNCT
ma-170	262	1	‖zn	‖zn	NUM
ma-170	262	2	−	−	NOUN
ma-170	262	3	yn‖	yn‖	NOUN
ma-170	262	4	≤	≤	PROPN
ma-170	262	5	cn	cn	PROPN
ma-170	262	6	−	−	PROPN
ma-170	262	7	bn	bn	PROPN
ma-170	262	8	,	,	PUNCT
ma-170	262	9	(	(	PUNCT
ma-170	262	10	3.26	3.26	NUM
ma-170	262	11	)	)	PUNCT
ma-170	262	12	‖xn+1	‖xn+1	NUM
ma-170	262	13	−	−	PROPN
ma-170	262	14	zn‖	zn‖	PROPN
ma-170	262	15	≤	≤	NUM
ma-170	262	16	an+1	an+1	AUX
ma-170	262	17	−	−	PROPN
ma-170	262	18	cn	cn	PROPN
ma-170	262	19	,	,	PUNCT
ma-170	262	20	(	(	PUNCT
ma-170	262	21	3.27	3.27	NUM
ma-170	262	22	)	)	PUNCT
ma-170	263	1	and	and	CCONJ
ma-170	263	2	there	there	PRON
ma-170	263	3	exists	exist	VERB
ma-170	263	4	a	a	DET
ma-170	263	5	solution	solution	NOUN
ma-170	263	6	x∗	x∗	PROPN
ma-170	263	7	of	of	ADP
ma-170	263	8	the	the	DET
ma-170	263	9	equation	equation	NOUN
ma-170	263	10	f	f	X
ma-170	263	11	(	(	PUNCT
ma-170	263	12	x	x	X
ma-170	263	13	)	)	PUNCT
ma-170	263	14	=	=	SYM
ma-170	263	15	0	0	NUM
ma-170	263	16	such	such	ADJ
ma-170	263	17	that	that	PRON
ma-170	263	18	‖x∗	‖x∗	PUNCT
ma-170	264	1	−	−	NOUN
ma-170	264	2	xn‖	xn‖	PROPN
ma-170	264	3	≤	≤	NOUN
ma-170	264	4	a∗	a∗	PROPN
ma-170	264	5	−	−	PROPN
ma-170	264	6	an	an	NOUN
ma-170	264	7	.	.	PUNCT
ma-170	265	1	(	(	PUNCT
ma-170	265	2	3.28	3.28	NUM
ma-170	265	3	)	)	PUNCT
ma-170	265	4	proof	proof	NOUN
ma-170	265	5	.	.	PUNCT
ma-170	266	1	the	the	DET
ma-170	266	2	items	item	NOUN
ma-170	266	3	(	(	PUNCT
ma-170	266	4	3.24)-(3.27	3.24)-(3.27	NUM
ma-170	266	5	)	)	PUNCT
ma-170	266	6	are	be	AUX
ma-170	266	7	shown	show	VERB
ma-170	266	8	by	by	ADP
ma-170	266	9	induction	induction	NOUN
ma-170	266	10	.	.	PUNCT
ma-170	267	1	notice	notice	VERB
ma-170	267	2	that	that	SCONJ
ma-170	267	3	the	the	DET
ma-170	267	4	iterates	iterate	NOUN
ma-170	267	5	y0	y0	PROPN
ma-170	267	6	,	,	PUNCT
ma-170	267	7	z0	z0	PROPN
ma-170	267	8	,	,	PUNCT
ma-170	267	9	x1	x1	PROPN
ma-170	267	10	existsby	existsby	NOUN
ma-170	267	11	the	the	DET
ma-170	267	12	invertibility	invertibility	NOUN
ma-170	267	13	of	of	ADP
ma-170	267	14	[	[	X
ma-170	267	15	u0	u0	ADJ
ma-170	267	16	,	,	PUNCT
ma-170	267	17	v0;f	v0;f	PROPN
ma-170	267	18	]	]	PUNCT
ma-170	267	19	and	and	CCONJ
ma-170	267	20	the	the	DET
ma-170	267	21	method	method	NOUN
ma-170	267	22	(	(	PUNCT
ma-170	267	23	1.3	1.3	NUM
ma-170	267	24	)	)	PUNCT
ma-170	267	25	.	.	PUNCT
ma-170	268	1	the	the	DET
ma-170	268	2	estimate	estimate	NOUN
ma-170	268	3	(	(	PUNCT
ma-170	268	4	3.25	3.25	NUM
ma-170	268	5	)	)	PUNCT
ma-170	268	6	is	be	AUX
ma-170	268	7	validated	validate	VERB
ma-170	268	8	for	for	ADP
ma-170	268	9	n	n	NOUN
ma-170	268	10	=	=	SYM
ma-170	268	11	0,since	0,since	NOUN
ma-170	268	12	by	by	ADP
ma-170	268	13	the	the	DET
ma-170	268	14	condition	condition	NOUN
ma-170	268	15	(	(	PUNCT
ma-170	268	16	c4	c4	NOUN
ma-170	268	17	)	)	PUNCT
ma-170	268	18	‖y0	‖y0	NOUN
ma-170	268	19	−	−	PROPN
ma-170	269	1	x0‖	x0‖	PROPN
ma-170	269	2	=	=	SYM
ma-170	269	3	‖[u0	‖[u0	NOUN
ma-170	269	4	,	,	PUNCT
ma-170	269	5	v0;f	v0;f	PROPN
ma-170	269	6	]	]	SYM
ma-170	269	7	−1f	−1f	PROPN
ma-170	269	8	(	(	PUNCT
ma-170	269	9	x0)‖	x0)‖	PROPN
ma-170	269	10	≤	≤	NUM
ma-170	269	11	b0	b0	NOUN
ma-170	269	12	=	=	PUNCT
ma-170	269	13	b0	b0	PROPN
ma-170	269	14	−	−	PROPN
ma-170	269	15	a0	a0	PROPN
ma-170	269	16	≤	≤	ADJ
ma-170	269	17	a∗	a∗	NOUN
ma-170	269	18	(	(	PUNCT
ma-170	269	19	3.29	3.29	NUM
ma-170	269	20	)	)	PUNCT
ma-170	269	21	and	and	CCONJ
ma-170	269	22	the	the	DET
ma-170	269	23	iterate	iterate	NOUN
ma-170	269	24	y0	y0	PROPN
ma-170	269	25	∈	∈	NOUN
ma-170	269	26	b(x0	b(x0	NOUN
ma-170	269	27	,	,	PUNCT
ma-170	269	28	a	a	DET
ma-170	269	29	∗).then	∗).then	ADV
ma-170	269	30	,	,	PUNCT
ma-170	269	31	as	as	ADP
ma-170	269	32	in	in	ADP
ma-170	269	33	the	the	DET
ma-170	269	34	local	local	ADJ
ma-170	269	35	convergence	convergence	NOUN
ma-170	269	36	case	case	NOUN
ma-170	269	37	but	but	CCONJ
ma-170	269	38	using	use	VERB
ma-170	269	39	x0	x0	PROPN
ma-170	269	40	,	,	PUNCT
ma-170	269	41	(	(	PUNCT
ma-170	269	42	c	c	NOUN
ma-170	269	43	)	)	PUNCT
ma-170	269	44	instead	instead	ADV
ma-170	269	45	of	of	ADP
ma-170	269	46	x∗	x∗	PROPN
ma-170	269	47	,	,	PUNCT
ma-170	269	48	(	(	PUNCT
ma-170	269	49	h	h	NOUN
ma-170	269	50	)	)	PUNCT
ma-170	269	51	,	,	PUNCT
ma-170	269	52	we	we	PRON
ma-170	269	53	obtain	obtain	VERB
ma-170	269	54	from	from	ADP
ma-170	269	55	f	f	PROPN
ma-170	269	56	(	(	PUNCT
ma-170	269	57	yn	yn	PROPN
ma-170	269	58	)	)	PUNCT
ma-170	269	59	=	=	SYM
ma-170	269	60	f	f	PROPN
ma-170	269	61	(	(	PUNCT
ma-170	269	62	yn)−	yn)−	PROPN
ma-170	269	63	f	f	PROPN
ma-170	269	64	(	(	PUNCT
ma-170	269	65	xn)−d(yn	xn)−d(yn	PROPN
ma-170	269	66	−	−	PROPN
ma-170	269	67	xn	xn	NUM
ma-170	269	68	)	)	PUNCT
ma-170	269	69	=	=	SYM
ma-170	270	1	(	(	PUNCT
ma-170	270	2	[	[	X
ma-170	270	3	yn	yn	X
ma-170	270	4	,	,	PUNCT
ma-170	270	5	xn;f	xn;f	PUNCT
ma-170	271	1	]	]	PUNCT
ma-170	271	2	−d)(yn	−d)(yn	ADJ
ma-170	271	3	−	−	NOUN
ma-170	271	4	xn	xn	NUM
ma-170	271	5	)	)	PUNCT
ma-170	271	6	,	,	PUNCT
ma-170	271	7	so	so	ADV
ma-170	271	8	‖l−1f	‖l−1f	PROPN
ma-170	271	9	(	(	PUNCT
ma-170	271	10	yn)‖	yn)‖	PROPN
ma-170	271	11	≤	≤	PROPN
ma-170	271	12	w2(‖xn	w2(‖xn	PROPN
ma-170	271	13	−	−	PUNCT
ma-170	271	14	x0‖	x0‖	PROPN
ma-170	271	15	,	,	PUNCT
ma-170	271	16	‖yn	‖yn	PROPN
ma-170	271	17	−	−	NOUN
ma-170	271	18	x0‖	x0‖	PROPN
ma-170	271	19	,	,	PUNCT
ma-170	271	20	‖un	‖un	PROPN
ma-170	271	21	−	−	PROPN
ma-170	271	22	x0‖	x0‖	PROPN
ma-170	271	23	,	,	PUNCT
ma-170	271	24	‖vn	‖vn	PROPN
ma-170	271	25	−	−	PROPN
ma-170	271	26	x0‖	x0‖	PROPN
ma-170	271	27	)	)	PUNCT
ma-170	271	28	.	.	PUNCT
ma-170	272	1	(	(	PUNCT
ma-170	272	2	3.30	3.30	NUM
ma-170	272	3	)	)	PUNCT
ma-170	272	4	hence	hence	ADV
ma-170	272	5	,	,	PUNCT
ma-170	272	6	by	by	ADP
ma-170	272	7	the	the	DET
ma-170	272	8	second	second	ADJ
ma-170	272	9	substep	substep	NOUN
ma-170	272	10	zn	zn	PROPN
ma-170	272	11	−	−	PROPN
ma-170	272	12	yn	yn	PROPN
ma-170	272	13	=	=	PROPN
ma-170	272	14	−d−1f	−d−1f	PROPN
ma-170	272	15	(	(	PUNCT
ma-170	272	16	yn)−	yn)−	PROPN
ma-170	272	17	2d−1(d	2d−1(d	NUM
ma-170	272	18	−	−	PROPN
ma-170	273	1	[	[	X
ma-170	273	2	yn	yn	X
ma-170	273	3	,	,	PUNCT
ma-170	273	4	xn;f	xn;f	PUNCT
ma-170	274	1	]	]	PUNCT
ma-170	274	2	)	)	PUNCT
ma-170	274	3	−1d−1f	−1d−1f	NOUN
ma-170	274	4	(	(	PUNCT
ma-170	274	5	yn	yn	NOUN
ma-170	274	6	)	)	PUNCT
ma-170	274	7	,	,	PUNCT
ma-170	274	8	and	and	CCONJ
ma-170	274	9	‖zn	‖zn	NUM
ma-170	274	10	−	−	NOUN
ma-170	274	11	yn‖	yn‖	NOUN
ma-170	274	12	≤	≤	PROPN
ma-170	275	1	[	[	X
ma-170	275	2	w2(‖xn	w2(‖xn	PROPN
ma-170	275	3	−	−	PROPN
ma-170	275	4	x0‖	x0‖	PROPN
ma-170	275	5	,	,	PUNCT
ma-170	275	6	‖yn	‖yn	PROPN
ma-170	275	7	−	−	NOUN
ma-170	275	8	x0‖	x0‖	PROPN
ma-170	275	9	,	,	PUNCT
ma-170	275	10	‖un	‖un	PROPN
ma-170	275	11	−	−	PROPN
ma-170	275	12	x0‖	x0‖	PROPN
ma-170	275	13	,	,	PUNCT
ma-170	275	14	‖vn	‖vn	PROPN
ma-170	275	15	−	−	PROPN
ma-170	275	16	x0‖	x0‖	PROPN
ma-170	275	17	)	)	PUNCT
ma-170	275	18	1−	1−	NUM
ma-170	275	19	w0(f1(‖xn	w0(f1(‖xn	X
ma-170	275	20	−	−	PROPN
ma-170	275	21	x0‖	x0‖	PROPN
ma-170	275	22	)	)	PUNCT
ma-170	275	23	,	,	PUNCT
ma-170	275	24	f2(‖xn	f2(‖xn	PROPN
ma-170	275	25	−	−	NOUN
ma-170	275	26	x0‖	x0‖	PROPN
ma-170	275	27	)	)	PUNCT
ma-170	275	28	)	)	PUNCT
ma-170	276	1	+	+	CCONJ
ma-170	276	2	2	2	X
ma-170	276	3	(	(	PUNCT
ma-170	276	4	w2(‖xn	w2(‖xn	PROPN
ma-170	276	5	−	−	PROPN
ma-170	276	6	x0‖	x0‖	PROPN
ma-170	276	7	,	,	PUNCT
ma-170	276	8	‖yn	‖yn	PROPN
ma-170	276	9	−	−	NOUN
ma-170	276	10	x0‖	x0‖	PROPN
ma-170	276	11	,	,	PUNCT
ma-170	276	12	‖un	‖un	PROPN
ma-170	276	13	−	−	PROPN
ma-170	276	14	x0‖	x0‖	PROPN
ma-170	276	15	,	,	PUNCT
ma-170	276	16	‖vn	‖vn	PROPN
ma-170	276	17	−	−	PROPN
ma-170	276	18	x0‖	x0‖	PROPN
ma-170	276	19	)	)	PUNCT
ma-170	276	20	1−	1−	NUM
ma-170	276	21	w0(f1(‖xn	w0(f1(‖xn	X
ma-170	276	22	−	−	PROPN
ma-170	276	23	x0‖	x0‖	PROPN
ma-170	276	24	)	)	PUNCT
ma-170	276	25	,	,	PUNCT
ma-170	276	26	f2(‖xn	f2(‖xn	PROPN
ma-170	276	27	−	−	NOUN
ma-170	276	28	x0‖	x0‖	PROPN
ma-170	276	29	)	)	PUNCT
ma-170	276	30	)	)	PUNCT
ma-170	276	31	)	)	PUNCT
ma-170	277	1	2	2	X
ma-170	277	2	]	]	PUNCT
ma-170	277	3	‖yn	‖yn	NUM
ma-170	277	4	−	−	NOUN
ma-170	277	5	xn‖	xn‖	PROPN
ma-170	277	6	≤	≤	VERB
ma-170	277	7	an	an	DET
ma-170	277	8	−	−	PROPN
ma-170	277	9	bn	bn	NOUN
ma-170	277	10	(	(	PUNCT
ma-170	277	11	3.31	3.31	NUM
ma-170	277	12	)	)	PUNCT
ma-170	277	13	and	and	CCONJ
ma-170	278	1	‖zn	‖zn	NUM
ma-170	278	2	−	−	NOUN
ma-170	278	3	x0‖	x0‖	PROPN
ma-170	278	4	≤	≤	PROPN
ma-170	279	1	‖zn	‖zn	NUM
ma-170	279	2	−	−	PROPN
ma-170	279	3	yn‖+	yn‖+	PROPN
ma-170	279	4	‖yn	‖yn	PROPN
ma-170	279	5	−	−	PROPN
ma-170	279	6	x0‖	x0‖	PROPN
ma-170	279	7	≤	≤	PROPN
ma-170	279	8	an	an	DET
ma-170	279	9	−	−	PROPN
ma-170	279	10	bn	bn	NOUN
ma-170	279	11	+	+	CCONJ
ma-170	279	12	bn	bn	NOUN
ma-170	279	13	−	−	PROPN
ma-170	279	14	a0	a0	NOUN
ma-170	279	15	=	=	SYM
ma-170	279	16	cn	cn	PROPN
ma-170	279	17	<	<	X
ma-170	279	18	a∗	a∗	PROPN
ma-170	279	19	,	,	PUNCT
ma-170	279	20	thus	thus	ADV
ma-170	279	21	the	the	DET
ma-170	279	22	item	item	NOUN
ma-170	279	23	(	(	PUNCT
ma-170	279	24	3.26	3.26	NUM
ma-170	279	25	)	)	PUNCT
ma-170	279	26	holds	hold	NOUN
ma-170	279	27	and	and	CCONJ
ma-170	279	28	the	the	DET
ma-170	279	29	iterate	iterate	NOUN
ma-170	279	30	z0	z0	PROPN
ma-170	279	31	∈	∈	PROPN
ma-170	279	32	b(x0	b(x0	NOUN
ma-170	279	33	,	,	PUNCT
ma-170	279	34	a	a	DET
ma-170	279	35	∗).moreover	∗).moreover	NOUN
ma-170	279	36	,	,	PUNCT
ma-170	279	37	by	by	ADP
ma-170	279	38	the	the	DET
ma-170	279	39	third	third	ADJ
ma-170	279	40	substep	substep	NOUN
ma-170	279	41	xn+1	xn+1	PROPN
ma-170	280	1	−	−	PROPN
ma-170	281	1	zn	zn	NOUN
ma-170	282	1	=	=	SYM
ma-170	283	1	−bd−1f	−bd−1f	PROPN
ma-170	283	2	(	(	PUNCT
ma-170	283	3	zn	zn	PROPN
ma-170	283	4	)	)	PUNCT
ma-170	283	5	,	,	PUNCT
ma-170	283	6	(	(	PUNCT
ma-170	283	7	3.32	3.32	NUM
ma-170	283	8	)	)	PUNCT
ma-170	283	9	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	NOUN
ma-170	283	10	eur	eur	PROPN
ma-170	283	11	.	.	PUNCT
ma-170	284	1	j.	j.	PROPN
ma-170	284	2	math	math	PROPN
ma-170	284	3	.	.	PUNCT
ma-170	285	1	anal	anal	PROPN
ma-170	285	2	.	.	PUNCT
ma-170	286	1	10.28924	10.28924	NUM
ma-170	286	2	/	/	SYM
ma-170	286	3	ada	ada	PROPN
ma-170	286	4	/	/	SYM
ma-170	286	5	ma.3.24	ma.3.24	PROPN
ma-170	286	6	10where	10where	X
ma-170	287	1	b	b	X
ma-170	287	2	=	=	SYM
ma-170	287	3	−	−	PROPN
ma-170	287	4	1	1	NUM
ma-170	287	5	4	4	NUM
ma-170	287	6	(	(	PUNCT
ma-170	287	7	13i	13i	NOUN
ma-170	287	8	−	−	PROPN
ma-170	287	9	14d−1[zn	14d−1[zn	NUM
ma-170	287	10	,	,	PUNCT
ma-170	287	11	yn;f	yn;f	ADJ
ma-170	287	12	]	]	PUNCT
ma-170	288	1	+	+	CCONJ
ma-170	288	2	5(d−1[zn	5(d−1[zn	NUM
ma-170	288	3	,	,	PUNCT
ma-170	288	4	yn;f	yn;f	NOUN
ma-170	288	5	]	]	PUNCT
ma-170	288	6	)	)	PUNCT
ma-170	288	7	2	2	X
ma-170	288	8	)	)	PUNCT
ma-170	288	9	=	=	SYM
ma-170	289	1	−	−	PROPN
ma-170	289	2	1	1	NUM
ma-170	289	3	4	4	NUM
ma-170	289	4	(	(	PUNCT
ma-170	289	5	5(d−1[zn	5(d−1[zn	NUM
ma-170	289	6	,	,	PUNCT
ma-170	289	7	yn;f	yn;f	NOUN
ma-170	289	8	]	]	PUNCT
ma-170	289	9	−	−	PROPN
ma-170	289	10	i)2	i)2	ADJ
ma-170	289	11	−	−	PROPN
ma-170	289	12	4(d−1[zn	4(d−1[zn	NUM
ma-170	289	13	,	,	PUNCT
ma-170	289	14	yn;f	yn;f	NOUN
ma-170	289	15	]	]	PUNCT
ma-170	289	16	−	−	PROPN
ma-170	290	1	i	i	NOUN
ma-170	290	2	)	)	PUNCT
ma-170	291	1	+	+	CCONJ
ma-170	291	2	4i	4i	NOUN
ma-170	291	3	)	)	PUNCT
ma-170	291	4	,	,	PUNCT
ma-170	291	5	thus	thus	ADV
ma-170	291	6	‖b‖	‖b‖	VERB
ma-170	291	7	≤	≤	NUM
ma-170	291	8	1	1	NUM
ma-170	291	9	4	4	NUM
ma-170	291	10	(	(	PUNCT
ma-170	291	11	5	5	NUM
ma-170	291	12	(	(	PUNCT
ma-170	291	13	w2(‖xn	w2(‖xn	PROPN
ma-170	291	14	−	−	PROPN
ma-170	291	15	x0‖	x0‖	PROPN
ma-170	291	16	,	,	PUNCT
ma-170	291	17	‖yn	‖yn	PROPN
ma-170	291	18	−	−	NOUN
ma-170	291	19	x0‖	x0‖	PROPN
ma-170	291	20	,	,	PUNCT
ma-170	291	21	‖un	‖un	PROPN
ma-170	291	22	−	−	PROPN
ma-170	291	23	x0‖	x0‖	PROPN
ma-170	291	24	,	,	PUNCT
ma-170	291	25	‖vn	‖vn	PROPN
ma-170	291	26	−	−	PROPN
ma-170	291	27	x0‖	x0‖	PROPN
ma-170	291	28	)	)	PUNCT
ma-170	291	29	1−	1−	NUM
ma-170	291	30	w0(f1(‖xn	w0(f1(‖xn	X
ma-170	291	31	−	−	PROPN
ma-170	291	32	x0‖	x0‖	PROPN
ma-170	291	33	)	)	PUNCT
ma-170	291	34	,	,	PUNCT
ma-170	291	35	f2(‖xn	f2(‖xn	PROPN
ma-170	291	36	−	−	NOUN
ma-170	291	37	x0‖	x0‖	PROPN
ma-170	291	38	)	)	PUNCT
ma-170	291	39	)	)	PUNCT
ma-170	291	40	)	)	PUNCT
ma-170	292	1	2	2	NUM
ma-170	292	2	+	+	NUM
ma-170	292	3	4	4	NUM
ma-170	292	4	(	(	PUNCT
ma-170	292	5	w2(‖xn	w2(‖xn	PROPN
ma-170	292	6	−	−	PROPN
ma-170	292	7	x0‖	x0‖	PROPN
ma-170	292	8	,	,	PUNCT
ma-170	292	9	‖yn	‖yn	PROPN
ma-170	292	10	−	−	NOUN
ma-170	292	11	x0‖	x0‖	PROPN
ma-170	292	12	,	,	PUNCT
ma-170	292	13	‖un	‖un	PROPN
ma-170	292	14	−	−	PROPN
ma-170	292	15	x0‖	x0‖	PROPN
ma-170	292	16	,	,	PUNCT
ma-170	292	17	‖vn	‖vn	PROPN
ma-170	292	18	−	−	PROPN
ma-170	292	19	x0‖	x0‖	PROPN
ma-170	292	20	)	)	PUNCT
ma-170	292	21	1−	1−	NUM
ma-170	292	22	w0(f1(‖xn	w0(f1(‖xn	X
ma-170	293	1	−	−	PROPN
ma-170	294	1	x0‖	x0‖	PROPN
ma-170	294	2	)	)	PUNCT
ma-170	294	3	,	,	PUNCT
ma-170	294	4	f2(‖xn	f2(‖xn	PROPN
ma-170	294	5	−	−	NOUN
ma-170	294	6	x0‖	x0‖	PROPN
ma-170	294	7	)	)	PUNCT
ma-170	294	8	)	)	PUNCT
ma-170	294	9	)	)	PUNCT
ma-170	295	1	+	+	CCONJ
ma-170	295	2	4	4	X
ma-170	295	3	)	)	PUNCT
ma-170	295	4	=	=	PUNCT
ma-170	295	5	β̄	β̄	ADJ
ma-170	295	6	<	<	X
ma-170	295	7	βn	βn	NOUN
ma-170	295	8	.	.	PUNCT
ma-170	296	1	consequently	consequently	ADV
ma-170	296	2	,	,	PUNCT
ma-170	296	3	we	we	PRON
ma-170	296	4	have	have	VERB
ma-170	296	5	‖xn+1	‖xn+1	NUM
ma-170	296	6	−	−	PROPN
ma-170	296	7	zn‖	zn‖	PROPN
ma-170	296	8	≤	≤	X
ma-170	296	9	β̄n(1	β̄n(1	NUM
ma-170	296	10	+	+	CCONJ
ma-170	296	11	w0(‖yn	w0(‖yn	ADP
ma-170	296	12	−	−	X
ma-170	296	13	x0‖	x0‖	PROPN
ma-170	296	14	,	,	PUNCT
ma-170	296	15	‖zn	‖zn	PROPN
ma-170	296	16	−	−	PROPN
ma-170	297	1	x0‖))‖zn	x0‖))‖zn	ADV
ma-170	297	2	−	−	NOUN
ma-170	298	1	yn‖	yn‖	NOUN
ma-170	298	2	1−	1−	NUM
ma-170	298	3	w0(f1(‖xn	w0(f1(‖xn	PROPN
ma-170	298	4	−	−	PROPN
ma-170	298	5	x0‖	x0‖	PROPN
ma-170	298	6	)	)	PUNCT
ma-170	298	7	,	,	PUNCT
ma-170	298	8	f2(‖xn	f2(‖xn	PROPN
ma-170	298	9	−	−	NOUN
ma-170	298	10	x0‖	x0‖	PROPN
ma-170	298	11	)	)	PUNCT
ma-170	298	12	)	)	PUNCT
ma-170	298	13	≤	≤	PUNCT
ma-170	299	1	βn(1	βn(1	X
ma-170	299	2	+	+	CCONJ
ma-170	299	3	w0(βn	w0(βn	PROPN
ma-170	299	4	,	,	PUNCT
ma-170	299	5	cn))(cn	cn))(cn	ADJ
ma-170	299	6	−	−	PROPN
ma-170	299	7	bn	bn	NOUN
ma-170	299	8	)	)	PUNCT
ma-170	299	9	1−	1−	NUM
ma-170	299	10	w0(f1(an	w0(f1(an	NUM
ma-170	299	11	)	)	PUNCT
ma-170	299	12	,	,	PUNCT
ma-170	299	13	f2(an	f2(an	PROPN
ma-170	299	14	)	)	PUNCT
ma-170	299	15	)	)	PUNCT
ma-170	300	1	=	=	PUNCT
ma-170	300	2	an+1	an+1	AUX
ma-170	300	3	−	−	PROPN
ma-170	301	1	cn	cn	X
ma-170	301	2	<	<	X
ma-170	301	3	βn	βn	X
ma-170	301	4	(	(	PUNCT
ma-170	301	5	3.33	3.33	NUM
ma-170	301	6	)	)	PUNCT
ma-170	301	7	and	and	CCONJ
ma-170	301	8	‖xn+1	‖xn+1	NUM
ma-170	302	1	−	−	PROPN
ma-170	302	2	x0‖	x0‖	PROPN
ma-170	302	3	≤	≤	PROPN
ma-170	302	4	‖xn+1	‖xn+1	PUNCT
ma-170	302	5	−	−	PROPN
ma-170	303	1	zn‖+	zn‖+	PROPN
ma-170	304	1	‖zn	‖zn	NUM
ma-170	304	2	−	−	PROPN
ma-170	304	3	x0‖	x0‖	PROPN
ma-170	304	4	≤	≤	PROPN
ma-170	304	5	an+1	an+1	AUX
ma-170	305	1	−	−	PROPN
ma-170	305	2	cn	cn	INTJ
ma-170	305	3	+	+	CCONJ
ma-170	305	4	cn	cn	PROPN
ma-170	305	5	−	−	PROPN
ma-170	305	6	a0	a0	NOUN
ma-170	305	7	=	=	SYM
ma-170	305	8	an+1	an+1	X
ma-170	305	9	<	<	X
ma-170	305	10	a∗.hence	a∗.hence	PROPN
ma-170	305	11	,	,	PUNCT
ma-170	305	12	the	the	DET
ma-170	305	13	item	item	NOUN
ma-170	305	14	(	(	PUNCT
ma-170	305	15	3.27	3.27	NUM
ma-170	305	16	)	)	PUNCT
ma-170	305	17	is	be	AUX
ma-170	305	18	validated	validate	VERB
ma-170	305	19	and	and	CCONJ
ma-170	305	20	iterate	iterate	VERB
ma-170	305	21	xn+1	xn+1	PROPN
ma-170	305	22	∈	∈	PROPN
ma-170	305	23	b(x0	b(x0	NOUN
ma-170	305	24	,	,	PUNCT
ma-170	305	25	a	a	DET
ma-170	305	26	∗	∗	NOUN
ma-170	305	27	)	)	PUNCT
ma-170	305	28	.	.	PUNCT
ma-170	306	1	�	�	PROPN
ma-170	306	2	remark	remark	VERB
ma-170	306	3	3.3	3.3	NUM
ma-170	306	4	as	as	ADP
ma-170	306	5	in	in	ADP
ma-170	306	6	the	the	DET
ma-170	306	7	local	local	ADJ
ma-170	306	8	case	case	NOUN
ma-170	306	9	the	the	DET
ma-170	306	10	functions	function	NOUN
ma-170	306	11	g1	g1	VERB
ma-170	306	12	and	and	CCONJ
ma-170	306	13	g2	g2	PROPN
ma-170	306	14	can	can	AUX
ma-170	306	15	be	be	AUX
ma-170	306	16	expressed	express	VERB
ma-170	306	17	in	in	ADP
ma-170	306	18	terms	term	NOUN
ma-170	306	19	of	of	ADP
ma-170	306	20	the	the	DET
ma-170	306	21	rest	rest	NOUN
ma-170	306	22	ofthe	ofthe	NOUN
ma-170	306	23	conditions.assume	conditions.assume	PROPN
ma-170	306	24	that	that	SCONJ
ma-170	306	25	there	there	PRON
ma-170	306	26	exists	exist	VERB
ma-170	306	27	a	a	DET
ma-170	306	28	cn	cn	PROPN
ma-170	306	29	function	function	NOUN
ma-170	306	30	ϕ1	ϕ1	NOUN
ma-170	306	31	:	:	PUNCT
ma-170	306	32	t	t	X
ma-170	306	33	→	→	SYM
ma-170	306	34	r	r	NOUN
ma-170	306	35	such	such	ADJ
ma-170	306	36	that	that	PRON
ma-170	306	37	for	for	SCONJ
ma-170	306	38	each	each	DET
ma-170	306	39	x	x	SYM
ma-170	306	40	∈	∈	PROPN
ma-170	306	41	ω	ω	NOUN
ma-170	306	42	‖l−1([x	‖l−1([x	ADJ
ma-170	306	43	,	,	PUNCT
ma-170	306	44	x0;f	x0;f	PROPN
ma-170	306	45	]	]	X
ma-170	306	46	−	−	PROPN
ma-170	306	47	l)‖	l)‖	NOUN
ma-170	306	48	≤	≤	NUM
ma-170	306	49	ϕ1(‖x	ϕ1(‖x	NOUN
ma-170	306	50	−	−	PROPN
ma-170	306	51	x0‖	x0‖	PROPN
ma-170	306	52	)	)	PUNCT
ma-170	306	53	.	.	PUNCT
ma-170	307	1	then	then	ADV
ma-170	307	2	,	,	PUNCT
ma-170	307	3	from	from	ADP
ma-170	307	4	the	the	DET
ma-170	307	5	estimate	estimate	NOUN
ma-170	307	6	un	un	PROPN
ma-170	307	7	−	−	PROPN
ma-170	307	8	x0	x0	PROPN
ma-170	308	1	=	=	PUNCT
ma-170	308	2	xn	xn	PROPN
ma-170	309	1	−	−	NUM
ma-170	309	2	x0	x0	PROPN
ma-170	310	1	+	+	CCONJ
ma-170	310	2	f	f	X
ma-170	310	3	(	(	PUNCT
ma-170	310	4	xn)−	xn)−	X
ma-170	310	5	f	f	X
ma-170	310	6	(	(	PUNCT
ma-170	310	7	x0	x0	PROPN
ma-170	310	8	)	)	PUNCT
ma-170	311	1	+	+	CCONJ
ma-170	311	2	f	f	X
ma-170	311	3	(	(	PUNCT
ma-170	311	4	x	x	NOUN
ma-170	311	5	)	)	PUNCT
ma-170	311	6	=(	=(	NOUN
ma-170	311	7	i	i	PRON
ma-170	311	8	+	+	CCONJ
ma-170	311	9	l+	l+	NOUN
ma-170	311	10	ll−1([xn	ll−1([xn	NOUN
ma-170	311	11	,	,	PUNCT
ma-170	311	12	x0;f	x0;f	PROPN
ma-170	311	13	]	]	X
ma-170	311	14	−	−	PROPN
ma-170	312	1	l))(xn	l))(xn	NOUN
ma-170	312	2	−	−	NOUN
ma-170	312	3	x0	x0	PROPN
ma-170	312	4	)	)	PUNCT
ma-170	313	1	+	+	CCONJ
ma-170	313	2	f	f	X
ma-170	313	3	(	(	PUNCT
ma-170	313	4	x0	x0	PROPN
ma-170	313	5	)	)	PUNCT
ma-170	313	6	,	,	PUNCT
ma-170	313	7	so	so	SCONJ
ma-170	313	8	we	we	PRON
ma-170	313	9	can	can	AUX
ma-170	313	10	choose	choose	VERB
ma-170	313	11	g1(t	g1(t	ADP
ma-170	313	12	)	)	PUNCT
ma-170	313	13	=	=	SYM
ma-170	313	14	(	(	PUNCT
ma-170	313	15	‖1	‖1	NOUN
ma-170	313	16	+	+	CCONJ
ma-170	313	17	l‖+	l‖+	ADJ
ma-170	313	18	‖l‖ϕ1(t))t	‖l‖ϕ1(t))t	NOUN
ma-170	313	19	+	+	X
ma-170	313	20	‖f	‖f	ADP
ma-170	313	21	(	(	PUNCT
ma-170	313	22	x0)‖and	x0)‖and	NUM
ma-170	313	23	similarly	similarly	ADV
ma-170	313	24	g2(t	g2(t	NOUN
ma-170	313	25	)	)	PUNCT
ma-170	314	1	=	=	PRON
ma-170	314	2	(	(	PUNCT
ma-170	314	3	‖1−	‖1−	ADV
ma-170	314	4	l‖+	l‖+	ADJ
ma-170	314	5	‖l‖ϕ1(t))t	‖l‖ϕ1(t))t	ADV
ma-170	314	6	+	+	X
ma-170	314	7	‖f	‖f	ADP
ma-170	314	8	(	(	PUNCT
ma-170	314	9	x0)‖.under	x0)‖.under	X
ma-170	314	10	these	these	DET
ma-170	314	11	choices	choice	NOUN
ma-170	314	12	of	of	ADP
ma-170	314	13	g1	g1	NOUN
ma-170	314	14	and	and	CCONJ
ma-170	314	15	g2	g2	PROPN
ma-170	314	16	‖u	‖u	PROPN
ma-170	315	1	−	−	PROPN
ma-170	315	2	x0‖	x0‖	PROPN
ma-170	316	1	=	=	PUNCT
ma-170	316	2	g1(‖x	g1(‖x	PROPN
ma-170	316	3	−	−	PROPN
ma-170	316	4	x0‖	x0‖	PROPN
ma-170	316	5	)	)	PUNCT
ma-170	316	6	,	,	PUNCT
ma-170	316	7	‖v	‖v	NOUN
ma-170	316	8	−	−	PROPN
ma-170	316	9	x0‖	x0‖	PROPN
ma-170	317	1	=	=	PRON
ma-170	317	2	g2(‖x	g2(‖x	PROPN
ma-170	317	3	−	−	PROPN
ma-170	317	4	x0‖	x0‖	PROPN
ma-170	317	5	)	)	PUNCT
ma-170	317	6	and	and	CCONJ
ma-170	317	7	the	the	DET
ma-170	317	8	second	second	ADJ
ma-170	317	9	and	and	CCONJ
ma-170	317	10	third	third	ADJ
ma-170	317	11	conditions	condition	NOUN
ma-170	317	12	in	in	ADP
ma-170	317	13	(	(	PUNCT
ma-170	317	14	h3	h3	NOUN
ma-170	317	15	)	)	PUNCT
ma-170	317	16	can	can	AUX
ma-170	317	17	be	be	AUX
ma-170	317	18	dropped.possible	dropped.possible	ADJ
ma-170	317	19	choices	choice	NOUN
ma-170	317	20	for	for	ADP
ma-170	317	21	l	l	NOUN
ma-170	317	22	are	be	AUX
ma-170	317	23	l	l	NOUN
ma-170	317	24	=	=	SYM
ma-170	317	25	f	f	PROPN
ma-170	317	26	′(x0	′(x0	NOUN
ma-170	317	27	)	)	PUNCT
ma-170	317	28	(	(	PUNCT
ma-170	317	29	the	the	DET
ma-170	317	30	differentiable	differentiable	ADJ
ma-170	317	31	case	case	NOUN
ma-170	317	32	)	)	PUNCT
ma-170	317	33	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	NOUN
ma-170	317	34	eur	eur	PROPN
ma-170	317	35	.	.	PUNCT
ma-170	318	1	j.	j.	PROPN
ma-170	318	2	math	math	PROPN
ma-170	318	3	.	.	PUNCT
ma-170	319	1	anal	anal	PROPN
ma-170	319	2	.	.	PUNCT
ma-170	320	1	10.28924	10.28924	NUM
ma-170	320	2	/	/	SYM
ma-170	320	3	ada	ada	PROPN
ma-170	320	4	/	/	SYM
ma-170	320	5	ma.3.24	ma.3.24	PROPN
ma-170	320	6	11or	11or	ADJ
ma-170	320	7	l	l	NOUN
ma-170	320	8	=	=	PUNCT
ma-170	321	1	[	[	X
ma-170	321	2	.	.	X
ma-170	321	3	,	,	PUNCT
ma-170	321	4	.;f	.;f	PUNCT
ma-170	321	5	]	]	PUNCT
ma-170	321	6	(	(	PUNCT
ma-170	321	7	the	the	DET
ma-170	321	8	non	non	ADJ
ma-170	321	9	-	-	ADJ
ma-170	321	10	differentiable	differentiable	ADJ
ma-170	321	11	case).the	case).the	DET
ma-170	321	12	condition	condition	NOUN
ma-170	321	13	(	(	PUNCT
ma-170	321	14	c6	c6	PROPN
ma-170	321	15	)	)	PUNCT
ma-170	321	16	can	can	AUX
ma-170	321	17	be	be	AUX
ma-170	321	18	replaced	replace	VERB
ma-170	321	19	by	by	ADP
ma-170	321	20	(	(	PUNCT
ma-170	321	21	c6	c6	PROPN
ma-170	321	22	)	)	PUNCT
ma-170	321	23	′	′	NUM
ma-170	321	24	b[x0	b[x0	ADV
ma-170	321	25	,	,	PUNCT
ma-170	321	26	ā	ā	X
ma-170	321	27	]	]	X
ma-170	321	28	⊂	⊂	PROPN
ma-170	321	29	ω	ω	PROPN
ma-170	321	30	,	,	PUNCT
ma-170	321	31	where	where	SCONJ
ma-170	321	32	ā	ā	NOUN
ma-170	321	33	=	=	SYM
ma-170	321	34	max{a∗	max{a∗	PROPN
ma-170	321	35	,	,	PUNCT
ma-170	321	36	g1(a∗	g1(a∗	X
ma-170	321	37	)	)	PUNCT
ma-170	321	38	,	,	PUNCT
ma-170	321	39	g2(a∗)}.a	g2(a∗)}.a	PROPN
ma-170	321	40	uniqueness	uniqueness	NOUN
ma-170	321	41	of	of	ADP
ma-170	321	42	the	the	DET
ma-170	321	43	solution	solution	NOUN
ma-170	321	44	set	set	VERB
ma-170	321	45	is	be	AUX
ma-170	321	46	specified	specify	VERB
ma-170	321	47	.	.	PUNCT
ma-170	322	1	proposition	proposition	NOUN
ma-170	322	2	3.4	3.4	NUM
ma-170	322	3	assume	assume	VERB
ma-170	322	4	:	:	PUNCT
ma-170	322	5	there	there	PRON
ma-170	322	6	exists	exist	VERB
ma-170	322	7	a	a	DET
ma-170	322	8	solution	solution	NOUN
ma-170	322	9	d	d	PROPN
ma-170	322	10	∈	∈	PROPN
ma-170	322	11	b(x0	b(x0	NOUN
ma-170	322	12	,	,	PUNCT
ma-170	322	13	δ6	δ6	NOUN
ma-170	322	14	)	)	PUNCT
ma-170	322	15	of	of	ADP
ma-170	322	16	the	the	DET
ma-170	322	17	equation	equation	NOUN
ma-170	323	1	f	f	X
ma-170	323	2	(	(	PUNCT
ma-170	323	3	x	x	X
ma-170	323	4	)	)	PUNCT
ma-170	323	5	=	=	SYM
ma-170	323	6	0	0	NUM
ma-170	324	1	for	for	ADP
ma-170	324	2	some	some	DET
ma-170	324	3	δ6	δ6	NOUN
ma-170	324	4	>	>	X
ma-170	324	5	0	0	NUM
ma-170	324	6	;	;	PUNCT
ma-170	324	7	the	the	DET
ma-170	324	8	first	first	ADJ
ma-170	324	9	condition	condition	NOUN
ma-170	324	10	in	in	ADP
ma-170	324	11	(	(	PUNCT
ma-170	324	12	h3	h3	NOUN
ma-170	324	13	)	)	PUNCT
ma-170	324	14	holds	hold	VERB
ma-170	324	15	in	in	ADP
ma-170	324	16	the	the	DET
ma-170	324	17	ball	ball	NOUN
ma-170	324	18	b(x0	b(x0	NOUN
ma-170	324	19	,	,	PUNCT
ma-170	324	20	δ6	δ6	NOUN
ma-170	324	21	)	)	PUNCT
ma-170	324	22	and	and	CCONJ
ma-170	324	23	there	there	PRON
ma-170	324	24	exists	exist	VERB
ma-170	324	25	δ7	δ7	NOUN
ma-170	324	26	≥	≥	NOUN
ma-170	324	27	δ6	δ6	VERB
ma-170	324	28	such	such	DET
ma-170	324	29	that	that	DET
ma-170	324	30	w0(δ6	w0(δ6	PROPN
ma-170	324	31	,	,	PUNCT
ma-170	324	32	δ7	δ7	NOUN
ma-170	324	33	)	)	PUNCT
ma-170	324	34	<	<	X
ma-170	325	1	1	1	X
ma-170	325	2	.	.	PUNCT
ma-170	325	3	let	let	VERB
ma-170	325	4	b3	b3	PROPN
ma-170	325	5	=	=	SYM
ma-170	325	6	b[x0	b[x0	ADV
ma-170	325	7	,	,	PUNCT
ma-170	325	8	δ7	δ7	NOUN
ma-170	325	9	]	]	PUNCT
ma-170	325	10	∩ω	∩ω	PROPN
ma-170	325	11	.	.	PUNCT
ma-170	326	1	then	then	ADV
ma-170	326	2	,	,	PUNCT
ma-170	326	3	the	the	DET
ma-170	326	4	point	point	NOUN
ma-170	326	5	d	d	NOUN
ma-170	326	6	is	be	AUX
ma-170	326	7	the	the	DET
ma-170	326	8	only	only	ADJ
ma-170	326	9	solution	solution	NOUN
ma-170	326	10	of	of	ADP
ma-170	326	11	the	the	DET
ma-170	326	12	equation	equation	NOUN
ma-170	326	13	f	f	X
ma-170	326	14	(	(	PUNCT
ma-170	326	15	x	x	X
ma-170	326	16	)	)	PUNCT
ma-170	326	17	=	=	SYM
ma-170	326	18	0	0	NUM
ma-170	326	19	in	in	ADP
ma-170	326	20	the	the	DET
ma-170	326	21	set	set	NOUN
ma-170	326	22	b3	b3	PROPN
ma-170	326	23	.	.	PUNCT
ma-170	327	1	proof	proof	NOUN
ma-170	327	2	.	.	PUNCT
ma-170	328	1	let	let	VERB
ma-170	328	2	d1	d1	PROPN
ma-170	328	3	∈	∈	PROPN
ma-170	328	4	b3	b3	PROPN
ma-170	328	5	be	be	VERB
ma-170	328	6	such	such	ADJ
ma-170	328	7	that	that	SCONJ
ma-170	328	8	f	f	PROPN
ma-170	328	9	(	(	PUNCT
ma-170	328	10	d1	d1	PROPN
ma-170	328	11	)	)	PUNCT
ma-170	328	12	=	=	SYM
ma-170	328	13	0	0	X
ma-170	328	14	.	.	PUNCT
ma-170	328	15	define	define	VERB
ma-170	328	16	the	the	DET
ma-170	328	17	divided	divide	VERB
ma-170	328	18	difference	difference	NOUN
ma-170	328	19	[	[	X
ma-170	328	20	d	d	X
ma-170	328	21	,	,	PUNCT
ma-170	328	22	d1;f	d1;f	PROPN
ma-170	328	23	]	]	PUNCT
ma-170	328	24	.	.	PUNCT
ma-170	329	1	then	then	ADV
ma-170	329	2	,	,	PUNCT
ma-170	329	3	‖l−1([d	‖l−1([d	VERB
ma-170	329	4	,	,	PUNCT
ma-170	329	5	d1;f	d1;f	PROPN
ma-170	329	6	]	]	SYM
ma-170	329	7	−	−	PROPN
ma-170	329	8	l)‖	l)‖	NOUN
ma-170	329	9	≤	≤	PUNCT
ma-170	330	1	w0(‖d	w0(‖d	PROPN
ma-170	330	2	−	−	PROPN
ma-170	330	3	x0‖	x0‖	PROPN
ma-170	330	4	,	,	PUNCT
ma-170	330	5	‖d1	‖d1	PROPN
ma-170	330	6	−	−	PROPN
ma-170	330	7	x0‖	x0‖	PROPN
ma-170	330	8	)	)	PUNCT
ma-170	330	9	≤	≤	NOUN
ma-170	331	1	w0(δ6	w0(δ6	PROPN
ma-170	331	2	,	,	PUNCT
ma-170	331	3	δ7	δ7	NOUN
ma-170	331	4	)	)	PUNCT
ma-170	331	5	<	<	X
ma-170	331	6	1	1	NUM
ma-170	331	7	,	,	PUNCT
ma-170	331	8	thus	thus	ADV
ma-170	331	9	d1	d1	PROPN
ma-170	331	10	=	=	SYM
ma-170	331	11	d.	d.	PROPN
ma-170	331	12	�	�	PROPN
ma-170	331	13	remark	remark	VERB
ma-170	331	14	3.5	3.5	NUM
ma-170	331	15	if	if	SCONJ
ma-170	331	16	all	all	DET
ma-170	331	17	the	the	DET
ma-170	331	18	conditions	condition	NOUN
ma-170	331	19	(	(	PUNCT
ma-170	331	20	c1)−	c1)−	NOUN
ma-170	331	21	(	(	PUNCT
ma-170	331	22	c6	c6	PROPN
ma-170	331	23	)	)	PUNCT
ma-170	331	24	hold	hold	VERB
ma-170	331	25	,	,	PUNCT
ma-170	331	26	then	then	ADV
ma-170	331	27	set	set	VERB
ma-170	331	28	d	d	PROPN
ma-170	331	29	=	=	PUNCT
ma-170	331	30	x∗	x∗	PROPN
ma-170	331	31	and	and	CCONJ
ma-170	331	32	δ6	δ6	NOUN
ma-170	331	33	=	=	SYM
ma-170	331	34	a∗.	a∗.	NOUN
ma-170	332	1	4	4	NUM
ma-170	332	2	.	.	PUNCT
ma-170	332	3	numerical	numerical	ADJ
ma-170	332	4	tests	test	NOUN
ma-170	332	5	in	in	ADP
ma-170	332	6	order	order	NOUN
ma-170	332	7	to	to	PART
ma-170	332	8	validate	validate	VERB
ma-170	332	9	the	the	DET
ma-170	332	10	theoretical	theoretical	ADJ
ma-170	332	11	deductions	deduction	NOUN
ma-170	332	12	,	,	PUNCT
ma-170	332	13	we	we	PRON
ma-170	332	14	take	take	VERB
ma-170	332	15	into	into	ADP
ma-170	332	16	account	account	NOUN
ma-170	332	17	the	the	DET
ma-170	332	18	following	follow	VERB
ma-170	332	19	numericalexamples	numericalexample	NOUN
ma-170	332	20	to	to	PART
ma-170	332	21	estimate	estimate	VERB
ma-170	332	22	the	the	DET
ma-170	332	23	real	real	ADJ
ma-170	332	24	parameters	parameter	NOUN
ma-170	332	25	defined	define	VERB
ma-170	332	26	in	in	ADP
ma-170	332	27	the	the	DET
ma-170	332	28	preceding	precede	VERB
ma-170	332	29	sections	section	NOUN
ma-170	332	30	:	:	PUNCT
ma-170	332	31	example	example	NOUN
ma-170	333	1	1	1	X
ma-170	333	2	.	.	PUNCT
ma-170	333	3	let	let	VERB
ma-170	333	4	z	z	NOUN
ma-170	333	5	=	=	PUNCT
ma-170	333	6	r×	r×	NOUN
ma-170	333	7	r×	r×	NOUN
ma-170	333	8	r	r	NOUN
ma-170	333	9	and	and	CCONJ
ma-170	333	10	ω	ω	NUM
ma-170	333	11	=	=	SYM
ma-170	333	12	b(ξ∗	b(ξ∗	NOUN
ma-170	333	13	,	,	PUNCT
ma-170	333	14	1	1	NUM
ma-170	333	15	)	)	PUNCT
ma-170	333	16	with	with	ADP
ma-170	333	17	ξ∗	ξ∗	NOUN
ma-170	333	18	=	=	SYM
ma-170	333	19	(	(	PUNCT
ma-170	333	20	0	0	NUM
ma-170	333	21	,	,	PUNCT
ma-170	333	22	0	0	NUM
ma-170	333	23	,	,	PUNCT
ma-170	333	24	0)t	0)t	INTJ
ma-170	333	25	.	.	PUNCT
ma-170	334	1	define	define	VERB
ma-170	334	2	the	the	DET
ma-170	334	3	mapping	mapping	NOUN
ma-170	334	4	f	f	NOUN
ma-170	334	5	for	for	ADP
ma-170	334	6	ξ	ξ	PROPN
ma-170	334	7	=	=	SYM
ma-170	334	8	(	(	PUNCT
ma-170	334	9	ξ1	ξ1	PROPN
ma-170	334	10	,	,	PUNCT
ma-170	334	11	ξ2	ξ2	ADJ
ma-170	334	12	,	,	PUNCT
ma-170	334	13	ξ3	ξ3	NOUN
ma-170	334	14	)	)	PUNCT
ma-170	334	15	t	t	NOUN
ma-170	334	16	,	,	PUNCT
ma-170	334	17	ξi	ξi	NOUN
ma-170	334	18	∈	∈	NOUN
ma-170	334	19	r	r	NOUN
ma-170	334	20	by	by	ADP
ma-170	334	21	f	f	PROPN
ma-170	334	22	(	(	PUNCT
ma-170	334	23	ξ	ξ	PROPN
ma-170	334	24	)	)	PUNCT
ma-170	334	25	=	=	SYM
ma-170	334	26	(	(	PUNCT
ma-170	334	27	ξ1	ξ1	NOUN
ma-170	334	28	,	,	PUNCT
ma-170	334	29	e	e	X
ma-170	334	30	ξ2	ξ2	NOUN
ma-170	334	31	−	−	PROPN
ma-170	334	32	1	1	NUM
ma-170	334	33	,	,	PUNCT
ma-170	334	34	(	(	PUNCT
ma-170	334	35	e	e	NOUN
ma-170	334	36	−	−	PROPN
ma-170	334	37	1	1	NUM
ma-170	334	38	)	)	SYM
ma-170	334	39	2	2	NUM
ma-170	334	40	ξ23	ξ23	NOUN
ma-170	334	41	+	+	CCONJ
ma-170	334	42	ξ3	ξ3	NOUN
ma-170	334	43	)	)	PUNCT
ma-170	334	44	t	t	PROPN
ma-170	334	45	.	.	PUNCT
ma-170	335	1	this	this	DET
ma-170	335	2	definition	definition	NOUN
ma-170	335	3	gives	give	VERB
ma-170	335	4	that	that	SCONJ
ma-170	335	5	the	the	DET
ma-170	335	6	f	f	NOUN
ma-170	335	7	′	′	NOUN
ma-170	335	8	of	of	ADP
ma-170	335	9	the	the	DET
ma-170	335	10	mapping	mapping	NOUN
ma-170	335	11	f	f	X
ma-170	335	12	is	be	AUX
ma-170	335	13	the	the	DET
ma-170	335	14	jacobian	jacobian	ADJ
ma-170	335	15	matrix	matrix	NOUN
ma-170	335	16	f	f	PROPN
ma-170	335	17	′(ξ	′(ξ	PROPN
ma-170	335	18	)	)	PUNCT
ma-170	335	19	=	=	SYM
ma-170	336	1	1	1	PROPN
ma-170	336	2	0	0	NUM
ma-170	336	3	0	0	NUM
ma-170	336	4	0	0	NUM
ma-170	337	1	eξ2	eξ2	NOUN
ma-170	337	2	0	0	NUM
ma-170	337	3	0	0	NUM
ma-170	337	4	0	0	NUM
ma-170	338	1	(	(	PUNCT
ma-170	338	2	e	e	X
ma-170	338	3	−	−	PROPN
ma-170	338	4	1)ξ3	1)ξ3	PROPN
ma-170	338	5	+	+	CCONJ
ma-170	338	6	1	1	NUM
ma-170	338	7			NOUN
ma-170	338	8	.	.	PUNCT
ma-170	339	1	notice	notice	VERB
ma-170	339	2	that	that	SCONJ
ma-170	340	1	f	f	PROPN
ma-170	340	2	(	(	PUNCT
ma-170	340	3	ξ∗	ξ∗	ADJ
ma-170	340	4	)	)	PUNCT
ma-170	340	5	=	=	SYM
ma-170	340	6	o	o	PROPN
ma-170	340	7	and	and	CCONJ
ma-170	340	8	f	f	PROPN
ma-170	340	9	′(ξ∗	′(ξ∗	NOUN
ma-170	340	10	)	)	PUNCT
ma-170	341	1	=	=	SYM
ma-170	341	2	i.	i.	NOUN
ma-170	341	3	then	then	ADV
ma-170	341	4	,	,	PUNCT
ma-170	341	5	the	the	DET
ma-170	341	6	conditions	condition	NOUN
ma-170	341	7	(	(	PUNCT
ma-170	341	8	h1)−	h1)−	PROPN
ma-170	341	9	(	(	PUNCT
ma-170	341	10	h4	h4	PROPN
ma-170	341	11	)	)	PUNCT
ma-170	341	12	are	be	AUX
ma-170	341	13	validated	validate	VERB
ma-170	341	14	if	if	SCONJ
ma-170	341	15	w0(t1	w0(t1	NOUN
ma-170	341	16	,	,	PUNCT
ma-170	341	17	t2	t2	NOUN
ma-170	341	18	)	)	PUNCT
ma-170	341	19	=	=	SYM
ma-170	341	20	1	1	NUM
ma-170	341	21	2	2	NUM
ma-170	341	22	(	(	PUNCT
ma-170	341	23	e	e	NOUN
ma-170	341	24	−	−	PROPN
ma-170	341	25	1)(t1	1)(t1	NUM
ma-170	341	26	+	+	CCONJ
ma-170	341	27	t2	t2	NOUN
ma-170	341	28	)	)	PUNCT
ma-170	341	29	,	,	PUNCT
ma-170	341	30	w(t	w(t	PROPN
ma-170	341	31	)	)	PUNCT
ma-170	341	32	=	=	SYM
ma-170	341	33	1	1	NUM
ma-170	341	34	2	2	NUM
ma-170	341	35	(	(	PUNCT
ma-170	341	36	e	e	NOUN
ma-170	341	37	−	−	PROPN
ma-170	341	38	1)t	1)t	PROPN
ma-170	341	39	,	,	PUNCT
ma-170	341	40	w1(t1	w1(t1	NOUN
ma-170	341	41	,	,	PUNCT
ma-170	341	42	t2	t2	NOUN
ma-170	341	43	,	,	PUNCT
ma-170	341	44	t3	t3	PROPN
ma-170	341	45	)	)	PUNCT
ma-170	341	46	=	=	SYM
ma-170	341	47	1	1	NUM
ma-170	341	48	2	2	NUM
ma-170	341	49	(	(	PUNCT
ma-170	341	50	e	e	NOUN
ma-170	341	51	−	−	PROPN
ma-170	341	52	1)(t1	1)(t1	NUM
ma-170	342	1	+	+	CCONJ
ma-170	342	2	t2	t2	PROPN
ma-170	342	3	+	+	CCONJ
ma-170	342	4	t3	t3	PROPN
ma-170	342	5	)	)	PUNCT
ma-170	342	6	,	,	PUNCT
ma-170	342	7	w2(t1	w2(t1	NOUN
ma-170	342	8	,	,	PUNCT
ma-170	342	9	t2	t2	NOUN
ma-170	342	10	,	,	PUNCT
ma-170	342	11	t3	t3	PROPN
ma-170	342	12	,	,	PUNCT
ma-170	342	13	t4	t4	PROPN
ma-170	342	14	)	)	PUNCT
ma-170	342	15	=	=	SYM
ma-170	342	16	1	1	NUM
ma-170	342	17	2	2	NUM
ma-170	342	18	(	(	PUNCT
ma-170	342	19	e	e	NOUN
ma-170	342	20	−	−	PROPN
ma-170	342	21	1)(t1	1)(t1	NUM
ma-170	343	1	+	+	CCONJ
ma-170	343	2	t2	t2	PROPN
ma-170	343	3	+	+	CCONJ
ma-170	343	4	t3	t3	PROPN
ma-170	343	5	+	+	CCONJ
ma-170	343	6	t4	t4	PROPN
ma-170	343	7	)	)	PUNCT
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ma-170	343	9	eur	eur	PROPN
ma-170	343	10	.	.	PUNCT
ma-170	344	1	j.	j.	PROPN
ma-170	344	2	math	math	PROPN
ma-170	344	3	.	.	PUNCT
ma-170	345	1	anal	anal	PROPN
ma-170	345	2	.	.	PUNCT
ma-170	346	1	10.28924	10.28924	NUM
ma-170	346	2	/	/	SYM
ma-170	346	3	ada	ada	PROPN
ma-170	346	4	/	/	SYM
ma-170	346	5	ma.3.24	ma.3.24	PROPN
ma-170	346	6	12and	12and	NOUN
ma-170	346	7	the	the	DET
ma-170	346	8	functions	function	NOUN
ma-170	346	9	f1	f1	NOUN
ma-170	346	10	and	and	CCONJ
ma-170	346	11	f2	f2	PROPN
ma-170	346	12	are	be	AUX
ma-170	346	13	given	give	VERB
ma-170	346	14	in	in	ADP
ma-170	346	15	remark	remark	NOUN
ma-170	346	16	2.2	2.2	NUM
ma-170	346	17	.	.	PUNCT
ma-170	347	1	then	then	ADV
ma-170	347	2	,	,	PUNCT
ma-170	347	3	the	the	DET
ma-170	347	4	radius	radius	NOUN
ma-170	347	5	δ∗	δ∗	NOUN
ma-170	347	6	using	use	VERB
ma-170	347	7	(	(	PUNCT
ma-170	347	8	2.5	2.5	NUM
ma-170	347	9	)	)	PUNCT
ma-170	347	10	is	be	AUX
ma-170	347	11	δ1	δ1	NOUN
ma-170	347	12	=	=	SYM
ma-170	347	13	0.20415	0.20415	NUM
ma-170	347	14	,	,	PUNCT
ma-170	347	15	δ2	δ2	VERB
ma-170	347	16	=	=	SYM
ma-170	347	17	0.13109	0.13109	NUM
ma-170	347	18	,	,	PUNCT
ma-170	347	19	δ3	δ3	PROPN
ma-170	347	20	=	=	PROPN
ma-170	347	21	0.11960	0.11960	NUM
ma-170	347	22	and	and	CCONJ
ma-170	347	23	δ∗	δ∗	NOUN
ma-170	347	24	=	=	SYM
ma-170	347	25	0.11960	0.11960	NUM
ma-170	347	26	.	.	PUNCT
ma-170	348	1	figure	figure	NOUN
ma-170	348	2	1	1	NUM
ma-170	348	3	.	.	PUNCT
ma-170	349	1	graph	graph	NOUN
ma-170	349	2	of	of	ADP
ma-170	349	3	radius	radius	NOUN
ma-170	349	4	of	of	ADP
ma-170	349	5	convergence	convergence	NOUN
ma-170	349	6	of	of	ADP
ma-170	349	7	example	example	NOUN
ma-170	349	8	1	1	NUM
ma-170	349	9	.	.	PUNCT
ma-170	350	1	∆1	∆1	PROPN
ma-170	350	2	∆2	∆2	PROPN
ma-170	350	3	∆3	∆3	PROPN
ma-170	350	4	-0.2	-0.2	PROPN
ma-170	350	5	-0.1	-0.1	PROPN
ma-170	350	6	0.0	0.0	NUM
ma-170	350	7	0.1	0.1	NUM
ma-170	350	8	0.2	0.2	NUM
ma-170	350	9	-1.0	-1.0	PROPN
ma-170	350	10	-0.5	-0.5	X
ma-170	350	11	0.0	0.0	NUM
ma-170	350	12	0.5	0.5	NUM
ma-170	350	13	1.0	1.0	NUM
ma-170	350	14	1.5	1.5	NUM
ma-170	350	15	2.0	2.0	NUM
ma-170	350	16	t	t	NOUN
ma-170	351	1	h	h	NOUN
ma-170	352	1	i	i	PRON
ma-170	352	2	t	t	NOUN
ma-170	353	1	h	h	NOUN
ma-170	354	1	i	i	PRON
ma-170	354	2	h1	h1	VERB
ma-170	354	3	h2	h2	NOUN
ma-170	354	4	h3	h3	NOUN
ma-170	354	5	example	example	NOUN
ma-170	354	6	2	2	X
ma-170	354	7	.	.	PUNCT
ma-170	355	1	let	let	VERB
ma-170	355	2	z	z	NOUN
ma-170	355	3	=	=	SYM
ma-170	355	4	c[0	c[0	PROPN
ma-170	355	5	,	,	PUNCT
ma-170	355	6	1	1	NUM
ma-170	355	7	]	]	PUNCT
ma-170	355	8	be	be	AUX
ma-170	355	9	the	the	DET
ma-170	355	10	space	space	NOUN
ma-170	355	11	of	of	ADP
ma-170	355	12	continuous	continuous	ADJ
ma-170	355	13	functions	function	NOUN
ma-170	355	14	defined	define	VERB
ma-170	355	15	in	in	ADP
ma-170	355	16	[	[	X
ma-170	355	17	0	0	NUM
ma-170	355	18	,	,	PUNCT
ma-170	355	19	1	1	NUM
ma-170	355	20	]	]	PUNCT
ma-170	355	21	and	and	CCONJ
ma-170	355	22	ω	ω	NUM
ma-170	355	23	=	=	SYM
ma-170	355	24	b̄(l∗	b̄(l∗	NOUN
ma-170	355	25	,	,	PUNCT
ma-170	355	26	1).consider	1).consider	NUM
ma-170	355	27	the	the	DET
ma-170	355	28	integral	integral	ADJ
ma-170	355	29	equation	equation	NOUN
ma-170	355	30	of	of	ADP
ma-170	355	31	the	the	DET
ma-170	355	32	mixed	mixed	ADJ
ma-170	355	33	hammerstein	hammerstein	NOUN
ma-170	355	34	-	-	PUNCT
ma-170	355	35	type	type	NOUN
ma-170	355	36	[	[	X
ma-170	355	37	6	6	NUM
ma-170	355	38	,	,	PUNCT
ma-170	355	39	12	12	NUM
ma-170	355	40	]	]	PUNCT
ma-170	355	41	by	by	ADP
ma-170	355	42	l(d	l(d	PROPN
ma-170	355	43	)	)	PUNCT
ma-170	356	1	=	=	SYM
ma-170	356	2	∫	∫	PROPN
ma-170	356	3	1	1	NUM
ma-170	356	4	0	0	NUM
ma-170	356	5	t	t	PROPN
ma-170	356	6	(	(	PUNCT
ma-170	356	7	d	d	PROPN
ma-170	356	8	,	,	PUNCT
ma-170	356	9	ω	ω	NOUN
ma-170	356	10	)	)	PUNCT
ma-170	356	11	(	(	PUNCT
ma-170	356	12	l(ω)3/2	l(ω)3/2	PROPN
ma-170	357	1	+	+	CCONJ
ma-170	357	2	l(ω)2	l(ω)2	PROPN
ma-170	357	3	2	2	NUM
ma-170	357	4	)	)	PUNCT
ma-170	357	5	dω	dω	ADP
ma-170	357	6	,	,	PUNCT
ma-170	357	7	(	(	PUNCT
ma-170	357	8	4.34	4.34	NUM
ma-170	357	9	)	)	PUNCT
ma-170	357	10	t	t	NOUN
ma-170	357	11	(	(	PUNCT
ma-170	357	12	d	d	PROPN
ma-170	357	13	,	,	PUNCT
ma-170	357	14	ω	ω	NOUN
ma-170	357	15	)	)	PUNCT
ma-170	357	16	=	=	PRON
ma-170	357	17	{	{	PUNCT
ma-170	357	18	(	(	PUNCT
ma-170	357	19	1−	1−	NUM
ma-170	357	20	d)ω	d)ω	NOUN
ma-170	357	21	,	,	PUNCT
ma-170	357	22	ω	ω	PROPN
ma-170	357	23	≤	≤	NUM
ma-170	357	24	d	d	PROPN
ma-170	357	25	,	,	PUNCT
ma-170	357	26	d(1−	d(1−	PROPN
ma-170	357	27	ω	ω	PROPN
ma-170	357	28	)	)	PUNCT
ma-170	357	29	,	,	PUNCT
ma-170	357	30	d	d	X
ma-170	357	31	≤	≤	ADJ
ma-170	357	32	ω.notice	ω.notice	NOUN
ma-170	357	33	that	that	PRON
ma-170	357	34	l∗(d	l∗(d	PROPN
ma-170	357	35	)	)	PUNCT
ma-170	357	36	=	=	SYM
ma-170	357	37	0	0	X
ma-170	357	38	.	.	X
ma-170	357	39	define	define	VERB
ma-170	357	40	h	h	NOUN
ma-170	357	41	:	:	PUNCT
ma-170	357	42	ω	ω	NUM
ma-170	357	43	⊆	⊆	NUM
ma-170	357	44	[	[	X
ma-170	357	45	0	0	NUM
ma-170	357	46	,	,	PUNCT
ma-170	357	47	1]→	1]→	ADJ
ma-170	357	48	c[0	c[0	PROPN
ma-170	357	49	,	,	PUNCT
ma-170	357	50	1	1	NUM
ma-170	357	51	]	]	PUNCT
ma-170	357	52	as	as	ADP
ma-170	357	53	h(l)(d	h(l)(d	NOUN
ma-170	357	54	)	)	PUNCT
ma-170	357	55	=	=	PUNCT
ma-170	358	1	l(d)−	l(d)−	PROPN
ma-170	358	2	∫	∫	PROPN
ma-170	358	3	1	1	NUM
ma-170	358	4	0	0	NUM
ma-170	358	5	t	t	PROPN
ma-170	358	6	(	(	PUNCT
ma-170	358	7	d	d	PROPN
ma-170	358	8	,	,	PUNCT
ma-170	358	9	ω	ω	NOUN
ma-170	358	10	)	)	PUNCT
ma-170	358	11	(	(	PUNCT
ma-170	358	12	l(ω)3/2	l(ω)3/2	PROPN
ma-170	359	1	+	+	CCONJ
ma-170	359	2	l(ω)2	l(ω)2	PROPN
ma-170	359	3	2	2	NUM
ma-170	359	4	)	)	PUNCT
ma-170	359	5	dω	dω	ADV
ma-170	359	6	.	.	PUNCT
ma-170	360	1	the	the	DET
ma-170	360	2	derivative	derivative	ADJ
ma-170	360	3	h′	h′	NOUN
ma-170	360	4	is	be	AUX
ma-170	360	5	given	give	VERB
ma-170	360	6	by	by	ADP
ma-170	360	7	h′(l)q(d	h′(l)q(d	PROPN
ma-170	360	8	)	)	PUNCT
ma-170	360	9	=	=	VERB
ma-170	361	1	q(d)−	q(d)−	PROPN
ma-170	361	2	∫	∫	PROPN
ma-170	361	3	1	1	NUM
ma-170	361	4	0	0	NUM
ma-170	361	5	t	t	PROPN
ma-170	361	6	(	(	PUNCT
ma-170	361	7	d	d	PROPN
ma-170	361	8	,	,	PUNCT
ma-170	361	9	ω	ω	NOUN
ma-170	361	10	)	)	PUNCT
ma-170	361	11	(	(	PUNCT
ma-170	361	12	3	3	NUM
ma-170	361	13	2	2	NUM
ma-170	361	14	l(ω)1/2	l(ω)1/2	NUM
ma-170	361	15	+	+	CCONJ
ma-170	361	16	l(ω	l(ω	PROPN
ma-170	361	17	)	)	PUNCT
ma-170	361	18	)	)	PUNCT
ma-170	362	1	dω	dω	ADP
ma-170	362	2	,	,	PUNCT
ma-170	362	3	since	since	SCONJ
ma-170	362	4	h′(l∗(d	h′(l∗(d	NOUN
ma-170	362	5	)	)	PUNCT
ma-170	362	6	)	)	PUNCT
ma-170	363	1	=	=	SYM
ma-170	363	2	1	1	X
ma-170	363	3	,	,	PUNCT
ma-170	363	4	it	it	PRON
ma-170	363	5	follows	follow	VERB
ma-170	363	6	‖h′(α)−1(h′(l)−h′(q))‖	‖h′(α)−1(h′(l)−h′(q))‖	VERB
ma-170	363	7	≤	≤	NUM
ma-170	363	8	5	5	NUM
ma-170	363	9	16	16	NUM
ma-170	363	10	‖l	‖l	NOUN
ma-170	363	11	−	−	NOUN
ma-170	363	12	q‖.	q‖.	NOUN
ma-170	363	13	(	(	PUNCT
ma-170	363	14	4.35	4.35	NUM
ma-170	363	15	)	)	PUNCT
ma-170	363	16	in	in	ADP
ma-170	363	17	(	(	PUNCT
ma-170	363	18	4.35	4.35	NUM
ma-170	363	19	)	)	PUNCT
ma-170	363	20	,	,	PUNCT
ma-170	363	21	switch	switch	VERB
ma-170	363	22	q	q	NOUN
ma-170	363	23	by	by	ADP
ma-170	363	24	l0	l0	PROPN
ma-170	363	25	‖h′(α)−1(h′(l)−h′(l0))‖	‖h′(α)−1(h′(l)−h′(l0))‖	ADJ
ma-170	363	26	≤	≤	NUM
ma-170	363	27	5	5	NUM
ma-170	363	28	16	16	NUM
ma-170	363	29	‖l	‖l	NOUN
ma-170	363	30	−	−	PROPN
ma-170	364	1	l0‖.thus	l0‖.thus	PROPN
ma-170	364	2	,	,	PUNCT
ma-170	364	3	we	we	PRON
ma-170	364	4	take	take	VERB
ma-170	364	5	w0(t1	w0(t1	NOUN
ma-170	364	6	,	,	PUNCT
ma-170	364	7	t2	t2	NOUN
ma-170	364	8	)	)	PUNCT
ma-170	365	1	=	=	SYM
ma-170	366	1	t1	t1	NOUN
ma-170	366	2	+	+	NUM
ma-170	366	3	t2	t2	NOUN
ma-170	366	4	,	,	PUNCT
ma-170	366	5	w(t	w(t	PROPN
ma-170	366	6	)	)	PUNCT
ma-170	366	7	=	=	SYM
ma-170	366	8	t	t	PROPN
ma-170	366	9	,	,	PUNCT
ma-170	366	10	w1(t1	w1(t1	NOUN
ma-170	366	11	,	,	PUNCT
ma-170	366	12	t2	t2	NOUN
ma-170	366	13	,	,	PUNCT
ma-170	366	14	t3	t3	PROPN
ma-170	366	15	)	)	PUNCT
ma-170	366	16	=	=	PUNCT
ma-170	367	1	t1	t1	NOUN
ma-170	367	2	+	+	NUM
ma-170	367	3	t2	t2	PROPN
ma-170	367	4	+	+	CCONJ
ma-170	367	5	t3	t3	PROPN
ma-170	367	6	,	,	PUNCT
ma-170	367	7	w2(t1	w2(t1	NOUN
ma-170	367	8	,	,	PUNCT
ma-170	367	9	t2	t2	NOUN
ma-170	367	10	,	,	PUNCT
ma-170	367	11	t3	t3	PROPN
ma-170	367	12	,	,	PUNCT
ma-170	367	13	t4	t4	PROPN
ma-170	367	14	)	)	PUNCT
ma-170	367	15	=	=	PUNCT
ma-170	367	16	5	5	X
ma-170	367	17	.	.	NOUN
ma-170	367	18	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	PROPN
ma-170	367	19	eur	eur	PROPN
ma-170	367	20	.	.	PUNCT
ma-170	368	1	j.	j.	PROPN
ma-170	368	2	math	math	PROPN
ma-170	368	3	.	.	PUNCT
ma-170	369	1	anal	anal	PROPN
ma-170	369	2	.	.	PUNCT
ma-170	370	1	10.28924	10.28924	NUM
ma-170	370	2	/	/	SYM
ma-170	370	3	ada	ada	PROPN
ma-170	370	4	/	/	SYM
ma-170	370	5	ma.3.24	ma.3.24	PROPN
ma-170	370	6	13hence	13hence	NUM
ma-170	370	7	,	,	PUNCT
ma-170	370	8	we	we	PRON
ma-170	370	9	obtain	obtain	VERB
ma-170	370	10	δ1	δ1	NOUN
ma-170	370	11	=	=	SYM
ma-170	370	12	0.17539	0.17539	NUM
ma-170	370	13	,	,	PUNCT
ma-170	370	14	δ2	δ2	VERB
ma-170	370	15	=	=	ADJ
ma-170	370	16	0.02678	0.02678	NUM
ma-170	370	17	,	,	PUNCT
ma-170	370	18	δ3	δ3	PROPN
ma-170	370	19	=	=	NOUN
ma-170	370	20	0.90819×	0.90819×	NUM
ma-170	370	21	10−3	10−3	NUM
ma-170	370	22	and	and	CCONJ
ma-170	370	23	δ∗	δ∗	NOUN
ma-170	370	24	=	=	SYM
ma-170	370	25	0.90819×	0.90819×	NUM
ma-170	370	26	10−3	10−3	NUM
ma-170	370	27	.	.	PUNCT
ma-170	371	1	figure	figure	NOUN
ma-170	371	2	2	2	NUM
ma-170	371	3	.	.	PUNCT
ma-170	371	4	graph	graph	NOUN
ma-170	371	5	of	of	ADP
ma-170	371	6	radius	radius	NOUN
ma-170	371	7	of	of	ADP
ma-170	371	8	convergence	convergence	NOUN
ma-170	371	9	of	of	ADP
ma-170	371	10	example	example	NOUN
ma-170	371	11	2	2	NUM
ma-170	371	12	.	.	PUNCT
ma-170	372	1	∆1	∆1	PROPN
ma-170	372	2	∆2	∆2	PROPN
ma-170	372	3	∆3	∆3	PROPN
ma-170	372	4	-0.6	-0.6	PROPN
ma-170	372	5	-0.4	-0.4	X
ma-170	372	6	-0.2	-0.2	PROPN
ma-170	372	7	0.0	0.0	NUM
ma-170	372	8	0.2	0.2	NUM
ma-170	372	9	-20	-20	NUM
ma-170	372	10	0	0	NUM
ma-170	372	11	20	20	NUM
ma-170	372	12	40	40	NUM
ma-170	372	13	60	60	NUM
ma-170	372	14	80	80	NUM
ma-170	372	15	t	t	NOUN
ma-170	372	16	h	h	NOUN
ma-170	373	1	i	i	PRON
ma-170	373	2	t	t	NOUN
ma-170	374	1	h	h	NOUN
ma-170	375	1	i	i	PRON
ma-170	375	2	h1	h1	VERB
ma-170	375	3	h2	h2	NOUN
ma-170	375	4	h3	h3	NOUN
ma-170	375	5	example	example	NOUN
ma-170	375	6	3	3	X
ma-170	375	7	.	.	PUNCT
ma-170	376	1	let	let	VERB
ma-170	376	2	z	z	NOUN
ma-170	376	3	=	=	SYM
ma-170	376	4	c[0	c[0	PROPN
ma-170	376	5	,	,	PUNCT
ma-170	376	6	1	1	NUM
ma-170	376	7	]	]	PUNCT
ma-170	376	8	be	be	AUX
ma-170	376	9	the	the	DET
ma-170	376	10	space	space	NOUN
ma-170	376	11	of	of	ADP
ma-170	376	12	continuous	continuous	ADJ
ma-170	376	13	functions	function	NOUN
ma-170	376	14	[	[	X
ma-170	376	15	12	12	NUM
ma-170	376	16	]	]	PUNCT
ma-170	376	17	defined	define	VERB
ma-170	376	18	on	on	ADP
ma-170	376	19	the	the	DET
ma-170	376	20	interval	interval	NOUN
ma-170	376	21	[	[	X
ma-170	376	22	0	0	NUM
ma-170	376	23	,	,	PUNCT
ma-170	376	24	1]and	1]and	PROPN
ma-170	376	25	ω	ω	NUM
ma-170	376	26	=	=	SYM
ma-170	376	27	b̄(0	b̄(0	PROPN
ma-170	376	28	,	,	PUNCT
ma-170	376	29	1	1	NUM
ma-170	376	30	)	)	PUNCT
ma-170	376	31	.	.	PUNCT
ma-170	377	1	define	define	VERB
ma-170	377	2	the	the	DET
ma-170	377	3	function	function	NOUN
ma-170	377	4	h	h	NOUN
ma-170	377	5	on	on	ADP
ma-170	377	6	ω	ω	NUM
ma-170	377	7	by	by	ADP
ma-170	377	8	h(ϕ)(l	h(ϕ)(l	NUM
ma-170	377	9	)	)	PUNCT
ma-170	378	1	=	=	PUNCT
ma-170	378	2	ϕ(l)−	ϕ(l)−	PROPN
ma-170	378	3	10	10	NUM
ma-170	378	4	∫	∫	NOUN
ma-170	378	5	1	1	NUM
ma-170	378	6	0	0	NUM
ma-170	379	1	lρϕ(ρ)3dρ	lρϕ(ρ)3dρ	ADJ
ma-170	379	2	.	.	PUNCT
ma-170	380	1	it	it	PRON
ma-170	380	2	follows	follow	VERB
ma-170	380	3	that	that	PRON
ma-170	380	4	h′(ϕ(ξ))(l	h′(ϕ(ξ))(l	NOUN
ma-170	380	5	)	)	PUNCT
ma-170	380	6	=	=	SYM
ma-170	380	7	ξ(l)−	ξ(l)−	PROPN
ma-170	380	8	30	30	NUM
ma-170	380	9	∫	∫	NOUN
ma-170	380	10	1	1	NUM
ma-170	380	11	0	0	NUM
ma-170	380	12	lρϕ(ρ)2ξ(ρ)dρ	lρϕ(ρ)2ξ(ρ)dρ	PROPN
ma-170	380	13	,	,	PUNCT
ma-170	380	14	for	for	ADP
ma-170	380	15	each	each	DET
ma-170	380	16	ξ	ξ	PROPN
ma-170	380	17	∈	∈	PROPN
ma-170	380	18	ω	ω	PROPN
ma-170	380	19	.	.	PUNCT
ma-170	381	1	since	since	SCONJ
ma-170	381	2	l∗	l∗	PROPN
ma-170	381	3	=	=	SYM
ma-170	381	4	0	0	NUM
ma-170	381	5	,	,	PUNCT
ma-170	381	6	so	so	SCONJ
ma-170	381	7	we	we	PRON
ma-170	381	8	can	can	AUX
ma-170	381	9	set	set	VERB
ma-170	381	10	w0(t1	w0(t1	PROPN
ma-170	381	11	,	,	PUNCT
ma-170	381	12	t2	t2	NOUN
ma-170	381	13	)	)	PUNCT
ma-170	381	14	=	=	SYM
ma-170	382	1	2(t1	2(t1	NUM
ma-170	382	2	+	+	NUM
ma-170	382	3	t2	t2	NOUN
ma-170	382	4	)	)	PUNCT
ma-170	382	5	,	,	PUNCT
ma-170	382	6	w(t	w(t	PROPN
ma-170	382	7	)	)	PUNCT
ma-170	383	1	=	=	SYM
ma-170	383	2	t	t	PROPN
ma-170	383	3	5	5	NUM
ma-170	383	4	,	,	PUNCT
ma-170	383	5	w1(t1	w1(t1	NOUN
ma-170	383	6	,	,	PUNCT
ma-170	383	7	t2	t2	NOUN
ma-170	383	8	,	,	PUNCT
ma-170	383	9	t3	t3	PROPN
ma-170	383	10	)	)	PUNCT
ma-170	384	1	=	=	SYM
ma-170	384	2	2(t1	2(t1	NUM
ma-170	385	1	+	+	NUM
ma-170	385	2	t2	t2	PROPN
ma-170	385	3	+	+	CCONJ
ma-170	385	4	t3	t3	PROPN
ma-170	385	5	)	)	PUNCT
ma-170	385	6	,	,	PUNCT
ma-170	385	7	w2(t1	w2(t1	NOUN
ma-170	385	8	,	,	PUNCT
ma-170	385	9	t2	t2	NOUN
ma-170	385	10	,	,	PUNCT
ma-170	385	11	t3	t3	PROPN
ma-170	385	12	,	,	PUNCT
ma-170	385	13	t4	t4	PROPN
ma-170	385	14	)	)	PUNCT
ma-170	385	15	=	=	SYM
ma-170	386	1	2(t1	2(t1	NUM
ma-170	387	1	+	+	NUM
ma-170	387	2	t2	t2	PROPN
ma-170	387	3	+	+	CCONJ
ma-170	387	4	t3	t3	PROPN
ma-170	387	5	+	+	CCONJ
ma-170	387	6	t4	t4	PROPN
ma-170	387	7	)	)	PUNCT
ma-170	387	8	.	.	PUNCT
ma-170	388	1	hence	hence	ADV
ma-170	388	2	,	,	PUNCT
ma-170	388	3	we	we	PRON
ma-170	388	4	obtain	obtain	VERB
ma-170	388	5	δ1	δ1	NOUN
ma-170	388	6	=	=	SYM
ma-170	388	7	0.98449×	0.98449×	NOUN
ma-170	388	8	10−1	10−1	NUM
ma-170	388	9	,	,	PUNCT
ma-170	388	10	δ2	δ2	VERB
ma-170	388	11	=	=	PUNCT
ma-170	388	12	0.62003×	0.62003×	NUM
ma-170	388	13	10−1	10−1	NUM
ma-170	388	14	,	,	PUNCT
ma-170	388	15	δ3	δ3	PROPN
ma-170	388	16	=	=	SYM
ma-170	388	17	0.55704×	0.55704×	PROPN
ma-170	388	18	10−1	10−1	NUM
ma-170	388	19	and	and	CCONJ
ma-170	388	20	δ∗	δ∗	PROPN
ma-170	388	21	=	=	SYM
ma-170	388	22	0.55704×	0.55704×	PROPN
ma-170	389	1	10−1	10−1	NUM
ma-170	389	2	.	.	PUNCT
ma-170	389	3	example	example	NOUN
ma-170	389	4	4	4	X
ma-170	389	5	.	.	PUNCT
ma-170	390	1	lastly	lastly	ADV
ma-170	390	2	,	,	PUNCT
ma-170	390	3	a	a	DET
ma-170	390	4	nondifferentiable	nondifferentiable	ADJ
ma-170	390	5	nonlinear	nonlinear	ADJ
ma-170	390	6	system	system	NOUN
ma-170	390	7	on	on	ADP
ma-170	390	8	r	r	NOUN
ma-170	390	9	×	×	NOUN
ma-170	390	10	r	r	NOUN
ma-170	390	11	is	be	AUX
ma-170	390	12	solved	solve	VERB
ma-170	390	13	using	use	VERB
ma-170	390	14	the	the	DET
ma-170	390	15	method(1.3	method(1.3	NOUN
ma-170	390	16	)	)	PUNCT
ma-170	390	17	,	,	PUNCT
ma-170	390	18	where	where	SCONJ
ma-170	390	19	the	the	DET
ma-170	390	20	divided	divided	ADJ
ma-170	390	21	difference	difference	NOUN
ma-170	390	22	is	be	AUX
ma-170	390	23	defined	define	VERB
ma-170	390	24	by	by	ADP
ma-170	390	25	the	the	DET
ma-170	390	26	2	2	NUM
ma-170	390	27	×	×	NOUN
ma-170	390	28	2	2	NUM
ma-170	390	29	matrix	matrix	NOUN
ma-170	390	30	given	give	VERB
ma-170	390	31	for	for	ADP
ma-170	390	32	t̄	t̄	NOUN
ma-170	390	33	=	=	SYM
ma-170	390	34	(	(	PUNCT
ma-170	390	35	t1	t1	NOUN
ma-170	390	36	,	,	PUNCT
ma-170	390	37	t2	t2	NOUN
ma-170	390	38	)	)	PUNCT
ma-170	390	39	∈	∈	PROPN
ma-170	390	40	r	r	NOUN
ma-170	390	41	×	×	NOUN
ma-170	390	42	r	r	NOUN
ma-170	390	43	,	,	PUNCT
ma-170	390	44	t̃	t̃	PROPN
ma-170	390	45	=	=	SYM
ma-170	390	46	(	(	PUNCT
ma-170	390	47	t3	t3	PROPN
ma-170	390	48	,	,	PUNCT
ma-170	390	49	t4	t4	PROPN
ma-170	390	50	)	)	PUNCT
ma-170	390	51	∈	∈	PROPN
ma-170	390	52	r×	r×	NOUN
ma-170	390	53	r	r	NOUN
ma-170	390	54	,	,	PUNCT
ma-170	390	55	and	and	CCONJ
ma-170	390	56	f	f	X
ma-170	390	57	=	=	PUNCT
ma-170	390	58	(	(	PUNCT
ma-170	390	59	f1	f1	PROPN
ma-170	390	60	,	,	PUNCT
ma-170	390	61	f2	f2	PROPN
ma-170	390	62	)	)	PUNCT
ma-170	390	63	by	by	ADP
ma-170	390	64	[	[	X
ma-170	390	65	t̄	t̄	NOUN
ma-170	390	66	,	,	PUNCT
ma-170	390	67	t̃;f	t̃;f	ADP
ma-170	390	68	]	]	X
ma-170	390	69	i	i	PRON
ma-170	390	70	,	,	PUNCT
ma-170	390	71	1	1	X
ma-170	390	72	=	=	SYM
ma-170	390	73	fi(t3	fi(t3	PROPN
ma-170	390	74	,	,	PUNCT
ma-170	390	75	t4)−	t4)−	NOUN
ma-170	390	76	fi(s1	fi(s1	NOUN
ma-170	390	77	,	,	PUNCT
ma-170	390	78	s4	s4	PROPN
ma-170	390	79	)	)	PUNCT
ma-170	390	80	t3	t3	PROPN
ma-170	390	81	−	−	PROPN
ma-170	390	82	t1	t1	PROPN
ma-170	390	83	t3	t3	PROPN
ma-170	391	1	6=	6=	PROPN
ma-170	391	2	t1	t1	NOUN
ma-170	391	3	and	and	CCONJ
ma-170	391	4	[	[	X
ma-170	391	5	t̄	t̄	NOUN
ma-170	391	6	,	,	PUNCT
ma-170	391	7	t̃;f	t̃;f	ADP
ma-170	391	8	]	]	X
ma-170	391	9	i	i	PRON
ma-170	391	10	,	,	PUNCT
ma-170	391	11	2	2	NUM
ma-170	391	12	=	=	SYM
ma-170	391	13	fi(s1	fi(s1	NOUN
ma-170	391	14	,	,	PUNCT
ma-170	391	15	s4)−	s4)−	PROPN
ma-170	391	16	fi(s1	fi(s1	NOUN
ma-170	391	17	,	,	PUNCT
ma-170	391	18	s2	s2	PROPN
ma-170	391	19	)	)	PUNCT
ma-170	391	20	s4	s4	PROPN
ma-170	391	21	−	−	PROPN
ma-170	391	22	s2	s2	PROPN
ma-170	391	23	.	.	PUNCT
ma-170	392	1	s4	s4	PROPN
ma-170	392	2	6=	6=	PROPN
ma-170	392	3	s2	s2	PROPN
ma-170	392	4	.	.	PUNCT
ma-170	392	5	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	PROPN
ma-170	392	6	eur	eur	PROPN
ma-170	392	7	.	.	PUNCT
ma-170	393	1	j.	j.	PROPN
ma-170	393	2	math	math	PROPN
ma-170	393	3	.	.	PUNCT
ma-170	394	1	anal	anal	PROPN
ma-170	394	2	.	.	PUNCT
ma-170	395	1	10.28924	10.28924	NUM
ma-170	395	2	/	/	SYM
ma-170	395	3	ada	ada	PROPN
ma-170	395	4	/	/	SYM
ma-170	395	5	ma.3.24	ma.3.24	ADJ
ma-170	395	6	14	14	NUM
ma-170	395	7	figure	figure	NOUN
ma-170	395	8	3	3	NUM
ma-170	395	9	.	.	PUNCT
ma-170	395	10	graph	graph	NOUN
ma-170	395	11	of	of	ADP
ma-170	395	12	radius	radius	NOUN
ma-170	395	13	of	of	ADP
ma-170	395	14	convergence	convergence	NOUN
ma-170	395	15	of	of	ADP
ma-170	395	16	example	example	NOUN
ma-170	395	17	3	3	X
ma-170	395	18	.	.	PUNCT
ma-170	395	19	∆2	∆2	PROPN
ma-170	396	1	∆1	∆1	PROPN
ma-170	396	2	∆3	∆3	X
ma-170	396	3	-0.20	-0.20	PROPN
ma-170	396	4	-0.15	-0.15	NUM
ma-170	396	5	-0.10	-0.10	NUM
ma-170	396	6	-0.05	-0.05	NUM
ma-170	397	1	0.00	0.00	NUM
ma-170	397	2	0.05	0.05	NUM
ma-170	397	3	0.10	0.10	NUM
ma-170	397	4	-1	-1	SYM
ma-170	397	5	0	0	NUM
ma-170	397	6	1	1	NUM
ma-170	397	7	2	2	NUM
ma-170	397	8	t	t	NOUN
ma-170	397	9	h	h	NOUN
ma-170	398	1	i	i	PRON
ma-170	398	2	t	t	NOUN
ma-170	399	1	h	h	NOUN
ma-170	400	1	i	i	PRON
ma-170	400	2	h1	h1	VERB
ma-170	400	3	h2	h2	NOUN
ma-170	400	4	h3	h3	NOUN
ma-170	400	5	otherwise	otherwise	ADV
ma-170	400	6	,	,	PUNCT
ma-170	400	7	we	we	PRON
ma-170	400	8	set	set	VERB
ma-170	400	9	[	[	X
ma-170	400	10	.	.	PUNCT
ma-170	400	11	,	,	PUNCT
ma-170	400	12	.	.	PUNCT
ma-170	400	13	;	;	PUNCT
ma-170	400	14	.	.	PUNCT
ma-170	400	15	]	]	PUNCT
ma-170	401	1	=	=	PUNCT
ma-170	401	2	o.	o.	NOUN
ma-170	401	3	7	7	NUM
ma-170	401	4	let	let	VERB
ma-170	401	5	us	we	PRON
ma-170	401	6	consider	consider	VERB
ma-170	401	7	the	the	DET
ma-170	401	8	nonlinear	nonlinear	ADJ
ma-170	401	9	and	and	CCONJ
ma-170	401	10	nondifferentiable	nondifferentiable	ADJ
ma-170	401	11	system	system	NOUN
ma-170	401	12	as	as	ADP
ma-170	401	13	3t21	3t21	NUM
ma-170	401	14	t2	t2	NOUN
ma-170	401	15	+	+	CCONJ
ma-170	401	16	t22	t22	PROPN
ma-170	401	17	−	−	PROPN
ma-170	401	18	1	1	NUM
ma-170	401	19	+	+	CCONJ
ma-170	401	20	|t1	|t1	NOUN
ma-170	401	21	−	−	PROPN
ma-170	401	22	1|	1|	NUM
ma-170	401	23	=	=	SYM
ma-170	401	24	0	0	NUM
ma-170	401	25	,	,	PUNCT
ma-170	401	26	t41	t41	NOUN
ma-170	402	1	+	+	CCONJ
ma-170	402	2	t1	t1	PROPN
ma-170	402	3	t	t	NOUN
ma-170	402	4	3	3	NUM
ma-170	402	5	2	2	NUM
ma-170	402	6	−	−	NUM
ma-170	402	7	1	1	NUM
ma-170	402	8	+	+	NOUN
ma-170	402	9	|t2|	|t2|	NOUN
ma-170	402	10	=	=	SYM
ma-170	402	11	0	0	X
ma-170	402	12	.	.	PUNCT
ma-170	403	1	then	then	ADV
ma-170	403	2	,	,	PUNCT
ma-170	403	3	we	we	PRON
ma-170	403	4	set	set	VERB
ma-170	403	5	f	f	PROPN
ma-170	403	6	=	=	PRON
ma-170	403	7	(	(	PUNCT
ma-170	403	8	f1	f1	PROPN
ma-170	403	9	,	,	PUNCT
ma-170	403	10	f2	f2	PROPN
ma-170	403	11	)	)	PUNCT
ma-170	403	12	,	,	PUNCT
ma-170	403	13	where	where	SCONJ
ma-170	403	14	f1(t1	f1(t1	X
ma-170	403	15	,	,	PUNCT
ma-170	403	16	t2	t2	NOUN
ma-170	403	17	)	)	PUNCT
ma-170	403	18	=	=	SYM
ma-170	403	19	f1	f1	NOUN
ma-170	403	20	=	=	SYM
ma-170	403	21	3t21	3t21	PROPN
ma-170	403	22	t2	t2	NOUN
ma-170	403	23	+	+	CCONJ
ma-170	403	24	t22	t22	PROPN
ma-170	403	25	−	−	PROPN
ma-170	403	26	1	1	NUM
ma-170	403	27	+	+	CCONJ
ma-170	403	28	|t1	|t1	NOUN
ma-170	403	29	−	−	PROPN
ma-170	403	30	1|	1|	NUM
ma-170	403	31	=	=	SYM
ma-170	403	32	0	0	NUM
ma-170	403	33	and	and	CCONJ
ma-170	403	34	f2(t1	f2(t1	PRON
ma-170	403	35	,	,	PUNCT
ma-170	403	36	t2	t2	NOUN
ma-170	403	37	)	)	PUNCT
ma-170	403	38	=	=	SYM
ma-170	403	39	f2	f2	PROPN
ma-170	403	40	=	=	SYM
ma-170	403	41	t41	t41	PROPN
ma-170	404	1	+	+	CCONJ
ma-170	404	2	t1	t1	PROPN
ma-170	404	3	t	t	NOUN
ma-170	404	4	3	3	NUM
ma-170	404	5	2	2	NUM
ma-170	404	6	−	−	NUM
ma-170	404	7	1	1	NUM
ma-170	404	8	+	+	NOUN
ma-170	404	9	|t2|	|t2|	NOUN
ma-170	404	10	=	=	SYM
ma-170	404	11	0	0	X
ma-170	404	12	.	.	PUNCT
ma-170	404	13	choose	choose	VERB
ma-170	404	14	initial	initial	ADJ
ma-170	404	15	points	point	NOUN
ma-170	404	16	(	(	PUNCT
ma-170	404	17	5	5	NUM
ma-170	404	18	,	,	PUNCT
ma-170	404	19	5	5	NUM
ma-170	404	20	)	)	PUNCT
ma-170	404	21	and	and	CCONJ
ma-170	404	22	(	(	PUNCT
ma-170	404	23	1	1	NUM
ma-170	404	24	,	,	PUNCT
ma-170	404	25	0	0	NUM
ma-170	404	26	)	)	PUNCT
ma-170	404	27	.	.	PUNCT
ma-170	405	1	then	then	ADV
ma-170	405	2	,	,	PUNCT
ma-170	405	3	using	use	VERB
ma-170	405	4	the	the	DET
ma-170	405	5	aforementioned	aforementioned	ADJ
ma-170	405	6	divided	divide	VERB
ma-170	405	7	difference	difference	NOUN
ma-170	405	8	andthe	andthe	NOUN
ma-170	405	9	method	method	NOUN
ma-170	405	10	(	(	PUNCT
ma-170	405	11	1.3	1.3	NUM
ma-170	405	12	)	)	PUNCT
ma-170	405	13	we	we	PRON
ma-170	405	14	obtain	obtain	VERB
ma-170	405	15	the	the	DET
ma-170	405	16	solution	solution	NOUN
ma-170	405	17	x∗	x∗	PROPN
ma-170	406	1	=	=	PUNCT
ma-170	407	1	(	(	PUNCT
ma-170	407	2	x∗1	x∗1	ADV
ma-170	407	3	,	,	PUNCT
ma-170	407	4	x	x	X
ma-170	407	5	∗	∗	NOUN
ma-170	407	6	2	2	NUM
ma-170	407	7	)	)	PUNCT
ma-170	407	8	after	after	ADP
ma-170	407	9	three	three	NUM
ma-170	407	10	iterations	iteration	NOUN
ma-170	407	11	with	with	ADP
ma-170	407	12	x∗1	x∗1	ADJ
ma-170	407	13	=	=	SYM
ma-170	407	14	0.894655074966771	0.894655074966771	NUM
ma-170	407	15	and	and	CCONJ
ma-170	407	16	x∗2	x∗2	PROPN
ma-170	407	17	=	=	NOUN
ma-170	407	18	0.327826643198819	0.327826643198819	NUM
ma-170	407	19	.	.	PUNCT
ma-170	408	1	5	5	NUM
ma-170	408	2	.	.	X
ma-170	408	3	conclusion	conclusion	VERB
ma-170	408	4	the	the	DET
ma-170	408	5	focus	focus	NOUN
ma-170	408	6	of	of	ADP
ma-170	408	7	this	this	DET
ma-170	408	8	paper	paper	NOUN
ma-170	408	9	is	be	AUX
ma-170	408	10	to	to	PART
ma-170	408	11	provide	provide	VERB
ma-170	408	12	a	a	DET
ma-170	408	13	comprehensive	comprehensive	ADJ
ma-170	408	14	analysis	analysis	NOUN
ma-170	408	15	of	of	ADP
ma-170	408	16	the	the	DET
ma-170	408	17	local	local	ADJ
ma-170	408	18	and	and	CCONJ
ma-170	408	19	semilocal	semilocal	ADJ
ma-170	408	20	con	con	NOUN
ma-170	408	21	-	-	PUNCT
ma-170	408	22	vergence	vergence	NOUN
ma-170	408	23	of	of	ADP
ma-170	408	24	a	a	DET
ma-170	408	25	derivative	derivative	ADJ
ma-170	408	26	-	-	PUNCT
ma-170	408	27	free	free	ADJ
ma-170	408	28	seventh	seventh	ADJ
ma-170	408	29	-	-	PUNCT
ma-170	408	30	order	order	NOUN
ma-170	408	31	method	method	NOUN
ma-170	408	32	in	in	ADP
ma-170	408	33	banach	banach	NOUN
ma-170	408	34	space	space	NOUN
ma-170	408	35	.	.	PUNCT
ma-170	409	1	it	it	PRON
ma-170	409	2	is	be	AUX
ma-170	409	3	noteworthy	noteworthy	ADJ
ma-170	409	4	that	that	SCONJ
ma-170	409	5	theconvergence	theconvergence	NOUN
ma-170	409	6	has	have	AUX
ma-170	409	7	been	be	AUX
ma-170	409	8	investigated	investigate	VERB
ma-170	409	9	in	in	ADP
ma-170	409	10	earlier	early	ADJ
ma-170	409	11	studies	study	NOUN
ma-170	409	12	by	by	ADP
ma-170	409	13	assuming	assume	VERB
ma-170	409	14	the	the	DET
ma-170	409	15	existence	existence	NOUN
ma-170	409	16	of	of	ADP
ma-170	409	17	some	some	DET
ma-170	409	18	higherorder	higherorder	NOUN
ma-170	409	19	derivatives	derivative	NOUN
ma-170	409	20	,	,	PUNCT
ma-170	409	21	which	which	PRON
ma-170	409	22	in	in	ADP
ma-170	409	23	fact	fact	NOUN
ma-170	409	24	are	be	AUX
ma-170	409	25	not	not	PART
ma-170	409	26	used	use	VERB
ma-170	409	27	in	in	ADP
ma-170	409	28	the	the	DET
ma-170	409	29	iterative	iterative	NOUN
ma-170	409	30	method	method	NOUN
ma-170	409	31	.	.	PUNCT
ma-170	410	1	contrary	contrary	ADJ
ma-170	410	2	to	to	ADP
ma-170	410	3	this	this	PRON
ma-170	410	4	,	,	PUNCT
ma-170	410	5	our	our	PRON
ma-170	410	6	approachonly	approachonly	ADV
ma-170	410	7	considers	consider	VERB
ma-170	410	8	the	the	DET
ma-170	410	9	first	first	ADJ
ma-170	410	10	-	-	PUNCT
ma-170	410	11	order	order	NOUN
ma-170	410	12	divided	divide	VERB
ma-170	410	13	differences	difference	NOUN
ma-170	410	14	that	that	PRON
ma-170	410	15	are	be	AUX
ma-170	410	16	actually	actually	ADV
ma-170	410	17	present	present	ADJ
ma-170	410	18	in	in	ADP
ma-170	410	19	the	the	DET
ma-170	410	20	iterative	iterative	NOUN
ma-170	410	21	process.this	process.this	PRON
ma-170	410	22	unique	unique	ADJ
ma-170	410	23	feature	feature	NOUN
ma-170	410	24	makes	make	VERB
ma-170	410	25	the	the	DET
ma-170	410	26	method	method	NOUN
ma-170	410	27	applicable	applicable	ADJ
ma-170	410	28	to	to	ADP
ma-170	410	29	a	a	DET
ma-170	410	30	wider	wide	ADJ
ma-170	410	31	range	range	NOUN
ma-170	410	32	of	of	ADP
ma-170	410	33	functions	function	NOUN
ma-170	410	34	,	,	PUNCT
ma-170	410	35	thereby	thereby	ADV
ma-170	410	36	expandingits	expandingit	VERB
ma-170	410	37	utility	utility	NOUN
ma-170	410	38	.	.	PUNCT
ma-170	411	1	in	in	ADP
ma-170	411	2	the	the	DET
ma-170	411	3	analysis	analysis	NOUN
ma-170	411	4	,	,	PUNCT
ma-170	411	5	we	we	PRON
ma-170	411	6	present	present	VERB
ma-170	411	7	an	an	DET
ma-170	411	8	error	error	NOUN
ma-170	411	9	estimate	estimate	NOUN
ma-170	411	10	and	and	CCONJ
ma-170	411	11	convergence	convergence	NOUN
ma-170	411	12	ball	ball	NOUN
ma-170	411	13	that	that	PRON
ma-170	411	14	bounds	bound	VERB
ma-170	411	15	the	the	DET
ma-170	411	16	iter	iter	NOUN
ma-170	411	17	-	-	PUNCT
ma-170	411	18	ates	ates	PROPN
ma-170	411	19	,	,	PUNCT
ma-170	411	20	providing	provide	VERB
ma-170	411	21	further	further	ADJ
ma-170	411	22	benefits	benefit	NOUN
ma-170	411	23	to	to	ADP
ma-170	411	24	the	the	DET
ma-170	411	25	analysis	analysis	NOUN
ma-170	411	26	of	of	ADP
ma-170	411	27	convergence	convergence	NOUN
ma-170	411	28	.	.	PUNCT
ma-170	412	1	in	in	ADP
ma-170	412	2	addition	addition	NOUN
ma-170	412	3	,	,	PUNCT
ma-170	412	4	the	the	DET
ma-170	412	5	sufficient	sufficient	ADJ
ma-170	412	6	conditionsare	conditionsare	NOUN
ma-170	412	7	developed	develop	VERB
ma-170	412	8	to	to	PART
ma-170	412	9	show	show	VERB
ma-170	412	10	the	the	DET
ma-170	412	11	uniqueness	uniqueness	NOUN
ma-170	412	12	of	of	ADP
ma-170	412	13	solution	solution	NOUN
ma-170	412	14	in	in	ADP
ma-170	412	15	the	the	DET
ma-170	412	16	given	give	VERB
ma-170	412	17	domain	domain	NOUN
ma-170	412	18	.	.	PUNCT
ma-170	413	1	to	to	PART
ma-170	413	2	verify	verify	VERB
ma-170	413	3	the	the	DET
ma-170	413	4	theoreticalresults	theoreticalresult	NOUN
ma-170	413	5	,	,	PUNCT
ma-170	413	6	we	we	PRON
ma-170	413	7	have	have	AUX
ma-170	413	8	conducted	conduct	VERB
ma-170	413	9	numerical	numerical	ADJ
ma-170	413	10	tests	test	NOUN
ma-170	413	11	on	on	ADP
ma-170	413	12	several	several	ADJ
ma-170	413	13	problems	problem	NOUN
ma-170	413	14	,	,	PUNCT
ma-170	413	15	demonstrating	demonstrate	VERB
ma-170	413	16	the	the	DET
ma-170	413	17	effectiveness	effectiveness	NOUN
ma-170	413	18	ofthis	ofthis	ADJ
ma-170	413	19	approach	approach	NOUN
ma-170	413	20	.	.	PUNCT
ma-170	414	1	moreover	moreover	ADV
ma-170	414	2	,	,	PUNCT
ma-170	414	3	this	this	DET
ma-170	414	4	idea	idea	NOUN
ma-170	414	5	has	have	VERB
ma-170	414	6	the	the	DET
ma-170	414	7	potential	potential	NOUN
ma-170	414	8	to	to	PART
ma-170	414	9	be	be	AUX
ma-170	414	10	extended	extend	VERB
ma-170	414	11	to	to	ADP
ma-170	414	12	other	other	ADJ
ma-170	414	13	methods	method	NOUN
ma-170	414	14	,	,	PUNCT
ma-170	414	15	making	make	VERB
ma-170	414	16	it	it	PRON
ma-170	414	17	avaluable	avaluable	ADJ
ma-170	414	18	contribution	contribution	NOUN
ma-170	414	19	in	in	ADP
ma-170	414	20	the	the	DET
ma-170	414	21	field	field	NOUN
ma-170	414	22	of	of	ADP
ma-170	414	23	the	the	DET
ma-170	414	24	theory	theory	NOUN
ma-170	414	25	of	of	ADP
ma-170	414	26	iterative	iterative	NOUN
ma-170	414	27	functions	function	NOUN
ma-170	414	28	[	[	X
ma-170	414	29	1–17	1–17	NOUN
ma-170	414	30	]	]	PUNCT
ma-170	414	31	.	.	PUNCT
ma-170	415	1	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	PROPN
ma-170	415	2	eur	eur	PROPN
ma-170	415	3	.	.	PUNCT
ma-170	416	1	j.	j.	PROPN
ma-170	416	2	math	math	PROPN
ma-170	416	3	.	.	PUNCT
ma-170	417	1	anal	anal	PROPN
ma-170	417	2	.	.	PUNCT
ma-170	418	1	10.28924	10.28924	NUM
ma-170	418	2	/	/	SYM
ma-170	418	3	ada	ada	PROPN
ma-170	418	4	/	/	SYM
ma-170	418	5	ma.3.24	ma.3.24	ADJ
ma-170	418	6	15references	15reference	NOUN
ma-170	419	1	[	[	X
ma-170	419	2	1	1	NUM
ma-170	419	3	]	]	PUNCT
ma-170	419	4	a.	a.	NOUN
ma-170	419	5	cordero	cordero	PROPN
ma-170	419	6	,	,	PUNCT
ma-170	419	7	j.l	j.l	PROPN
ma-170	419	8	.	.	PROPN
ma-170	419	9	hueso	hueso	PROPN
ma-170	419	10	,	,	PUNCT
ma-170	419	11	e.	e.	PROPN
ma-170	419	12	martinez	martinez	PROPN
ma-170	419	13	,	,	PUNCT
ma-170	419	14	j.r	j.r	PROPN
ma-170	419	15	.	.	PROPN
ma-170	419	16	torregrosa	torregrosa	PROPN
ma-170	419	17	,	,	PUNCT
ma-170	419	18	a	a	DET
ma-170	419	19	modified	modify	VERB
ma-170	419	20	newton	newton	PROPN
ma-170	419	21	-	-	PUNCT
ma-170	419	22	jarratt	jarratt	PROPN
ma-170	419	23	’s	’s	PART
ma-170	419	24	composition	composition	NOUN
ma-170	419	25	,	,	PUNCT
ma-170	419	26	numer	numer	PROPN
ma-170	419	27	.	.	PROPN
ma-170	419	28	algor	algor	PROPN
ma-170	419	29	.	.	PUNCT
ma-170	420	1	55(2010	55(2010	NUM
ma-170	420	2	)	)	PUNCT
ma-170	420	3	87–99	87–99	NUM
ma-170	420	4	.	.	PUNCT
ma-170	421	1	https://doi.org/10.1007/s11075-009-9359-z.[2	https://doi.org/10.1007/s11075-009-9359-z.[2	PROPN
ma-170	421	2	]	]	X
ma-170	421	3	f.	f.	PROPN
ma-170	421	4	awawdeh	awawdeh	PROPN
ma-170	421	5	,	,	PUNCT
ma-170	421	6	on	on	ADP
ma-170	421	7	new	new	ADJ
ma-170	421	8	iterative	iterative	NOUN
ma-170	421	9	method	method	NOUN
ma-170	421	10	for	for	ADP
ma-170	421	11	solving	solve	VERB
ma-170	421	12	systems	system	NOUN
ma-170	421	13	of	of	ADP
ma-170	421	14	nonlinear	nonlinear	ADJ
ma-170	421	15	equations	equation	NOUN
ma-170	421	16	,	,	PUNCT
ma-170	421	17	numer	numer	PROPN
ma-170	421	18	.	.	PROPN
ma-170	421	19	algor	algor	PROPN
ma-170	421	20	.	.	PUNCT
ma-170	422	1	54	54	NUM
ma-170	422	2	(	(	PUNCT
ma-170	422	3	2010	2010	NUM
ma-170	422	4	)	)	PUNCT
ma-170	422	5	395–409	395–409	NUM
ma-170	422	6	.	.	PUNCT
ma-170	423	1	https://doi.org/10.1007/s11075-009-9342-8.[3	https://doi.org/10.1007/s11075-009-9342-8.[3	PROPN
ma-170	423	2	]	]	X
ma-170	423	3	f.	f.	PROPN
ma-170	423	4	a.	a.	PROPN
ma-170	423	5	potra	potra	PROPN
ma-170	423	6	,	,	PUNCT
ma-170	423	7	v.	v.	ADP
ma-170	423	8	pták	pták	ADJ
ma-170	423	9	,	,	PUNCT
ma-170	423	10	nondiscrete	nondiscrete	ADJ
ma-170	423	11	induction	induction	NOUN
ma-170	423	12	and	and	CCONJ
ma-170	423	13	iterative	iterative	NOUN
ma-170	423	14	processes	process	NOUN
ma-170	423	15	pitman	pitman	NOUN
ma-170	423	16	publishing	publishing	NOUN
ma-170	423	17	,	,	PUNCT
ma-170	423	18	boston	boston	PROPN
ma-170	423	19	,	,	PUNCT
ma-170	423	20	1984.[4	1984.[4	NUM
ma-170	423	21	]	]	X
ma-170	423	22	i.k	i.k	PROPN
ma-170	423	23	.	.	PROPN
ma-170	423	24	argyros	argyros	PROPN
ma-170	423	25	,	,	PUNCT
ma-170	423	26	computational	computational	ADJ
ma-170	423	27	theory	theory	NOUN
ma-170	423	28	of	of	ADP
ma-170	423	29	iterative	iterative	ADJ
ma-170	423	30	methods	method	NOUN
ma-170	423	31	,	,	PUNCT
ma-170	423	32	series	series	NOUN
ma-170	423	33	:	:	PUNCT
ma-170	423	34	studies	study	NOUN
ma-170	423	35	in	in	ADP
ma-170	423	36	computational	computational	ADJ
ma-170	423	37	mathematics	mathematic	NOUN
ma-170	423	38	,	,	PUNCT
ma-170	423	39	15	15	NUM
ma-170	423	40	,	,	PUNCT
ma-170	423	41	editors	editor	NOUN
ma-170	423	42	:	:	PUNCT
ma-170	423	43	chui	chui	PROPN
ma-170	423	44	c.k	c.k	PROPN
ma-170	423	45	.	.	PROPN
ma-170	423	46	and	and	CCONJ
ma-170	423	47	wuytack	wuytack	PROPN
ma-170	423	48	l	l	PROPN
ma-170	423	49	,	,	PUNCT
ma-170	423	50	elsevier	elsevier	PROPN
ma-170	423	51	publ	publ	PROPN
ma-170	423	52	.	.	PUNCT
ma-170	424	1	co.	co.	PROPN
ma-170	424	2	,	,	PUNCT
ma-170	424	3	new	new	PROPN
ma-170	424	4	york	york	PROPN
ma-170	424	5	,	,	PUNCT
ma-170	424	6	2007.[5	2007.[5	NUM
ma-170	424	7	]	]	X
ma-170	424	8	i.f	i.f	PROPN
ma-170	424	9	.	.	PROPN
ma-170	424	10	steffensen	steffensen	PROPN
ma-170	424	11	,	,	PUNCT
ma-170	424	12	remarks	remark	VERB
ma-170	424	13	on	on	ADP
ma-170	424	14	iteration	iteration	NOUN
ma-170	424	15	,	,	PUNCT
ma-170	424	16	scand	scand	PROPN
ma-170	424	17	.	.	PUNCT
ma-170	424	18	actuar	actuar	PROPN
ma-170	424	19	.	.	PUNCT
ma-170	425	1	j.	j.	PROPN
ma-170	425	2	16	16	NUM
ma-170	425	3	(	(	PUNCT
ma-170	425	4	1933	1933	NUM
ma-170	425	5	)	)	PUNCT
ma-170	425	6	64–72	64–72	NUM
ma-170	425	7	.	.	PUNCT
ma-170	426	1	https://doi.org/10.1080/03461238	https://doi.org/10.1080/03461238	NOUN
ma-170	426	2	.	.	PUNCT
ma-170	427	1	1933.10419209.[6	1933.10419209.[6	NUM
ma-170	427	2	]	]	X
ma-170	427	3	i.k	i.k	PROPN
ma-170	427	4	.	.	PROPN
ma-170	427	5	argyros	argyros	PROPN
ma-170	427	6	,	,	PUNCT
ma-170	427	7	á	á	PROPN
ma-170	427	8	.	.	PUNCT
ma-170	427	9	a.	a.	PROPN
ma-170	427	10	magreñán	magreñán	PROPN
ma-170	427	11	,	,	PUNCT
ma-170	427	12	iterative	iterative	NOUN
ma-170	427	13	methods	method	NOUN
ma-170	427	14	and	and	CCONJ
ma-170	427	15	their	their	PRON
ma-170	427	16	dynamics	dynamic	NOUN
ma-170	427	17	with	with	ADP
ma-170	427	18	applications	application	NOUN
ma-170	427	19	,	,	PUNCT
ma-170	427	20	crc	crc	NOUN
ma-170	427	21	press	press	NOUN
ma-170	427	22	:	:	PUNCT
ma-170	427	23	new	new	PROPN
ma-170	427	24	york	york	PROPN
ma-170	427	25	,	,	PUNCT
ma-170	427	26	ny	ny	PROPN
ma-170	427	27	,	,	PUNCT
ma-170	427	28	usa	usa	PROPN
ma-170	427	29	,	,	PUNCT
ma-170	427	30	2017.[7	2017.[7	NUM
ma-170	427	31	]	]	X
ma-170	427	32	j.a	j.a	PROPN
ma-170	427	33	.	.	PROPN
ma-170	427	34	ezquerro	ezquerro	PROPN
ma-170	427	35	,	,	PUNCT
ma-170	427	36	á	á	PROPN
ma-170	427	37	.	.	PUNCT
ma-170	428	1	grau	grau	PROPN
ma-170	428	2	,	,	PUNCT
ma-170	428	3	m.	m.	NOUN
ma-170	428	4	grau	grau	PROPN
ma-170	428	5	-	-	PUNCT
ma-170	428	6	sánchez	sánchez	PROPN
ma-170	428	7	,	,	PUNCT
ma-170	428	8	m.	m.	NOUN
ma-170	428	9	a.	a.	NOUN
ma-170	428	10	hernández	hernández	PROPN
ma-170	428	11	,	,	PUNCT
ma-170	428	12	m.	m.	NOUN
ma-170	428	13	noguera	noguera	NOUN
ma-170	428	14	,	,	PUNCT
ma-170	428	15	analysing	analyse	VERB
ma-170	428	16	the	the	DET
ma-170	428	17	efficiency	efficiency	NOUN
ma-170	428	18	of	of	ADP
ma-170	428	19	some	some	DET
ma-170	428	20	modifi	modifi	NOUN
ma-170	428	21	-	-	PUNCT
ma-170	428	22	cations	cation	NOUN
ma-170	428	23	of	of	ADP
ma-170	428	24	the	the	DET
ma-170	428	25	secant	secant	ADJ
ma-170	428	26	method	method	NOUN
ma-170	428	27	,	,	PUNCT
ma-170	428	28	comput	comput	NOUN
ma-170	428	29	.	.	PUNCT
ma-170	429	1	math	math	NOUN
ma-170	429	2	.	.	PUNCT
ma-170	430	1	appl	appl	PROPN
ma-170	430	2	.	.	PUNCT
ma-170	431	1	64	64	NUM
ma-170	431	2	(	(	PUNCT
ma-170	431	3	2012	2012	NUM
ma-170	431	4	)	)	PUNCT
ma-170	431	5	2066–2073	2066–2073	NUM
ma-170	431	6	.	.	PUNCT
ma-170	432	1	https://doi.org/10.1016/j.camwa	https://doi.org/10.1016/j.camwa	PROPN
ma-170	432	2	.	.	PUNCT
ma-170	433	1	2012.03.105.[8	2012.03.105.[8	PROPN
ma-170	433	2	]	]	X
ma-170	433	3	j.	j.	PROPN
ma-170	433	4	a.	a.	PROPN
ma-170	433	5	ezquerro	ezquerro	PROPN
ma-170	433	6	,	,	PUNCT
ma-170	433	7	m.	m.	NOUN
ma-170	433	8	a.	a.	NOUN
ma-170	433	9	hernández	hernández	PROPN
ma-170	433	10	,	,	PUNCT
ma-170	433	11	n.	n.	PROPN
ma-170	433	12	romero	romero	PROPN
ma-170	433	13	,	,	PUNCT
ma-170	433	14	solving	solve	VERB
ma-170	433	15	nonlinear	nonlinear	ADJ
ma-170	433	16	integral	integral	ADJ
ma-170	433	17	equations	equation	NOUN
ma-170	433	18	of	of	ADP
ma-170	433	19	fredholm	fredholm	NOUN
ma-170	433	20	type	type	NOUN
ma-170	433	21	with	with	ADP
ma-170	433	22	high	high	ADJ
ma-170	433	23	orderiterative	orderiterative	ADJ
ma-170	433	24	methods	method	NOUN
ma-170	433	25	,	,	PUNCT
ma-170	433	26	j.	j.	PROPN
ma-170	433	27	comput	comput	PROPN
ma-170	433	28	.	.	PUNCT
ma-170	434	1	appl	appl	PROPN
ma-170	434	2	.	.	PROPN
ma-170	434	3	math	math	PROPN
ma-170	434	4	.	.	PUNCT
ma-170	435	1	36	36	NUM
ma-170	435	2	(	(	PUNCT
ma-170	435	3	2011	2011	NUM
ma-170	435	4	)	)	PUNCT
ma-170	435	5	1449–1463	1449–1463	NUM
ma-170	435	6	.	.	PUNCT
ma-170	436	1	https://doi.org/10.1016/j.cam.2011.09.009.[9	https://doi.org/10.1016/j.cam.2011.09.009.[9	X
ma-170	436	2	]	]	X
ma-170	436	3	j.f	j.f	PROPN
ma-170	436	4	.	.	PROPN
ma-170	436	5	traub	traub	PROPN
ma-170	436	6	,	,	PUNCT
ma-170	436	7	iterative	iterative	NOUN
ma-170	436	8	methods	method	NOUN
ma-170	436	9	for	for	ADP
ma-170	436	10	the	the	DET
ma-170	436	11	solution	solution	NOUN
ma-170	436	12	of	of	ADP
ma-170	436	13	equations	equation	NOUN
ma-170	436	14	,	,	PUNCT
ma-170	436	15	prentice	prentice	NOUN
ma-170	436	16	-	-	PUNCT
ma-170	436	17	hall	hall	NOUN
ma-170	436	18	,	,	PUNCT
ma-170	436	19	englewood	englewood	PROPN
ma-170	436	20	cliffs	cliffs	PROPN
ma-170	436	21	,	,	PUNCT
ma-170	436	22	new	new	PROPN
ma-170	436	23	jersey	jersey	PROPN
ma-170	436	24	,	,	PUNCT
ma-170	436	25	1964.[10	1964.[10	NUM
ma-170	436	26	]	]	X
ma-170	436	27	j.m	j.m	PROPN
ma-170	436	28	.	.	PROPN
ma-170	436	29	ortega	ortega	PROPN
ma-170	436	30	,	,	PUNCT
ma-170	436	31	w.c	w.c	PROPN
ma-170	436	32	.	.	PROPN
ma-170	436	33	rheinboldt	rheinboldt	ADJ
ma-170	436	34	,	,	PUNCT
ma-170	436	35	iterative	iterative	ADJ
ma-170	436	36	solution	solution	NOUN
ma-170	436	37	of	of	ADP
ma-170	436	38	nonlinear	nonlinear	ADJ
ma-170	436	39	equations	equation	NOUN
ma-170	436	40	in	in	ADP
ma-170	436	41	several	several	ADJ
ma-170	436	42	variables	variable	NOUN
ma-170	436	43	,	,	PUNCT
ma-170	436	44	academic	academic	ADJ
ma-170	436	45	press	press	NOUN
ma-170	436	46	,	,	PUNCT
ma-170	436	47	newyork	newyork	NOUN
ma-170	436	48	,	,	PUNCT
ma-170	436	49	1970.[11	1970.[11	NUM
ma-170	436	50	]	]	X
ma-170	436	51	j.r	j.r	PROPN
ma-170	436	52	.	.	PROPN
ma-170	436	53	sharma	sharma	PROPN
ma-170	436	54	,	,	PUNCT
ma-170	436	55	h.	h.	PROPN
ma-170	436	56	arora	arora	PROPN
ma-170	436	57	,	,	PUNCT
ma-170	436	58	an	an	DET
ma-170	436	59	efficient	efficient	ADJ
ma-170	436	60	derivative	derivative	ADJ
ma-170	436	61	free	free	ADJ
ma-170	436	62	iterative	iterative	NOUN
ma-170	436	63	method	method	NOUN
ma-170	436	64	for	for	ADP
ma-170	436	65	solving	solve	VERB
ma-170	436	66	systems	system	NOUN
ma-170	436	67	of	of	ADP
ma-170	436	68	nonlinear	nonlinear	ADJ
ma-170	436	69	equations	equation	NOUN
ma-170	436	70	,	,	PUNCT
ma-170	436	71	appl.anal	appl.anal	NUM
ma-170	436	72	.	.	PUNCT
ma-170	436	73	discrete	discrete	ADJ
ma-170	436	74	math	math	NOUN
ma-170	436	75	.	.	PUNCT
ma-170	437	1	7	7	NUM
ma-170	437	2	(	(	PUNCT
ma-170	437	3	2013	2013	NUM
ma-170	437	4	)	)	PUNCT
ma-170	437	5	390–403	390–403	NUM
ma-170	437	6	.	.	PUNCT
ma-170	438	1	https://doi:10.2298	https://doi:10.2298	PROPN
ma-170	438	2	/	/	SYM
ma-170	438	3	aadm130725016s.[12	aadm130725016s.[12	PROPN
ma-170	438	4	]	]	X
ma-170	438	5	j.r	j.r	PROPN
ma-170	438	6	.	.	PROPN
ma-170	438	7	sharma	sharma	PROPN
ma-170	438	8	,	,	PUNCT
ma-170	438	9	s.	s.	PROPN
ma-170	438	10	kumar	kumar	PROPN
ma-170	438	11	,	,	PUNCT
ma-170	438	12	i.k	i.k	PROPN
ma-170	438	13	.	.	PROPN
ma-170	438	14	argyros	argyros	PROPN
ma-170	438	15	,	,	PUNCT
ma-170	438	16	generalized	generalized	ADJ
ma-170	438	17	kung	kung	ADJ
ma-170	438	18	-	-	PUNCT
ma-170	438	19	traub	traub	NOUN
ma-170	438	20	method	method	NOUN
ma-170	438	21	and	and	CCONJ
ma-170	438	22	its	its	PRON
ma-170	438	23	multi	multi	ADJ
ma-170	438	24	-	-	ADJ
ma-170	438	25	step	step	ADJ
ma-170	438	26	iteration	iteration	NOUN
ma-170	438	27	in	in	ADP
ma-170	438	28	banach	banach	NOUN
ma-170	438	29	spaces	space	NOUN
ma-170	438	30	,	,	PUNCT
ma-170	438	31	journal	journal	NOUN
ma-170	438	32	of	of	ADP
ma-170	438	33	complexity	complexity	NOUN
ma-170	438	34	54	54	NUM
ma-170	438	35	(	(	PUNCT
ma-170	438	36	2019	2019	NUM
ma-170	438	37	)	)	PUNCT
ma-170	438	38	101400	101400	NUM
ma-170	438	39	.	.	PUNCT
ma-170	439	1	https://doi.org/10.1016/j.jco.2019.02.003.[13	https://doi.org/10.1016/j.jco.2019.02.003.[13	PROPN
ma-170	439	2	]	]	PUNCT
ma-170	439	3	m.	m.	NOUN
ma-170	439	4	grau	grau	PROPN
ma-170	439	5	-	-	PUNCT
ma-170	439	6	sánchez	sánchez	PROPN
ma-170	439	7	,	,	PUNCT
ma-170	439	8	á	á	PROPN
ma-170	439	9	,	,	PUNCT
ma-170	439	10	grau	grau	NOUN
ma-170	439	11	,	,	PUNCT
ma-170	439	12	m.	m.	NOUN
ma-170	439	13	noguera	noguera	NOUN
ma-170	439	14	,	,	PUNCT
ma-170	439	15	frozen	freeze	VERB
ma-170	439	16	divided	divide	VERB
ma-170	439	17	difference	difference	NOUN
ma-170	439	18	scheme	scheme	NOUN
ma-170	439	19	for	for	ADP
ma-170	439	20	solving	solve	VERB
ma-170	439	21	systems	system	NOUN
ma-170	439	22	of	of	ADP
ma-170	439	23	nonlinear	nonlinear	ADJ
ma-170	439	24	equations	equation	NOUN
ma-170	439	25	,	,	PUNCT
ma-170	439	26	j.	j.	PROPN
ma-170	439	27	comput	comput	PROPN
ma-170	439	28	.	.	PUNCT
ma-170	440	1	appl	appl	PROPN
ma-170	440	2	.	.	PUNCT
ma-170	440	3	math	math	PROPN
ma-170	440	4	.	.	PUNCT
ma-170	441	1	235	235	NUM
ma-170	441	2	(	(	PUNCT
ma-170	441	3	2011	2011	NUM
ma-170	441	4	)	)	PUNCT
ma-170	441	5	1739–1743	1739–1743	NUM
ma-170	441	6	.	.	PUNCT
ma-170	442	1	https://doi.org/10.1016/j.cam.2010.09.019.[14	https://doi.org/10.1016/j.cam.2010.09.019.[14	PROPN
ma-170	442	2	]	]	PUNCT
ma-170	442	3	m.	m.	NOUN
ma-170	442	4	grau	grau	PROPN
ma-170	442	5	-	-	PUNCT
ma-170	442	6	sánchez	sánchez	PROPN
ma-170	442	7	,	,	PUNCT
ma-170	442	8	m.	m.	NOUN
ma-170	442	9	noguera	noguera	PROPN
ma-170	442	10	,	,	PUNCT
ma-170	442	11	a	a	DET
ma-170	442	12	technique	technique	NOUN
ma-170	442	13	to	to	PART
ma-170	442	14	choose	choose	VERB
ma-170	442	15	the	the	DET
ma-170	442	16	most	most	ADV
ma-170	442	17	efficient	efficient	ADJ
ma-170	442	18	method	method	NOUN
ma-170	442	19	between	between	ADP
ma-170	442	20	secant	secant	ADJ
ma-170	442	21	method	method	NOUN
ma-170	442	22	and	and	CCONJ
ma-170	442	23	somevariants	somevariant	NOUN
ma-170	442	24	,	,	PUNCT
ma-170	442	25	appl	appl	PROPN
ma-170	442	26	.	.	PROPN
ma-170	442	27	math	math	NOUN
ma-170	442	28	.	.	PUNCT
ma-170	443	1	comput	comput	NOUN
ma-170	443	2	.	.	PUNCT
ma-170	444	1	218	218	NUM
ma-170	444	2	(	(	PUNCT
ma-170	444	3	2012	2012	NUM
ma-170	444	4	)	)	PUNCT
ma-170	444	5	6415–6426	6415–6426	NUM
ma-170	444	6	.	.	PUNCT
ma-170	445	1	https://doi.org/10.1016/j.amc.2011.12.011.[15	https://doi.org/10.1016/j.amc.2011.12.011.[15	PROPN
ma-170	445	2	]	]	PUNCT
ma-170	445	3	m.	m.	NOUN
ma-170	445	4	grau	grau	PROPN
ma-170	445	5	-	-	PUNCT
ma-170	445	6	sanchez	sanchez	PROPN
ma-170	445	7	,	,	PUNCT
ma-170	445	8	m.	m.	NOUN
ma-170	445	9	noguera	noguera	PROPN
ma-170	445	10	,	,	PUNCT
ma-170	445	11	s.	s.	PROPN
ma-170	445	12	amat	amat	PROPN
ma-170	445	13	,	,	PUNCT
ma-170	445	14	on	on	ADP
ma-170	445	15	the	the	DET
ma-170	445	16	approximation	approximation	NOUN
ma-170	445	17	of	of	ADP
ma-170	445	18	derivatives	derivative	NOUN
ma-170	445	19	using	use	VERB
ma-170	445	20	divided	divided	ADJ
ma-170	445	21	difference	difference	NOUN
ma-170	445	22	operatorspreserving	operatorspreserve	VERB
ma-170	445	23	the	the	DET
ma-170	445	24	local	local	ADJ
ma-170	445	25	convergence	convergence	NOUN
ma-170	445	26	order	order	NOUN
ma-170	445	27	of	of	ADP
ma-170	445	28	iterative	iterative	ADJ
ma-170	445	29	methods	method	NOUN
ma-170	445	30	,	,	PUNCT
ma-170	445	31	j.	j.	PROPN
ma-170	445	32	comput	comput	PROPN
ma-170	445	33	.	.	PUNCT
ma-170	446	1	appl	appl	PROPN
ma-170	446	2	.	.	PROPN
ma-170	446	3	math	math	NOUN
ma-170	446	4	.	.	PUNCT
ma-170	447	1	237	237	NUM
ma-170	447	2	(	(	PUNCT
ma-170	447	3	2013	2013	NUM
ma-170	447	4	)	)	PUNCT
ma-170	448	1	363–372	363–372	NUM
ma-170	448	2	.	.	PUNCT
ma-170	448	3	https	https	NOUN
ma-170	448	4	:	:	PUNCT
ma-170	448	5	//doi.org/10.1016	//doi.org/10.1016	PROPN
ma-170	448	6	/	/	SYM
ma-170	448	7	j.cam.2012.06.005.[16	j.cam.2012.06.005.[16	NOUN
ma-170	448	8	]	]	PUNCT
ma-170	448	9	x.	x.	PROPN
ma-170	448	10	wang	wang	PROPN
ma-170	448	11	,	,	PUNCT
ma-170	448	12	t.	t.	PROPN
ma-170	448	13	zhang	zhang	PROPN
ma-170	448	14	,	,	PUNCT
ma-170	448	15	w.	w.	PROPN
ma-170	448	16	qian	qian	PROPN
ma-170	448	17	,	,	PUNCT
ma-170	448	18	m.	m.	NOUN
ma-170	448	19	teng	teng	PROPN
ma-170	448	20	,	,	PUNCT
ma-170	448	21	seventh	seventh	ADJ
ma-170	448	22	-	-	PUNCT
ma-170	448	23	order	order	NOUN
ma-170	448	24	derivative	derivative	ADJ
ma-170	448	25	-	-	PUNCT
ma-170	448	26	free	free	ADJ
ma-170	448	27	iterative	iterative	NOUN
ma-170	448	28	method	method	NOUN
ma-170	448	29	for	for	ADP
ma-170	448	30	solving	solve	VERB
ma-170	448	31	nonlinear	nonlinear	ADJ
ma-170	448	32	systems	system	NOUN
ma-170	448	33	,	,	PUNCT
ma-170	448	34	numer	numer	PROPN
ma-170	448	35	.	.	PROPN
ma-170	448	36	algor	algor	PROPN
ma-170	448	37	.	.	PUNCT
ma-170	449	1	70	70	NUM
ma-170	449	2	(	(	PUNCT
ma-170	449	3	2015	2015	NUM
ma-170	449	4	)	)	PUNCT
ma-170	450	1	545–558	545–558	NUM
ma-170	450	2	.	.	PUNCT
ma-170	451	1	https://doi.org/10.1007/s11075-015-9960-2.[17	https://doi.org/10.1007/s11075-015-9960-2.[17	PROPN
ma-170	451	2	]	]	PUNCT
ma-170	451	3	z.	z.	PROPN
ma-170	451	4	liu	liu	PROPN
ma-170	451	5	,	,	PUNCT
ma-170	451	6	q.	q.	PROPN
ma-170	451	7	zheng	zheng	PROPN
ma-170	451	8	,	,	PUNCT
ma-170	451	9	p.	p.	PROPN
ma-170	451	10	zhao	zhao	PROPN
ma-170	451	11	,	,	PUNCT
ma-170	451	12	a	a	DET
ma-170	451	13	variant	variant	NOUN
ma-170	451	14	of	of	ADP
ma-170	451	15	steffensen	steffensen	NOUN
ma-170	451	16	’s	’s	PART
ma-170	451	17	method	method	NOUN
ma-170	451	18	of	of	ADP
ma-170	451	19	fourth	fourth	ADJ
ma-170	451	20	-	-	PUNCT
ma-170	451	21	order	order	NOUN
ma-170	451	22	convergence	convergence	NOUN
ma-170	451	23	and	and	CCONJ
ma-170	451	24	its	its	PRON
ma-170	451	25	applications	application	NOUN
ma-170	451	26	,	,	PUNCT
ma-170	451	27	appl.math	appl.math	PROPN
ma-170	451	28	.	.	PUNCT
ma-170	451	29	comput	comput	NOUN
ma-170	451	30	.	.	PUNCT
ma-170	452	1	216	216	NUM
ma-170	452	2	(	(	PUNCT
ma-170	452	3	2010	2010	NUM
ma-170	452	4	)	)	PUNCT
ma-170	452	5	1978–1983	1978–1983	NUM
ma-170	452	6	.	.	PUNCT
ma-170	453	1	https://doi.org/10.1016/j.amc.2010.03.028	https://doi.org/10.1016/j.amc.2010.03.028	PROPN
ma-170	453	2	.	.	PUNCT
ma-170	453	3	https://doi.org/10.28924/ada/ma.3.24	https://doi.org/10.28924/ada/ma.3.24	PROPN
ma-170	454	1	https://doi.org/10.1007/s11075-009-9359-z	https://doi.org/10.1007/s11075-009-9359-z	PROPN
ma-170	454	2	https://doi.org/10.1007/s11075-009-9342-8	https://doi.org/10.1007/s11075-009-9342-8	PRON
ma-170	454	3	https://doi.org/10.1080/03461238.1933.10419209	https://doi.org/10.1080/03461238.1933.10419209	VERB
ma-170	454	4	https://doi.org/10.1080/03461238.1933.10419209	https://doi.org/10.1080/03461238.1933.10419209	VERB
ma-170	454	5	https://doi.org/10.1016/j.camwa.2012.03.105	https://doi.org/10.1016/j.camwa.2012.03.105	NOUN
ma-170	454	6	https://doi.org/10.1016/j.camwa.2012.03.105	https://doi.org/10.1016/j.camwa.2012.03.105	NOUN
ma-170	454	7	https://doi.org/10.1016/j.cam.2011.09.009	https://doi.org/10.1016/j.cam.2011.09.009	NUM
ma-170	454	8	https://doi:10.2298	https://doi:10.2298	NOUN
ma-170	454	9	/	/	SYM
ma-170	454	10	aadm130725016s	aadm130725016s	PROPN
ma-170	454	11	https://doi.org/10.1016/j.jco.2019.02.003	https://doi.org/10.1016/j.jco.2019.02.003	NOUN
ma-170	454	12	https://doi.org/10.1016/j.cam.2010.09.019	https://doi.org/10.1016/j.cam.2010.09.019	PROPN
ma-170	454	13	https://doi.org/10.1016/j.amc.2011.12.011	https://doi.org/10.1016/j.amc.2011.12.011	ADJ
ma-170	454	14	https://doi.org/10.1016/j.cam.2012.06.005	https://doi.org/10.1016/j.cam.2012.06.005	PROPN
ma-170	454	15	https://doi.org/10.1016/j.cam.2012.06.005	https://doi.org/10.1016/j.cam.2012.06.005	VERB
ma-170	454	16	https://doi.org/10.1007/s11075-015-9960-2	https://doi.org/10.1007/s11075-015-9960-2	NOUN
ma-170	454	17	https://doi.org/10.1016/j.amc.2010.03.028	https://doi.org/10.1016/j.amc.2010.03.028	NOUN
ma-170	454	18	1	1	NUM
ma-170	454	19	.	.	PUNCT
ma-170	454	20	introduction	introduction	NOUN
ma-170	454	21	2	2	NUM
ma-170	454	22	.	.	PUNCT
ma-170	454	23	local	local	ADJ
ma-170	454	24	convergence	convergence	NOUN
ma-170	454	25	3	3	NUM
ma-170	454	26	.	.	PUNCT
ma-170	455	1	semi	semi	ADJ
ma-170	455	2	-	-	ADJ
ma-170	455	3	local	local	ADJ
ma-170	455	4	analysis	analysis	NOUN
ma-170	455	5	4	4	NUM
ma-170	455	6	.	.	PUNCT
ma-170	455	7	numerical	numerical	ADJ
ma-170	455	8	tests	test	NOUN
ma-170	455	9	5	5	NUM
ma-170	455	10	.	.	PUNCT
ma-170	456	1	conclusion	conclusion	NOUN
ma-170	456	2	references	reference	NOUN