id	sid	tid	token	lemma	pos
ma-173	1	1	2023	2023	NUM
ma-173	1	2	ada	ada	PROPN
ma-173	1	3	academica	academica	PROPN
ma-173	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-173	1	5	.	.	PUNCT
ma-173	2	1	j.	j.	PROPN
ma-173	2	2	math	math	PROPN
ma-173	2	3	.	.	PUNCT
ma-173	3	1	anal	anal	ADJ
ma-173	3	2	.	.	PUNCT
ma-173	4	1	3	3	NUM
ma-173	4	2	(	(	PUNCT
ma-173	4	3	2023	2023	NUM
ma-173	4	4	)	)	PUNCT
ma-173	4	5	26doi	26doi	NOUN
ma-173	4	6	:	:	PUNCT
ma-173	4	7	10.28924	10.28924	NUM
ma-173	4	8	/	/	SYM
ma-173	4	9	ada	ada	NOUN
ma-173	4	10	/	/	SYM
ma-173	4	11	ma.3.26	ma.3.26	NOUN
ma-173	4	12	two	two	NUM
ma-173	4	13	point	point	NOUN
ma-173	4	14	iterative	iterative	NOUN
ma-173	4	15	schemes	scheme	NOUN
ma-173	4	16	for	for	ADP
ma-173	4	17	nondifferentiable	nondifferentiable	ADJ
ma-173	4	18	equations	equation	NOUN
ma-173	4	19	in	in	ADP
ma-173	4	20	banach	banach	NOUN
ma-173	4	21	space	space	NOUN
ma-173	4	22	ioannis	ioannis	PROPN
ma-173	4	23	k.	k.	PROPN
ma-173	4	24	argyros1,∗	argyros1,∗	PROPN
ma-173	4	25	,	,	PUNCT
ma-173	4	26	janak	janak	PROPN
ma-173	4	27	joshi2	joshi2	PROPN
ma-173	4	28	,	,	PUNCT
ma-173	4	29	samundra	samundra	NOUN
ma-173	4	30	regmi3	regmi3	PROPN
ma-173	4	31	1department	1department	NUM
ma-173	4	32	of	of	ADP
ma-173	4	33	computing	computing	NOUN
ma-173	4	34	and	and	CCONJ
ma-173	4	35	mathematical	mathematical	ADJ
ma-173	4	36	sciences	sciences	PROPN
ma-173	4	37	,	,	PUNCT
ma-173	4	38	cameron	cameron	PROPN
ma-173	4	39	university	university	PROPN
ma-173	4	40	,	,	PUNCT
ma-173	4	41	lawton	lawton	PROPN
ma-173	4	42	,	,	PUNCT
ma-173	4	43	ok	ok	PROPN
ma-173	4	44	73505	73505	NUM
ma-173	4	45	,	,	PUNCT
ma-173	4	46	usa	usa	PROPN
ma-173	4	47	iargyros@cameron.edu	iargyros@cameron.edu	PROPN
ma-173	5	1	2department	2department	NUM
ma-173	5	2	of	of	ADP
ma-173	5	3	mathematics	mathematic	NOUN
ma-173	5	4	,	,	PUNCT
ma-173	5	5	dallas	dallas	PROPN
ma-173	5	6	community	community	PROPN
ma-173	5	7	college	college	PROPN
ma-173	5	8	,	,	PUNCT
ma-173	5	9	dallas	dallas	PROPN
ma-173	5	10	,	,	PUNCT
ma-173	5	11	tx	tx	PROPN
ma-173	5	12	,	,	PUNCT
ma-173	5	13	usa	usa	PROPN
ma-173	5	14	janakrajjoshi2036@gmail.com	janakrajjoshi2036@gmail.com	PROPN
ma-173	6	1	3department	3department	NUM
ma-173	6	2	of	of	ADP
ma-173	6	3	mathematics	mathematic	NOUN
ma-173	6	4	,	,	PUNCT
ma-173	6	5	university	university	PROPN
ma-173	6	6	of	of	ADP
ma-173	6	7	houston	houston	PROPN
ma-173	6	8	,	,	PUNCT
ma-173	6	9	houston	houston	PROPN
ma-173	6	10	,	,	PUNCT
ma-173	6	11	77024	77024	NUM
ma-173	6	12	,	,	PUNCT
ma-173	6	13	tx	tx	PROPN
ma-173	6	14	,	,	PUNCT
ma-173	6	15	usa	usa	PROPN
ma-173	6	16	sregmi5@uh.edu	sregmi5@uh.edu	PROPN
ma-173	6	17	∗correspondence	∗correspondence	NOUN
ma-173	6	18	:	:	PUNCT
ma-173	6	19	iargyros@cameron.edu	iargyros@cameron.edu	X
ma-173	7	1	abstract	abstract	ADJ
ma-173	7	2	.	.	PUNCT
ma-173	8	1	the	the	DET
ma-173	8	2	local	local	ADJ
ma-173	8	3	as	as	ADV
ma-173	8	4	well	well	ADV
ma-173	8	5	as	as	ADP
ma-173	8	6	the	the	DET
ma-173	8	7	semi	semi	ADJ
ma-173	8	8	-	-	ADJ
ma-173	8	9	local	local	ADJ
ma-173	8	10	convergence	convergence	NOUN
ma-173	8	11	analysis	analysis	NOUN
ma-173	8	12	is	be	AUX
ma-173	8	13	established	establish	VERB
ma-173	8	14	for	for	ADP
ma-173	8	15	a	a	DET
ma-173	8	16	certain	certain	ADJ
ma-173	8	17	singlestep	singlestep	NOUN
ma-173	8	18	-	-	PUNCT
ma-173	8	19	two	two	NUM
ma-173	8	20	point	point	NOUN
ma-173	8	21	iterative	iterative	NOUN
ma-173	8	22	scheme	scheme	NOUN
ma-173	8	23	defined	define	VERB
ma-173	8	24	on	on	ADP
ma-173	8	25	a	a	DET
ma-173	8	26	banach	banach	NOUN
ma-173	8	27	space	space	NOUN
ma-173	8	28	setting	setting	NOUN
ma-173	8	29	.	.	PUNCT
ma-173	9	1	these	these	DET
ma-173	9	2	schemes	scheme	NOUN
ma-173	9	3	converge	converge	VERB
ma-173	9	4	to	to	ADP
ma-173	9	5	alocally	alocally	ADV
ma-173	9	6	unique	unique	ADJ
ma-173	9	7	solution	solution	NOUN
ma-173	9	8	of	of	ADP
ma-173	9	9	a	a	DET
ma-173	9	10	nonlinear	nonlinear	ADJ
ma-173	9	11	equation	equation	NOUN
ma-173	9	12	.	.	PUNCT
ma-173	10	1	both	both	DET
ma-173	10	2	types	type	NOUN
ma-173	10	3	of	of	ADP
ma-173	10	4	convergence	convergence	NOUN
ma-173	10	5	are	be	AUX
ma-173	10	6	based	base	VERB
ma-173	10	7	on	on	ADP
ma-173	10	8	w	w	NOUN
ma-173	10	9	-	-	PUNCT
ma-173	10	10	typecontinuity	typecontinuity	NOUN
ma-173	10	11	and	and	CCONJ
ma-173	10	12	majorizing	majorizing	NOUN
ma-173	10	13	functions	function	NOUN
ma-173	10	14	and	and	CCONJ
ma-173	10	15	sequences	sequence	NOUN
ma-173	10	16	.	.	PUNCT
ma-173	11	1	an	an	DET
ma-173	11	2	auxiliary	auxiliary	ADJ
ma-173	11	3	fixed	fix	VERB
ma-173	11	4	linear	linear	NOUN
ma-173	11	5	operator	operator	NOUN
ma-173	11	6	is	be	AUX
ma-173	11	7	utilizedto	utilizedto	ADJ
ma-173	11	8	assure	assure	VERB
ma-173	11	9	the	the	DET
ma-173	11	10	existence	existence	NOUN
ma-173	11	11	of	of	ADP
ma-173	11	12	inverses	inverse	NOUN
ma-173	11	13	of	of	ADP
ma-173	11	14	the	the	DET
ma-173	11	15	linear	linear	PROPN
ma-173	11	16	operators	operator	NOUN
ma-173	11	17	involved	involve	VERB
ma-173	11	18	as	as	ADV
ma-173	11	19	well	well	ADV
ma-173	11	20	as	as	ADP
ma-173	11	21	the	the	DET
ma-173	11	22	initial	initial	ADJ
ma-173	11	23	points	point	NOUN
ma-173	11	24	ofthe	ofthe	ADJ
ma-173	11	25	iterative	iterative	NOUN
ma-173	11	26	scheme	scheme	NOUN
ma-173	11	27	.	.	PUNCT
ma-173	12	1	the	the	DET
ma-173	12	2	local	local	ADJ
ma-173	12	3	analysis	analysis	NOUN
ma-173	12	4	provides	provide	VERB
ma-173	12	5	the	the	DET
ma-173	12	6	radius	radius	NOUN
ma-173	12	7	of	of	ADP
ma-173	12	8	convergence	convergence	NOUN
ma-173	12	9	,	,	PUNCT
ma-173	12	10	error	error	NOUN
ma-173	12	11	estimates	estimate	VERB
ma-173	12	12	andinformation	andinformation	NOUN
ma-173	12	13	on	on	ADP
ma-173	12	14	the	the	DET
ma-173	12	15	uniqueness	uniqueness	NOUN
ma-173	12	16	of	of	ADP
ma-173	12	17	the	the	DET
ma-173	12	18	solution	solution	NOUN
ma-173	12	19	.	.	PUNCT
ma-173	13	1	moreover	moreover	ADV
ma-173	13	2	,	,	PUNCT
ma-173	13	3	the	the	DET
ma-173	13	4	semi	semi	ADJ
ma-173	13	5	local	local	ADJ
ma-173	13	6	analysis	analysis	NOUN
ma-173	13	7	provides	provide	VERB
ma-173	13	8	sufficientconvergence	sufficientconvergence	NOUN
ma-173	13	9	conditions	condition	NOUN
ma-173	13	10	,	,	PUNCT
ma-173	13	11	error	error	NOUN
ma-173	13	12	estimates	estimate	NOUN
ma-173	13	13	and	and	CCONJ
ma-173	13	14	uniqueness	uniqueness	NOUN
ma-173	13	15	of	of	ADP
ma-173	13	16	the	the	DET
ma-173	13	17	solution	solution	NOUN
ma-173	13	18	results	result	NOUN
ma-173	13	19	.	.	PUNCT
ma-173	14	1	numerical	numerical	PROPN
ma-173	14	2	examplesfurther	examplesfurther	PROPN
ma-173	14	3	validate	validate	VERB
ma-173	14	4	the	the	DET
ma-173	14	5	theoretical	theoretical	ADJ
ma-173	14	6	results	result	NOUN
ma-173	14	7	.	.	PUNCT
ma-173	15	1	1	1	X
ma-173	15	2	.	.	X
ma-173	15	3	introduction	introduction	NOUN
ma-173	15	4	using	use	VERB
ma-173	15	5	mathematical	mathematical	ADJ
ma-173	15	6	modelling	modelling	NOUN
ma-173	15	7	,	,	PUNCT
ma-173	15	8	a	a	DET
ma-173	15	9	plethora	plethora	NOUN
ma-173	15	10	of	of	ADP
ma-173	15	11	applications	application	NOUN
ma-173	15	12	from	from	ADP
ma-173	15	13	diverse	diverse	ADJ
ma-173	15	14	disciplines	discipline	NOUN
ma-173	15	15	of	of	ADP
ma-173	15	16	science	science	NOUN
ma-173	15	17	andengineering	andengineering	NOUN
ma-173	15	18	reduce	reduce	VERB
ma-173	15	19	to	to	ADP
ma-173	15	20	determining	determine	VERB
ma-173	15	21	solutions	solution	NOUN
ma-173	15	22	denoted	denote	VERB
ma-173	15	23	by	by	ADP
ma-173	15	24	x∗	x∗	PROPN
ma-173	15	25	of	of	ADP
ma-173	15	26	a	a	DET
ma-173	15	27	nonlinear	nonlinear	ADJ
ma-173	15	28	equation	equation	NOUN
ma-173	15	29	like	like	ADP
ma-173	15	30	f	f	PROPN
ma-173	15	31	(	(	PUNCT
ma-173	15	32	x	x	NOUN
ma-173	15	33	)	)	PUNCT
ma-173	15	34	=	=	SYM
ma-173	16	1	0	0	X
ma-173	16	2	.	.	PUNCT
ma-173	17	1	(	(	PUNCT
ma-173	17	2	1.1	1.1	NUM
ma-173	17	3	)	)	PUNCT
ma-173	17	4	here	here	ADV
ma-173	17	5	,	,	PUNCT
ma-173	17	6	f	f	X
ma-173	17	7	:	:	PUNCT
ma-173	17	8	d	d	X
ma-173	17	9	⊂	⊂	PROPN
ma-173	17	10	b	b	X
ma-173	17	11	→	→	SYM
ma-173	17	12	b	b	PROPN
ma-173	17	13	is	be	AUX
ma-173	17	14	a	a	DET
ma-173	17	15	continuous	continuous	ADJ
ma-173	17	16	operator	operator	NOUN
ma-173	17	17	,	,	PUNCT
ma-173	17	18	b	b	NOUN
ma-173	17	19	stands	stand	VERB
ma-173	17	20	for	for	ADP
ma-173	17	21	a	a	DET
ma-173	17	22	banach	banach	NOUN
ma-173	17	23	space	space	NOUN
ma-173	17	24	and	and	CCONJ
ma-173	17	25	d	d	NOUN
ma-173	17	26	is	be	AUX
ma-173	17	27	an	an	DET
ma-173	17	28	open	open	ADJ
ma-173	17	29	setin	setin	NOUN
ma-173	17	30	b.	b.	PROPN
ma-173	17	31	the	the	DET
ma-173	17	32	analytic	analytic	ADJ
ma-173	17	33	form	form	NOUN
ma-173	17	34	of	of	ADP
ma-173	17	35	the	the	DET
ma-173	17	36	solution	solution	NOUN
ma-173	17	37	for	for	ADP
ma-173	17	38	(	(	PUNCT
ma-173	17	39	1.1	1.1	NUM
ma-173	17	40	)	)	PUNCT
ma-173	17	41	can	can	AUX
ma-173	17	42	be	be	AUX
ma-173	17	43	found	find	VERB
ma-173	17	44	only	only	ADV
ma-173	17	45	in	in	ADP
ma-173	17	46	special	special	ADJ
ma-173	17	47	cases	case	NOUN
ma-173	17	48	.	.	PUNCT
ma-173	18	1	that	that	SCONJ
ma-173	18	2	explainswhy	explainswhy	SCONJ
ma-173	18	3	researchers	researcher	NOUN
ma-173	18	4	and	and	CCONJ
ma-173	18	5	practitioners	practitioner	NOUN
ma-173	18	6	resort	resort	VERB
ma-173	18	7	to	to	ADP
ma-173	18	8	iterative	iterative	NOUN
ma-173	18	9	schemes	scheme	NOUN
ma-173	18	10	,	,	PUNCT
ma-173	18	11	when	when	SCONJ
ma-173	18	12	a	a	DET
ma-173	18	13	sequence	sequence	NOUN
ma-173	18	14	is	be	AUX
ma-173	18	15	generatedapproximating	generatedapproximate	VERB
ma-173	18	16	x∗	x∗	PROPN
ma-173	18	17	under	under	ADP
ma-173	18	18	certain	certain	ADJ
ma-173	18	19	conditions	condition	NOUN
ma-173	18	20	.	.	PUNCT
ma-173	19	1	numerous	numerous	ADJ
ma-173	19	2	studies	study	NOUN
ma-173	19	3	exist	exist	VERB
ma-173	19	4	in	in	ADP
ma-173	19	5	the	the	DET
ma-173	19	6	local	local	ADJ
ma-173	19	7	as	as	ADV
ma-173	19	8	well	well	ADV
ma-173	19	9	as	as	ADP
ma-173	19	10	the	the	DET
ma-173	19	11	semi	semi	ADJ
ma-173	19	12	-	-	ADJ
ma-173	19	13	local	local	ADJ
ma-173	19	14	convergence	convergence	NOUN
ma-173	19	15	analysis	analysis	NOUN
ma-173	19	16	of	of	ADP
ma-173	19	17	iter	iter	NOUN
ma-173	19	18	-	-	PUNCT
ma-173	19	19	ative	ative	ADJ
ma-173	19	20	schemes	scheme	NOUN
ma-173	19	21	[	[	X
ma-173	19	22	1–16	1–16	NOUN
ma-173	19	23	]	]	PUNCT
ma-173	19	24	.	.	PUNCT
ma-173	20	1	recently	recently	ADV
ma-173	20	2	,	,	PUNCT
ma-173	20	3	there	there	PRON
ma-173	20	4	has	have	AUX
ma-173	20	5	been	be	AUX
ma-173	20	6	a	a	DET
ma-173	20	7	surge	surge	NOUN
ma-173	20	8	in	in	ADP
ma-173	20	9	the	the	DET
ma-173	20	10	development	development	NOUN
ma-173	20	11	of	of	ADP
ma-173	20	12	schemes	scheme	NOUN
ma-173	20	13	for	for	ADP
ma-173	20	14	solving	solve	VERB
ma-173	20	15	received	receive	VERB
ma-173	20	16	:	:	PUNCT
ma-173	20	17	4	4	NUM
ma-173	20	18	may	may	PROPN
ma-173	20	19	2023	2023	NUM
ma-173	20	20	.	.	PUNCT
ma-173	21	1	key	key	ADJ
ma-173	21	2	words	word	NOUN
ma-173	21	3	and	and	CCONJ
ma-173	21	4	phrases	phrase	NOUN
ma-173	21	5	.	.	PUNCT
ma-173	22	1	two	two	NUM
ma-173	22	2	-	-	PUNCT
ma-173	22	3	point	point	NOUN
ma-173	22	4	iterative	iterative	NOUN
ma-173	22	5	method	method	NOUN
ma-173	22	6	;	;	PUNCT
ma-173	22	7	banach	banach	NOUN
ma-173	22	8	space	space	NOUN
ma-173	22	9	;	;	PUNCT
ma-173	22	10	local	local	ADJ
ma-173	22	11	-	-	PUNCT
ma-173	22	12	semi	semi	ADJ
ma-173	22	13	local	local	ADJ
ma-173	22	14	convergences.1	convergences.1	PROPN
ma-173	22	15	https://adac.ee	https://adac.ee	PROPN
ma-173	22	16	https://doi.org/10.28924/ada/ma.3.26	https://doi.org/10.28924/ada/ma.3.26	ADJ
ma-173	22	17	eur	eur	NOUN
ma-173	22	18	.	.	PUNCT
ma-173	23	1	j.	j.	PROPN
ma-173	23	2	math	math	PROPN
ma-173	23	3	.	.	PUNCT
ma-173	24	1	anal	anal	PROPN
ma-173	24	2	.	.	PUNCT
ma-173	25	1	10.28924	10.28924	NUM
ma-173	25	2	/	/	SYM
ma-173	25	3	ada	ada	NOUN
ma-173	25	4	/	/	SYM
ma-173	25	5	ma.3.26	ma.3.26	NOUN
ma-173	25	6	2equations	2equations	NUM
ma-173	25	7	or	or	CCONJ
ma-173	25	8	systems	system	NOUN
ma-173	25	9	of	of	ADP
ma-173	25	10	equations	equation	NOUN
ma-173	25	11	involving	involve	VERB
ma-173	25	12	nondifferentiable	nondifferentiable	ADJ
ma-173	25	13	operators	operator	NOUN
ma-173	25	14	.	.	PUNCT
ma-173	26	1	looking	look	VERB
ma-173	26	2	towards	towards	ADP
ma-173	26	3	thisdirection	thisdirection	NOUN
ma-173	26	4	,	,	PUNCT
ma-173	26	5	we	we	PRON
ma-173	26	6	develop	develop	VERB
ma-173	26	7	the	the	DET
ma-173	26	8	two	two	NUM
ma-173	26	9	-	-	PUNCT
ma-173	26	10	point	point	NOUN
ma-173	26	11	iterative	iterative	NOUN
ma-173	26	12	scheme	scheme	NOUN
ma-173	26	13	(	(	PUNCT
ma-173	26	14	tips	tip	NOUN
ma-173	26	15	):	):	PUNCT
ma-173	26	16	for	for	ADP
ma-173	26	17	x0	x0	PROPN
ma-173	26	18	∈	∈	PROPN
ma-173	26	19	d	d	NOUN
ma-173	26	20	and	and	CCONJ
ma-173	26	21	each	each	DET
ma-173	26	22	n	n	NOUN
ma-173	26	23	=	=	SYM
ma-173	26	24	0	0	NUM
ma-173	26	25	,	,	PUNCT
ma-173	26	26	1	1	NUM
ma-173	26	27	,	,	PUNCT
ma-173	26	28	2	2	NUM
ma-173	26	29	,	,	PUNCT
ma-173	26	30	.	.	PUNCT
ma-173	26	31	.	.	PUNCT
ma-173	26	32	.	.	PUNCT
ma-173	27	1	by	by	ADP
ma-173	27	2	xn+1	xn+1	PROPN
ma-173	27	3	=	=	SYM
ma-173	27	4	xn	xn	PROPN
ma-173	27	5	−	−	PROPN
ma-173	27	6	a(xn	a(xn	PROPN
ma-173	27	7	,	,	PUNCT
ma-173	27	8	xn−1)−1f	xn−1)−1f	PUNCT
ma-173	27	9	(	(	PUNCT
ma-173	27	10	xn	xn	PROPN
ma-173	27	11	)	)	PUNCT
ma-173	27	12	,	,	PUNCT
ma-173	27	13	(	(	PUNCT
ma-173	27	14	1.2	1.2	NUM
ma-173	27	15	)	)	PUNCT
ma-173	27	16	where	where	SCONJ
ma-173	27	17	a	a	DET
ma-173	27	18	:	:	PUNCT
ma-173	27	19	d	d	NOUN
ma-173	27	20	×d	×d	NOUN
ma-173	27	21	→	→	SYM
ma-173	27	22	l(b	l(b	PROPN
ma-173	27	23	)	)	PUNCT
ma-173	27	24	,	,	PUNCT
ma-173	27	25	the	the	DET
ma-173	27	26	space	space	NOUN
ma-173	27	27	of	of	ADP
ma-173	27	28	bounded	bounded	ADJ
ma-173	27	29	linear	linear	PROPN
ma-173	27	30	operators	operator	NOUN
ma-173	27	31	from	from	ADP
ma-173	27	32	b	b	PROPN
ma-173	27	33	into	into	ADP
ma-173	27	34	b.	b.	PROPN
ma-173	27	35	tpis	tpis	PROPN
ma-173	27	36	specialtiesto	specialtiesto	ADJ
ma-173	27	37	popular	popular	ADJ
ma-173	27	38	schemes	scheme	NOUN
ma-173	27	39	.	.	PUNCT
ma-173	28	1	case	case	NOUN
ma-173	28	2	1	1	NUM
ma-173	28	3	:	:	PUNCT
ma-173	28	4	(	(	PUNCT
ma-173	28	5	secant	secant	ADJ
ma-173	28	6	scheme	scheme	NOUN
ma-173	29	1	[	[	X
ma-173	29	2	1–4,12–15	1–4,12–15	NUM
ma-173	29	3	]	]	X
ma-173	29	4	)	)	PUNCT
ma-173	29	5	set	set	VERB
ma-173	29	6	a(x	a(x	PROPN
ma-173	29	7	,	,	PUNCT
ma-173	29	8	y	y	NOUN
ma-173	29	9	)	)	PUNCT
ma-173	29	10	=	=	PUNCT
ma-173	30	1	[	[	X
ma-173	30	2	x	x	X
ma-173	30	3	,	,	PUNCT
ma-173	30	4	y	y	PROPN
ma-173	30	5	;	;	PUNCT
ma-173	30	6	f	f	X
ma-173	31	1	]	]	X
ma-173	31	2	,	,	PUNCT
ma-173	31	3	where	where	SCONJ
ma-173	31	4	[	[	X
ma-173	31	5	·	·	PUNCT
ma-173	31	6	,	,	PUNCT
ma-173	31	7	·	·	PUNCT
ma-173	31	8	;	;	PUNCT
ma-173	31	9	f	f	X
ma-173	31	10	]	]	PUNCT
ma-173	31	11	:	:	PUNCT
ma-173	31	12	d	d	X
ma-173	31	13	×	×	PROPN
ma-173	31	14	d	d	X
ma-173	31	15	→	→	SYM
ma-173	31	16	(	(	PUNCT
ma-173	31	17	b	b	NOUN
ma-173	31	18	)	)	PUNCT
ma-173	31	19	is	be	AUX
ma-173	31	20	a	a	DET
ma-173	31	21	divided	divided	ADJ
ma-173	31	22	difference	difference	NOUN
ma-173	31	23	oforder	oforder	ADP
ma-173	31	24	one	one	NUM
ma-173	31	25	for	for	ADP
ma-173	31	26	the	the	DET
ma-173	31	27	operator	operator	NOUN
ma-173	32	1	f	f	PROPN
ma-173	33	1	[	[	X
ma-173	33	2	6–8	6–8	X
ma-173	33	3	]	]	X
ma-173	33	4	.	.	PUNCT
ma-173	34	1	under	under	ADP
ma-173	34	2	this	this	DET
ma-173	34	3	choice	choice	NOUN
ma-173	34	4	the	the	DET
ma-173	34	5	scheme	scheme	NOUN
ma-173	34	6	(	(	PUNCT
ma-173	34	7	1.2	1.2	NUM
ma-173	34	8	)	)	PUNCT
ma-173	34	9	specializes	specialize	VERB
ma-173	34	10	to	to	ADP
ma-173	34	11	xn+1	xn+1	PROPN
ma-173	34	12	=	=	SYM
ma-173	34	13	xn	xn	PROPN
ma-173	35	1	−	−	PROPN
ma-173	36	1	[	[	X
ma-173	36	2	xn	xn	X
ma-173	36	3	,	,	PUNCT
ma-173	36	4	xn−1;f	xn−1;f	PROPN
ma-173	36	5	]	]	X
ma-173	36	6	−1f	−1f	PROPN
ma-173	36	7	(	(	PUNCT
ma-173	36	8	xn	xn	PROPN
ma-173	36	9	)	)	PUNCT
ma-173	36	10	.	.	PUNCT
ma-173	37	1	(	(	PUNCT
ma-173	37	2	1.3	1.3	NUM
ma-173	37	3	)	)	PUNCT
ma-173	37	4	case	case	NOUN
ma-173	37	5	2	2	NUM
ma-173	37	6	:	:	PUNCT
ma-173	37	7	(	(	PUNCT
ma-173	37	8	kurchatov	kurchatov	PRON
ma-173	37	9	’s	’s	PART
ma-173	37	10	scheme	scheme	NOUN
ma-173	37	11	[	[	X
ma-173	37	12	12,13])set	12,13])set	NUM
ma-173	37	13	a(x	a(x	NOUN
ma-173	37	14	,	,	PUNCT
ma-173	37	15	y	y	NOUN
ma-173	37	16	)	)	PUNCT
ma-173	37	17	=	=	PUNCT
ma-173	38	1	[	[	X
ma-173	38	2	2x	2x	NUM
ma-173	38	3	−	−	PROPN
ma-173	38	4	y	y	PROPN
ma-173	38	5	,	,	PUNCT
ma-173	38	6	y	y	PROPN
ma-173	38	7	;	;	PUNCT
ma-173	38	8	f	f	PROPN
ma-173	38	9	]	]	PUNCT
ma-173	38	10	.	.	PUNCT
ma-173	39	1	then	then	ADV
ma-173	39	2	,	,	PUNCT
ma-173	39	3	the	the	DET
ma-173	39	4	scheme	scheme	NOUN
ma-173	39	5	(	(	PUNCT
ma-173	39	6	1.2	1.2	NUM
ma-173	39	7	)	)	PUNCT
ma-173	39	8	becomes	become	VERB
ma-173	39	9	:	:	PUNCT
ma-173	39	10	xn+1	xn+1	NUM
ma-173	39	11	=	=	SYM
ma-173	39	12	xn	xn	X
ma-173	40	1	−	−	PROPN
ma-173	41	1	[	[	X
ma-173	41	2	2xn	2xn	ADJ
ma-173	41	3	−	−	NOUN
ma-173	41	4	xn−1	xn−1	PROPN
ma-173	41	5	,	,	PUNCT
ma-173	41	6	xn−1;f	xn−1;f	PROPN
ma-173	41	7	]	]	X
ma-173	41	8	−1f	−1f	PROPN
ma-173	41	9	(	(	PUNCT
ma-173	41	10	xn	xn	PROPN
ma-173	41	11	)	)	PUNCT
ma-173	41	12	.	.	PUNCT
ma-173	42	1	(	(	PUNCT
ma-173	42	2	1.4	1.4	NUM
ma-173	42	3	)	)	PUNCT
ma-173	42	4	case	case	NOUN
ma-173	42	5	3	3	NUM
ma-173	42	6	:	:	PUNCT
ma-173	42	7	(	(	PUNCT
ma-173	42	8	steffensen	steffensen	PROPN
ma-173	42	9	’s	’s	PART
ma-173	42	10	scheme	scheme	NOUN
ma-173	43	1	[	[	X
ma-173	43	2	2	2	NUM
ma-173	43	3	,	,	PUNCT
ma-173	43	4	8	8	NUM
ma-173	43	5	,	,	PUNCT
ma-173	43	6	15])set	15])set	PROPN
ma-173	43	7	a(x	a(x	PROPN
ma-173	43	8	,	,	PUNCT
ma-173	43	9	y	y	NOUN
ma-173	43	10	)	)	PUNCT
ma-173	43	11	=	=	PUNCT
ma-173	44	1	[	[	X
ma-173	44	2	x	x	X
ma-173	44	3	+	+	NUM
ma-173	44	4	f	f	X
ma-173	44	5	(	(	PUNCT
ma-173	44	6	x	x	X
ma-173	44	7	)	)	PUNCT
ma-173	44	8	,	,	PUNCT
ma-173	44	9	y	y	PROPN
ma-173	44	10	;	;	PUNCT
ma-173	44	11	f	f	PROPN
ma-173	44	12	]	]	PUNCT
ma-173	44	13	.	.	PUNCT
ma-173	45	1	then	then	ADV
ma-173	45	2	,	,	PUNCT
ma-173	45	3	the	the	DET
ma-173	45	4	scheme	scheme	NOUN
ma-173	45	5	(	(	PUNCT
ma-173	45	6	1.2	1.2	NUM
ma-173	45	7	)	)	PUNCT
ma-173	45	8	becomes	become	VERB
ma-173	45	9	:	:	PUNCT
ma-173	45	10	xn+1	xn+1	NUM
ma-173	45	11	=	=	SYM
ma-173	45	12	xn	xn	X
ma-173	46	1	−	−	PROPN
ma-173	47	1	[	[	X
ma-173	47	2	x	x	X
ma-173	47	3	+	+	NUM
ma-173	47	4	f	f	X
ma-173	47	5	(	(	PUNCT
ma-173	47	6	x	x	X
ma-173	47	7	)	)	PUNCT
ma-173	47	8	,	,	PUNCT
ma-173	47	9	y	y	PROPN
ma-173	47	10	;	;	PUNCT
ma-173	47	11	f	f	PROPN
ma-173	47	12	]	]	X
ma-173	47	13	−1f	−1f	PROPN
ma-173	47	14	(	(	PUNCT
ma-173	47	15	xn	xn	PROPN
ma-173	47	16	)	)	PUNCT
ma-173	47	17	.	.	PUNCT
ma-173	48	1	(	(	PUNCT
ma-173	48	2	1.5	1.5	NUM
ma-173	48	3	)	)	PUNCT
ma-173	48	4	case	case	NOUN
ma-173	48	5	4	4	NUM
ma-173	48	6	:	:	PUNCT
ma-173	48	7	(	(	PUNCT
ma-173	48	8	picards	picard	NOUN
ma-173	48	9	’s	’s	PART
ma-173	48	10	scheme	scheme	NOUN
ma-173	49	1	[	[	X
ma-173	49	2	1	1	NUM
ma-173	49	3	,	,	PUNCT
ma-173	49	4	3	3	NUM
ma-173	49	5	,	,	PUNCT
ma-173	49	6	8–10,15,16])set	8–10,15,16])set	ADJ
ma-173	49	7	a(x	a(x	PROPN
ma-173	49	8	,	,	PUNCT
ma-173	49	9	y	y	NOUN
ma-173	49	10	)	)	PUNCT
ma-173	50	1	=	=	NOUN
ma-173	50	2	i	i	INTJ
ma-173	50	3	,	,	PUNCT
ma-173	50	4	where	where	SCONJ
ma-173	50	5	i	i	PRON
ma-173	50	6	stands	stand	VERB
ma-173	50	7	for	for	ADP
ma-173	50	8	the	the	DET
ma-173	50	9	identity	identity	NOUN
ma-173	50	10	operator	operator	NOUN
ma-173	50	11	on	on	ADP
ma-173	50	12	b.	b.	PROPN
ma-173	50	13	case	case	NOUN
ma-173	50	14	5	5	NUM
ma-173	50	15	:	:	PUNCT
ma-173	50	16	(	(	PUNCT
ma-173	50	17	newton	newton	PROPN
ma-173	50	18	’s	’s	PART
ma-173	50	19	scheme	scheme	NOUN
ma-173	51	1	[	[	X
ma-173	51	2	1–3,5	1–3,5	NUM
ma-173	51	3	,	,	PUNCT
ma-173	51	4	6	6	NUM
ma-173	51	5	,	,	PUNCT
ma-173	51	6	9	9	NUM
ma-173	51	7	,	,	PUNCT
ma-173	51	8	15,16])set	15,16])set	NUM
ma-173	51	9	a(x	a(x	PROPN
ma-173	51	10	,	,	PUNCT
ma-173	51	11	y	y	NOUN
ma-173	51	12	)	)	PUNCT
ma-173	51	13	=	=	SYM
ma-173	52	1	f	f	NOUN
ma-173	52	2	′(x	′(x	NOUN
ma-173	52	3	)	)	PUNCT
ma-173	52	4	,	,	PUNCT
ma-173	52	5	where	where	SCONJ
ma-173	52	6	f	f	PROPN
ma-173	52	7	′	′	NUM
ma-173	52	8	stands	stand	VERB
ma-173	52	9	for	for	ADP
ma-173	52	10	the	the	DET
ma-173	52	11	fréchet	fréchet	NOUN
ma-173	52	12	derivative	derivative	NOUN
ma-173	52	13	of	of	ADP
ma-173	52	14	the	the	DET
ma-173	52	15	operator	operator	NOUN
ma-173	53	1	f	f	PROPN
ma-173	53	2	.the	.the	PROPN
ma-173	53	3	local	local	ADJ
ma-173	53	4	as	as	ADV
ma-173	53	5	well	well	ADV
ma-173	53	6	as	as	ADP
ma-173	53	7	the	the	DET
ma-173	53	8	semi	semi	ADJ
ma-173	53	9	-	-	ADJ
ma-173	53	10	local	local	ADJ
ma-173	53	11	convergence	convergence	NOUN
ma-173	53	12	results	result	NOUN
ma-173	53	13	for	for	ADP
ma-173	53	14	the	the	DET
ma-173	53	15	aforementioned	aforementioned	ADJ
ma-173	53	16	schemes	scheme	NOUN
ma-173	53	17	involveassumptions	involveassumption	NOUN
ma-173	53	18	on	on	ADP
ma-173	53	19	derivatives	derivative	NOUN
ma-173	53	20	which	which	PRON
ma-173	53	21	do	do	AUX
ma-173	53	22	not	not	PART
ma-173	53	23	appear	appear	VERB
ma-173	53	24	on	on	ADP
ma-173	53	25	some	some	PRON
ma-173	53	26	of	of	ADP
ma-173	53	27	these	these	DET
ma-173	53	28	methods	method	NOUN
ma-173	53	29	(	(	PUNCT
ma-173	53	30	except	except	SCONJ
ma-173	53	31	case	case	NOUN
ma-173	53	32	5	5	NUM
ma-173	53	33	)	)	PUNCT
ma-173	53	34	.	.	PUNCT
ma-173	54	1	therefore	therefore	ADV
ma-173	54	2	,	,	PUNCT
ma-173	54	3	these	these	DET
ma-173	54	4	results	result	NOUN
ma-173	54	5	can	can	AUX
ma-173	54	6	not	not	PART
ma-173	54	7	be	be	AUX
ma-173	54	8	used	use	VERB
ma-173	54	9	to	to	PART
ma-173	54	10	solve	solve	VERB
ma-173	54	11	nondifferentiable	nondifferentiable	ADJ
ma-173	54	12	operator	operator	NOUN
ma-173	54	13	equations	equation	NOUN
ma-173	54	14	(	(	PUNCT
ma-173	54	15	seee.g	seee.g	PROPN
ma-173	54	16	.	.	PROPN
ma-173	54	17	,	,	PUNCT
ma-173	54	18	example	example	NOUN
ma-173	54	19	4.2	4.2	NUM
ma-173	54	20	)	)	PUNCT
ma-173	54	21	.	.	PUNCT
ma-173	55	1	other	other	ADJ
ma-173	55	2	conditions	condition	NOUN
ma-173	55	3	involve	involve	VERB
ma-173	55	4	approximations	approximation	NOUN
ma-173	55	5	to	to	ADP
ma-173	55	6	the	the	DET
ma-173	55	7	divided	divide	VERB
ma-173	55	8	difference	difference	NOUN
ma-173	55	9	and	and	CCONJ
ma-173	55	10	theselection	theselection	NOUN
ma-173	55	11	of	of	ADP
ma-173	55	12	an	an	DET
ma-173	55	13	initial	initial	ADJ
ma-173	55	14	point	point	NOUN
ma-173	55	15	x0	x0	PROPN
ma-173	56	1	so	so	SCONJ
ma-173	56	2	that	that	SCONJ
ma-173	56	3	the	the	DET
ma-173	56	4	first	first	ADJ
ma-173	56	5	iteration	iteration	NOUN
ma-173	56	6	is	be	AUX
ma-173	56	7	computable	computable	ADJ
ma-173	56	8	.	.	PUNCT
ma-173	57	1	in	in	ADP
ma-173	57	2	the	the	DET
ma-173	57	3	present	present	ADJ
ma-173	57	4	article	article	NOUN
ma-173	57	5	,	,	PUNCT
ma-173	57	6	the	the	DET
ma-173	57	7	local	local	ADJ
ma-173	57	8	and	and	CCONJ
ma-173	57	9	semi	semi	ADJ
ma-173	57	10	-	-	ADJ
ma-173	57	11	local	local	ADJ
ma-173	57	12	convergence	convergence	NOUN
ma-173	57	13	of	of	ADP
ma-173	57	14	the	the	DET
ma-173	57	15	scheme	scheme	NOUN
ma-173	57	16	(	(	PUNCT
ma-173	57	17	1.2	1.2	NUM
ma-173	57	18	)	)	PUNCT
ma-173	57	19	is	be	AUX
ma-173	57	20	investi	investi	PROPN
ma-173	57	21	-	-	PUNCT
ma-173	57	22	gated	gate	VERB
ma-173	57	23	under	under	ADP
ma-173	57	24	w	w	NOUN
ma-173	57	25	-	-	PUNCT
ma-173	57	26	continuity	continuity	NOUN
ma-173	57	27	-	-	PUNCT
ma-173	57	28	type	type	NOUN
ma-173	57	29	conditions	condition	NOUN
ma-173	57	30	.	.	PUNCT
ma-173	58	1	moreover	moreover	ADV
ma-173	58	2	,	,	PUNCT
ma-173	58	3	by	by	ADP
ma-173	58	4	introducing	introduce	VERB
ma-173	58	5	a	a	DET
ma-173	58	6	certain	certain	ADJ
ma-173	58	7	linear	linear	NOUN
ma-173	58	8	operator	operator	NOUN
ma-173	58	9	p	p	NOUN
ma-173	58	10	,	,	PUNCT
ma-173	58	11	then	then	ADV
ma-173	58	12	invertibility	invertibility	NOUN
ma-173	58	13	of	of	ADP
ma-173	58	14	the	the	DET
ma-173	58	15	linear	linear	ADJ
ma-173	58	16	operator	operator	NOUN
ma-173	58	17	a	a	PRON
ma-173	58	18	is	be	AUX
ma-173	58	19	assured	assure	VERB
ma-173	58	20	in	in	ADP
ma-173	58	21	a	a	DET
ma-173	58	22	certain	certain	ADJ
ma-173	58	23	subset	subset	NOUN
ma-173	58	24	of	of	ADP
ma-173	58	25	d	d	PROPN
ma-173	58	26	from	from	ADP
ma-173	58	27	which	which	PRON
ma-173	58	28	the	the	DET
ma-173	58	29	initial	initial	ADJ
ma-173	58	30	https://doi.org/10.28924/ada/ma.3.26	https://doi.org/10.28924/ada/ma.3.26	ADJ
ma-173	58	31	eur	eur	NOUN
ma-173	58	32	.	.	PUNCT
ma-173	59	1	j.	j.	PROPN
ma-173	59	2	math	math	PROPN
ma-173	59	3	.	.	PUNCT
ma-173	60	1	anal	anal	PROPN
ma-173	60	2	.	.	PUNCT
ma-173	61	1	10.28924	10.28924	NUM
ma-173	61	2	/	/	SYM
ma-173	61	3	ada	ada	NOUN
ma-173	61	4	/	/	SYM
ma-173	61	5	ma.3.26	ma.3.26	NOUN
ma-173	61	6	3point	3point	NUM
ma-173	61	7	is	be	AUX
ma-173	61	8	selected	select	VERB
ma-173	61	9	.	.	PUNCT
ma-173	62	1	the	the	DET
ma-173	62	2	rest	rest	NOUN
ma-173	62	3	of	of	ADP
ma-173	62	4	the	the	DET
ma-173	62	5	article	article	NOUN
ma-173	62	6	is	be	AUX
ma-173	62	7	structured	structure	VERB
ma-173	62	8	as	as	SCONJ
ma-173	62	9	follows	follow	VERB
ma-173	62	10	:	:	PUNCT
ma-173	62	11	the	the	DET
ma-173	62	12	local	local	ADJ
ma-173	62	13	and	and	CCONJ
ma-173	62	14	the	the	DET
ma-173	62	15	semi	semi	NOUN
ma-173	62	16	-	-	NOUN
ma-173	62	17	localconvergence	localconvergence	NOUN
ma-173	62	18	of	of	ADP
ma-173	62	19	the	the	DET
ma-173	62	20	scheme	scheme	NOUN
ma-173	62	21	(	(	PUNCT
ma-173	62	22	1.2	1.2	NUM
ma-173	62	23	)	)	PUNCT
ma-173	62	24	appear	appear	VERB
ma-173	62	25	in	in	ADP
ma-173	62	26	section	section	NOUN
ma-173	62	27	2	2	NUM
ma-173	62	28	and	and	CCONJ
ma-173	62	29	section	section	NOUN
ma-173	62	30	3	3	NUM
ma-173	62	31	,	,	PUNCT
ma-173	62	32	respectively	respectively	ADV
ma-173	62	33	.	.	PUNCT
ma-173	63	1	the	the	DET
ma-173	63	2	examplescan	examplescan	NOUN
ma-173	63	3	be	be	AUX
ma-173	63	4	found	find	VERB
ma-173	63	5	in	in	ADP
ma-173	63	6	section	section	NOUN
ma-173	63	7	4	4	NUM
ma-173	63	8	.	.	PUNCT
ma-173	64	1	the	the	DET
ma-173	64	2	article	article	NOUN
ma-173	64	3	is	be	AUX
ma-173	64	4	completed	complete	VERB
ma-173	64	5	the	the	DET
ma-173	64	6	conclusions	conclusion	NOUN
ma-173	64	7	in	in	ADP
ma-173	64	8	section	section	NOUN
ma-173	64	9	5	5	NUM
ma-173	64	10	.	.	NOUN
ma-173	64	11	2	2	NUM
ma-173	64	12	.	.	X
ma-173	64	13	convergence	convergence	NOUN
ma-173	65	1	i	i	PRON
ma-173	65	2	:	:	PUNCT
ma-173	65	3	local	local	VERB
ma-173	65	4	some	some	DET
ma-173	65	5	real	real	ADJ
ma-173	65	6	functions	function	NOUN
ma-173	65	7	are	be	AUX
ma-173	65	8	introduced	introduce	VERB
ma-173	65	9	that	that	PRON
ma-173	65	10	play	play	VERB
ma-173	65	11	a	a	DET
ma-173	65	12	role	role	NOUN
ma-173	65	13	in	in	ADP
ma-173	65	14	the	the	DET
ma-173	65	15	local	local	ADJ
ma-173	65	16	convergence	convergence	NOUN
ma-173	65	17	analysis	analysis	NOUN
ma-173	65	18	of	of	ADP
ma-173	65	19	thescheme	thescheme	NOUN
ma-173	65	20	(	(	PUNCT
ma-173	65	21	1.2	1.2	NUM
ma-173	65	22	)	)	PUNCT
ma-173	65	23	.	.	PUNCT
ma-173	66	1	let	let	VERB
ma-173	66	2	t	t	NOUN
ma-173	66	3	=	=	PUNCT
ma-173	67	1	[	[	X
ma-173	67	2	0,∞	0,∞	NUM
ma-173	67	3	)	)	PUNCT
ma-173	67	4	.	.	PUNCT
ma-173	68	1	assume	assume	VERB
ma-173	68	2	:	:	PUNCT
ma-173	68	3	(	(	PUNCT
ma-173	68	4	a1	a1	NOUN
ma-173	68	5	)	)	PUNCT
ma-173	68	6	there	there	PRON
ma-173	68	7	exists	exist	VERB
ma-173	68	8	a	a	DET
ma-173	68	9	continuous	continuous	ADJ
ma-173	68	10	and	and	CCONJ
ma-173	68	11	nondecreasing	nondecreasing	ADJ
ma-173	68	12	function	function	NOUN
ma-173	68	13	(	(	PUNCT
ma-173	68	14	cnf	cnf	PROPN
ma-173	68	15	)	)	PUNCT
ma-173	68	16	w0	w0	PROPN
ma-173	68	17	:	:	PUNCT
ma-173	68	18	t	t	PROPN
ma-173	68	19	×	×	PROPN
ma-173	68	20	t	t	PROPN
ma-173	68	21	→	→	SYM
ma-173	68	22	t	t	PROPN
ma-173	68	23	such	such	ADJ
ma-173	68	24	thatthe	thatthe	PRON
ma-173	68	25	equation	equation	NOUN
ma-173	68	26	w0(t	w0(t	PROPN
ma-173	68	27	,	,	PUNCT
ma-173	68	28	t)−	t)−	PROPN
ma-173	68	29	1	1	NUM
ma-173	69	1	=	=	SYM
ma-173	69	2	0has	0ha	NOUN
ma-173	69	3	a	a	DET
ma-173	69	4	smallest	small	ADJ
ma-173	69	5	solution	solution	NOUN
ma-173	69	6	r	r	NOUN
ma-173	69	7	∈	∈	PROPN
ma-173	69	8	t0	t0	PROPN
ma-173	70	1	−	−	PROPN
ma-173	70	2	{	{	PUNCT
ma-173	70	3	0}.set	0}.set	NOUN
ma-173	70	4	t0	t0	PROPN
ma-173	70	5	=	=	PUNCT
ma-173	71	1	[	[	X
ma-173	71	2	0	0	NUM
ma-173	71	3	,	,	PUNCT
ma-173	71	4	r0	r0	NOUN
ma-173	71	5	)	)	PUNCT
ma-173	71	6	and	and	CCONJ
ma-173	71	7	d1	d1	PROPN
ma-173	71	8	=	=	PUNCT
ma-173	72	1	d	d	X
ma-173	72	2	∪	∪	ADP
ma-173	72	3	u(x∗	u(x∗	PROPN
ma-173	72	4	,	,	PUNCT
ma-173	72	5	r	r	NOUN
ma-173	72	6	)	)	PUNCT
ma-173	72	7	.	.	PUNCT
ma-173	73	1	moreover	moreover	ADV
ma-173	73	2	,	,	PUNCT
ma-173	73	3	there	there	PRON
ma-173	73	4	exists	exist	VERB
ma-173	73	5	cnf	cnf	PROPN
ma-173	73	6	w	w	PROPN
ma-173	73	7	:	:	PUNCT
ma-173	73	8	t0	t0	PROPN
ma-173	73	9	→	→	PUNCT
ma-173	73	10	t	t	PROPN
ma-173	73	11	suchthat	suchthat	VERB
ma-173	73	12	the	the	DET
ma-173	73	13	equation	equation	NOUN
ma-173	73	14	h(t)−	h(t)−	PROPN
ma-173	73	15	1	1	NUM
ma-173	73	16	=	=	SYM
ma-173	73	17	0	0	PROPN
ma-173	73	18	has	have	VERB
ma-173	73	19	a	a	DET
ma-173	73	20	smallest	small	ADJ
ma-173	73	21	solution	solution	NOUN
ma-173	73	22	r	r	NOUN
ma-173	73	23	∈	∈	PROPN
ma-173	73	24	(	(	PUNCT
ma-173	73	25	0	0	NUM
ma-173	73	26	,	,	PUNCT
ma-173	73	27	r0	r0	NOUN
ma-173	73	28	)	)	PUNCT
ma-173	73	29	,	,	PUNCT
ma-173	73	30	where	where	SCONJ
ma-173	73	31	h(t	h(t	X
ma-173	73	32	)	)	PUNCT
ma-173	73	33	=	=	SYM
ma-173	73	34	w(t	w(t	PROPN
ma-173	73	35	,	,	PUNCT
ma-173	73	36	t	t	PROPN
ma-173	73	37	)	)	PUNCT
ma-173	73	38	1−	1−	NUM
ma-173	73	39	w0(t	w0(t	PROPN
ma-173	73	40	,	,	PUNCT
ma-173	73	41	t	t	PROPN
ma-173	73	42	)	)	PUNCT
ma-173	73	43	.	.	PUNCT
ma-173	74	1	let	let	VERB
ma-173	74	2	t1	t1	NOUN
ma-173	74	3	=	=	PUNCT
ma-173	75	1	[	[	X
ma-173	75	2	0	0	NUM
ma-173	75	3	,	,	PUNCT
ma-173	75	4	r	r	NOUN
ma-173	75	5	)	)	PUNCT
ma-173	75	6	.	.	PUNCT
ma-173	75	7	0	0	NUM
ma-173	76	1	≤	≤	NUM
ma-173	76	2	w0(t	w0(t	PROPN
ma-173	76	3	,	,	PUNCT
ma-173	76	4	t	t	PROPN
ma-173	76	5	)	)	PUNCT
ma-173	76	6	<	<	X
ma-173	76	7	1	1	NUM
ma-173	76	8	(	(	PUNCT
ma-173	76	9	2.6)and	2.6)and	NUM
ma-173	76	10	0	0	NUM
ma-173	76	11	≤	≤	NUM
ma-173	76	12	h(t	h(t	PROPN
ma-173	76	13	)	)	PUNCT
ma-173	76	14	<	<	X
ma-173	76	15	1	1	NUM
ma-173	76	16	(	(	PUNCT
ma-173	76	17	2.7)from	2.7)from	NUM
ma-173	76	18	now	now	ADV
ma-173	76	19	on	on	ADV
ma-173	76	20	we	we	PRON
ma-173	76	21	assume	assume	VERB
ma-173	76	22	that	that	SCONJ
ma-173	76	23	x∗	x∗	PROPN
ma-173	76	24	∈	∈	PROPN
ma-173	76	25	d	d	NOUN
ma-173	76	26	is	be	AUX
ma-173	76	27	a	a	DET
ma-173	76	28	solution	solution	NOUN
ma-173	76	29	of	of	ADP
ma-173	76	30	the	the	DET
ma-173	76	31	equation	equation	NOUN
ma-173	76	32	f	f	X
ma-173	76	33	(	(	PUNCT
ma-173	76	34	x	x	X
ma-173	76	35	)	)	PUNCT
ma-173	76	36	=	=	SYM
ma-173	76	37	0	0	NUM
ma-173	76	38	and	and	CCONJ
ma-173	76	39	the	the	DET
ma-173	76	40	divideddifference	divideddifference	NOUN
ma-173	77	1	[	[	X
ma-173	77	2	∗	∗	NOUN
ma-173	77	3	,	,	PUNCT
ma-173	77	4	∗;f	∗;f	NUM
ma-173	77	5	]	]	PUNCT
ma-173	77	6	exists	exist	VERB
ma-173	77	7	on	on	ADP
ma-173	77	8	d×d	d×d	PROPN
ma-173	77	9	.	.	PUNCT
ma-173	78	1	the	the	DET
ma-173	78	2	functions	function	NOUN
ma-173	78	3	w0	w0	PROPN
ma-173	78	4	and	and	CCONJ
ma-173	78	5	w	w	NOUN
ma-173	78	6	are	be	AUX
ma-173	78	7	connected	connect	VERB
ma-173	78	8	to	to	ADP
ma-173	78	9	the	the	DET
ma-173	78	10	operatorson	operatorson	NOUN
ma-173	78	11	the	the	DET
ma-173	78	12	scheme	scheme	NOUN
ma-173	78	13	(	(	PUNCT
ma-173	78	14	1.2	1.2	NUM
ma-173	78	15	)	)	PUNCT
ma-173	78	16	.	.	PUNCT
ma-173	79	1	(	(	PUNCT
ma-173	79	2	a2	a2	PROPN
ma-173	79	3	)	)	PUNCT
ma-173	79	4	there	there	PRON
ma-173	79	5	exists	exist	VERB
ma-173	79	6	an	an	DET
ma-173	79	7	invertible	invertible	ADJ
ma-173	79	8	operator	operator	NOUN
ma-173	79	9	p	p	PRON
ma-173	79	10	such	such	ADJ
ma-173	79	11	that	that	PRON
ma-173	79	12	for	for	ADP
ma-173	79	13	each	each	DET
ma-173	79	14	x	x	NOUN
ma-173	79	15	,	,	PUNCT
ma-173	79	16	y	y	PROPN
ma-173	79	17	∈	∈	PROPN
ma-173	79	18	d	d	X
ma-173	79	19	‖p−1(a(x	‖p−1(a(x	NOUN
ma-173	79	20	,	,	PUNCT
ma-173	79	21	y)−	y)−	PROPN
ma-173	79	22	p	p	NOUN
ma-173	79	23	)	)	PUNCT
ma-173	79	24	‖	‖	PROPN
ma-173	79	25	≤	≤	PROPN
ma-173	79	26	w0(‖x	w0(‖x	CCONJ
ma-173	79	27	−	−	PROPN
ma-173	79	28	x∗‖	x∗‖	PROPN
ma-173	79	29	,	,	PUNCT
ma-173	79	30	‖y	‖y	PUNCT
ma-173	79	31	−	−	PUNCT
ma-173	79	32	x∗‖	x∗‖	NUM
ma-173	79	33	)	)	PUNCT
ma-173	79	34	.	.	PUNCT
ma-173	80	1	(	(	PUNCT
ma-173	80	2	a3	a3	NOUN
ma-173	80	3	)	)	PUNCT
ma-173	80	4	‖p−1(a(x	‖p−1(a(x	PROPN
ma-173	80	5	,	,	PUNCT
ma-173	80	6	y)−	y)−	PROPN
ma-173	81	1	[	[	X
ma-173	81	2	x	x	X
ma-173	81	3	,	,	PUNCT
ma-173	81	4	x∗;f	x∗;f	PROPN
ma-173	81	5	]	]	X
ma-173	81	6	)	)	PUNCT
ma-173	81	7	‖	‖	PROPN
ma-173	81	8	≤	≤	NOUN
ma-173	81	9	w(‖x	w(‖x	PUNCT
ma-173	81	10	−	−	PROPN
ma-173	81	11	x∗‖	x∗‖	PROPN
ma-173	81	12	,	,	PUNCT
ma-173	81	13	‖y	‖y	PUNCT
ma-173	82	1	−	−	PROPN
ma-173	83	1	x∗‖	x∗‖	NUM
ma-173	83	2	)	)	PUNCT
ma-173	84	1	for	for	ADP
ma-173	84	2	each	each	DET
ma-173	84	3	x	x	NOUN
ma-173	84	4	,	,	PUNCT
ma-173	84	5	y	y	PROPN
ma-173	84	6	∈	∈	PROPN
ma-173	84	7	d1and	d1and	PROPN
ma-173	84	8	(	(	PUNCT
ma-173	84	9	a4	a4	NOUN
ma-173	84	10	)	)	PUNCT
ma-173	84	11	u[x	u[x	DET
ma-173	84	12	∗	∗	NOUN
ma-173	84	13	,	,	PUNCT
ma-173	84	14	r	r	NOUN
ma-173	84	15	]	]	PUNCT
ma-173	84	16	⊂	⊂	PROPN
ma-173	84	17	d.next	d.next	PROPN
ma-173	84	18	,	,	PUNCT
ma-173	84	19	the	the	DET
ma-173	84	20	local	local	ADJ
ma-173	84	21	convergence	convergence	NOUN
ma-173	84	22	of	of	ADP
ma-173	84	23	the	the	DET
ma-173	84	24	scheme	scheme	NOUN
ma-173	84	25	(	(	PUNCT
ma-173	84	26	1.2	1.2	NUM
ma-173	84	27	)	)	PUNCT
ma-173	84	28	is	be	AUX
ma-173	84	29	provided	provide	VERB
ma-173	84	30	based	base	VERB
ma-173	84	31	on	on	ADP
ma-173	84	32	the	the	DET
ma-173	84	33	conditions	condition	NOUN
ma-173	84	34	(	(	PUNCT
ma-173	84	35	a1	a1	NOUN
ma-173	84	36	)	)	PUNCT
ma-173	84	37	−	−	PROPN
ma-173	84	38	(	(	PUNCT
ma-173	84	39	a4)and	a4)and	ADP
ma-173	84	40	the	the	DET
ma-173	84	41	developed	develop	VERB
ma-173	84	42	terminology	terminology	NOUN
ma-173	84	43	.	.	PUNCT
ma-173	85	1	theorem	theorem	VERB
ma-173	85	2	2.1	2.1	NUM
ma-173	85	3	.	.	PUNCT
ma-173	86	1	assume	assume	VERB
ma-173	86	2	that	that	SCONJ
ma-173	86	3	the	the	DET
ma-173	86	4	conditions	condition	NOUN
ma-173	86	5	(	(	PUNCT
ma-173	86	6	a1)−(a4	a1)−(a4	NOUN
ma-173	86	7	)	)	PUNCT
ma-173	86	8	are	be	AUX
ma-173	86	9	validated	validate	VERB
ma-173	86	10	.	.	PUNCT
ma-173	87	1	if	if	SCONJ
ma-173	87	2	the	the	DET
ma-173	87	3	initial	initial	ADJ
ma-173	87	4	points	point	NOUN
ma-173	87	5	x−1	x−1	PROPN
ma-173	87	6	,	,	PUNCT
ma-173	87	7	x0	x0	PROPN
ma-173	87	8	∈	∈	PROPN
ma-173	87	9	u(x∗	u(x∗	PROPN
ma-173	87	10	,	,	PUNCT
ma-173	87	11	r)−{x∗	r)−{x∗	PROPN
ma-173	87	12	}	}	PUNCT
ma-173	87	13	,	,	PUNCT
ma-173	87	14	then	then	ADV
ma-173	87	15	the	the	DET
ma-173	87	16	sequence	sequence	NOUN
ma-173	87	17	{	{	PUNCT
ma-173	87	18	xn	xn	PROPN
ma-173	87	19	}	}	PUNCT
ma-173	87	20	generated	generate	VERB
ma-173	87	21	by	by	ADP
ma-173	87	22	the	the	DET
ma-173	87	23	scheme	scheme	NOUN
ma-173	87	24	(	(	PUNCT
ma-173	87	25	1.2	1.2	NUM
ma-173	87	26	)	)	PUNCT
ma-173	87	27	is	be	AUX
ma-173	87	28	well	well	ADV
ma-173	87	29	defined	define	VERB
ma-173	87	30	in	in	ADP
ma-173	87	31	u(x∗	u(x∗	PROPN
ma-173	87	32	,	,	PUNCT
ma-173	87	33	r	r	NOUN
ma-173	87	34	)	)	PUNCT
ma-173	87	35	for	for	ADP
ma-173	87	36	each	each	DET
ma-173	87	37	n	n	NOUN
ma-173	87	38	=	=	SYM
ma-173	87	39	0	0	NUM
ma-173	87	40	,	,	PUNCT
ma-173	87	41	1	1	NUM
ma-173	87	42	,	,	PUNCT
ma-173	87	43	2	2	NUM
ma-173	87	44	,	,	PUNCT
ma-173	87	45	3	3	NUM
ma-173	87	46	,	,	PUNCT
ma-173	87	47	.	.	PUNCT
ma-173	87	48	.	.	PUNCT
ma-173	87	49	.	.	PUNCT
ma-173	88	1	and	and	CCONJ
ma-173	88	2	is	be	AUX
ma-173	88	3	convergent	convergent	ADJ
ma-173	88	4	to	to	ADP
ma-173	88	5	the	the	DET
ma-173	88	6	solution	solution	NOUN
ma-173	88	7	x∗	x∗	PROPN
ma-173	88	8	of	of	ADP
ma-173	88	9	the	the	DET
ma-173	88	10	equation	equation	NOUN
ma-173	88	11	f	f	X
ma-173	88	12	(	(	PUNCT
ma-173	88	13	x	x	X
ma-173	88	14	)	)	PUNCT
ma-173	88	15	=	=	SYM
ma-173	88	16	0	0	NUM
ma-173	88	17	,	,	PUNCT
ma-173	88	18	so	so	SCONJ
ma-173	88	19	that	that	SCONJ
ma-173	88	20	‖xn+1	‖xn+1	NUM
ma-173	88	21	−	−	X
ma-173	88	22	x∗‖	x∗‖	PROPN
ma-173	88	23	≤	≤	PROPN
ma-173	88	24	h(‖xn	h(‖xn	PUNCT
ma-173	88	25	−	−	PROPN
ma-173	88	26	x∗‖)‖xn	x∗‖)‖xn	PUNCT
ma-173	89	1	−	−	PROPN
ma-173	89	2	x∗‖	x∗‖	PROPN
ma-173	89	3	≤	≤	NOUN
ma-173	90	1	‖xn	‖xn	PROPN
ma-173	90	2	−	−	PROPN
ma-173	91	1	x∗‖	x∗‖	X
ma-173	91	2	<	<	X
ma-173	91	3	r	r	X
ma-173	91	4	(	(	PUNCT
ma-173	91	5	2.8	2.8	NUM
ma-173	91	6	)	)	PUNCT
ma-173	91	7	https://doi.org/10.28924/ada/ma.3.26	https://doi.org/10.28924/ada/ma.3.26	ADJ
ma-173	91	8	eur	eur	NOUN
ma-173	91	9	.	.	PUNCT
ma-173	92	1	j.	j.	PROPN
ma-173	92	2	math	math	PROPN
ma-173	92	3	.	.	PUNCT
ma-173	93	1	anal	anal	PROPN
ma-173	93	2	.	.	PUNCT
ma-173	94	1	10.28924	10.28924	NUM
ma-173	94	2	/	/	SYM
ma-173	94	3	ada	ada	NOUN
ma-173	94	4	/	/	SYM
ma-173	94	5	ma.3.26	ma.3.26	NOUN
ma-173	94	6	4	4	NUM
ma-173	94	7	where	where	SCONJ
ma-173	94	8	the	the	DET
ma-173	94	9	radius	radius	NOUN
ma-173	94	10	of	of	ADP
ma-173	94	11	convergence	convergence	NOUN
ma-173	94	12	r	r	NOUN
ma-173	94	13	is	be	AUX
ma-173	94	14	defined	define	VERB
ma-173	94	15	in	in	ADP
ma-173	94	16	(	(	PUNCT
ma-173	94	17	a1	a1	NOUN
ma-173	94	18	)	)	PUNCT
ma-173	94	19	and	and	CCONJ
ma-173	94	20	the	the	DET
ma-173	94	21	function	function	NOUN
ma-173	94	22	h	h	NOUN
ma-173	94	23	is	be	AUX
ma-173	94	24	also	also	ADV
ma-173	94	25	given	give	VERB
ma-173	94	26	in	in	ADP
ma-173	94	27	(	(	PUNCT
ma-173	94	28	a1	a1	NOUN
ma-173	94	29	)	)	PUNCT
ma-173	94	30	.	.	PUNCT
ma-173	95	1	proof	proof	NOUN
ma-173	95	2	.	.	PUNCT
ma-173	96	1	by	by	ADP
ma-173	96	2	hypothesis	hypothesis	NOUN
ma-173	96	3	,	,	PUNCT
ma-173	96	4	x−1	x−1	PROPN
ma-173	96	5	,	,	PUNCT
ma-173	96	6	x0	x0	PROPN
ma-173	96	7	,	,	PUNCT
ma-173	96	8	(	(	PUNCT
ma-173	96	9	a2	a2	PROPN
ma-173	96	10	)	)	PUNCT
ma-173	96	11	and	and	CCONJ
ma-173	96	12	(	(	PUNCT
ma-173	96	13	a3	a3	NOUN
ma-173	96	14	)	)	PUNCT
ma-173	96	15	we	we	PRON
ma-173	96	16	obtain	obtain	VERB
ma-173	96	17	in	in	ADP
ma-173	96	18	turn	turn	NOUN
ma-173	96	19	that	that	PRON
ma-173	96	20	:	:	PUNCT
ma-173	96	21	‖p−1(a(x0	‖p−1(a(x0	ADP
ma-173	96	22	,	,	PUNCT
ma-173	96	23	x−1)−	x−1)−	NOUN
ma-173	96	24	p	p	NOUN
ma-173	96	25	)	)	PUNCT
ma-173	96	26	‖	‖	PROPN
ma-173	96	27	≤	≤	PROPN
ma-173	96	28	wo(‖x0	wo(‖x0	PROPN
ma-173	96	29	−	−	PROPN
ma-173	96	30	x∗‖	x∗‖	PROPN
ma-173	96	31	,	,	PUNCT
ma-173	96	32	‖x−1	‖x−1	ADP
ma-173	96	33	−	−	PROPN
ma-173	96	34	x∗‖	x∗‖	NUM
ma-173	96	35	)	)	PUNCT
ma-173	96	36	≤	≤	NOUN
ma-173	96	37	w0(r	w0(r	PROPN
ma-173	96	38	,	,	PUNCT
ma-173	96	39	r	r	NOUN
ma-173	96	40	)	)	PUNCT
ma-173	96	41	<	<	X
ma-173	96	42	1	1	NUM
ma-173	96	43	.	.	PUNCT
ma-173	96	44	(	(	PUNCT
ma-173	96	45	2.9	2.9	NUM
ma-173	96	46	)	)	PUNCT
ma-173	96	47	the	the	DET
ma-173	96	48	estimate	estimate	NOUN
ma-173	96	49	(	(	PUNCT
ma-173	96	50	2.9	2.9	NUM
ma-173	96	51	)	)	PUNCT
ma-173	96	52	and	and	CCONJ
ma-173	96	53	the	the	DET
ma-173	96	54	banach	banach	ADV
ma-173	96	55	lemma	lemma	PROPN
ma-173	96	56	on	on	ADP
ma-173	96	57	invertible	invertible	ADJ
ma-173	96	58	operators	operator	NOUN
ma-173	97	1	[	[	X
ma-173	97	2	1–3	1–3	NOUN
ma-173	97	3	,	,	PUNCT
ma-173	97	4	8	8	NUM
ma-173	97	5	,	,	PUNCT
ma-173	97	6	9	9	NUM
ma-173	97	7	]	]	PUNCT
ma-173	97	8	assure	assure	NOUN
ma-173	97	9	the	the	DET
ma-173	97	10	existenceof	existenceof	PROPN
ma-173	97	11	a(x0	a(x0	NOUN
ma-173	97	12	,	,	PUNCT
ma-173	97	13	x−1)−1l(b	x−1)−1l(b	PROPN
ma-173	97	14	)	)	PUNCT
ma-173	97	15	and	and	CCONJ
ma-173	97	16	‖a(x0	‖a(x0	NUM
ma-173	97	17	,	,	PUNCT
ma-173	97	18	x−1)−1p‖	x−1)−1p‖	PROPN
ma-173	97	19	≤	≤	NOUN
ma-173	97	20	1	1	NUM
ma-173	97	21	1−	1−	NUM
ma-173	98	1	w0(‖x0	w0(‖x0	PROPN
ma-173	98	2	−	−	PROPN
ma-173	98	3	x∗‖	x∗‖	PROPN
ma-173	98	4	,	,	PUNCT
ma-173	98	5	‖x−1	‖x−1	ADP
ma-173	98	6	−	−	PROPN
ma-173	98	7	x∗‖	x∗‖	NUM
ma-173	98	8	)	)	PUNCT
ma-173	98	9	.	.	PUNCT
ma-173	99	1	(	(	PUNCT
ma-173	99	2	2.10	2.10	NUM
ma-173	99	3	)	)	PUNCT
ma-173	99	4	moreover	moreover	ADV
ma-173	99	5	,	,	PUNCT
ma-173	99	6	the	the	DET
ma-173	99	7	iterate	iterate	NOUN
ma-173	99	8	x1	x1	PRON
ma-173	99	9	is	be	AUX
ma-173	99	10	well	well	ADV
ma-173	99	11	defined	define	VERB
ma-173	99	12	by	by	ADP
ma-173	99	13	the	the	DET
ma-173	99	14	first	first	ADJ
ma-173	99	15	subset	subset	NOUN
ma-173	99	16	of	of	ADP
ma-173	99	17	the	the	DET
ma-173	99	18	scheme	scheme	NOUN
ma-173	99	19	(	(	PUNCT
ma-173	99	20	1.2	1.2	NUM
ma-173	99	21	)	)	PUNCT
ma-173	99	22	.	.	PUNCT
ma-173	100	1	then	then	ADV
ma-173	100	2	,	,	PUNCT
ma-173	100	3	we	we	PRON
ma-173	100	4	can	can	AUX
ma-173	100	5	write	write	VERB
ma-173	100	6	:	:	PUNCT
ma-173	100	7	x1	x1	PROPN
ma-173	100	8	−	−	NOUN
ma-173	100	9	x∗	x∗	PROPN
ma-173	101	1	=	=	PUNCT
ma-173	101	2	x0	x0	PROPN
ma-173	102	1	−	−	PROPN
ma-173	102	2	x∗	x∗	PROPN
ma-173	102	3	−	−	PROPN
ma-173	102	4	a(x0	a(x0	VERB
ma-173	102	5	−	−	PROPN
ma-173	102	6	x−1)−1f	x−1)−1f	PROPN
ma-173	102	7	(	(	PUNCT
ma-173	102	8	x0	x0	PROPN
ma-173	102	9	)	)	PUNCT
ma-173	102	10	=	=	PRON
ma-173	102	11	a(x0	a(x0	VERB
ma-173	102	12	−	−	PROPN
ma-173	102	13	x−1)(a(x0	x−1)(a(x0	PROPN
ma-173	102	14	,	,	PUNCT
ma-173	102	15	x−1)−	x−1)−	PUNCT
ma-173	103	1	[	[	X
ma-173	103	2	x0	x0	PROPN
ma-173	103	3	,	,	PUNCT
ma-173	103	4	x∗;f	x∗;f	PROPN
ma-173	103	5	]	]	PUNCT
ma-173	103	6	)	)	PUNCT
ma-173	103	7	(	(	PUNCT
ma-173	103	8	x0	x0	PROPN
ma-173	103	9	−	−	PROPN
ma-173	103	10	x∗	x∗	PROPN
ma-173	103	11	)	)	PUNCT
ma-173	103	12	(	(	PUNCT
ma-173	103	13	2.11	2.11	NUM
ma-173	103	14	)	)	PUNCT
ma-173	103	15	using	use	VERB
ma-173	103	16	(	(	PUNCT
ma-173	103	17	2.7	2.7	NUM
ma-173	103	18	)	)	PUNCT
ma-173	103	19	,	,	PUNCT
ma-173	103	20	(	(	PUNCT
ma-173	103	21	a3	a3	NOUN
ma-173	103	22	)	)	PUNCT
ma-173	103	23	,	,	PUNCT
ma-173	103	24	(	(	PUNCT
ma-173	103	25	2.10	2.10	NUM
ma-173	103	26	)	)	PUNCT
ma-173	103	27	,	,	PUNCT
ma-173	103	28	(	(	PUNCT
ma-173	103	29	a2	a2	PROPN
ma-173	103	30	)	)	PUNCT
ma-173	103	31	and	and	CCONJ
ma-173	103	32	(	(	PUNCT
ma-173	103	33	2.11	2.11	NUM
ma-173	103	34	)	)	PUNCT
ma-173	103	35	we	we	PRON
ma-173	103	36	get	get	VERB
ma-173	103	37	in	in	ADP
ma-173	103	38	turn	turn	NOUN
ma-173	103	39	that	that	PRON
ma-173	103	40	:	:	PUNCT
ma-173	103	41	‖x1	‖x1	NOUN
ma-173	103	42	−	−	PROPN
ma-173	103	43	x∗‖	x∗‖	PUNCT
ma-173	103	44	=	=	PUNCT
ma-173	103	45	w(‖x0	w(‖x0	ADP
ma-173	103	46	−	−	PROPN
ma-173	103	47	x∗‖	x∗‖	PROPN
ma-173	103	48	,	,	PUNCT
ma-173	103	49	‖x−1	‖x−1	VERB
ma-173	103	50	−	−	PROPN
ma-173	103	51	x∗‖)‖x0	x∗‖)‖x0	PROPN
ma-173	103	52	−	−	PROPN
ma-173	103	53	x∗‖	x∗‖	PROPN
ma-173	103	54	1−	1−	NUM
ma-173	103	55	w0(‖x0	w0(‖x0	PROPN
ma-173	103	56	−	−	PROPN
ma-173	103	57	x∗‖	x∗‖	PROPN
ma-173	103	58	,	,	PUNCT
ma-173	103	59	‖x−1	‖x−1	ADP
ma-173	103	60	−	−	PROPN
ma-173	103	61	x∗‖	x∗‖	NUM
ma-173	103	62	)	)	PUNCT
ma-173	103	63	≤	≤	NUM
ma-173	103	64	h(‖x0	h(‖x0	NOUN
ma-173	103	65	−	−	PROPN
ma-173	103	66	x∗‖)‖x0	x∗‖)‖x0	NOUN
ma-173	103	67	−	−	PROPN
ma-173	103	68	x∗‖	x∗‖	PROPN
ma-173	103	69	≤	≤	NUM
ma-173	103	70	‖x0	‖x0	NOUN
ma-173	103	71	−	−	PROPN
ma-173	103	72	x∗‖	x∗‖	PROPN
ma-173	103	73	<	<	X
ma-173	103	74	r,(2.12)thus	r,(2.12)thus	PROPN
ma-173	103	75	,	,	PUNCT
ma-173	103	76	the	the	DET
ma-173	103	77	iterate	iterate	NOUN
ma-173	103	78	x1	x1	PROPN
ma-173	103	79	∈	∈	PROPN
ma-173	103	80	u(x∗	u(x∗	NOUN
ma-173	103	81	,	,	PUNCT
ma-173	103	82	r	r	NOUN
ma-173	103	83	)	)	PUNCT
ma-173	103	84	and	and	CCONJ
ma-173	103	85	the	the	DET
ma-173	103	86	item	item	NOUN
ma-173	103	87	(	(	PUNCT
ma-173	103	88	2.8	2.8	NUM
ma-173	103	89	)	)	PUNCT
ma-173	103	90	holds	hold	VERB
ma-173	103	91	for	for	ADP
ma-173	103	92	n	n	NOUN
ma-173	103	93	=	=	SYM
ma-173	103	94	0	0	X
ma-173	103	95	.	.	PUNCT
ma-173	103	96	simply	simply	ADV
ma-173	103	97	replace	replace	VERB
ma-173	103	98	x−1	x−1	PROPN
ma-173	103	99	,	,	PUNCT
ma-173	103	100	x0	x0	PROPN
ma-173	103	101	,	,	PUNCT
ma-173	103	102	x1	x1	NUM
ma-173	103	103	by	by	ADP
ma-173	103	104	xm−1	xm−1	PROPN
ma-173	103	105	,	,	PUNCT
ma-173	103	106	xm	xm	PROPN
ma-173	103	107	,	,	PUNCT
ma-173	103	108	xm+1	xm+1	PROPN
ma-173	103	109	in	in	ADP
ma-173	103	110	the	the	DET
ma-173	103	111	preceding	precede	VERB
ma-173	103	112	calculations	calculation	NOUN
ma-173	103	113	to	to	PART
ma-173	103	114	terminate	terminate	VERB
ma-173	103	115	the	the	DET
ma-173	103	116	induction	induction	NOUN
ma-173	103	117	for	for	ADP
ma-173	103	118	items	item	NOUN
ma-173	103	119	(	(	PUNCT
ma-173	103	120	2.8	2.8	NUM
ma-173	103	121	)	)	PUNCT
ma-173	103	122	.	.	PUNCT
ma-173	104	1	then	then	ADV
ma-173	104	2	,	,	PUNCT
ma-173	104	3	fromthe	fromthe	ADJ
ma-173	104	4	estimation	estimation	NOUN
ma-173	104	5	:	:	PUNCT
ma-173	104	6	‖xm+1	‖xm+1	PUNCT
ma-173	104	7	−	−	PROPN
ma-173	104	8	x∗‖	x∗‖	PROPN
ma-173	104	9	≤	≤	NOUN
ma-173	105	1	c‖xm	c‖xm	PROPN
ma-173	105	2	−	−	PROPN
ma-173	106	1	x∗‖	x∗‖	X
ma-173	106	2	<	<	X
ma-173	106	3	r	r	NOUN
ma-173	106	4	,	,	PUNCT
ma-173	106	5	(	(	PUNCT
ma-173	106	6	2.13)where	2.13)where	NUM
ma-173	106	7	c	c	NOUN
ma-173	106	8	=	=	SYM
ma-173	106	9	h(‖x0	h(‖x0	PROPN
ma-173	106	10	−	−	PROPN
ma-173	106	11	x∗‖	x∗‖	PROPN
ma-173	106	12	)	)	PUNCT
ma-173	106	13	∈	∈	PROPN
ma-173	107	1	[	[	X
ma-173	107	2	0	0	NUM
ma-173	107	3	,	,	PUNCT
ma-173	107	4	1	1	NUM
ma-173	107	5	)	)	PUNCT
ma-173	107	6	.	.	PUNCT
ma-173	108	1	we	we	PRON
ma-173	108	2	conclude	conclude	VERB
ma-173	108	3	that	that	SCONJ
ma-173	108	4	limm→∞	limm→∞	PROPN
ma-173	108	5	xm	xm	PROPN
ma-173	109	1	=	=	PUNCT
ma-173	109	2	x∗	x∗	PROPN
ma-173	109	3	and	and	CCONJ
ma-173	109	4	that	that	SCONJ
ma-173	109	5	the	the	DET
ma-173	109	6	iterate	iterate	NOUN
ma-173	109	7	xm+1	xm+1	PROPN
ma-173	109	8	∈	∈	PROPN
ma-173	109	9	u(x∗	u(x∗	NOUN
ma-173	109	10	,	,	PUNCT
ma-173	109	11	r	r	NOUN
ma-173	109	12	)	)	PUNCT
ma-173	109	13	.	.	PUNCT
ma-173	110	1	�	�	PROPN
ma-173	110	2	the	the	DET
ma-173	110	3	uniqueness	uniqueness	NOUN
ma-173	110	4	of	of	ADP
ma-173	110	5	the	the	DET
ma-173	110	6	solution	solution	NOUN
ma-173	110	7	region	region	NOUN
ma-173	110	8	is	be	AUX
ma-173	110	9	given	give	VERB
ma-173	110	10	in	in	ADP
ma-173	110	11	the	the	DET
ma-173	110	12	next	next	ADJ
ma-173	110	13	result	result	NOUN
ma-173	110	14	.	.	PUNCT
ma-173	111	1	proposition	proposition	NOUN
ma-173	111	2	2.2	2.2	NUM
ma-173	111	3	.	.	PUNCT
ma-173	112	1	assume	assume	VERB
ma-173	112	2	:	:	PUNCT
ma-173	112	3	there	there	PRON
ma-173	112	4	exists	exist	VERB
ma-173	112	5	a	a	DET
ma-173	112	6	solution	solution	NOUN
ma-173	112	7	z	z	PROPN
ma-173	112	8	∈	∈	PROPN
ma-173	112	9	u(x∗	u(x∗	PROPN
ma-173	112	10	,	,	PUNCT
ma-173	112	11	r1	r1	PROPN
ma-173	112	12	)	)	PUNCT
ma-173	112	13	of	of	ADP
ma-173	112	14	the	the	DET
ma-173	112	15	equation	equation	NOUN
ma-173	112	16	f	f	X
ma-173	112	17	(	(	PUNCT
ma-173	112	18	x	x	X
ma-173	112	19	)	)	PUNCT
ma-173	112	20	=	=	SYM
ma-173	112	21	0	0	NUM
ma-173	112	22	for	for	ADP
ma-173	112	23	some	some	DET
ma-173	112	24	r1	r1	PROPN
ma-173	112	25	≥	≥	NOUN
ma-173	112	26	0	0	NUM
ma-173	112	27	;	;	PUNCT
ma-173	112	28	the	the	DET
ma-173	112	29	condition	condition	NOUN
ma-173	112	30	(	(	PUNCT
ma-173	112	31	a2	a2	PROPN
ma-173	112	32	)	)	PUNCT
ma-173	112	33	holds	hold	VERB
ma-173	112	34	in	in	ADP
ma-173	112	35	the	the	DET
ma-173	112	36	ball	ball	NOUN
ma-173	112	37	u(x∗	u(x∗	NOUN
ma-173	112	38	,	,	PUNCT
ma-173	112	39	r1	r1	PROPN
ma-173	112	40	)	)	PUNCT
ma-173	112	41	for	for	ADP
ma-173	112	42	a	a	DET
ma-173	112	43	being	being	AUX
ma-173	112	44	[	[	X
ma-173	112	45	·	·	PUNCT
ma-173	112	46	,	,	PUNCT
ma-173	112	47	·	·	PUNCT
ma-173	112	48	;	;	PUNCT
ma-173	112	49	f	f	X
ma-173	112	50	]	]	PUNCT
ma-173	112	51	,	,	PUNCT
ma-173	112	52	and	and	CCONJ
ma-173	112	53	there	there	PRON
ma-173	112	54	exists	exist	VERB
ma-173	112	55	r2	r2	PROPN
ma-173	112	56	≥	≥	PROPN
ma-173	112	57	r1	r1	PROPN
ma-173	112	58	such	such	ADJ
ma-173	112	59	that	that	SCONJ
ma-173	112	60	:	:	PUNCT
ma-173	112	61	w0(r1	w0(r1	NOUN
ma-173	112	62	,	,	PUNCT
ma-173	112	63	r2	r2	PROPN
ma-173	112	64	)	)	PUNCT
ma-173	112	65	<	<	X
ma-173	113	1	1	1	X
ma-173	113	2	.	.	PUNCT
ma-173	113	3	(	(	PUNCT
ma-173	113	4	2.14	2.14	NUM
ma-173	113	5	)	)	PUNCT
ma-173	113	6	define	define	VERB
ma-173	113	7	the	the	DET
ma-173	113	8	region	region	NOUN
ma-173	113	9	d2	d2	PROPN
ma-173	113	10	=	=	PUNCT
ma-173	114	1	d	d	X
ma-173	114	2	∪	∪	ADP
ma-173	114	3	u[x∗	u[x∗	PROPN
ma-173	114	4	,	,	PUNCT
ma-173	114	5	r2	r2	PROPN
ma-173	114	6	]	]	PUNCT
ma-173	114	7	.	.	PUNCT
ma-173	115	1	then	then	ADV
ma-173	115	2	,	,	PUNCT
ma-173	115	3	x∗	x∗	PROPN
ma-173	115	4	is	be	AUX
ma-173	115	5	the	the	DET
ma-173	115	6	only	only	ADJ
ma-173	115	7	solution	solution	NOUN
ma-173	115	8	of	of	ADP
ma-173	115	9	the	the	DET
ma-173	115	10	equation	equation	NOUN
ma-173	115	11	f	f	X
ma-173	115	12	(	(	PUNCT
ma-173	115	13	x	x	X
ma-173	115	14	)	)	PUNCT
ma-173	115	15	=	=	SYM
ma-173	115	16	0	0	NUM
ma-173	115	17	in	in	ADP
ma-173	115	18	the	the	DET
ma-173	115	19	region	region	NOUN
ma-173	115	20	d2	d2	PROPN
ma-173	115	21	.	.	PUNCT
ma-173	116	1	proof	proof	NOUN
ma-173	116	2	.	.	PUNCT
ma-173	117	1	if	if	SCONJ
ma-173	117	2	z	z	PROPN
ma-173	117	3	6=	6=	ADP
ma-173	117	4	x∗	x∗	NOUN
ma-173	117	5	,	,	PUNCT
ma-173	117	6	then	then	ADV
ma-173	117	7	the	the	DET
ma-173	117	8	divided	divided	ADJ
ma-173	117	9	difference	difference	NOUN
ma-173	117	10	e	e	NOUN
ma-173	117	11	=	=	PUNCT
ma-173	118	1	[	[	X
ma-173	118	2	x∗	x∗	X
ma-173	118	3	,	,	PUNCT
ma-173	118	4	z	z	NOUN
ma-173	118	5	;	;	PUNCT
ma-173	118	6	f	f	X
ma-173	118	7	]	]	PUNCT
ma-173	118	8	is	be	AUX
ma-173	118	9	well	well	ADV
ma-173	118	10	defined	define	VERB
ma-173	118	11	.	.	PUNCT
ma-173	119	1	using	use	VERB
ma-173	119	2	(	(	PUNCT
ma-173	119	3	a2	a2	PROPN
ma-173	119	4	)	)	PUNCT
ma-173	119	5	and	and	CCONJ
ma-173	119	6	(	(	PUNCT
ma-173	119	7	2.14),we	2.14),we	NOUN
ma-173	119	8	get	get	VERB
ma-173	119	9	in	in	ADP
ma-173	119	10	turn	turn	NOUN
ma-173	119	11	that	that	PRON
ma-173	119	12	‖p−1(e	‖p−1(e	NOUN
ma-173	120	1	−	−	PROPN
ma-173	121	1	p	p	NOUN
ma-173	121	2	)	)	PUNCT
ma-173	121	3	‖|	‖|	PROPN
ma-173	121	4	≤	≤	NUM
ma-173	121	5	w0(‖x∗	w0(‖x∗	PROPN
ma-173	121	6	−	−	PROPN
ma-173	121	7	x∗‖	x∗‖	PROPN
ma-173	121	8	,	,	PUNCT
ma-173	121	9	‖z	‖z	NOUN
ma-173	121	10	−	−	NOUN
ma-173	121	11	x∗‖	x∗‖	NUM
ma-173	121	12	)	)	PUNCT
ma-173	121	13	≤	≤	NOUN
ma-173	121	14	w0(0	w0(0	PROPN
ma-173	121	15	,	,	PUNCT
ma-173	121	16	r2	r2	PROPN
ma-173	121	17	)	)	PUNCT
ma-173	121	18	<	<	X
ma-173	121	19	1	1	X
ma-173	121	20	.	.	PUNCT
ma-173	122	1	thus	thus	ADV
ma-173	122	2	,	,	PUNCT
ma-173	122	3	e−1	e−1	PROPN
ma-173	122	4	∈	∈	PROPN
ma-173	122	5	l(b	l(b	PROPN
ma-173	122	6	)	)	PUNCT
ma-173	122	7	.	.	PUNCT
ma-173	123	1	moreover	moreover	ADV
ma-173	123	2	,	,	PUNCT
ma-173	123	3	from	from	ADP
ma-173	123	4	the	the	DET
ma-173	123	5	identity	identity	NOUN
ma-173	123	6	z	z	NOUN
ma-173	123	7	−	−	NOUN
ma-173	123	8	x∗	x∗	PROPN
ma-173	124	1	=	=	SYM
ma-173	124	2	e−1(f	e−1(f	PROPN
ma-173	124	3	(	(	PUNCT
ma-173	124	4	z)−	z)−	PROPN
ma-173	124	5	f	f	X
ma-173	124	6	(	(	PUNCT
ma-173	124	7	x∗	x∗	PROPN
ma-173	124	8	)	)	PUNCT
ma-173	124	9	)	)	PUNCT
ma-173	125	1	=	=	SYM
ma-173	125	2	e−1(0	e−1(0	NOUN
ma-173	125	3	)	)	PUNCT
ma-173	125	4	=	=	SYM
ma-173	126	1	0	0	X
ma-173	126	2	.	.	PUNCT
ma-173	127	1	https://doi.org/10.28924/ada/ma.3.26	https://doi.org/10.28924/ada/ma.3.26	ADJ
ma-173	127	2	eur	eur	PROPN
ma-173	127	3	.	.	PUNCT
ma-173	128	1	j.	j.	PROPN
ma-173	128	2	math	math	PROPN
ma-173	128	3	.	.	PUNCT
ma-173	129	1	anal	anal	PROPN
ma-173	129	2	.	.	PUNCT
ma-173	130	1	10.28924	10.28924	NUM
ma-173	130	2	/	/	SYM
ma-173	130	3	ada	ada	NOUN
ma-173	130	4	/	/	SYM
ma-173	130	5	ma.3.26	ma.3.26	NOUN
ma-173	130	6	5hence	5hence	NUM
ma-173	130	7	,	,	PUNCT
ma-173	130	8	we	we	PRON
ma-173	130	9	conclude	conclude	VERB
ma-173	130	10	that	that	PRON
ma-173	130	11	z	z	NOUN
ma-173	130	12	=	=	SYM
ma-173	130	13	x∗.	x∗.	SYM
ma-173	130	14	�	�	PROPN
ma-173	130	15	3	3	NUM
ma-173	130	16	.	.	PUNCT
ma-173	130	17	convergence	convergence	PROPN
ma-173	130	18	ii	ii	PROPN
ma-173	130	19	:	:	PUNCT
ma-173	130	20	semi	semi	ADJ
ma-173	130	21	-	-	ADJ
ma-173	130	22	local	local	ADJ
ma-173	130	23	a	a	DET
ma-173	130	24	certain	certain	ADJ
ma-173	130	25	real	real	ADJ
ma-173	130	26	sequence	sequence	NOUN
ma-173	130	27	is	be	AUX
ma-173	130	28	developed	develop	VERB
ma-173	130	29	that	that	PRON
ma-173	130	30	is	be	AUX
ma-173	130	31	shown	show	VERB
ma-173	130	32	in	in	ADP
ma-173	130	33	theorem	theorem	ADJ
ma-173	130	34	3.1	3.1	NUM
ma-173	130	35	to	to	PART
ma-173	130	36	be	be	AUX
ma-173	130	37	majorizing	majorize	VERB
ma-173	130	38	for	for	ADP
ma-173	130	39	thescheme	thescheme	PROPN
ma-173	130	40	(	(	PUNCT
ma-173	130	41	1.2	1.2	NUM
ma-173	130	42	)	)	PUNCT
ma-173	130	43	.	.	PUNCT
ma-173	131	1	assume	assume	VERB
ma-173	131	2	:	:	PUNCT
ma-173	131	3	(	(	PUNCT
ma-173	131	4	h1	h1	PROPN
ma-173	131	5	)	)	PUNCT
ma-173	131	6	:	:	PUNCT
ma-173	131	7	there	there	PRON
ma-173	131	8	exists	exist	VERB
ma-173	131	9	a	a	DET
ma-173	131	10	continuous	continuous	ADJ
ma-173	131	11	and	and	CCONJ
ma-173	131	12	nondecreasing	nondecreasing	ADJ
ma-173	131	13	function	function	NOUN
ma-173	131	14	v0	v0	NOUN
ma-173	131	15	:	:	PUNCT
ma-173	131	16	t	t	PROPN
ma-173	131	17	→	→	SYM
ma-173	131	18	t	t	PROPN
ma-173	131	19	such	such	ADJ
ma-173	131	20	that	that	DET
ma-173	131	21	v0(t	v0(t	PROPN
ma-173	131	22	,	,	PUNCT
ma-173	131	23	t)−1	t)−1	NOUN
ma-173	131	24	=	=	SYM
ma-173	131	25	0has	0ha	NOUN
ma-173	131	26	a	a	DET
ma-173	131	27	unique	unique	ADJ
ma-173	131	28	positive	positive	ADJ
ma-173	131	29	solution	solution	NOUN
ma-173	131	30	denoted	denote	VERB
ma-173	131	31	by	by	ADP
ma-173	131	32	δ.let	δ.let	NOUN
ma-173	131	33	t2	t2	NOUN
ma-173	131	34	=	=	PUNCT
ma-173	132	1	[	[	X
ma-173	132	2	0	0	NUM
ma-173	132	3	,	,	PUNCT
ma-173	132	4	δ	δ	PROPN
ma-173	132	5	)	)	PUNCT
ma-173	132	6	.	.	PUNCT
ma-173	133	1	(	(	PUNCT
ma-173	133	2	h2	h2	PROPN
ma-173	133	3	)	)	PUNCT
ma-173	133	4	:	:	PUNCT
ma-173	133	5	there	there	PRON
ma-173	133	6	exists	exist	VERB
ma-173	133	7	a	a	DET
ma-173	133	8	cnf	cnf	PROPN
ma-173	133	9	v	v	NOUN
ma-173	133	10	:	:	PUNCT
ma-173	133	11	t2×	t2×	X
ma-173	133	12	t2	t2	PROPN
ma-173	133	13	→	→	SYM
ma-173	133	14	t	t	PROPN
ma-173	133	15	.	.	PUNCT
ma-173	134	1	define	define	VERB
ma-173	134	2	a	a	DET
ma-173	134	3	sequence	sequence	NOUN
ma-173	134	4	{	{	PUNCT
ma-173	134	5	γn	γn	NOUN
ma-173	134	6	}	}	PUNCT
ma-173	134	7	for	for	ADP
ma-173	134	8	γ−1	γ−1	PROPN
ma-173	134	9	=	=	SYM
ma-173	134	10	0	0	NUM
ma-173	134	11	,	,	PUNCT
ma-173	134	12	γ0	γ0	NOUN
ma-173	134	13	=	=	SYM
ma-173	134	14	α	α	PROPN
ma-173	134	15	,	,	PUNCT
ma-173	134	16	some	some	DET
ma-173	134	17	γ1	γ1	NOUN
ma-173	134	18	≥	≥	NOUN
ma-173	134	19	α	α	X
ma-173	134	20	by	by	ADP
ma-173	134	21	:	:	PUNCT
ma-173	134	22	γn+2	γn+2	NUM
ma-173	134	23	=	=	SYM
ma-173	134	24	γn+1	γn+1	PROPN
ma-173	134	25	+	+	CCONJ
ma-173	134	26	v(γn+1	v(γn+1	PROPN
ma-173	134	27	−	−	NOUN
ma-173	134	28	γn	γn	NOUN
ma-173	134	29	,	,	PUNCT
ma-173	134	30	γn	γn	ADV
ma-173	134	31	−	−	NOUN
ma-173	134	32	γn+1)(γn+1	γn+1)(γn+1	NOUN
ma-173	134	33	−	−	NOUN
ma-173	134	34	γn	γn	NUM
ma-173	134	35	)	)	PUNCT
ma-173	134	36	1−	1−	NUM
ma-173	135	1	v0(γn	v0(γn	PROPN
ma-173	135	2	−	−	PROPN
ma-173	135	3	γ0	γ0	PROPN
ma-173	135	4	,	,	PUNCT
ma-173	135	5	γn+1	γn+1	ADP
ma-173	135	6	−	−	PROPN
ma-173	135	7	γ0	γ0	NOUN
ma-173	135	8	)	)	PUNCT
ma-173	135	9	.	.	PUNCT
ma-173	136	1	(	(	PUNCT
ma-173	136	2	h3	h3	NOUN
ma-173	136	3	)	)	PUNCT
ma-173	136	4	:	:	PUNCT
ma-173	137	1	v0(γn	v0(γn	PROPN
ma-173	137	2	−	−	PROPN
ma-173	137	3	γ0	γ0	PROPN
ma-173	137	4	,	,	PUNCT
ma-173	137	5	γn+1	γn+1	ADP
ma-173	137	6	−	−	PROPN
ma-173	137	7	γ0	γ0	NOUN
ma-173	137	8	)	)	PUNCT
ma-173	137	9	<	<	X
ma-173	137	10	1	1	NUM
ma-173	137	11	and	and	CCONJ
ma-173	137	12	γn	γn	ADP
ma-173	137	13	≤	≤	NUM
ma-173	137	14	γ	γ	X
ma-173	137	15	<	<	X
ma-173	137	16	δ.clearly	δ.clearly	ADV
ma-173	137	17	,	,	PUNCT
ma-173	137	18	by	by	ADP
ma-173	137	19	the	the	DET
ma-173	137	20	definition	definition	NOUN
ma-173	137	21	of	of	ADP
ma-173	137	22	the	the	DET
ma-173	137	23	sequence	sequence	NOUN
ma-173	137	24	γn	γn	NOUN
ma-173	137	25	and	and	CCONJ
ma-173	137	26	(	(	PUNCT
ma-173	137	27	h3	h3	NOUN
ma-173	137	28	)	)	PUNCT
ma-173	137	29	,	,	PUNCT
ma-173	137	30	this	this	DET
ma-173	137	31	sequence	sequence	NOUN
ma-173	137	32	is	be	AUX
ma-173	137	33	nondecreasingly	nondecreasingly	ADV
ma-173	137	34	convergentto	convergentto	VERB
ma-173	137	35	its	its	PRON
ma-173	137	36	unique	unique	ADJ
ma-173	137	37	least	least	ADV
ma-173	137	38	upper	upper	ADJ
ma-173	137	39	bound	bind	VERB
ma-173	137	40	denoted	denote	VERB
ma-173	137	41	by	by	ADP
ma-173	137	42	γ∗.	γ∗.	ADJ
ma-173	137	43	the	the	DET
ma-173	137	44	functions	function	NOUN
ma-173	137	45	v0	v0	NOUN
ma-173	137	46	,	,	PUNCT
ma-173	137	47	v	v	NOUN
ma-173	137	48	and	and	CCONJ
ma-173	137	49	the	the	DET
ma-173	137	50	limit	limit	NOUN
ma-173	137	51	point	point	NOUN
ma-173	137	52	γ∗	γ∗	PROPN
ma-173	137	53	areconnected	areconnecte	VERB
ma-173	137	54	to	to	ADP
ma-173	137	55	the	the	DET
ma-173	137	56	operators	operator	NOUN
ma-173	137	57	on	on	ADP
ma-173	137	58	the	the	DET
ma-173	137	59	scheme	scheme	NOUN
ma-173	137	60	as	as	SCONJ
ma-173	137	61	follows	follow	VERB
ma-173	137	62	:	:	PUNCT
ma-173	137	63	(	(	PUNCT
ma-173	137	64	h4	h4	PROPN
ma-173	137	65	)	)	PUNCT
ma-173	137	66	:	:	PUNCT
ma-173	137	67	there	there	PRON
ma-173	137	68	exists	exist	VERB
ma-173	137	69	an	an	DET
ma-173	137	70	invertible	invertible	ADJ
ma-173	137	71	operator	operator	NOUN
ma-173	137	72	p	p	PROPN
ma-173	137	73	∈	∈	PROPN
ma-173	137	74	l(b	l(b	PROPN
ma-173	137	75	)	)	PUNCT
ma-173	137	76	such	such	ADJ
ma-173	137	77	that	that	SCONJ
ma-173	137	78	p−1	p−1	PROPN
ma-173	137	79	∈	∈	PROPN
ma-173	137	80	l(b	l(b	PROPN
ma-173	137	81	)	)	PUNCT
ma-173	137	82	and	and	CCONJ
ma-173	137	83	for	for	ADP
ma-173	137	84	each	each	DET
ma-173	137	85	x	x	NOUN
ma-173	137	86	,	,	PUNCT
ma-173	137	87	y	y	PROPN
ma-173	137	88	∈	∈	PROPN
ma-173	137	89	d	d	X
ma-173	137	90	‖p−1(a(x	‖p−1(a(x	NOUN
ma-173	137	91	,	,	PUNCT
ma-173	137	92	y)−	y)−	PROPN
ma-173	137	93	p	p	NOUN
ma-173	137	94	)	)	PUNCT
ma-173	137	95	‖	‖	PROPN
ma-173	137	96	≤	≤	NOUN
ma-173	137	97	v0(‖x	v0(‖x	PUNCT
ma-173	137	98	−	−	PROPN
ma-173	137	99	x0‖	x0‖	PROPN
ma-173	137	100	,	,	PUNCT
ma-173	137	101	‖y	‖y	PUNCT
ma-173	137	102	−	−	PROPN
ma-173	138	1	x0‖	x0‖	PROPN
ma-173	138	2	)	)	PUNCT
ma-173	138	3	.	.	PUNCT
ma-173	139	1	it	it	PRON
ma-173	139	2	follows	follow	VERB
ma-173	139	3	by	by	ADP
ma-173	139	4	(	(	PUNCT
ma-173	139	5	h1	h1	PROPN
ma-173	139	6	)	)	PUNCT
ma-173	139	7	that	that	SCONJ
ma-173	139	8	:	:	PUNCT
ma-173	139	9	if	if	SCONJ
ma-173	139	10	x−1	x−1	PROPN
ma-173	139	11	,	,	PUNCT
ma-173	139	12	x0	x0	PROPN
ma-173	139	13	∈	∈	PROPN
ma-173	140	1	d	d	X
ma-173	140	2	with	with	ADP
ma-173	140	3	‖x−1	‖x−1	NUM
ma-173	140	4	−	−	PROPN
ma-173	140	5	x0‖	x0‖	PROPN
ma-173	140	6	≤	≤	PROPN
ma-173	140	7	α	α	X
ma-173	140	8	,	,	PUNCT
ma-173	140	9	v0(‖x−1	v0(‖x−1	NOUN
ma-173	140	10	−	−	PROPN
ma-173	140	11	x0‖	x0‖	PROPN
ma-173	140	12	,	,	PUNCT
ma-173	140	13	‖x0	‖x0	NOUN
ma-173	140	14	−	−	PROPN
ma-173	140	15	x0‖	x0‖	PROPN
ma-173	140	16	)	)	PUNCT
ma-173	140	17	≤	≤	PROPN
ma-173	140	18	v0(α	v0(α	PROPN
ma-173	140	19	,	,	PUNCT
ma-173	140	20	0	0	NUM
ma-173	140	21	)	)	PUNCT
ma-173	140	22	<	<	X
ma-173	140	23	1	1	X
ma-173	140	24	.	.	PUNCT
ma-173	140	25	thus	thus	ADV
ma-173	140	26	a(x0	a(x0	VERB
ma-173	140	27	,	,	PUNCT
ma-173	140	28	x−1)−1	x−1)−1	PROPN
ma-173	140	29	∈	∈	PROPN
ma-173	140	30	l(b	l(b	PROPN
ma-173	140	31	)	)	PUNCT
ma-173	140	32	.	.	PUNCT
ma-173	141	1	let	let	VERB
ma-173	141	2	‖a(x0	‖a(x0	NOUN
ma-173	141	3	,	,	PUNCT
ma-173	141	4	x−1)−1f	x−1)−1f	PROPN
ma-173	141	5	(	(	PUNCT
ma-173	141	6	x0)‖	x0)‖	PROPN
ma-173	141	7	≤	≤	NUM
ma-173	141	8	γ1	γ1	NOUN
ma-173	141	9	−	−	PROPN
ma-173	141	10	γ0	γ0	PROPN
ma-173	141	11	.	.	PUNCT
ma-173	142	1	set	set	VERB
ma-173	142	2	d3	d3	PROPN
ma-173	142	3	=	=	SYM
ma-173	143	1	d	d	X
ma-173	143	2	∪	∪	ADJ
ma-173	143	3	u(x0	u(x0	PROPN
ma-173	143	4	,	,	PUNCT
ma-173	143	5	γ	γ	NOUN
ma-173	143	6	)	)	PUNCT
ma-173	143	7	.	.	PUNCT
ma-173	144	1	‖p−1(a(x	‖p−1(a(x	NOUN
ma-173	144	2	,	,	PUNCT
ma-173	144	3	y)−	y)−	PROPN
ma-173	144	4	[	[	X
ma-173	144	5	y	y	PROPN
ma-173	144	6	,	,	PUNCT
ma-173	144	7	z	z	PROPN
ma-173	144	8	;	;	PUNCT
ma-173	144	9	f	f	PROPN
ma-173	144	10	]	]	X
ma-173	144	11	)	)	PUNCT
ma-173	144	12	‖	‖	PROPN
ma-173	144	13	≤	≤	NOUN
ma-173	144	14	(	(	PUNCT
ma-173	144	15	‖x	‖x	NOUN
ma-173	144	16	−	−	PROPN
ma-173	144	17	y‖	y‖	PROPN
ma-173	144	18	,	,	PUNCT
ma-173	144	19	‖y	‖y	PUNCT
ma-173	144	20	−	−	NOUN
ma-173	144	21	z‖	z‖	NOUN
ma-173	144	22	)	)	PUNCT
ma-173	144	23	for	for	ADP
ma-173	144	24	each	each	DET
ma-173	144	25	x	x	PROPN
ma-173	144	26	,	,	PUNCT
ma-173	144	27	y	y	PROPN
ma-173	144	28	,	,	PUNCT
ma-173	144	29	z	z	PROPN
ma-173	144	30	∈	∈	PROPN
ma-173	144	31	d3	d3	PROPN
ma-173	144	32	and	and	CCONJ
ma-173	144	33	(	(	PUNCT
ma-173	144	34	h5	h5	PROPN
ma-173	144	35	)	)	PUNCT
ma-173	144	36	:	:	PUNCT
ma-173	144	37	u[x0	u[x0	ADV
ma-173	144	38	,	,	PUNCT
ma-173	144	39	γ∗	γ∗	PROPN
ma-173	144	40	]	]	X
ma-173	144	41	⊂	⊂	PROPN
ma-173	144	42	d.next	d.next	PROPN
ma-173	144	43	,	,	PUNCT
ma-173	144	44	we	we	PRON
ma-173	144	45	present	present	VERB
ma-173	144	46	the	the	DET
ma-173	144	47	semi	semi	ADJ
ma-173	144	48	-	-	ADJ
ma-173	144	49	local	local	ADJ
ma-173	144	50	convergence	convergence	NOUN
ma-173	144	51	analysis	analysis	NOUN
ma-173	144	52	of	of	ADP
ma-173	144	53	the	the	DET
ma-173	144	54	scheme	scheme	NOUN
ma-173	144	55	(	(	PUNCT
ma-173	144	56	1.2	1.2	NUM
ma-173	144	57	)	)	PUNCT
ma-173	144	58	under	under	ADP
ma-173	144	59	the	the	DET
ma-173	144	60	conditions	condition	NOUN
ma-173	144	61	(	(	PUNCT
ma-173	144	62	h1)−	h1)−	PROPN
ma-173	144	63	(	(	PUNCT
ma-173	144	64	h5	h5	PROPN
ma-173	144	65	)	)	PUNCT
ma-173	144	66	and	and	CCONJ
ma-173	144	67	the	the	DET
ma-173	144	68	preceding	precede	VERB
ma-173	144	69	terminology	terminology	NOUN
ma-173	144	70	.	.	PUNCT
ma-173	145	1	theorem	theorem	VERB
ma-173	145	2	3.1	3.1	NUM
ma-173	145	3	.	.	PUNCT
ma-173	146	1	assume	assume	VERB
ma-173	146	2	that	that	SCONJ
ma-173	146	3	the	the	DET
ma-173	146	4	conditions	condition	NOUN
ma-173	146	5	(	(	PUNCT
ma-173	146	6	h1)−(h5	h1)−(h5	NOUN
ma-173	146	7	)	)	PUNCT
ma-173	146	8	hold	hold	NOUN
ma-173	146	9	.	.	PUNCT
ma-173	147	1	then	then	ADV
ma-173	147	2	the	the	DET
ma-173	147	3	sequence	sequence	NOUN
ma-173	147	4	{	{	PUNCT
ma-173	147	5	xn	xn	PROPN
ma-173	147	6	}	}	PUNCT
ma-173	147	7	generated	generate	VERB
ma-173	147	8	by	by	ADP
ma-173	147	9	the	the	DET
ma-173	147	10	scheme	scheme	NOUN
ma-173	147	11	(	(	PUNCT
ma-173	147	12	1.2	1.2	NUM
ma-173	147	13	)	)	PUNCT
ma-173	147	14	is	be	AUX
ma-173	147	15	well	well	ADV
ma-173	147	16	defined	define	VERB
ma-173	147	17	in	in	ADP
ma-173	147	18	u(x0	u(x0	NOUN
ma-173	147	19	,	,	PUNCT
ma-173	147	20	γ0	γ0	PROPN
ma-173	147	21	)	)	PUNCT
ma-173	147	22	,	,	PUNCT
ma-173	147	23	remains	remain	VERB
ma-173	147	24	in	in	ADP
ma-173	147	25	u(x0	u(x0	NOUN
ma-173	147	26	,	,	PUNCT
ma-173	147	27	γ0	γ0	NOUN
ma-173	147	28	)	)	PUNCT
ma-173	147	29	for	for	ADP
ma-173	147	30	each	each	DET
ma-173	147	31	n	n	NOUN
ma-173	147	32	=	=	SYM
ma-173	147	33	0	0	NUM
ma-173	147	34	,	,	PUNCT
ma-173	147	35	1	1	NUM
ma-173	147	36	,	,	PUNCT
ma-173	147	37	2	2	NUM
ma-173	147	38	,	,	PUNCT
ma-173	147	39	.	.	PUNCT
ma-173	147	40	.	.	PUNCT
ma-173	148	1	.	.	PUNCT
ma-173	149	1	and	and	CCONJ
ma-173	149	2	converges	converge	VERB
ma-173	149	3	to	to	ADP
ma-173	149	4	a	a	DET
ma-173	149	5	solution	solution	NOUN
ma-173	149	6	x∗	x∗	PROPN
ma-173	149	7	∈	∈	PROPN
ma-173	149	8	u(x0	u(x0	NOUN
ma-173	149	9	,	,	PUNCT
ma-173	149	10	γ0	γ0	PROPN
ma-173	149	11	)	)	PUNCT
ma-173	149	12	of	of	ADP
ma-173	149	13	the	the	DET
ma-173	149	14	equation	equation	NOUN
ma-173	149	15	f	f	X
ma-173	149	16	(	(	PUNCT
ma-173	149	17	x	x	X
ma-173	149	18	)	)	PUNCT
ma-173	149	19	=	=	SYM
ma-173	149	20	0	0	X
ma-173	149	21	.	.	PUNCT
ma-173	150	1	moreover	moreover	ADV
ma-173	150	2	,	,	PUNCT
ma-173	150	3	the	the	DET
ma-173	150	4	following	follow	VERB
ma-173	150	5	items	item	NOUN
ma-173	150	6	hold	hold	VERB
ma-173	150	7	:	:	PUNCT
ma-173	150	8	‖x∗	‖x∗	PUNCT
ma-173	151	1	−	−	NOUN
ma-173	151	2	xn‖	xn‖	PROPN
ma-173	151	3	≤	≤	PROPN
ma-173	151	4	γn+1	γn+1	NUM
ma-173	151	5	−	−	NUM
ma-173	151	6	γn	γn	NOUN
ma-173	151	7	(	(	PUNCT
ma-173	151	8	3.15	3.15	NUM
ma-173	151	9	)	)	PUNCT
ma-173	151	10	https://doi.org/10.28924/ada/ma.3.26	https://doi.org/10.28924/ada/ma.3.26	ADJ
ma-173	151	11	eur	eur	NOUN
ma-173	151	12	.	.	PUNCT
ma-173	152	1	j.	j.	PROPN
ma-173	152	2	math	math	PROPN
ma-173	152	3	.	.	PUNCT
ma-173	153	1	anal	anal	PROPN
ma-173	153	2	.	.	PUNCT
ma-173	154	1	10.28924	10.28924	NUM
ma-173	154	2	/	/	SYM
ma-173	154	3	ada	ada	NOUN
ma-173	154	4	/	/	SYM
ma-173	154	5	ma.3.26	ma.3.26	NOUN
ma-173	154	6	6	6	NUM
ma-173	154	7	and	and	CCONJ
ma-173	154	8	‖x∗	‖x∗	NUM
ma-173	154	9	−	−	NOUN
ma-173	154	10	xn‖	xn‖	PROPN
ma-173	154	11	≤	≤	PROPN
ma-173	154	12	γ∗	γ∗	PROPN
ma-173	154	13	−	−	NOUN
ma-173	154	14	γn	γn	NOUN
ma-173	154	15	,	,	PUNCT
ma-173	154	16	(	(	PUNCT
ma-173	154	17	3.16	3.16	NUM
ma-173	154	18	)	)	PUNCT
ma-173	154	19	where	where	SCONJ
ma-173	154	20	the	the	DET
ma-173	154	21	sequence	sequence	NOUN
ma-173	154	22	{	{	PUNCT
ma-173	154	23	γn	γn	NOUN
ma-173	154	24	}	}	PUNCT
ma-173	154	25	and	and	CCONJ
ma-173	154	26	the	the	DET
ma-173	154	27	point	point	NOUN
ma-173	154	28	x∗	x∗	PROPN
ma-173	154	29	are	be	AUX
ma-173	154	30	defined	define	VERB
ma-173	154	31	in	in	ADP
ma-173	154	32	(	(	PUNCT
ma-173	154	33	h3	h3	NOUN
ma-173	154	34	)	)	PUNCT
ma-173	154	35	.	.	PUNCT
ma-173	155	1	proof	proof	NOUN
ma-173	155	2	.	.	PUNCT
ma-173	156	1	the	the	DET
ma-173	156	2	inequality	inequality	NOUN
ma-173	156	3	(	(	PUNCT
ma-173	156	4	3.15	3.15	NUM
ma-173	156	5	)	)	PUNCT
ma-173	156	6	holds	hold	VERB
ma-173	156	7	for	for	ADP
ma-173	156	8	n	n	NOUN
ma-173	156	9	=	=	SYM
ma-173	156	10	0	0	NUM
ma-173	156	11	,	,	PUNCT
ma-173	156	12	since	since	SCONJ
ma-173	156	13	:	:	PUNCT
ma-173	156	14	‖x1	‖x1	NOUN
ma-173	156	15	−	−	PROPN
ma-173	156	16	x0‖	x0‖	PROPN
ma-173	156	17	=	=	SYM
ma-173	156	18	‖a(x0	‖a(x0	PROPN
ma-173	156	19	,	,	PUNCT
ma-173	156	20	x−1)−1f	x−1)−1f	PROPN
ma-173	157	1	(	(	PUNCT
ma-173	157	2	x0)‖	x0)‖	PROPN
ma-173	157	3	≤	≤	NUM
ma-173	157	4	γ1	γ1	NOUN
ma-173	157	5	−	−	PROPN
ma-173	157	6	γ0	γ0	PROPN
ma-173	157	7	<	<	X
ma-173	157	8	γ∗	γ∗	PROPN
ma-173	157	9	−	−	PROPN
ma-173	157	10	γ0	γ0	PROPN
ma-173	157	11	.	.	PUNCT
ma-173	158	1	�	�	PROPN
ma-173	158	2	thus	thus	ADV
ma-173	158	3	,	,	PUNCT
ma-173	158	4	the	the	DET
ma-173	158	5	iterate	iterate	NOUN
ma-173	158	6	x1	x1	PROPN
ma-173	158	7	∈	∈	PROPN
ma-173	158	8	u(x0	u(x0	NOUN
ma-173	158	9	,	,	PUNCT
ma-173	158	10	γ0	γ0	NOUN
ma-173	158	11	)	)	PUNCT
ma-173	158	12	.	.	PUNCT
ma-173	159	1	let	let	VERB
ma-173	159	2	xn	xn	X
ma-173	159	3	,	,	PUNCT
ma-173	159	4	xn−1	xn−1	PROPN
ma-173	159	5	∈	∈	PROPN
ma-173	159	6	u(x0	u(x0	NOUN
ma-173	159	7	,	,	PUNCT
ma-173	159	8	γ0	γ0	NOUN
ma-173	159	9	)	)	PUNCT
ma-173	159	10	.	.	PUNCT
ma-173	160	1	using	use	VERB
ma-173	160	2	(	(	PUNCT
ma-173	160	3	h3	h3	NOUN
ma-173	160	4	)	)	PUNCT
ma-173	160	5	and	and	CCONJ
ma-173	160	6	(	(	PUNCT
ma-173	160	7	h4	h4	PROPN
ma-173	160	8	)	)	PUNCT
ma-173	160	9	,	,	PUNCT
ma-173	160	10	we	we	PRON
ma-173	160	11	have	have	VERB
ma-173	160	12	inturn	inturn	NOUN
ma-173	160	13	,	,	PUNCT
ma-173	160	14	‖p−1(a(xn	‖p−1(a(xn	NOUN
ma-173	160	15	,	,	PUNCT
ma-173	160	16	xn−1)−	xn−1)−	PROPN
ma-173	160	17	p	p	NOUN
ma-173	160	18	)	)	PUNCT
ma-173	161	1	‖	‖	PROPN
ma-173	161	2	≤	≤	PROPN
ma-173	161	3	v0(‖xn	v0(‖xn	PUNCT
ma-173	162	1	−	−	PROPN
ma-173	162	2	x0‖	x0‖	PROPN
ma-173	162	3	,	,	PUNCT
ma-173	162	4	‖xn−1	‖xn−1	ADP
ma-173	162	5	−	−	PROPN
ma-173	162	6	x0‖	x0‖	PROPN
ma-173	162	7	)	)	PUNCT
ma-173	162	8	≤	≤	NOUN
ma-173	163	1	v0(γ0	v0(γ0	ADP
ma-173	163	2	,	,	PUNCT
ma-173	163	3	γ0	γ0	PROPN
ma-173	163	4	)	)	PUNCT
ma-173	163	5	<	<	X
ma-173	163	6	1.so	1.so	NUM
ma-173	163	7	,	,	PUNCT
ma-173	163	8	a(xn	a(xn	NOUN
ma-173	163	9	,	,	PUNCT
ma-173	163	10	xn−1)−1l(b	xn−1)−1l(b	NOUN
ma-173	163	11	)	)	PUNCT
ma-173	163	12	and	and	CCONJ
ma-173	163	13	‖a(xn	‖a(xn	PROPN
ma-173	163	14	,	,	PUNCT
ma-173	163	15	xn−1)−1p‖	xn−1)−1p‖	PROPN
ma-173	163	16	≤	≤	NUM
ma-173	163	17	1	1	NUM
ma-173	163	18	1−	1−	NUM
ma-173	163	19	v0(‖xn	v0(‖xn	PROPN
ma-173	163	20	−	−	PROPN
ma-173	163	21	x0‖	x0‖	PROPN
ma-173	163	22	,	,	PUNCT
ma-173	163	23	‖xn−1	‖xn−1	ADP
ma-173	163	24	−	−	PROPN
ma-173	163	25	x0‖	x0‖	PROPN
ma-173	163	26	)	)	PUNCT
ma-173	163	27	.	.	PUNCT
ma-173	164	1	(	(	PUNCT
ma-173	164	2	3.17	3.17	NUM
ma-173	164	3	)	)	PUNCT
ma-173	164	4	moreover	moreover	ADV
ma-173	164	5	,	,	PUNCT
ma-173	164	6	the	the	DET
ma-173	164	7	iterate	iterate	NOUN
ma-173	164	8	xn+1	xn+1	PART
ma-173	164	9	is	be	AUX
ma-173	164	10	well	well	ADV
ma-173	164	11	defined	define	VERB
ma-173	164	12	by	by	ADP
ma-173	164	13	the	the	DET
ma-173	164	14	scheme	scheme	NOUN
ma-173	164	15	(	(	PUNCT
ma-173	164	16	1.2	1.2	NUM
ma-173	164	17	)	)	PUNCT
ma-173	164	18	and	and	CCONJ
ma-173	164	19	(	(	PUNCT
ma-173	164	20	3.17	3.17	NUM
ma-173	164	21	)	)	PUNCT
ma-173	164	22	.	.	PUNCT
ma-173	165	1	further	far	ADV
ma-173	165	2	we	we	PRON
ma-173	165	3	can	can	AUX
ma-173	165	4	writerby	writerby	VERB
ma-173	165	5	the	the	DET
ma-173	165	6	scheme	scheme	NOUN
ma-173	165	7	(	(	PUNCT
ma-173	165	8	1.2	1.2	NUM
ma-173	165	9	)	)	PUNCT
ma-173	165	10	f	f	NOUN
ma-173	165	11	(	(	PUNCT
ma-173	165	12	xn+1	xn+1	X
ma-173	165	13	)	)	PUNCT
ma-173	165	14	=	=	SYM
ma-173	165	15	f	f	PROPN
ma-173	165	16	(	(	PUNCT
ma-173	165	17	xn+1)−	xn+1)−	PROPN
ma-173	165	18	f	f	PROPN
ma-173	165	19	(	(	PUNCT
ma-173	165	20	xn)−	xn)−	X
ma-173	165	21	a(xn	a(xn	PROPN
ma-173	165	22	,	,	PUNCT
ma-173	165	23	xn−1)(xn+1	xn−1)(xn+1	PROPN
ma-173	165	24	−	−	PROPN
ma-173	165	25	xn	xn	X
ma-173	165	26	)	)	PUNCT
ma-173	165	27	=	=	SYM
ma-173	166	1	(	(	PUNCT
ma-173	166	2	[	[	X
ma-173	166	3	xn+1	xn+1	X
ma-173	166	4	,	,	PUNCT
ma-173	166	5	xn;f	xn;f	PUNCT
ma-173	166	6	]	]	X
ma-173	166	7	−	−	X
ma-173	166	8	a(xn	a(xn	PROPN
ma-173	166	9	,	,	PUNCT
ma-173	166	10	xn−1))(xn+1	xn−1))(xn+1	PROPN
ma-173	166	11	−	−	PROPN
ma-173	166	12	xn	xn	PROPN
ma-173	166	13	)	)	PUNCT
ma-173	166	14	.	.	PUNCT
ma-173	167	1	(	(	PUNCT
ma-173	167	2	3.18	3.18	NUM
ma-173	167	3	)	)	PUNCT
ma-173	167	4	in	in	ADP
ma-173	167	5	view	view	NOUN
ma-173	167	6	of	of	ADP
ma-173	167	7	(	(	PUNCT
ma-173	167	8	h4	h4	NOUN
ma-173	167	9	)	)	PUNCT
ma-173	167	10	and	and	CCONJ
ma-173	167	11	(	(	PUNCT
ma-173	167	12	3.18	3.18	NUM
ma-173	167	13	)	)	PUNCT
ma-173	167	14	we	we	PRON
ma-173	167	15	get	get	VERB
ma-173	167	16	:	:	PUNCT
ma-173	167	17	‖p−1f	‖p−1f	NOUN
ma-173	167	18	(	(	PUNCT
ma-173	167	19	xn+1)‖	xn+1)‖	PROPN
ma-173	167	20	≤	≤	PROPN
ma-173	167	21	‖p−1([xn+1	‖p−1([xn+1	PROPN
ma-173	167	22	,	,	PUNCT
ma-173	167	23	xn;f	xn;f	PUNCT
ma-173	167	24	]	]	PUNCT
ma-173	167	25	−	−	X
ma-173	167	26	a(xn	a(xn	PROPN
ma-173	167	27	,	,	PUNCT
ma-173	167	28	xn−1))‖‖xn+1	xn−1))‖‖xn+1	NOUN
ma-173	167	29	−	−	PROPN
ma-173	167	30	xn‖	xn‖	PROPN
ma-173	167	31	≤	≤	PROPN
ma-173	167	32	v(‖xn+1	v(‖xn+1	NOUN
ma-173	167	33	−	−	PROPN
ma-173	167	34	xn‖	xn‖	PROPN
ma-173	167	35	,	,	PUNCT
ma-173	167	36	‖xn	‖xn	PROPN
ma-173	167	37	−	−	NUM
ma-173	167	38	xn−1‖)‖xn+1	xn−1‖)‖xn+1	PROPN
ma-173	168	1	−	−	PROPN
ma-173	168	2	xn‖	xn‖	PROPN
ma-173	168	3	≤	≤	NOUN
ma-173	168	4	v(‖γn+1	v(‖γn+1	NOUN
ma-173	168	5	−	−	PROPN
ma-173	168	6	γn‖	γn‖	PROPN
ma-173	168	7	,	,	PUNCT
ma-173	168	8	‖γn	‖γn	PROPN
ma-173	168	9	−	−	PROPN
ma-173	168	10	γn−1‖)‖γn+1	γn−1‖)‖γn+1	PROPN
ma-173	168	11	−	−	NOUN
ma-173	168	12	γn‖.	γn‖.	NOUN
ma-173	168	13	(	(	PUNCT
ma-173	168	14	3.19	3.19	NUM
ma-173	168	15	)	)	PUNCT
ma-173	168	16	then	then	ADV
ma-173	168	17	,	,	PUNCT
ma-173	168	18	by	by	ADP
ma-173	168	19	the	the	DET
ma-173	168	20	scheme	scheme	NOUN
ma-173	168	21	(	(	PUNCT
ma-173	168	22	1.2	1.2	NUM
ma-173	168	23	)	)	PUNCT
ma-173	168	24	for	for	ADP
ma-173	168	25	n	n	PRON
ma-173	168	26	replaced	replace	VERB
ma-173	168	27	by	by	ADP
ma-173	168	28	n	n	PROPN
ma-173	168	29	+	+	NOUN
ma-173	168	30	1	1	NUM
ma-173	168	31	,	,	PUNCT
ma-173	168	32	we	we	PRON
ma-173	168	33	obtain	obtain	VERB
ma-173	168	34	:	:	PUNCT
ma-173	168	35	‖xn+2	‖xn+2	ADV
ma-173	168	36	−	−	PROPN
ma-173	169	1	xn+1‖	xn+1‖	PROPN
ma-173	169	2	≤	≤	PROPN
ma-173	169	3	‖a(xn+1	‖a(xn+1	PROPN
ma-173	169	4	,	,	PUNCT
ma-173	169	5	xn)−1p‖‖pf	xn)−1p‖‖pf	PROPN
ma-173	169	6	(	(	PUNCT
ma-173	169	7	xn+1)‖	xn+1)‖	PROPN
ma-173	169	8	≤	≤	PROPN
ma-173	169	9	v(γn+1	v(γn+1	PROPN
ma-173	169	10	−	−	NOUN
ma-173	169	11	γn	γn	NOUN
ma-173	169	12	,	,	PUNCT
ma-173	169	13	γn	γn	ADP
ma-173	169	14	−	−	PROPN
ma-173	169	15	γn−1	γn−1	PROPN
ma-173	169	16	)	)	PUNCT
ma-173	169	17	1−	1−	NUM
ma-173	170	1	v0(‖xn+1	v0(‖xn+1	PROPN
ma-173	170	2	−	−	PROPN
ma-173	170	3	x0‖	x0‖	PROPN
ma-173	170	4	,	,	PUNCT
ma-173	170	5	‖xn	‖xn	PROPN
ma-173	170	6	−	−	PROPN
ma-173	170	7	x0‖	x0‖	PROPN
ma-173	170	8	)	)	PUNCT
ma-173	170	9	≤	≤	NUM
ma-173	171	1	v(γn+1	v(γn+1	NOUN
ma-173	171	2	−	−	NOUN
ma-173	171	3	γn	γn	NOUN
ma-173	171	4	,	,	PUNCT
ma-173	171	5	γn	γn	ADP
ma-173	171	6	−	−	PROPN
ma-173	171	7	γn−1)(γn+1	γn−1)(γn+1	PROPN
ma-173	171	8	−	−	NOUN
ma-173	171	9	γn	γn	NUM
ma-173	171	10	)	)	PUNCT
ma-173	171	11	1−	1−	NUM
ma-173	171	12	v0(γn+1	v0(γn+1	NOUN
ma-173	171	13	,	,	PUNCT
ma-173	171	14	γn)and	γn)and	PUNCT
ma-173	171	15	‖xn+2	‖xn+2	PUNCT
ma-173	172	1	−	−	PROPN
ma-173	172	2	x0‖	x0‖	PROPN
ma-173	172	3	≤	≤	PROPN
ma-173	172	4	‖xn+2	‖xn+2	ADV
ma-173	172	5	−	−	PROPN
ma-173	172	6	xn+1‖+	xn+1‖+	PUNCT
ma-173	173	1	‖xn+1	‖xn+1	NUM
ma-173	173	2	−	−	PROPN
ma-173	173	3	x0‖	x0‖	PROPN
ma-173	173	4	≤	≤	PROPN
ma-173	173	5	γn+2	γn+2	NUM
ma-173	174	1	−	−	PART
ma-173	174	2	γn+1	γn+1	NUM
ma-173	175	1	+	+	CCONJ
ma-173	175	2	γn+1	γn+1	NUM
ma-173	175	3	−	−	NOUN
ma-173	175	4	γ0	γ0	NOUN
ma-173	175	5	<	<	X
ma-173	175	6	γ∗	γ∗	PROPN
ma-173	175	7	−	−	PROPN
ma-173	175	8	γ0	γ0	PROPN
ma-173	175	9	.	.	PUNCT
ma-173	176	1	therefore	therefore	ADV
ma-173	176	2	,	,	PUNCT
ma-173	176	3	the	the	DET
ma-173	176	4	induction	induction	NOUN
ma-173	176	5	for	for	ADP
ma-173	176	6	the	the	DET
ma-173	176	7	item	item	NOUN
ma-173	176	8	(	(	PUNCT
ma-173	176	9	3.15	3.15	NUM
ma-173	176	10	)	)	PUNCT
ma-173	176	11	is	be	AUX
ma-173	176	12	terminated	terminate	VERB
ma-173	176	13	and	and	CCONJ
ma-173	176	14	{	{	PUNCT
ma-173	176	15	xn	xn	PROPN
ma-173	176	16	}	}	PUNCT
ma-173	176	17	⊂	⊂	PROPN
ma-173	176	18	u(x0	u(x0	NOUN
ma-173	176	19	,	,	PUNCT
ma-173	176	20	γ	γ	PROPN
ma-173	176	21	∗	∗	NOUN
ma-173	176	22	−	−	PROPN
ma-173	176	23	γ0	γ0	PROPN
ma-173	176	24	)	)	PUNCT
ma-173	176	25	.	.	PUNCT
ma-173	177	1	but	but	CCONJ
ma-173	177	2	thesequence	thesequence	NOUN
ma-173	177	3	{	{	PUNCT
ma-173	177	4	γn	γn	NOUN
ma-173	177	5	}	}	PUNCT
ma-173	177	6	is	be	AUX
ma-173	177	7	complete	complete	ADJ
ma-173	177	8	.	.	PUNCT
ma-173	178	1	thus	thus	ADV
ma-173	178	2	,	,	PUNCT
ma-173	178	3	the	the	DET
ma-173	178	4	sequence	sequence	NOUN
ma-173	178	5	{	{	PUNCT
ma-173	178	6	xn	xn	NOUN
ma-173	178	7	}	}	PUNCT
ma-173	178	8	is	be	AUX
ma-173	178	9	also	also	ADV
ma-173	178	10	complete	complete	ADJ
ma-173	178	11	in	in	ADP
ma-173	178	12	a	a	DET
ma-173	178	13	banach	banach	NOUN
ma-173	178	14	space	space	NOUN
ma-173	178	15	b.	b.	PROPN
ma-173	178	16	hencethere	hencethere	PROPN
ma-173	178	17	exists	exist	VERB
ma-173	178	18	x∗	x∗	PROPN
ma-173	178	19	∈	∈	PROPN
ma-173	178	20	u[x0	u[x0	NOUN
ma-173	178	21	,	,	PUNCT
ma-173	178	22	γ∗	γ∗	PROPN
ma-173	178	23	−	−	PROPN
ma-173	178	24	γ0	γ0	PROPN
ma-173	178	25	]	]	PUNCT
ma-173	178	26	such	such	ADJ
ma-173	178	27	that	that	SCONJ
ma-173	178	28	limn→∞	limn→∞	PROPN
ma-173	178	29	xn	xn	PUNCT
ma-173	179	1	=	=	SYM
ma-173	179	2	x∗.	x∗.	PROPN
ma-173	180	1	https://doi.org/10.28924/ada/ma.3.26	https://doi.org/10.28924/ada/ma.3.26	ADJ
ma-173	180	2	eur	eur	PROPN
ma-173	180	3	.	.	PUNCT
ma-173	181	1	j.	j.	PROPN
ma-173	181	2	math	math	PROPN
ma-173	181	3	.	.	PUNCT
ma-173	182	1	anal	anal	PROPN
ma-173	182	2	.	.	PUNCT
ma-173	183	1	10.28924	10.28924	NUM
ma-173	183	2	/	/	SYM
ma-173	183	3	ada	ada	NOUN
ma-173	183	4	/	/	SYM
ma-173	183	5	ma.3.26	ma.3.26	PROPN
ma-173	183	6	7by	7by	NOUN
ma-173	183	7	letting	let	VERB
ma-173	183	8	n	n	X
ma-173	183	9	→	→	SYM
ma-173	183	10	+	+	ADJ
ma-173	183	11	∞	∞	PROPN
ma-173	183	12	in	in	ADP
ma-173	183	13	(	(	PUNCT
ma-173	183	14	3.19	3.19	NUM
ma-173	183	15	)	)	PUNCT
ma-173	183	16	and	and	CCONJ
ma-173	183	17	using	use	VERB
ma-173	183	18	the	the	DET
ma-173	183	19	continuity	continuity	NOUN
ma-173	183	20	of	of	ADP
ma-173	183	21	the	the	DET
ma-173	183	22	operator	operator	NOUN
ma-173	183	23	f	f	NOUN
ma-173	183	24	,	,	PUNCT
ma-173	183	25	we	we	PRON
ma-173	183	26	deduce	deduce	VERB
ma-173	183	27	f	f	X
ma-173	183	28	(	(	PUNCT
ma-173	183	29	x∗	x∗	X
ma-173	183	30	)	)	PUNCT
ma-173	183	31	=	=	SYM
ma-173	184	1	0	0	X
ma-173	184	2	.	.	PUNCT
ma-173	185	1	then	then	ADV
ma-173	185	2	from	from	ADP
ma-173	185	3	the	the	DET
ma-173	185	4	estimation	estimation	NOUN
ma-173	185	5	:	:	PUNCT
ma-173	186	1	‖xn+i	‖xn+i	PROPN
ma-173	186	2	−	−	PROPN
ma-173	186	3	xn‖	xn‖	PROPN
ma-173	186	4	≤	≤	PROPN
ma-173	186	5	γn+i	γn+i	VERB
ma-173	186	6	−	−	NOUN
ma-173	186	7	γn	γn	NOUN
ma-173	186	8	,	,	PUNCT
ma-173	186	9	(	(	PUNCT
ma-173	186	10	3.20	3.20	NUM
ma-173	186	11	)	)	PUNCT
ma-173	186	12	the	the	DET
ma-173	186	13	item	item	NOUN
ma-173	186	14	(	(	PUNCT
ma-173	186	15	3.16	3.16	NUM
ma-173	186	16	)	)	PUNCT
ma-173	186	17	is	be	AUX
ma-173	186	18	obtained	obtain	VERB
ma-173	186	19	by	by	ADP
ma-173	186	20	letting	let	VERB
ma-173	186	21	i	i	PRON
ma-173	186	22	→	→	PUNCT
ma-173	187	1	+	+	ADJ
ma-173	187	2	∞	∞	PROPN
ma-173	187	3	in	in	ADP
ma-173	187	4	(	(	PUNCT
ma-173	187	5	3.20	3.20	NUM
ma-173	187	6	)	)	PUNCT
ma-173	187	7	.	.	PUNCT
ma-173	188	1	a	a	DET
ma-173	188	2	uniqueness	uniqueness	NOUN
ma-173	188	3	of	of	ADP
ma-173	188	4	the	the	DET
ma-173	188	5	solution	solution	NOUN
ma-173	188	6	region	region	NOUN
ma-173	188	7	is	be	AUX
ma-173	188	8	determined	determine	VERB
ma-173	188	9	in	in	ADP
ma-173	188	10	the	the	DET
ma-173	188	11	next	next	ADJ
ma-173	188	12	result	result	NOUN
ma-173	188	13	.	.	PUNCT
ma-173	189	1	proposition	proposition	NOUN
ma-173	189	2	3.2	3.2	NUM
ma-173	189	3	.	.	PUNCT
ma-173	190	1	assume	assume	VERB
ma-173	190	2	:	:	PUNCT
ma-173	190	3	there	there	PRON
ma-173	190	4	exists	exist	VERB
ma-173	190	5	a	a	DET
ma-173	190	6	solution	solution	NOUN
ma-173	190	7	z	z	PROPN
ma-173	190	8	∈	∈	PROPN
ma-173	190	9	u(x0	u(x0	PROPN
ma-173	190	10	,	,	PUNCT
ma-173	190	11	δ1	δ1	NOUN
ma-173	190	12	)	)	PUNCT
ma-173	190	13	of	of	ADP
ma-173	190	14	the	the	DET
ma-173	190	15	equation	equation	NOUN
ma-173	190	16	f	f	X
ma-173	190	17	(	(	PUNCT
ma-173	190	18	x	x	X
ma-173	190	19	)	)	PUNCT
ma-173	190	20	=	=	SYM
ma-173	190	21	0	0	NUM
ma-173	190	22	for	for	ADP
ma-173	190	23	some	some	DET
ma-173	190	24	δ1	δ1	NOUN
ma-173	190	25	>	>	X
ma-173	190	26	0	0	NUM
ma-173	190	27	;	;	PUNCT
ma-173	190	28	the	the	DET
ma-173	190	29	condition	condition	NOUN
ma-173	190	30	(	(	PUNCT
ma-173	190	31	h4	h4	PROPN
ma-173	190	32	)	)	PUNCT
ma-173	190	33	holds	hold	VERB
ma-173	190	34	for	for	ADP
ma-173	190	35	[	[	NOUN
ma-173	190	36	∗	∗	NOUN
ma-173	190	37	,	,	PUNCT
ma-173	190	38	∗	∗	NOUN
ma-173	190	39	,	,	PUNCT
ma-173	190	40	;	;	PUNCT
ma-173	191	1	f	f	X
ma-173	191	2	]	]	PUNCT
ma-173	191	3	replacing	replace	VERB
ma-173	191	4	a	a	PRON
ma-173	191	5	on	on	ADP
ma-173	191	6	the	the	DET
ma-173	191	7	ball	ball	NOUN
ma-173	191	8	u(x0	u(x0	PROPN
ma-173	191	9	,	,	PUNCT
ma-173	191	10	δ1	δ1	NOUN
ma-173	191	11	)	)	PUNCT
ma-173	191	12	and	and	CCONJ
ma-173	191	13	there	there	PRON
ma-173	191	14	exists	exist	VERB
ma-173	191	15	δ2	δ2	ADJ
ma-173	191	16	≥	≥	NOUN
ma-173	191	17	δ1	δ1	NOUN
ma-173	191	18	such	such	ADJ
ma-173	191	19	that	that	SCONJ
ma-173	191	20	v0(δ1	v0(δ1	NOUN
ma-173	191	21	,	,	PUNCT
ma-173	191	22	δ2	δ2	ADV
ma-173	191	23	)	)	PUNCT
ma-173	191	24	<	<	X
ma-173	192	1	1	1	X
ma-173	192	2	.	.	PUNCT
ma-173	192	3	(	(	PUNCT
ma-173	192	4	3.21	3.21	NUM
ma-173	192	5	)	)	PUNCT
ma-173	192	6	define	define	VERB
ma-173	192	7	the	the	DET
ma-173	192	8	region	region	NOUN
ma-173	192	9	d4	d4	PROPN
ma-173	192	10	=	=	SYM
ma-173	192	11	d	d	PROPN
ma-173	192	12	∩	∩	ADJ
ma-173	192	13	u[x0	u[x0	X
ma-173	192	14	,	,	PUNCT
ma-173	192	15	δ2	δ2	VERB
ma-173	192	16	]	]	PUNCT
ma-173	192	17	.	.	PUNCT
ma-173	193	1	then	then	ADV
ma-173	193	2	,	,	PUNCT
ma-173	193	3	the	the	DET
ma-173	193	4	only	only	ADJ
ma-173	193	5	solution	solution	NOUN
ma-173	193	6	of	of	ADP
ma-173	193	7	the	the	DET
ma-173	193	8	equation	equation	NOUN
ma-173	193	9	f	f	X
ma-173	193	10	(	(	PUNCT
ma-173	193	11	x	x	X
ma-173	193	12	)	)	PUNCT
ma-173	194	1	=	=	SYM
ma-173	194	2	0	0	NUM
ma-173	194	3	in	in	ADP
ma-173	194	4	the	the	DET
ma-173	194	5	region	region	NOUN
ma-173	194	6	d4	d4	PROPN
ma-173	194	7	is	be	AUX
ma-173	194	8	z	z	NOUN
ma-173	194	9	.	.	PUNCT
ma-173	195	1	proof	proof	NOUN
ma-173	195	2	.	.	PUNCT
ma-173	196	1	as	as	ADP
ma-173	196	2	in	in	ADP
ma-173	196	3	proposition	proposition	NOUN
ma-173	196	4	2.2	2.2	NUM
ma-173	196	5	,	,	PUNCT
ma-173	196	6	consider	consider	VERB
ma-173	196	7	z1	z1	NUM
ma-173	196	8	∈	∈	PROPN
ma-173	196	9	d4	d4	PROPN
ma-173	196	10	with	with	ADP
ma-173	196	11	f	f	PROPN
ma-173	196	12	(	(	PUNCT
ma-173	196	13	z1	z1	PROPN
ma-173	196	14	)	)	PUNCT
ma-173	196	15	=	=	SYM
ma-173	196	16	0	0	NUM
ma-173	196	17	and	and	CCONJ
ma-173	196	18	define	define	VERB
ma-173	196	19	e1	e1	NOUN
ma-173	196	20	=	=	PUNCT
ma-173	197	1	[	[	X
ma-173	197	2	z	z	X
ma-173	197	3	,	,	PUNCT
ma-173	197	4	z1;f	z1;f	PROPN
ma-173	197	5	]	]	PUNCT
ma-173	197	6	for	for	ADP
ma-173	197	7	z	z	PROPN
ma-173	197	8	6=	6=	PUNCT
ma-173	197	9	z1.then	z1.then	PROPN
ma-173	197	10	,	,	PUNCT
ma-173	197	11	the	the	DET
ma-173	197	12	application	application	NOUN
ma-173	197	13	of	of	ADP
ma-173	197	14	(	(	PUNCT
ma-173	197	15	h4	h4	PROPN
ma-173	197	16	)	)	PUNCT
ma-173	197	17	and	and	CCONJ
ma-173	197	18	(	(	PUNCT
ma-173	197	19	3.21	3.21	NUM
ma-173	197	20	)	)	PUNCT
ma-173	197	21	give	give	VERB
ma-173	197	22	‖p−1(e1	‖p−1(e1	PUNCT
ma-173	197	23	−	−	PROPN
ma-173	197	24	p	p	NOUN
ma-173	197	25	)	)	PUNCT
ma-173	197	26	‖	‖	PROPN
ma-173	197	27	≤	≤	PRON
ma-173	198	1	v0(‖z	v0(‖z	CCONJ
ma-173	198	2	−	−	PROPN
ma-173	198	3	z0‖	z0‖	PROPN
ma-173	198	4	,	,	PUNCT
ma-173	198	5	‖z1	‖z1	NOUN
ma-173	198	6	−	−	PROPN
ma-173	198	7	x0‖	x0‖	PROPN
ma-173	198	8	)	)	PUNCT
ma-173	198	9	≤	≤	NUM
ma-173	198	10	v0(δ1	v0(δ1	NOUN
ma-173	198	11	,	,	PUNCT
ma-173	198	12	δ2	δ2	ADV
ma-173	198	13	)	)	PUNCT
ma-173	198	14	<	<	X
ma-173	198	15	1	1	X
ma-173	198	16	.	.	PUNCT
ma-173	199	1	consequently	consequently	ADV
ma-173	199	2	,	,	PUNCT
ma-173	199	3	it	it	PRON
ma-173	199	4	follows	follow	VERB
ma-173	199	5	again	again	ADV
ma-173	199	6	that	that	SCONJ
ma-173	199	7	z1	z1	PROPN
ma-173	199	8	=	=	SYM
ma-173	199	9	z0	z0	PROPN
ma-173	199	10	.	.	PUNCT
ma-173	199	11	�	�	PROPN
ma-173	199	12	remark	remark	VERB
ma-173	199	13	3.3	3.3	NUM
ma-173	199	14	.	.	PUNCT
ma-173	200	1	(	(	PUNCT
ma-173	200	2	i	i	NOUN
ma-173	200	3	)	)	PUNCT
ma-173	200	4	possible	possible	ADJ
ma-173	200	5	choices	choice	NOUN
ma-173	200	6	but	but	CCONJ
ma-173	200	7	not	not	PART
ma-173	200	8	the	the	DET
ma-173	200	9	only	only	ADJ
ma-173	200	10	ones	one	NOUN
ma-173	200	11	for	for	ADP
ma-173	200	12	the	the	DET
ma-173	200	13	linear	linear	ADJ
ma-173	200	14	operator	operator	NOUN
ma-173	200	15	p	p	NOUN
ma-173	200	16	are	be	AUX
ma-173	200	17	:	:	PUNCT
ma-173	200	18	–	–	PUNCT
ma-173	200	19	differential	differential	ADJ
ma-173	200	20	case	case	NOUN
ma-173	200	21	:	:	PUNCT
ma-173	201	1	p	p	X
ma-173	201	2	=	=	PUNCT
ma-173	201	3	f	f	PROPN
ma-173	201	4	′(x∗	′(x∗	NOUN
ma-173	201	5	)	)	PUNCT
ma-173	201	6	and	and	CCONJ
ma-173	201	7	–	–	PUNCT
ma-173	201	8	non	non	ADJ
ma-173	201	9	-	-	ADJ
ma-173	201	10	differential	differential	ADJ
ma-173	201	11	case	case	NOUN
ma-173	201	12	:	:	PUNCT
ma-173	201	13	p	p	X
ma-173	202	1	=	=	PUNCT
ma-173	203	1	[	[	X
ma-173	203	2	x−1	x−1	PROPN
ma-173	203	3	,	,	PUNCT
ma-173	203	4	x0;f	x0;f	PROPN
ma-173	203	5	]	]	PUNCT
ma-173	203	6	.	.	PUNCT
ma-173	204	1	p	p	NOUN
ma-173	204	2	should	should	AUX
ma-173	204	3	be	be	AUX
ma-173	204	4	chosen	choose	VERB
ma-173	204	5	in	in	ADP
ma-173	204	6	general	general	ADJ
ma-173	204	7	,	,	PUNCT
ma-173	204	8	so	so	CCONJ
ma-173	204	9	the	the	DET
ma-173	204	10	majorant	majorant	NOUN
ma-173	204	11	functions	function	NOUN
ma-173	204	12	are	be	AUX
ma-173	204	13	as	as	ADV
ma-173	204	14	tight	tight	ADJ
ma-173	204	15	as	as	ADP
ma-173	204	16	possible	possible	ADJ
ma-173	204	17	in	in	ADP
ma-173	204	18	both	both	CCONJ
ma-173	204	19	the	the	DET
ma-173	204	20	local	local	ADJ
ma-173	204	21	and	and	CCONJ
ma-173	204	22	semi	semi	ADJ
ma-173	204	23	-	-	ADJ
ma-173	204	24	local	local	ADJ
ma-173	204	25	analysis	analysis	NOUN
ma-173	204	26	(	(	PUNCT
ma-173	204	27	see	see	VERB
ma-173	204	28	the	the	DET
ma-173	204	29	numerical	numerical	ADJ
ma-173	204	30	section	section	NOUN
ma-173	204	31	4	4	NUM
ma-173	204	32	that	that	PRON
ma-173	204	33	follows).(ii	follows).(ii	X
ma-173	204	34	)	)	PUNCT
ma-173	204	35	the	the	DET
ma-173	204	36	limit	limit	NOUN
ma-173	204	37	point	point	VERB
ma-173	204	38	γ∗	γ∗	NOUN
ma-173	204	39	in	in	ADP
ma-173	204	40	(	(	PUNCT
ma-173	204	41	h5	h5	PROPN
ma-173	204	42	)	)	PUNCT
ma-173	204	43	is	be	AUX
ma-173	204	44	replaced	replace	VERB
ma-173	204	45	by	by	ADP
ma-173	204	46	δ	δ	PROPN
ma-173	204	47	given	give	VERB
ma-173	204	48	in	in	ADP
ma-173	204	49	(	(	PUNCT
ma-173	204	50	h1).(iii	h1).(iii	NOUN
ma-173	204	51	)	)	PUNCT
ma-173	204	52	notice	notice	NOUN
ma-173	204	53	that	that	SCONJ
ma-173	204	54	only	only	ADV
ma-173	204	55	(	(	PUNCT
ma-173	204	56	h4	h4	PROPN
ma-173	204	57	)	)	PUNCT
ma-173	204	58	out	out	ADP
ma-173	204	59	of	of	ADP
ma-173	204	60	conditions	condition	NOUN
ma-173	204	61	(	(	PUNCT
ma-173	204	62	h1)−	h1)−	PROPN
ma-173	204	63	(	(	PUNCT
ma-173	204	64	h5	h5	PROPN
ma-173	204	65	)	)	PUNCT
ma-173	204	66	is	be	AUX
ma-173	204	67	used	use	VERB
ma-173	204	68	in	in	ADP
ma-173	204	69	proposition	proposition	NOUN
ma-173	204	70	3.2	3.2	NUM
ma-173	204	71	.	.	PUNCT
ma-173	205	1	however	however	ADV
ma-173	205	2	,	,	PUNCT
ma-173	205	3	if	if	SCONJ
ma-173	205	4	all	all	DET
ma-173	205	5	conditions	condition	NOUN
ma-173	205	6	are	be	AUX
ma-173	205	7	used	use	VERB
ma-173	205	8	,	,	PUNCT
ma-173	205	9	let	let	VERB
ma-173	205	10	δ1	δ1	NOUN
ma-173	205	11	=	=	PUNCT
ma-173	205	12	γ∗	γ∗	PROPN
ma-173	205	13	and	and	CCONJ
ma-173	205	14	z	z	NOUN
ma-173	205	15	=	=	SYM
ma-173	205	16	x∗.	x∗.	PROPN
ma-173	206	1	4	4	X
ma-173	206	2	.	.	X
ma-173	206	3	numerical	numerical	ADJ
ma-173	206	4	examples	example	NOUN
ma-173	206	5	example	example	NOUN
ma-173	206	6	4.1	4.1	NUM
ma-173	206	7	.	.	PUNCT
ma-173	207	1	let	let	VERB
ma-173	207	2	b	b	NOUN
ma-173	207	3	=	=	SYM
ma-173	207	4	r×	r×	NOUN
ma-173	207	5	r	r	NOUN
ma-173	207	6	and	and	CCONJ
ma-173	207	7	d	d	PROPN
ma-173	207	8	=	=	SYM
ma-173	207	9	u[x∗	u[x∗	PROPN
ma-173	207	10	,	,	PUNCT
ma-173	207	11	1	1	NUM
ma-173	207	12	]	]	PUNCT
ma-173	207	13	with	with	ADP
ma-173	207	14	x∗	x∗	PROPN
ma-173	207	15	=	=	SYM
ma-173	207	16	(	(	PUNCT
ma-173	207	17	0	0	NUM
ma-173	207	18	,	,	PUNCT
ma-173	207	19	0	0	NUM
ma-173	207	20	,	,	PUNCT
ma-173	207	21	0)t	0)t	INTJ
ma-173	207	22	.	.	PUNCT
ma-173	208	1	define	define	VERB
ma-173	208	2	the	the	DET
ma-173	208	3	mapping	mapping	NOUN
ma-173	208	4	f	f	NOUN
ma-173	208	5	on	on	ADP
ma-173	208	6	d	d	PROPN
ma-173	208	7	for	for	ADP
ma-173	208	8	y	y	PROPN
ma-173	208	9	=	=	SYM
ma-173	208	10	(	(	PUNCT
ma-173	208	11	y1	y1	PROPN
ma-173	208	12	,	,	PUNCT
ma-173	208	13	y2	y2	PROPN
ma-173	208	14	,	,	PUNCT
ma-173	208	15	y3)t	y3)t	ADJ
ma-173	208	16	as	as	ADP
ma-173	208	17	:	:	PUNCT
ma-173	208	18	f	f	PROPN
ma-173	208	19	(	(	PUNCT
ma-173	208	20	y	y	NOUN
ma-173	208	21	)	)	PUNCT
ma-173	208	22	=	=	SYM
ma-173	209	1	(	(	PUNCT
ma-173	209	2	ey1	ey1	ADV
ma-173	209	3	−	−	ADP
ma-173	209	4	1	1	NUM
ma-173	209	5	,	,	PUNCT
ma-173	209	6	y2	y2	INTJ
ma-173	209	7	,	,	PUNCT
ma-173	209	8	e	e	NOUN
ma-173	209	9	−	−	PROPN
ma-173	209	10	1	1	NUM
ma-173	209	11	2	2	NUM
ma-173	209	12	y23	y23	NOUN
ma-173	209	13	+	+	CCONJ
ma-173	209	14	y3	y3	NOUN
ma-173	209	15	)	)	PUNCT
ma-173	209	16	t	t	PROPN
ma-173	209	17	.	.	PUNCT
ma-173	210	1	https://doi.org/10.28924/ada/ma.3.26	https://doi.org/10.28924/ada/ma.3.26	ADJ
ma-173	210	2	eur	eur	PROPN
ma-173	210	3	.	.	PUNCT
ma-173	211	1	j.	j.	PROPN
ma-173	211	2	math	math	PROPN
ma-173	211	3	.	.	PUNCT
ma-173	212	1	anal	anal	PROPN
ma-173	212	2	.	.	PUNCT
ma-173	213	1	10.28924	10.28924	NUM
ma-173	213	2	/	/	SYM
ma-173	213	3	ada	ada	NOUN
ma-173	213	4	/	/	SYM
ma-173	213	5	ma.3.26	ma.3.26	NOUN
ma-173	213	6	8	8	NUM
ma-173	213	7	then	then	ADV
ma-173	213	8	,	,	PUNCT
ma-173	213	9	by	by	ADP
ma-173	213	10	the	the	DET
ma-173	213	11	definition	definition	NOUN
ma-173	213	12	of	of	ADP
ma-173	213	13	the	the	DET
ma-173	213	14	fréchet	fréchet	NOUN
ma-173	213	15	derivative	derivative	ADJ
ma-173	213	16	f	f	NOUN
ma-173	213	17	′	′	NUM
ma-173	213	18	of	of	ADP
ma-173	213	19	f	f	PROPN
ma-173	213	20	is	be	AUX
ma-173	213	21	given	give	VERB
ma-173	213	22	by	by	ADP
ma-173	213	23	:	:	PUNCT
ma-173	213	24	f	f	PROPN
ma-173	213	25	′(y	′(y	PROPN
ma-173	213	26	)	)	PUNCT
ma-173	214	1	=	=	PUNCT
ma-173	215	1	e	e	NOUN
ma-173	215	2	y1	y1	NOUN
ma-173	215	3	0	0	NUM
ma-173	215	4	0	0	NUM
ma-173	215	5	0	0	NUM
ma-173	215	6	1	1	NUM
ma-173	215	7	0	0	NUM
ma-173	215	8	0	0	NUM
ma-173	215	9	0	0	NUM
ma-173	215	10	(	(	PUNCT
ma-173	215	11	e	e	X
ma-173	215	12	−	−	PROPN
ma-173	215	13	1)y3	1)y3	NUM
ma-173	215	14	+	+	CCONJ
ma-173	215	15	1	1	NUM
ma-173	215	16			NOUN
ma-173	215	17	it	it	PRON
ma-173	215	18	follows	follow	VERB
ma-173	215	19	that	that	SCONJ
ma-173	215	20	f	f	PROPN
ma-173	215	21	′(x∗	′(x∗	PROPN
ma-173	215	22	)	)	PUNCT
ma-173	216	1	=	=	NOUN
ma-173	217	1	i	i	PRON
ma-173	217	2	.	.	PUNCT
ma-173	218	1	then	then	ADV
ma-173	218	2	,	,	PUNCT
ma-173	218	3	the	the	DET
ma-173	218	4	convergence	convergence	NOUN
ma-173	218	5	conditions	condition	NOUN
ma-173	218	6	(	(	PUNCT
ma-173	218	7	a3)−(a5	a3)−(a5	ADV
ma-173	218	8	)	)	PUNCT
ma-173	218	9	are	be	AUX
ma-173	218	10	validated	validate	VERB
ma-173	218	11	,	,	PUNCT
ma-173	218	12	respectively	respectively	ADV
ma-173	218	13	for	for	ADP
ma-173	218	14	:	:	PUNCT
ma-173	218	15	case	case	NOUN
ma-173	218	16	1	1	NUM
ma-173	218	17	:	:	PUNCT
ma-173	218	18	w0(s1	w0(s1	ADJ
ma-173	218	19	,	,	PUNCT
ma-173	218	20	s2	s2	PROPN
ma-173	218	21	)	)	PUNCT
ma-173	218	22	=	=	SYM
ma-173	218	23	1	1	NUM
ma-173	218	24	2	2	NUM
ma-173	218	25	(	(	PUNCT
ma-173	218	26	e	e	NOUN
ma-173	218	27	−	−	PROPN
ma-173	218	28	1)(s1	1)(s1	NUM
ma-173	218	29	+	+	NUM
ma-173	218	30	s2	s2	NOUN
ma-173	218	31	)	)	PUNCT
ma-173	218	32	,	,	PUNCT
ma-173	218	33	w(s1	w(s1	VERB
ma-173	218	34	,	,	PUNCT
ma-173	218	35	s2	s2	PROPN
ma-173	218	36	)	)	PUNCT
ma-173	218	37	=	=	SYM
ma-173	218	38	1	1	NUM
ma-173	218	39	2	2	NUM
ma-173	218	40	(	(	PUNCT
ma-173	218	41	e	e	NOUN
ma-173	218	42	−	−	PROPN
ma-173	218	43	1)s1	1)s1	NUM
ma-173	218	44	,	,	PUNCT
ma-173	218	45	and	and	CCONJ
ma-173	218	46	u[x∗	u[x∗	NOUN
ma-173	218	47	,	,	PUNCT
ma-173	218	48	r	r	NOUN
ma-173	218	49	]	]	PUNCT
ma-173	218	50	⊂	⊂	PROPN
ma-173	218	51	d.	d.	PROPN
ma-173	218	52	case	case	NOUN
ma-173	218	53	2	2	NUM
ma-173	218	54	:	:	PUNCT
ma-173	218	55	w0(s1	w0(s1	ADJ
ma-173	218	56	,	,	PUNCT
ma-173	218	57	s2	s2	PROPN
ma-173	218	58	)	)	PUNCT
ma-173	218	59	=	=	SYM
ma-173	218	60	1	1	NUM
ma-173	218	61	2	2	NUM
ma-173	218	62	(	(	PUNCT
ma-173	218	63	e	e	NOUN
ma-173	218	64	−	−	PROPN
ma-173	218	65	1)(s1	1)(s1	NUM
ma-173	218	66	+	+	NUM
ma-173	218	67	s2	s2	NOUN
ma-173	218	68	)	)	PUNCT
ma-173	218	69	,	,	PUNCT
ma-173	218	70	w(s1	w(s1	VERB
ma-173	218	71	,	,	PUNCT
ma-173	218	72	s2	s2	PROPN
ma-173	218	73	)	)	PUNCT
ma-173	218	74	=	=	SYM
ma-173	218	75	1	1	NUM
ma-173	218	76	2	2	NUM
ma-173	218	77	(	(	PUNCT
ma-173	218	78	e	e	NOUN
ma-173	218	79	−	−	PROPN
ma-173	218	80	1)(2s1	1)(2s1	NUM
ma-173	218	81	+	+	NUM
ma-173	218	82	s2	s2	PROPN
ma-173	218	83	)	)	PUNCT
ma-173	218	84	,	,	PUNCT
ma-173	218	85	and	and	CCONJ
ma-173	218	86	u[x∗	u[x∗	PROPN
ma-173	218	87	,	,	PUNCT
ma-173	218	88	3r	3r	NUM
ma-173	218	89	]	]	PUNCT
ma-173	219	1	⊂	⊂	PROPN
ma-173	219	2	d.	d.	PROPN
ma-173	219	3	case	case	NOUN
ma-173	219	4	3	3	NUM
ma-173	219	5	:	:	PUNCT
ma-173	219	6	w0(s1	w0(s1	ADJ
ma-173	219	7	,	,	PUNCT
ma-173	219	8	s2	s2	PROPN
ma-173	219	9	)	)	PUNCT
ma-173	219	10	=	=	SYM
ma-173	219	11	1	1	NUM
ma-173	219	12	2	2	NUM
ma-173	219	13	(	(	PUNCT
ma-173	219	14	e	e	NOUN
ma-173	219	15	−	−	PROPN
ma-173	219	16	1)(s1	1)(s1	NUM
ma-173	219	17	+	+	NUM
ma-173	219	18	s2	s2	NOUN
ma-173	219	19	)	)	PUNCT
ma-173	219	20	,	,	PUNCT
ma-173	219	21	w(s1	w(s1	VERB
ma-173	219	22	,	,	PUNCT
ma-173	219	23	s2	s2	PROPN
ma-173	219	24	)	)	PUNCT
ma-173	219	25	=	=	SYM
ma-173	219	26	1	1	NUM
ma-173	219	27	2	2	NUM
ma-173	219	28	(	(	PUNCT
ma-173	219	29	e	e	NOUN
ma-173	219	30	−	−	PROPN
ma-173	219	31	1)(s1	1)(s1	NUM
ma-173	219	32	+	+	CCONJ
ma-173	219	33	2s2	2s2	NUM
ma-173	219	34	)	)	PUNCT
ma-173	219	35	,	,	PUNCT
ma-173	219	36	and	and	CCONJ
ma-173	219	37	u[x∗	u[x∗	NOUN
ma-173	219	38	,	,	PUNCT
ma-173	219	39	r	r	NOUN
ma-173	219	40	]	]	PUNCT
ma-173	219	41	⊂	⊂	PROPN
ma-173	220	1	d	d	X
ma-173	220	2	,	,	PUNCT
ma-173	220	3	where	where	SCONJ
ma-173	220	4	r	r	NOUN
ma-173	220	5	=	=	SYM
ma-173	220	6	max{r	max{r	NOUN
ma-173	220	7	,	,	PUNCT
ma-173	220	8	f	f	PROPN
ma-173	220	9	(	(	PUNCT
ma-173	220	10	r	r	NOUN
ma-173	220	11	)	)	PUNCT
ma-173	220	12	}	}	PUNCT
ma-173	220	13	and	and	CCONJ
ma-173	220	14	f	f	PROPN
ma-173	220	15	(	(	PUNCT
ma-173	220	16	t	t	PROPN
ma-173	220	17	)	)	PUNCT
ma-173	220	18	=	=	SYM
ma-173	221	1	(	(	PUNCT
ma-173	221	2	‖i	‖i	NOUN
ma-173	221	3	+	+	CCONJ
ma-173	221	4	p‖+	p‖+	PROPN
ma-173	221	5	e	e	NOUN
ma-173	221	6	−	−	PROPN
ma-173	221	7	1	1	NUM
ma-173	221	8	2	2	NUM
ma-173	221	9	t	t	NOUN
ma-173	221	10	)	)	PUNCT
ma-173	221	11	t	t	PROPN
ma-173	221	12	or	or	CCONJ
ma-173	221	13	f	f	PROPN
ma-173	221	14	(	(	PUNCT
ma-173	221	15	t	t	PROPN
ma-173	221	16	)	)	PUNCT
ma-173	221	17	=	=	PUNCT
ma-173	222	1	(	(	PUNCT
ma-173	222	2	2	2	NUM
ma-173	222	3	+	+	CCONJ
ma-173	222	4	e	e	NOUN
ma-173	222	5	−	−	PROPN
ma-173	222	6	1	1	NUM
ma-173	222	7	t	t	NOUN
ma-173	222	8	)	)	PUNCT
ma-173	223	1	t.	t.	NOUN
ma-173	223	2	case	case	NOUN
ma-173	223	3	4	4	NUM
ma-173	223	4	:	:	PUNCT
ma-173	223	5	w0(s1	w0(s1	ADJ
ma-173	223	6	,	,	PUNCT
ma-173	223	7	s2	s2	PROPN
ma-173	223	8	)	)	PUNCT
ma-173	223	9	=	=	SYM
ma-173	223	10	0	0	NUM
ma-173	223	11	,	,	PUNCT
ma-173	223	12	w(s1	w(s1	VERB
ma-173	223	13	,	,	PUNCT
ma-173	223	14	s2	s2	PROPN
ma-173	223	15	)	)	PUNCT
ma-173	223	16	=	=	SYM
ma-173	223	17	1	1	NUM
ma-173	223	18	2	2	NUM
ma-173	223	19	(	(	PUNCT
ma-173	223	20	e	e	NOUN
ma-173	223	21	−	−	PROPN
ma-173	223	22	1)s1	1)s1	NUM
ma-173	223	23	,	,	PUNCT
ma-173	223	24	and	and	CCONJ
ma-173	223	25	u[x∗	u[x∗	NOUN
ma-173	223	26	,	,	PUNCT
ma-173	223	27	r	r	NOUN
ma-173	223	28	]	]	PUNCT
ma-173	223	29	⊂	⊂	PROPN
ma-173	223	30	d.	d.	PROPN
ma-173	223	31	case	case	NOUN
ma-173	223	32	5	5	NUM
ma-173	223	33	:	:	PUNCT
ma-173	223	34	w0(s1	w0(s1	ADJ
ma-173	223	35	,	,	PUNCT
ma-173	223	36	s2	s2	PROPN
ma-173	223	37	)	)	PUNCT
ma-173	223	38	=	=	SYM
ma-173	223	39	1	1	NUM
ma-173	223	40	2	2	NUM
ma-173	223	41	(	(	PUNCT
ma-173	223	42	e	e	NOUN
ma-173	223	43	−	−	PROPN
ma-173	223	44	1)(s1	1)(s1	NUM
ma-173	223	45	+	+	NUM
ma-173	223	46	s2	s2	NOUN
ma-173	223	47	)	)	PUNCT
ma-173	223	48	,	,	PUNCT
ma-173	223	49	w(s1	w(s1	VERB
ma-173	223	50	,	,	PUNCT
ma-173	223	51	s2	s2	PROPN
ma-173	223	52	)	)	PUNCT
ma-173	223	53	=	=	SYM
ma-173	223	54	1	1	NUM
ma-173	223	55	2	2	NUM
ma-173	223	56	(	(	PUNCT
ma-173	223	57	e	e	NOUN
ma-173	223	58	−	−	PROPN
ma-173	223	59	1)s1	1)s1	NUM
ma-173	223	60	,	,	PUNCT
ma-173	223	61	and	and	CCONJ
ma-173	223	62	u[x∗	u[x∗	PROPN
ma-173	223	63	,	,	PUNCT
ma-173	223	64	3r	3r	NUM
ma-173	223	65	]	]	PUNCT
ma-173	224	1	⊂	⊂	PROPN
ma-173	224	2	d.	d.	PROPN
ma-173	224	3	the	the	DET
ma-173	224	4	exact	exact	ADJ
ma-173	224	5	radius	radius	NOUN
ma-173	224	6	r	r	NOUN
ma-173	224	7	can	can	AUX
ma-173	224	8	be	be	AUX
ma-173	224	9	then	then	ADV
ma-173	224	10	computed	compute	VERB
ma-173	224	11	immediately	immediately	ADV
ma-173	224	12	using	use	VERB
ma-173	224	13	the	the	DET
ma-173	224	14	condition	condition	NOUN
ma-173	224	15	(	(	PUNCT
ma-173	224	16	a2	a2	PROPN
ma-173	224	17	)	)	PUNCT
ma-173	224	18	.	.	PUNCT
ma-173	225	1	as	as	ADP
ma-173	225	2	an	an	DET
ma-173	225	3	example	example	NOUN
ma-173	225	4	,	,	PUNCT
ma-173	225	5	for	for	ADP
ma-173	225	6	the	the	DET
ma-173	225	7	case	case	NOUN
ma-173	225	8	5	5	NUM
ma-173	225	9	,	,	PUNCT
ma-173	225	10	we	we	PRON
ma-173	225	11	must	must	AUX
ma-173	225	12	solve	solve	VERB
ma-173	225	13	:	:	PUNCT
ma-173	225	14	1	1	NUM
ma-173	225	15	2(e	2(e	NUM
ma-173	225	16	−	−	PROPN
ma-173	225	17	1)t	1)t	PROPN
ma-173	225	18	1−	1−	NUM
ma-173	225	19	(	(	PUNCT
ma-173	225	20	e	e	X
ma-173	225	21	−	−	PROPN
ma-173	225	22	1)t	1)t	PROPN
ma-173	225	23	=	=	SYM
ma-173	225	24	0	0	NUM
ma-173	225	25	,	,	PUNCT
ma-173	225	26	leading	lead	VERB
ma-173	225	27	to	to	ADP
ma-173	225	28	t	t	NOUN
ma-173	225	29	=	=	SYM
ma-173	225	30	r	r	NOUN
ma-173	225	31	=	=	SYM
ma-173	225	32	2	2	NUM
ma-173	225	33	3(e	3(e	NUM
ma-173	225	34	−	−	NOUN
ma-173	225	35	1	1	NUM
ma-173	225	36	)	)	PUNCT
ma-173	225	37	.concerning	.concerne	VERB
ma-173	225	38	the	the	DET
ma-173	225	39	semi	semi	ADJ
ma-173	225	40	-	-	ADJ
ma-173	225	41	local	local	ADJ
ma-173	225	42	case	case	NOUN
ma-173	225	43	and	and	CCONJ
ma-173	225	44	the	the	DET
ma-173	225	45	application	application	NOUN
ma-173	225	46	of	of	ADP
ma-173	225	47	the	the	DET
ma-173	225	48	method	method	NOUN
ma-173	225	49	(	(	PUNCT
ma-173	225	50	1.2	1.2	NUM
ma-173	225	51	)	)	PUNCT
ma-173	225	52	,	,	PUNCT
ma-173	225	53	we	we	PRON
ma-173	225	54	present	present	VERB
ma-173	225	55	anotherexample	anotherexample	NOUN
ma-173	225	56	:	:	PUNCT
ma-173	225	57	example	example	NOUN
ma-173	225	58	4.2	4.2	NUM
ma-173	225	59	.	.	PUNCT
ma-173	226	1	let	let	VERB
ma-173	226	2	b	b	NOUN
ma-173	226	3	=	=	SYM
ma-173	226	4	r	r	NOUN
ma-173	226	5	×	×	NOUN
ma-173	226	6	r	r	NOUN
ma-173	226	7	×	×	PROPN
ma-173	226	8	r.	r.	NOUN
ma-173	226	9	the	the	DET
ma-173	226	10	two	two	NUM
ma-173	226	11	by	by	ADP
ma-173	226	12	two	two	NUM
ma-173	226	13	nonlinear	nonlinear	ADJ
ma-173	226	14	and	and	CCONJ
ma-173	226	15	nondifferentiable	nondifferentiable	ADJ
ma-173	226	16	system	system	NOUN
ma-173	226	17	to	to	PART
ma-173	226	18	be	be	AUX
ma-173	226	19	solved	solve	VERB
ma-173	226	20	is	be	AUX
ma-173	226	21	:	:	PUNCT
ma-173	226	22	3s21	3s21	NOUN
ma-173	226	23	s2	s2	NOUN
ma-173	226	24	+	+	CCONJ
ma-173	226	25	s	s	NOUN
ma-173	226	26	2	2	NUM
ma-173	226	27	2	2	NUM
ma-173	226	28	−	−	NUM
ma-173	226	29	1	1	NUM
ma-173	226	30	+	+	NOUN
ma-173	226	31	|s1	|s1	NOUN
ma-173	226	32	−	−	PROPN
ma-173	226	33	1|	1|	NUM
ma-173	226	34	=	=	SYM
ma-173	226	35	0	0	NUM
ma-173	226	36	,	,	PUNCT
ma-173	226	37	s41	s41	ADJ
ma-173	226	38	+	+	CCONJ
ma-173	226	39	s1s	s1s	PROPN
ma-173	226	40	3	3	NUM
ma-173	226	41	2	2	NUM
ma-173	226	42	−	−	NUM
ma-173	226	43	1	1	NUM
ma-173	226	44	+	+	NUM
ma-173	226	45	|s2|	|s2|	NOUN
ma-173	226	46	=	=	SYM
ma-173	226	47	0	0	X
ma-173	226	48	.	.	PUNCT
ma-173	227	1	https://doi.org/10.28924/ada/ma.3.26	https://doi.org/10.28924/ada/ma.3.26	ADJ
ma-173	227	2	eur	eur	PROPN
ma-173	227	3	.	.	PUNCT
ma-173	228	1	j.	j.	PROPN
ma-173	228	2	math	math	PROPN
ma-173	228	3	.	.	PUNCT
ma-173	229	1	anal	anal	PROPN
ma-173	229	2	.	.	PUNCT
ma-173	230	1	10.28924	10.28924	NUM
ma-173	230	2	/	/	SYM
ma-173	230	3	ada	ada	NOUN
ma-173	230	4	/	/	SYM
ma-173	230	5	ma.3.26	ma.3.26	NOUN
ma-173	230	6	9	9	NUM
ma-173	230	7	then	then	ADV
ma-173	230	8	,	,	PUNCT
ma-173	230	9	the	the	DET
ma-173	230	10	system	system	NOUN
ma-173	230	11	can	can	AUX
ma-173	230	12	be	be	AUX
ma-173	230	13	described	describe	VERB
ma-173	230	14	as	as	ADP
ma-173	230	15	q	q	PROPN
ma-173	230	16	=	=	SYM
ma-173	230	17	(	(	PUNCT
ma-173	230	18	q1	q1	PROPN
ma-173	230	19	,	,	PUNCT
ma-173	230	20	q2	q2	NOUN
ma-173	230	21	)	)	PUNCT
ma-173	230	22	,	,	PUNCT
ma-173	230	23	where	where	SCONJ
ma-173	230	24	q1(s1	q1(s1	NOUN
ma-173	230	25	,	,	PUNCT
ma-173	230	26	s2	s2	PROPN
ma-173	230	27	)	)	PUNCT
ma-173	230	28	=	=	PUNCT
ma-173	231	1	3s	3s	NUM
ma-173	231	2	2	2	NUM
ma-173	231	3	1	1	NUM
ma-173	231	4	s2	s2	NOUN
ma-173	231	5	+	+	CCONJ
ma-173	231	6	s	s	NOUN
ma-173	231	7	2	2	NUM
ma-173	231	8	1	1	NUM
ma-173	231	9	−	−	NUM
ma-173	231	10	1	1	NUM
ma-173	231	11	+	+	NOUN
ma-173	231	12	|s1	|s1	NOUN
ma-173	231	13	−	−	PROPN
ma-173	231	14	1|	1|	NUM
ma-173	231	15	and	and	CCONJ
ma-173	231	16	q2(s1	q2(s1	ADJ
ma-173	231	17	,	,	PUNCT
ma-173	231	18	s2	s2	PROPN
ma-173	231	19	)	)	PUNCT
ma-173	232	1	=	=	SYM
ma-173	232	2	s	s	VERB
ma-173	232	3	4	4	NUM
ma-173	232	4	1	1	NUM
ma-173	232	5	+	+	NUM
ma-173	232	6	s1s	s1s	PROPN
ma-173	232	7	3	3	NUM
ma-173	232	8	2	2	NUM
ma-173	232	9	−	−	NUM
ma-173	232	10	1	1	NUM
ma-173	232	11	+	+	NUM
ma-173	232	12	|s2|	|s2|	NOUN
ma-173	232	13	.	.	PUNCT
ma-173	233	1	the	the	DET
ma-173	233	2	system	system	NOUN
ma-173	233	3	becomes	become	VERB
ma-173	233	4	q(s1	q(s1	ADJ
ma-173	233	5	,	,	PUNCT
ma-173	233	6	s2	s2	PROPN
ma-173	233	7	)	)	PUNCT
ma-173	233	8	=	=	SYM
ma-173	234	1	0	0	X
ma-173	234	2	.	.	PUNCT
ma-173	235	1	then	then	ADV
ma-173	235	2	as	as	ADP
ma-173	235	3	a	a	PRON
ma-173	235	4	=	=	PUNCT
ma-173	236	1	[	[	X
ma-173	236	2	∗	∗	NOUN
ma-173	236	3	,	,	PUNCT
ma-173	236	4	∗;q	∗;q	NOUN
ma-173	236	5	]	]	X
ma-173	236	6	,	,	PUNCT
ma-173	236	7	which	which	PRON
ma-173	236	8	is	be	AUX
ma-173	236	9	an	an	DET
ma-173	236	10	2	2	NUM
ma-173	236	11	×	×	NOUN
ma-173	236	12	2	2	NUM
ma-173	236	13	real	real	ADJ
ma-173	236	14	matrix	matrix	NOUN
ma-173	236	15	defined	define	VERB
ma-173	236	16	for	for	ADP
ma-173	236	17	s	s	NOUN
ma-173	236	18	=	=	PUNCT
ma-173	237	1	[	[	X
ma-173	237	2	s1	s1	NOUN
ma-173	237	3	,	,	PUNCT
ma-173	237	4	s2]t	s2]t	PROPN
ma-173	237	5	and	and	CCONJ
ma-173	237	6	s̃	s̃	PROPN
ma-173	237	7	=	=	PUNCT
ma-173	238	1	[	[	X
ma-173	238	2	s3	s3	PROPN
ma-173	238	3	,	,	PUNCT
ma-173	238	4	s4]t	s4]t	X
ma-173	238	5	by	by	ADP
ma-173	238	6	:	:	PUNCT
ma-173	238	7	[	[	X
ma-173	238	8	s̃	s̃	PROPN
ma-173	238	9	,	,	PUNCT
ma-173	238	10	s̃;q]i	s̃;q]i	ADJ
ma-173	238	11	,	,	PUNCT
ma-173	238	12	1	1	NUM
ma-173	238	13	=	=	SYM
ma-173	238	14	qi	qi	X
ma-173	238	15	[	[	X
ma-173	238	16	(	(	PUNCT
ma-173	238	17	s1	s1	NOUN
ma-173	238	18	,	,	PUNCT
ma-173	238	19	s4)−qi(s1	s4)−qi(s1	PROPN
ma-173	238	20	,	,	PUNCT
ma-173	238	21	s2	s2	PROPN
ma-173	238	22	)	)	PUNCT
ma-173	238	23	]	]	PUNCT
ma-173	238	24	s4	s4	PROPN
ma-173	238	25	−	−	PROPN
ma-173	238	26	s2	s2	PROPN
ma-173	238	27	for	for	ADP
ma-173	238	28	s2	s2	PROPN
ma-173	238	29	6=	6=	X
ma-173	238	30	s4	s4	PROPN
ma-173	238	31	,	,	PUNCT
ma-173	238	32	i	i	PRON
ma-173	238	33	=	=	NOUN
ma-173	238	34	1	1	NUM
ma-173	238	35	,	,	PUNCT
ma-173	238	36	2	2	NUM
ma-173	238	37	.	.	PUNCT
ma-173	238	38	otherwise	otherwise	ADV
ma-173	238	39	,	,	PUNCT
ma-173	238	40	set	set	VERB
ma-173	238	41	[	[	NOUN
ma-173	238	42	∗	∗	NOUN
ma-173	238	43	,	,	PUNCT
ma-173	238	44	∗;q	∗;q	NOUN
ma-173	238	45	]	]	X
ma-173	238	46	=	=	SYM
ma-173	239	1	0	0	X
ma-173	239	2	.	.	PUNCT
ma-173	240	1	let	let	VERB
ma-173	240	2	us	we	PRON
ma-173	240	3	choose	choose	VERB
ma-173	240	4	s0	s0	NOUN
ma-173	240	5	=	=	SYM
ma-173	240	6	(	(	PUNCT
ma-173	240	7	5	5	NUM
ma-173	240	8	,	,	PUNCT
ma-173	240	9	5	5	NUM
ma-173	240	10	)	)	PUNCT
ma-173	240	11	and	and	CCONJ
ma-173	240	12	s−1	s−1	PROPN
ma-173	240	13	=	=	SYM
ma-173	240	14	(	(	PUNCT
ma-173	240	15	1	1	NUM
ma-173	240	16	,	,	PUNCT
ma-173	240	17	0	0	NUM
ma-173	240	18	)	)	PUNCT
ma-173	240	19	to	to	PART
ma-173	240	20	be	be	AUX
ma-173	240	21	the	the	DET
ma-173	240	22	starters	starter	NOUN
ma-173	240	23	for	for	ADP
ma-173	240	24	the	the	DET
ma-173	240	25	scheme	scheme	NOUN
ma-173	240	26	(	(	PUNCT
ma-173	240	27	1.2	1.2	NUM
ma-173	240	28	)	)	PUNCT
ma-173	240	29	.	.	PUNCT
ma-173	241	1	then	then	ADV
ma-173	241	2	,	,	PUNCT
ma-173	241	3	n	n	CCONJ
ma-173	241	4	x	x	X
ma-173	241	5	(	(	PUNCT
ma-173	241	6	1	1	NUM
ma-173	241	7	)	)	PUNCT
ma-173	241	8	n	n	NOUN
ma-173	241	9	x	x	SYM
ma-173	241	10	(	(	PUNCT
ma-173	241	11	2	2	NUM
ma-173	241	12	)	)	PUNCT
ma-173	241	13	n	n	PROPN
ma-173	241	14	‖xn	‖xn	PROPN
ma-173	241	15	−	−	PROPN
ma-173	241	16	xn−1‖	xn−1‖	PROPN
ma-173	241	17	0	0	NUM
ma-173	241	18	5	5	NUM
ma-173	241	19	5	5	NUM
ma-173	241	20	1	1	NUM
ma-173	241	21	1	1	NUM
ma-173	241	22	0	0	NUM
ma-173	241	23	5	5	NUM
ma-173	241	24	2	2	NUM
ma-173	241	25	0.98909090909090909	0.98909090909090909	NUM
ma-173	241	26	0.363636363636364	0.363636363636364	NUM
ma-173	241	27	3.636e-01	3.636e-01	NUM
ma-173	241	28	3	3	NUM
ma-173	241	29	0.894886945874111	0.894886945874111	NUM
ma-173	241	30	0.329098638203090	0.329098638203090	NUM
ma-173	241	31	3.453e-02	3.453e-02	NUM
ma-173	241	32	4	4	NUM
ma-173	241	33	0.894655531991499	0.894655531991499	NUM
ma-173	241	34	0.327827544745569	0.327827544745569	NUM
ma-173	241	35	1.271e-03	1.271e-03	NUM
ma-173	241	36	5	5	NUM
ma-173	241	37	0.894655373334793	0.894655373334793	NUM
ma-173	241	38	0.327826521746906	0.327826521746906	NUM
ma-173	241	39	1.022e-06	1.022e-06	NUM
ma-173	241	40	6	6	NUM
ma-173	241	41	0.894655373334687	0.894655373334687	NUM
ma-173	241	42	0.327826421746298	0.327826421746298	NUM
ma-173	241	43	6.089e-13	6.089e-13	NUM
ma-173	241	44	7	7	NUM
ma-173	241	45	0.894655373334687	0.894655373334687	NUM
ma-173	241	46	0.327826421746298	0.327826421746298	NUM
ma-173	241	47	2.701e-20	2.701e-20	NUM
ma-173	241	48	therefore	therefore	ADV
ma-173	241	49	,	,	PUNCT
ma-173	241	50	the	the	DET
ma-173	241	51	solution	solution	NOUN
ma-173	241	52	s∗	s∗	PROPN
ma-173	241	53	=	=	SYM
ma-173	241	54	(	(	PUNCT
ma-173	241	55	s∗1	s∗1	NOUN
ma-173	241	56	,	,	PUNCT
ma-173	241	57	s∗2)t	s∗2)t	PROPN
ma-173	241	58	of	of	ADP
ma-173	241	59	the	the	DET
ma-173	241	60	system	system	NOUN
ma-173	241	61	is	be	AUX
ma-173	241	62	s∗1	s∗1	ADJ
ma-173	241	63	=	=	SYM
ma-173	241	64	0.894655373334687	0.894655373334687	NUM
ma-173	241	65	and	and	CCONJ
ma-173	241	66	s∗2	s∗2	PROPN
ma-173	241	67	=	=	SYM
ma-173	241	68	0.327826421746298	0.327826421746298	NUM
ma-173	241	69	.	.	PUNCT
ma-173	242	1	remark	remark	PROPN
ma-173	242	2	4.3	4.3	NUM
ma-173	242	3	.	.	PUNCT
ma-173	243	1	a	a	DET
ma-173	243	2	more	more	ADV
ma-173	243	3	targeted	target	VERB
ma-173	243	4	choice	choice	NOUN
ma-173	243	5	for	for	ADP
ma-173	243	6	l	l	NOUN
ma-173	243	7	than	than	SCONJ
ma-173	243	8	the	the	DET
ma-173	243	9	two	two	NUM
ma-173	243	10	mentioned	mention	VERB
ma-173	243	11	already	already	ADV
ma-173	243	12	can	can	AUX
ma-173	243	13	give	give	VERB
ma-173	243	14	a	a	DET
ma-173	243	15	larger	large	ADJ
ma-173	243	16	radius	radius	NOUN
ma-173	243	17	of	of	ADP
ma-173	243	18	convergence	convergence	NOUN
ma-173	243	19	.	.	PUNCT
ma-173	244	1	indeed	indeed	ADV
ma-173	244	2	,	,	PUNCT
ma-173	244	3	assume	assume	VERB
ma-173	244	4	the	the	DET
ma-173	244	5	conditions	condition	NOUN
ma-173	244	6	instead	instead	ADV
ma-173	244	7	of	of	ADP
ma-173	244	8	(	(	PUNCT
ma-173	244	9	a3	a3	NOUN
ma-173	244	10	)	)	PUNCT
ma-173	244	11	and	and	CCONJ
ma-173	244	12	(	(	PUNCT
ma-173	244	13	a4	a4	NOUN
ma-173	244	14	)	)	PUNCT
ma-173	244	15	(	(	PUNCT
ma-173	244	16	a3	a3	NOUN
ma-173	244	17	)	)	PUNCT
ma-173	244	18	′	′	NUM
ma-173	245	1	‖p−1(f	‖p−1(f	NUM
ma-173	245	2	′(x)−	′(x)−	NOUN
ma-173	245	3	p	p	NOUN
ma-173	245	4	)	)	PUNCT
ma-173	246	1	‖	‖	PROPN
ma-173	246	2	<	<	X
ma-173	246	3	1	1	NUM
ma-173	246	4	and	and	CCONJ
ma-173	246	5	(	(	PUNCT
ma-173	246	6	a4	a4	NOUN
ma-173	246	7	)	)	PUNCT
ma-173	246	8	′	′	NUM
ma-173	247	1	‖p−1(f	‖p−1(f	NUM
ma-173	247	2	′(x∗	′(x∗	NOUN
ma-173	248	1	+	+	CCONJ
ma-173	248	2	θ(x	θ(x	PROPN
ma-173	248	3	−	−	PROPN
ma-173	248	4	x∗))−	x∗))−	NOUN
ma-173	248	5	f	f	PROPN
ma-173	248	6	′(x))‖	′(x))‖	PROPN
ma-173	248	7	≤	≤	PROPN
ma-173	248	8	g4(θ)‖x	g4(θ)‖x	PROPN
ma-173	248	9	−	−	PROPN
ma-173	248	10	x∗‖	x∗‖	PROPN
ma-173	248	11	for	for	ADP
ma-173	248	12	each	each	PRON
ma-173	248	13	x	x	SYM
ma-173	248	14	∈	∈	PROPN
ma-173	248	15	d.	d.	NOUN
ma-173	248	16	consider	consider	VERB
ma-173	248	17	an	an	DET
ma-173	248	18	example	example	NOUN
ma-173	249	1	f	f	X
ma-173	249	2	(	(	PUNCT
ma-173	249	3	x	x	X
ma-173	249	4	)	)	PUNCT
ma-173	249	5	=	=	SYM
ma-173	249	6	ex	ex	PRON
ma-173	249	7	−	−	PROPN
ma-173	249	8	1	1	NUM
ma-173	249	9	https://doi.org/10.28924/ada/ma.3.26	https://doi.org/10.28924/ada/ma.3.26	ADJ
ma-173	249	10	eur	eur	NOUN
ma-173	249	11	.	.	PUNCT
ma-173	250	1	j.	j.	PROPN
ma-173	250	2	math	math	PROPN
ma-173	250	3	.	.	PUNCT
ma-173	251	1	anal	anal	PROPN
ma-173	251	2	.	.	PUNCT
ma-173	252	1	10.28924	10.28924	NUM
ma-173	252	2	/	/	SYM
ma-173	252	3	ada	ada	NOUN
ma-173	252	4	/	/	SYM
ma-173	252	5	ma.3.26	ma.3.26	NOUN
ma-173	252	6	10with	10with	NUM
ma-173	252	7	d	d	NOUN
ma-173	252	8	=	=	SYM
ma-173	252	9	u[x∗	u[x∗	PROPN
ma-173	252	10	,	,	PUNCT
ma-173	252	11	1	1	NUM
ma-173	252	12	]	]	PUNCT
ma-173	252	13	.	.	PUNCT
ma-173	253	1	then	then	ADV
ma-173	253	2	x∗	x∗	PROPN
ma-173	253	3	=	=	SYM
ma-173	253	4	0	0	X
ma-173	253	5	.	.	PUNCT
ma-173	254	1	choose	choose	VERB
ma-173	254	2	p	p	NOUN
ma-173	254	3	=	=	SYM
ma-173	254	4	1	1	NUM
ma-173	254	5	be	be	NOUN
ma-173	254	6	x	x	PUNCT
ma-173	254	7	for	for	ADP
ma-173	254	8	b	b	PROPN
ma-173	254	9	∈	∈	PROPN
ma-173	254	10	(	(	PUNCT
ma-173	254	11	0	0	NUM
ma-173	254	12	,	,	PUNCT
ma-173	254	13	2	2	NUM
ma-173	254	14	)	)	PUNCT
ma-173	254	15	.	.	PUNCT
ma-173	255	1	then	then	ADV
ma-173	255	2	the	the	DET
ma-173	255	3	newton	newton	PROPN
ma-173	255	4	’s	’s	PART
ma-173	255	5	scheme	scheme	NOUN
ma-173	255	6	gives	give	VERB
ma-173	255	7	:	:	PUNCT
ma-173	255	8	xn+1	xn+1	NUM
ma-173	255	9	−	−	NOUN
ma-173	255	10	x∗	x∗	PROPN
ma-173	256	1	=	=	PUNCT
ma-173	256	2	xn	xn	PROPN
ma-173	257	1	−	−	PROPN
ma-173	257	2	x∗	x∗	PROPN
ma-173	257	3	−	−	PROPN
ma-173	257	4	f	f	PROPN
ma-173	257	5	′(xn)−1f	′(xn)−1f	PROPN
ma-173	257	6	(	(	PUNCT
ma-173	257	7	xn	xn	PROPN
ma-173	257	8	)	)	PUNCT
ma-173	257	9	=	=	PUNCT
ma-173	257	10	s0f	s0f	NOUN
ma-173	257	11	′(xn	′(xn	PROPN
ma-173	257	12	)	)	PUNCT
ma-173	257	13	−1	−1	NOUN
ma-173	257	14	(	(	PUNCT
ma-173	257	15	f	f	PROPN
ma-173	257	16	′(x∗	′(x∗	PROPN
ma-173	257	17	+	+	PUNCT
ma-173	257	18	θ(xn	θ(xn	ADP
ma-173	257	19	−	−	PROPN
ma-173	257	20	x∗))−	x∗))−	PROPN
ma-173	257	21	f	f	PROPN
ma-173	257	22	′(xn	′(xn	NOUN
ma-173	257	23	)	)	PUNCT
ma-173	257	24	)	)	PUNCT
ma-173	258	1	(	(	PUNCT
ma-173	258	2	xn	xn	NOUN
ma-173	258	3	−	−	PROPN
ma-173	258	4	x∗	x∗	PROPN
ma-173	258	5	)	)	PUNCT
ma-173	258	6	leading	lead	VERB
ma-173	258	7	by	by	ADP
ma-173	258	8	(	(	PUNCT
ma-173	258	9	a3)′	a3)′	PROPN
ma-173	258	10	and	and	CCONJ
ma-173	258	11	(	(	PUNCT
ma-173	258	12	a4)′	a4)′	X
ma-173	258	13	to	to	ADP
ma-173	258	14	‖xn+1	‖xn+1	PROPN
ma-173	258	15	−	−	PROPN
ma-173	258	16	x∗‖	x∗‖	PROPN
ma-173	258	17	≤	≤	NUM
ma-173	258	18	|b|(e	|b|(e	CCONJ
ma-173	259	1	−	−	PROPN
ma-173	260	1	2)‖xn	2)‖xn	NUM
ma-173	260	2	−	−	NOUN
ma-173	260	3	x∗‖2	x∗‖2	PROPN
ma-173	260	4	1−	1−	NUM
ma-173	260	5	|1−	|1−	PROPN
ma-173	260	6	b|	b|	PROPN
ma-173	260	7	,	,	PUNCT
ma-173	260	8	where	where	SCONJ
ma-173	260	9	we	we	PRON
ma-173	260	10	also	also	ADV
ma-173	260	11	used	use	VERB
ma-173	260	12	‖p−1(f	‖p−1(f	PROPN
ma-173	260	13	′(x)−	′(x)−	NOUN
ma-173	260	14	p	p	NOUN
ma-173	260	15	)	)	PUNCT
ma-173	261	1	‖	‖	PROPN
ma-173	261	2	=	=	SYM
ma-173	261	3	∥∥∥∥be−x	∥∥∥∥be−x	ADJ
ma-173	261	4	(	(	PUNCT
ma-173	261	5	ex	ex	NOUN
ma-173	261	6	−	−	PROPN
ma-173	261	7	1bex	1bex	NUM
ma-173	261	8	)	)	PUNCT
ma-173	261	9	∥∥∥∥	∥∥∥∥	PUNCT
ma-173	262	1	=	=	SYM
ma-173	262	2	|b	|b	ADJ
ma-173	262	3	−	−	PROPN
ma-173	262	4	1|	1|	NUM
ma-173	262	5	<	<	X
ma-173	262	6	1	1	NUM
ma-173	262	7	.	.	PUNCT
ma-173	263	1	thus	thus	ADV
ma-173	263	2	,	,	PUNCT
ma-173	263	3	‖p−1(f	‖p−1(f	PROPN
ma-173	263	4	′(x)−	′(x)−	NOUN
ma-173	263	5	p	p	NOUN
ma-173	263	6	)	)	PUNCT
ma-173	263	7	‖	‖	PROPN
ma-173	263	8	≤	≤	PROPN
ma-173	263	9	1	1	NUM
ma-173	263	10	1−	1−	NUM
ma-173	263	11	|1−	|1−	NOUN
ma-173	263	12	b|	b|	PROPN
ma-173	263	13	,	,	PUNCT
ma-173	263	14	and	and	CCONJ
ma-173	263	15	‖p−1(f	‖p−1(f	DET
ma-173	263	16	′(x∗	′(x∗	NOUN
ma-173	264	1	+	+	CCONJ
ma-173	264	2	θ(x	θ(x	PROPN
ma-173	264	3	−	−	PROPN
ma-173	264	4	x∗))−	x∗))−	NOUN
ma-173	264	5	f	f	X
ma-173	264	6	′(x))‖	′(x))‖	PROPN
ma-173	264	7	≤	≤	NOUN
ma-173	264	8	|b|(e	|b|(e	CCONJ
ma-173	264	9	−	−	PROPN
ma-173	264	10	2	2	NUM
ma-173	264	11	)	)	PUNCT
ma-173	264	12	.	.	PUNCT
ma-173	265	1	the	the	DET
ma-173	265	2	last	last	ADJ
ma-173	265	3	estimate	estimate	NOUN
ma-173	265	4	is	be	AUX
ma-173	265	5	obtained	obtain	VERB
ma-173	265	6	,	,	PUNCT
ma-173	265	7	since	since	SCONJ
ma-173	265	8	for	for	ADP
ma-173	265	9	y	y	NOUN
ma-173	265	10	=	=	SYM
ma-173	265	11	x∗	x∗	PROPN
ma-173	266	1	+	+	CCONJ
ma-173	266	2	θ(x	θ(x	PROPN
ma-173	266	3	−	−	NUM
ma-173	266	4	x∗	x∗	NOUN
ma-173	266	5	)	)	PUNCT
ma-173	267	1	e−x(e−y	e−x(e−y	PRON
ma-173	267	2	−	−	PROPN
ma-173	267	3	ex	ex	NOUN
ma-173	267	4	)	)	PUNCT
ma-173	267	5	=	=	PUNCT
ma-173	268	1	ey	ey	INTJ
ma-173	268	2	−	−	NOUN
ma-173	268	3	1	1	NUM
ma-173	268	4	=	=	SYM
ma-173	268	5	1	1	NUM
ma-173	268	6	+	+	NUM
ma-173	268	7	y	y	PROPN
ma-173	268	8	+	+	CCONJ
ma-173	268	9	y2	y2	PROPN
ma-173	268	10	2	2	NUM
ma-173	268	11	!	!	PUNCT
ma-173	269	1	+	+	CCONJ
ma-173	269	2	·	·	PUNCT
ma-173	269	3	·	·	PUNCT
ma-173	269	4	·	·	PUNCT
ma-173	269	5	+	+	NUM
ma-173	269	6	y	y	PROPN
ma-173	269	7	k	k	PROPN
ma-173	269	8	k	k	PROPN
ma-173	269	9	!	!	PUNCT
ma-173	270	1	+	+	CCONJ
ma-173	270	2	·	·	PUNCT
ma-173	270	3	·	·	PUNCT
ma-173	270	4	·	·	PUNCT
ma-173	271	1	−	−	NOUN
ma-173	271	2	1	1	NUM
ma-173	271	3	=	=	SYM
ma-173	271	4	y	y	PROPN
ma-173	271	5	(	(	PUNCT
ma-173	271	6	1	1	NUM
ma-173	271	7	+	+	NUM
ma-173	271	8	y	y	PROPN
ma-173	271	9	2	2	NUM
ma-173	271	10	!	!	PUNCT
ma-173	272	1	+	+	CCONJ
ma-173	272	2	·	·	PUNCT
ma-173	272	3	·	·	PUNCT
ma-173	272	4	·	·	PUNCT
ma-173	272	5	+	+	NUM
ma-173	272	6	y	y	PROPN
ma-173	272	7	k−1	k−1	PROPN
ma-173	272	8	k	k	PROPN
ma-173	272	9	!	!	PUNCT
ma-173	273	1	+	+	CCONJ
ma-173	273	2	.	.	PUNCT
ma-173	273	3	.	.	PUNCT
ma-173	273	4	.	.	PUNCT
ma-173	273	5	)	)	PUNCT
ma-173	273	6	.	.	PUNCT
ma-173	274	1	hence	hence	ADV
ma-173	274	2	,	,	PUNCT
ma-173	274	3	‖ex(ey	‖ex(ey	PROPN
ma-173	274	4	−	−	NOUN
ma-173	274	5	ex)‖	ex)‖	NOUN
ma-173	274	6	=	=	SYM
ma-173	274	7	(	(	PUNCT
ma-173	274	8	1−	1−	NUM
ma-173	274	9	θ)gn‖x	θ)gn‖x	NOUN
ma-173	274	10	−	−	PROPN
ma-173	274	11	x∗‖,where	x∗‖,where	PROPN
ma-173	274	12	,	,	PUNCT
ma-173	274	13	gn	gn	PROPN
ma-173	274	14	=	=	PUNCT
ma-173	274	15	1	1	NUM
ma-173	274	16	+	+	NUM
ma-173	274	17	1−	1−	NUM
ma-173	274	18	θ	θ	NOUN
ma-173	274	19	2	2	NUM
ma-173	274	20	!	!	PUNCT
ma-173	275	1	+	+	CCONJ
ma-173	275	2	·	·	PUNCT
ma-173	275	3	·	·	PUNCT
ma-173	275	4	·	·	PUNCT
ma-173	275	5	+	+	PUNCT
ma-173	275	6	(	(	PUNCT
ma-173	275	7	1−	1−	NUM
ma-173	275	8	θ)n−1	θ)n−1	PROPN
ma-173	275	9	n	n	X
ma-173	275	10	!	!	PUNCT
ma-173	276	1	+	+	CCONJ
ma-173	276	2	.	.	PUNCT
ma-173	276	3	.	.	PUNCT
ma-173	277	1	.	.	PUNCT
ma-173	278	1	,	,	PUNCT
ma-173	278	2	and	and	CCONJ
ma-173	278	3	∫	∫	PROPN
ma-173	278	4	1	1	NUM
ma-173	278	5	0	0	NUM
ma-173	278	6	(	(	PUNCT
ma-173	278	7	1−	1−	NUM
ma-173	278	8	θ)ndθ	θ)ndθ	PROPN
ma-173	278	9	=	=	SYM
ma-173	278	10	1	1	NUM
ma-173	278	11	n	n	NOUN
ma-173	278	12	+	+	NUM
ma-173	278	13	1	1	NUM
ma-173	278	14	.	.	PUNCT
ma-173	279	1	but	but	CCONJ
ma-173	279	2	,	,	PUNCT
ma-173	279	3	∫	∫	PROPN
ma-173	279	4	1	1	NUM
ma-173	279	5	0	0	NUM
ma-173	279	6	(	(	PUNCT
ma-173	279	7	1−	1−	NUM
ma-173	279	8	θ)ngndθ	θ)ngndθ	PROPN
ma-173	279	9	=	=	SYM
ma-173	279	10	∫	∫	PROPN
ma-173	279	11	1	1	NUM
ma-173	279	12	0	0	NUM
ma-173	279	13	(	(	PUNCT
ma-173	279	14	1−	1−	NUM
ma-173	279	15	θ)dθt	θ)dθt	PROPN
ma-173	279	16	+	+	CCONJ
ma-173	279	17	∫	∫	PROPN
ma-173	279	18	1	1	NUM
ma-173	279	19	0	0	NUM
ma-173	279	20	(	(	PUNCT
ma-173	279	21	1−	1−	NUM
ma-173	279	22	θ)2	θ)2	NOUN
ma-173	279	23	2	2	NUM
ma-173	279	24	!	!	PUNCT
ma-173	280	1	dθt2	dθt2	NOUN
ma-173	280	2	+	+	CCONJ
ma-173	280	3	·	·	PUNCT
ma-173	280	4	·	·	PUNCT
ma-173	280	5	·	·	PUNCT
ma-173	281	1	+	+	NUM
ma-173	281	2	∫	∫	PROPN
ma-173	281	3	1	1	NUM
ma-173	281	4	0	0	NUM
ma-173	281	5	(	(	PUNCT
ma-173	281	6	1−	1−	NUM
ma-173	281	7	θ)n	θ)n	NOUN
ma-173	281	8	n	n	X
ma-173	281	9	!	!	PUNCT
ma-173	282	1	dθtn−1	dθtn−1	PROPN
ma-173	283	1	+	+	CCONJ
ma-173	283	2	.	.	PUNCT
ma-173	283	3	.	.	PUNCT
ma-173	283	4	.	.	PUNCT
ma-173	284	1	=	=	SYM
ma-173	284	2	1	1	NUM
ma-173	284	3	2	2	NUM
ma-173	284	4	t	t	NOUN
ma-173	284	5	+	+	NOUN
ma-173	284	6	1	1	NUM
ma-173	284	7	3	3	NUM
ma-173	284	8	·	·	PUNCT
ma-173	284	9	2!t	2!t	NUM
ma-173	284	10	2	2	NUM
ma-173	284	11	+	+	CCONJ
ma-173	284	12	·	·	PUNCT
ma-173	284	13	·	·	PUNCT
ma-173	284	14	·	·	PUNCT
ma-173	285	1	+	+	SYM
ma-173	285	2	1	1	NUM
ma-173	285	3	(	(	PUNCT
ma-173	285	4	n	n	NOUN
ma-173	285	5	+	+	CCONJ
ma-173	285	6	1)n	1)n	X
ma-173	285	7	!	!	PUNCT
ma-173	286	1	tn−1	tn−1	PROPN
ma-173	286	2	+	+	CCONJ
ma-173	286	3	·	·	PUNCT
ma-173	286	4	·	·	PUNCT
ma-173	286	5	·	·	PUNCT
ma-173	287	1	≤	≤	NUM
ma-173	288	1	e	e	X
ma-173	288	2	−	−	PROPN
ma-173	288	3	2	2	NUM
ma-173	288	4	.	.	PUNCT
ma-173	288	5	consequently	consequently	ADV
ma-173	288	6	,	,	PUNCT
ma-173	288	7	it	it	PRON
ma-173	288	8	follows	follow	VERB
ma-173	288	9	from	from	ADP
ma-173	288	10	the	the	DET
ma-173	288	11	error	error	NOUN
ma-173	288	12	estimate	estimate	NOUN
ma-173	288	13	that	that	PRON
ma-173	288	14	:	:	PUNCT
ma-173	289	1	ra	ra	PROPN
ma-173	289	2	=	=	SYM
ma-173	289	3	1−	1−	NUM
ma-173	289	4	|1−	|1−	NOUN
ma-173	289	5	b|	b|	PROPN
ma-173	289	6	|b|(e	|b|(e	CCONJ
ma-173	289	7	−	−	NOUN
ma-173	289	8	2	2	NUM
ma-173	289	9	)	)	PUNCT
ma-173	289	10	.let	.let	PUNCT
ma-173	290	1	us	we	PRON
ma-173	290	2	compare	compare	VERB
ma-173	290	3	the	the	DET
ma-173	290	4	new	new	ADJ
ma-173	290	5	radius	radius	NOUN
ma-173	290	6	with	with	ADP
ma-173	290	7	the	the	DET
ma-173	290	8	ones	one	NOUN
ma-173	290	9	already	already	ADV
ma-173	290	10	in	in	ADP
ma-173	290	11	the	the	DET
ma-173	290	12	literature	literature	NOUN
ma-173	290	13	developed	develop	VERB
ma-173	290	14	independently	independently	ADV
ma-173	290	15	byrheinboldt	byrheinboldt	ADJ
ma-173	291	1	[	[	X
ma-173	291	2	11	11	NUM
ma-173	291	3	]	]	PUNCT
ma-173	291	4	and	and	CCONJ
ma-173	291	5	traub	traub	NOUN
ma-173	291	6	[	[	X
ma-173	291	7	15	15	NUM
ma-173	291	8	]	]	PUNCT
ma-173	291	9	.	.	PUNCT
ma-173	292	1	the	the	DET
ma-173	292	2	condition	condition	NOUN
ma-173	292	3	used	use	VERB
ma-173	292	4	is	be	AUX
ma-173	292	5	:	:	PUNCT
ma-173	292	6	‖f	‖f	PRON
ma-173	292	7	′(x∗)−1(f	′(x∗)−1(f	NOUN
ma-173	293	1	′(x)−	′(x)−	PROPN
ma-173	293	2	f	f	PROPN
ma-173	293	3	′(y))‖	′(y))‖	PROPN
ma-173	293	4	≤	≤	X
ma-173	293	5	l‖x	l‖x	PROPN
ma-173	293	6	−	−	PROPN
ma-173	293	7	y‖	y‖	PROPN
ma-173	294	1	https://doi.org/10.28924/ada/ma.3.26	https://doi.org/10.28924/ada/ma.3.26	PROPN
ma-173	294	2	eur	eur	PROPN
ma-173	294	3	.	.	PUNCT
ma-173	295	1	j.	j.	PROPN
ma-173	295	2	math	math	PROPN
ma-173	295	3	.	.	PUNCT
ma-173	296	1	anal	anal	PROPN
ma-173	296	2	.	.	PUNCT
ma-173	297	1	10.28924	10.28924	NUM
ma-173	297	2	/	/	SYM
ma-173	297	3	ada	ada	PROPN
ma-173	297	4	/	/	SYM
ma-173	297	5	ma.3.26	ma.3.26	NOUN
ma-173	297	6	11for	11for	NOUN
ma-173	297	7	each	each	DET
ma-173	297	8	x	x	NOUN
ma-173	297	9	,	,	PUNCT
ma-173	297	10	y	y	PROPN
ma-173	297	11	∈	∈	PROPN
ma-173	298	1	d	d	X
ma-173	298	2	to	to	PART
ma-173	298	3	obtain	obtain	VERB
ma-173	298	4	the	the	DET
ma-173	298	5	error	error	NOUN
ma-173	298	6	estimate	estimate	NOUN
ma-173	298	7	:	:	PUNCT
ma-173	298	8	‖xn+1	‖xn+1	NUM
ma-173	299	1	−	−	PROPN
ma-173	299	2	x∗‖	x∗‖	PROPN
ma-173	299	3	≤	≤	PROPN
ma-173	300	1	l‖xn	l‖xn	PROPN
ma-173	300	2	−	−	PROPN
ma-173	300	3	x∗‖2	x∗‖2	PROPN
ma-173	301	1	2(1−	2(1−	PROPN
ma-173	301	2	‖xn	‖xn	PROPN
ma-173	301	3	−	−	NUM
ma-173	301	4	x∗‖	x∗‖	NUM
ma-173	301	5	)	)	PUNCT
ma-173	301	6	,	,	PUNCT
ma-173	301	7	and	and	CCONJ
ma-173	301	8	the	the	DET
ma-173	301	9	radius	radius	NOUN
ma-173	301	10	is	be	AUX
ma-173	301	11	rtr	rtr	NOUN
ma-173	301	12	=	=	PUNCT
ma-173	301	13	2	2	NUM
ma-173	301	14	3l	3l	NUM
ma-173	301	15	.but	.but	PUNCT
ma-173	302	1	l	l	NOUN
ma-173	302	2	=	=	PUNCT
ma-173	302	3	e	e	NOUN
ma-173	302	4	for	for	ADP
ma-173	302	5	the	the	DET
ma-173	302	6	example	example	NOUN
ma-173	302	7	,	,	PUNCT
ma-173	302	8	so	so	ADV
ma-173	302	9	:	:	PUNCT
ma-173	302	10	rtr	rtr	PROPN
ma-173	302	11	=	=	PUNCT
ma-173	302	12	3	3	NUM
ma-173	302	13	2e	2e	NOUN
ma-173	302	14	<	<	X
ma-173	302	15	ra	ra	PROPN
ma-173	302	16	,	,	PUNCT
ma-173	302	17	say	say	VERB
ma-173	302	18	for	for	ADP
ma-173	302	19	b	b	NOUN
ma-173	302	20	=	=	SYM
ma-173	302	21	1	1	NUM
ma-173	302	22	.	.	PUNCT
ma-173	303	1	therefore	therefore	ADV
ma-173	303	2	,	,	PUNCT
ma-173	303	3	the	the	DET
ma-173	303	4	new	new	ADJ
ma-173	303	5	radius	radius	NOUN
ma-173	303	6	of	of	ADP
ma-173	303	7	convergence	convergence	NOUN
ma-173	303	8	is	be	AUX
ma-173	303	9	larger	large	ADJ
ma-173	303	10	allowing	allow	VERB
ma-173	303	11	for	for	ADP
ma-173	303	12	a	a	DET
ma-173	303	13	wider	wide	ADJ
ma-173	303	14	choice	choice	NOUN
ma-173	303	15	of	of	ADP
ma-173	303	16	initial	initial	ADJ
ma-173	303	17	points.other	points.other	ADJ
ma-173	303	18	choices	choice	NOUN
ma-173	303	19	of	of	ADP
ma-173	303	20	p	p	NOUN
ma-173	303	21	can	can	AUX
ma-173	303	22	lead	lead	VERB
ma-173	303	23	to	to	ADP
ma-173	303	24	even	even	ADV
ma-173	303	25	larger	large	ADJ
ma-173	303	26	radius	radius	NOUN
ma-173	303	27	of	of	ADP
ma-173	303	28	convergence	convergence	NOUN
ma-173	303	29	.	.	PUNCT
ma-173	304	1	we	we	PRON
ma-173	304	2	leave	leave	VERB
ma-173	304	3	the	the	DET
ma-173	304	4	detail	detail	NOUN
ma-173	304	5	to	to	ADP
ma-173	304	6	themotivated	themotivated	ADJ
ma-173	304	7	reader	reader	NOUN
ma-173	304	8	.	.	PUNCT
ma-173	305	1	5	5	X
ma-173	305	2	.	.	X
ma-173	305	3	conclusion	conclusion	NOUN
ma-173	305	4	a	a	DET
ma-173	305	5	finer	fine	ADJ
ma-173	305	6	and	and	CCONJ
ma-173	305	7	more	more	ADV
ma-173	305	8	flexible	flexible	ADJ
ma-173	305	9	local	local	ADJ
ma-173	305	10	and	and	CCONJ
ma-173	305	11	semi	semi	ADJ
ma-173	305	12	-	-	ADJ
ma-173	305	13	local	local	ADJ
ma-173	305	14	convergence	convergence	NOUN
ma-173	305	15	analysis	analysis	NOUN
ma-173	305	16	for	for	ADP
ma-173	305	17	the	the	DET
ma-173	305	18	scheme	scheme	NOUN
ma-173	305	19	(	(	PUNCT
ma-173	305	20	1.2	1.2	NUM
ma-173	305	21	)	)	PUNCT
ma-173	305	22	is	be	AUX
ma-173	305	23	devel	devel	NOUN
ma-173	305	24	-	-	PUNCT
ma-173	305	25	oped	ope	VERB
ma-173	305	26	involving	involve	VERB
ma-173	305	27	an	an	DET
ma-173	305	28	invertible	invertible	ADJ
ma-173	305	29	operator	operator	NOUN
ma-173	305	30	p	p	NOUN
ma-173	305	31	,	,	PUNCT
ma-173	305	32	which	which	PRON
ma-173	305	33	if	if	SCONJ
ma-173	305	34	chosen	choose	VERB
ma-173	305	35	appropriately	appropriately	ADV
ma-173	305	36	leads	lead	VERB
ma-173	305	37	to	to	ADP
ma-173	305	38	weaker	weak	ADJ
ma-173	305	39	convergenceconditions	convergencecondition	NOUN
ma-173	305	40	,	,	PUNCT
ma-173	305	41	better	well	ADJ
ma-173	305	42	uniqueness	uniqueness	NOUN
ma-173	305	43	of	of	ADP
ma-173	305	44	the	the	DET
ma-173	305	45	solution	solution	NOUN
ma-173	305	46	and	and	CCONJ
ma-173	305	47	a	a	DET
ma-173	305	48	larger	large	ADJ
ma-173	305	49	radius	radius	NOUN
ma-173	305	50	of	of	ADP
ma-173	305	51	convergence	convergence	NOUN
ma-173	305	52	than	than	SCONJ
ma-173	305	53	if	if	SCONJ
ma-173	305	54	p	p	NOUN
ma-173	305	55	is	be	AUX
ma-173	305	56	chosento	chosento	NOUN
ma-173	305	57	be	be	AUX
ma-173	305	58	as	as	ADP
ma-173	305	59	in	in	ADP
ma-173	305	60	earlier	early	ADJ
ma-173	305	61	studies	study	NOUN
ma-173	305	62	f	f	PROPN
ma-173	305	63	′(x∗	′(x∗	PROPN
ma-173	305	64	)	)	PUNCT
ma-173	305	65	or	or	CCONJ
ma-173	305	66	f	f	PROPN
ma-173	305	67	′(x0	′(x0	NOUN
ma-173	305	68	)	)	PUNCT
ma-173	305	69	or	or	CCONJ
ma-173	306	1	[	[	X
ma-173	306	2	x0	x0	PROPN
ma-173	306	3	,	,	PUNCT
ma-173	306	4	x−1;f	x−1;f	PROPN
ma-173	306	5	]	]	PUNCT
ma-173	306	6	.	.	PUNCT
ma-173	307	1	this	this	DET
ma-173	307	2	idea	idea	NOUN
ma-173	307	3	can	can	AUX
ma-173	307	4	be	be	AUX
ma-173	307	5	extended	extend	VERB
ma-173	307	6	to	to	ADP
ma-173	307	7	multistepand	multistepand	NOUN
ma-173	307	8	multipoint	multipoint	NOUN
ma-173	307	9	schemes	scheme	NOUN
ma-173	307	10	[	[	X
ma-173	307	11	1–16	1–16	NOUN
ma-173	307	12	]	]	PUNCT
ma-173	307	13	.	.	PUNCT
ma-173	308	1	this	this	PRON
ma-173	308	2	is	be	AUX
ma-173	308	3	the	the	DET
ma-173	308	4	direction	direction	NOUN
ma-173	308	5	of	of	ADP
ma-173	308	6	our	our	PRON
ma-173	308	7	future	future	ADJ
ma-173	308	8	research	research	NOUN
ma-173	308	9	.	.	PUNCT
ma-173	309	1	references	reference	NOUN
ma-173	309	2	[	[	X
ma-173	309	3	1	1	NUM
ma-173	309	4	]	]	X
ma-173	309	5	i.k	i.k	PROPN
ma-173	309	6	.	.	PROPN
ma-173	309	7	argyros	argyros	PROPN
ma-173	309	8	,	,	PUNCT
ma-173	309	9	unified	unified	ADJ
ma-173	309	10	convergence	convergence	NOUN
ma-173	309	11	criteria	criterion	NOUN
ma-173	309	12	for	for	ADP
ma-173	309	13	iterative	iterative	NOUN
ma-173	309	14	banach	banach	NOUN
ma-173	309	15	space	space	NOUN
ma-173	309	16	valued	value	VERB
ma-173	309	17	methods	method	NOUN
ma-173	309	18	with	with	ADP
ma-173	309	19	applications	application	NOUN
ma-173	309	20	,	,	PUNCT
ma-173	309	21	mathematics,9	mathematics,9	NOUN
ma-173	309	22	(	(	PUNCT
ma-173	309	23	2021	2021	NUM
ma-173	309	24	)	)	PUNCT
ma-173	309	25	1942.[2	1942.[2	NUM
ma-173	309	26	]	]	X
ma-173	309	27	i.k	i.k	PROPN
ma-173	309	28	.	.	PROPN
ma-173	309	29	argyros	argyros	PROPN
ma-173	309	30	,	,	PUNCT
ma-173	309	31	theory	theory	NOUN
ma-173	309	32	and	and	CCONJ
ma-173	309	33	applications	application	NOUN
ma-173	309	34	of	of	ADP
ma-173	309	35	iterative	iterative	ADJ
ma-173	309	36	methods	method	NOUN
ma-173	309	37	,	,	PUNCT
ma-173	309	38	2nd	2nd	PROPN
ma-173	309	39	edition	edition	NOUN
ma-173	309	40	engineering	engineering	NOUN
ma-173	309	41	series	series	NOUN
ma-173	309	42	.	.	PUNCT
ma-173	310	1	crc	crc	PROPN
ma-173	310	2	press	press	PROPN
ma-173	310	3	-	-	PUNCT
ma-173	310	4	taylor	taylor	PROPN
ma-173	310	5	andfrancis	andfrancis	PROPN
ma-173	310	6	group	group	PROPN
ma-173	310	7	,	,	PUNCT
ma-173	310	8	boca	boca	PROPN
ma-173	310	9	raton	raton	PROPN
ma-173	310	10	,	,	PUNCT
ma-173	310	11	florida	florida	PROPN
ma-173	310	12	,	,	PUNCT
ma-173	310	13	usa	usa	PROPN
ma-173	310	14	,	,	PUNCT
ma-173	310	15	2022.[3	2022.[3	NUM
ma-173	310	16	]	]	PUNCT
ma-173	310	17	i.k	i.k	PROPN
ma-173	310	18	.	.	PROPN
ma-173	310	19	argyros	argyros	PROPN
ma-173	310	20	,	,	PUNCT
ma-173	310	21	convergence	convergence	NOUN
ma-173	310	22	and	and	CCONJ
ma-173	310	23	application	application	NOUN
ma-173	310	24	of	of	ADP
ma-173	310	25	newton	newton	PROPN
ma-173	310	26	-	-	PUNCT
ma-173	310	27	type	type	NOUN
ma-173	310	28	iterations	iteration	NOUN
ma-173	310	29	,	,	PUNCT
ma-173	310	30	springer	springer	NOUN
ma-173	310	31	,	,	PUNCT
ma-173	310	32	new	new	PROPN
ma-173	310	33	york	york	PROPN
ma-173	310	34	,	,	PUNCT
ma-173	310	35	2008.[4	2008.[4	NUM
ma-173	310	36	]	]	X
ma-173	310	37	j.a	j.a	PROPN
ma-173	310	38	.	.	PROPN
ma-173	310	39	ezquerro	ezquerro	PROPN
ma-173	310	40	,	,	PUNCT
ma-173	310	41	m.	m.	NOUN
ma-173	310	42	grau	grau	PROPN
ma-173	310	43	-	-	PUNCT
ma-173	310	44	sanchez	sanchez	PROPN
ma-173	310	45	,	,	PUNCT
ma-173	310	46	m.a	m.a	PROPN
ma-173	310	47	.	.	PROPN
ma-173	310	48	hernandez	hernandez	PROPN
ma-173	310	49	,	,	PUNCT
ma-173	310	50	m.	m.	NOUN
ma-173	310	51	nouguera	nouguera	NOUN
ma-173	310	52	,	,	PUNCT
ma-173	310	53	semilocal	semilocal	ADJ
ma-173	310	54	convergence	convergence	NOUN
ma-173	310	55	of	of	ADP
ma-173	310	56	secant	secant	ADJ
ma-173	310	57	-	-	PUNCT
ma-173	310	58	like	like	ADJ
ma-173	310	59	methods	method	NOUN
ma-173	310	60	fordifferentiable	fordifferentiable	ADJ
ma-173	310	61	and	and	CCONJ
ma-173	310	62	nondifferentiable	nondifferentiable	ADJ
ma-173	310	63	operator	operator	NOUN
ma-173	310	64	equations	equation	NOUN
ma-173	310	65	,	,	PUNCT
ma-173	310	66	j.	j.	PROPN
ma-173	310	67	math	math	PROPN
ma-173	310	68	.	.	PUNCT
ma-173	311	1	anal	anal	PROPN
ma-173	311	2	.	.	PUNCT
ma-173	311	3	appl	appl	PROPN
ma-173	311	4	.	.	PUNCT
ma-173	312	1	398	398	NUM
ma-173	312	2	(	(	PUNCT
ma-173	312	3	2013	2013	NUM
ma-173	312	4	)	)	PUNCT
ma-173	313	1	110–112.[5	110–112.[5	NUM
ma-173	313	2	]	]	X
ma-173	313	3	s.	s.	PROPN
ma-173	313	4	george	george	PROPN
ma-173	313	5	,	,	PUNCT
ma-173	313	6	k.	k.	PROPN
ma-173	313	7	kanagaraj	kanagaraj	PROPN
ma-173	313	8	,	,	PUNCT
ma-173	313	9	derivative	derivative	ADJ
ma-173	313	10	free	free	ADJ
ma-173	313	11	regularization	regularization	NOUN
ma-173	313	12	method	method	NOUN
ma-173	313	13	for	for	ADP
ma-173	313	14	nonlinear	nonlinear	ADJ
ma-173	313	15	ill	ill	ADV
ma-173	313	16	-	-	PUNCT
ma-173	313	17	posed	pose	VERB
ma-173	313	18	equations	equation	NOUN
ma-173	313	19	in	in	ADP
ma-173	313	20	hilbert	hilbert	NOUN
ma-173	313	21	scales	scale	NOUN
ma-173	313	22	,	,	PUNCT
ma-173	313	23	comp	comp	NOUN
ma-173	313	24	.	.	PUNCT
ma-173	313	25	meth	meth	NOUN
ma-173	313	26	.	.	PUNCT
ma-173	314	1	appl	appl	PROPN
ma-173	314	2	.	.	PROPN
ma-173	314	3	math	math	PROPN
ma-173	314	4	.	.	PUNCT
ma-173	315	1	19	19	NUM
ma-173	315	2	(	(	PUNCT
ma-173	315	3	2019	2019	NUM
ma-173	315	4	)	)	PUNCT
ma-173	316	1	765–778.[6	765–778.[6	NUM
ma-173	316	2	]	]	PUNCT
ma-173	316	3	l.v	l.v	PROPN
ma-173	316	4	.	.	PROPN
ma-173	316	5	kantorovich	kantorovich	PROPN
ma-173	316	6	,	,	PUNCT
ma-173	316	7	g.p	g.p	PROPN
ma-173	316	8	.	.	PROPN
ma-173	316	9	akilov	akilov	PROPN
ma-173	316	10	,	,	PUNCT
ma-173	316	11	functional	functional	ADJ
ma-173	316	12	analysis	analysis	NOUN
ma-173	316	13	,	,	PUNCT
ma-173	316	14	pergamom	pergamom	NOUN
ma-173	316	15	press	press	NOUN
ma-173	316	16	,	,	PUNCT
ma-173	316	17	oxford	oxford	PROPN
ma-173	316	18	,	,	PUNCT
ma-173	316	19	1982.[7	1982.[7	NUM
ma-173	316	20	]	]	X
ma-173	316	21	a.a	a.a	PROPN
ma-173	316	22	.	.	PROPN
ma-173	316	23	magrenan	magrenan	PROPN
ma-173	316	24	,	,	PUNCT
ma-173	316	25	a	a	DET
ma-173	316	26	new	new	ADJ
ma-173	316	27	tool	tool	NOUN
ma-173	316	28	to	to	PART
ma-173	316	29	study	study	VERB
ma-173	316	30	real	real	ADJ
ma-173	316	31	dynamics	dynamic	NOUN
ma-173	316	32	:	:	PUNCT
ma-173	316	33	the	the	DET
ma-173	316	34	convergence	convergence	NOUN
ma-173	316	35	plane	plane	NOUN
ma-173	316	36	,	,	PUNCT
ma-173	316	37	appl	appl	PROPN
ma-173	316	38	.	.	PROPN
ma-173	316	39	math	math	PROPN
ma-173	316	40	.	.	PUNCT
ma-173	317	1	comp	comp	NOUN
ma-173	317	2	.	.	PUNCT
ma-173	318	1	248	248	NUM
ma-173	318	2	(	(	PUNCT
ma-173	318	3	2014	2014	NUM
ma-173	318	4	)	)	PUNCT
ma-173	318	5	215–224[8	215–224[8	NOUN
ma-173	318	6	]	]	X
ma-173	318	7	j.m	j.m	PROPN
ma-173	318	8	.	.	PROPN
ma-173	318	9	ortega	ortega	PROPN
ma-173	318	10	,	,	PUNCT
ma-173	318	11	w.c	w.c	PROPN
ma-173	318	12	.	.	PROPN
ma-173	318	13	rheinboldt	rheinboldt	ADJ
ma-173	318	14	,	,	PUNCT
ma-173	318	15	iterative	iterative	ADJ
ma-173	318	16	solution	solution	NOUN
ma-173	318	17	of	of	ADP
ma-173	318	18	nonlinear	nonlinear	ADJ
ma-173	318	19	equations	equation	NOUN
ma-173	318	20	in	in	ADP
ma-173	318	21	several	several	ADJ
ma-173	318	22	variables	variable	NOUN
ma-173	318	23	,	,	PUNCT
ma-173	318	24	academic	academic	ADJ
ma-173	318	25	press	press	NOUN
ma-173	318	26	,	,	PUNCT
ma-173	318	27	new	new	ADJ
ma-173	318	28	-	-	PUNCT
ma-173	318	29	york	york	NOUN
ma-173	318	30	,	,	PUNCT
ma-173	318	31	1970.[9	1970.[9	NUM
ma-173	318	32	]	]	X
ma-173	318	33	p.	p.	NOUN
ma-173	318	34	deuflhard	deuflhard	NOUN
ma-173	318	35	,	,	PUNCT
ma-173	318	36	g.	g.	PROPN
ma-173	318	37	heindl	heindl	PROPN
ma-173	318	38	,	,	PUNCT
ma-173	318	39	affine	affine	NOUN
ma-173	318	40	invariant	invariant	ADJ
ma-173	318	41	convergence	convergence	NOUN
ma-173	318	42	theorems	theorem	NOUN
ma-173	318	43	for	for	ADP
ma-173	318	44	newton	newton	PROPN
ma-173	318	45	’s	’s	PART
ma-173	318	46	method	method	NOUN
ma-173	318	47	and	and	CCONJ
ma-173	318	48	extensions	extension	NOUN
ma-173	318	49	to	to	ADP
ma-173	318	50	relatedmethods	relatedmethod	NOUN
ma-173	318	51	,	,	PUNCT
ma-173	318	52	siam	siam	PROPN
ma-173	318	53	j.	j.	PROPN
ma-173	318	54	numer	numer	PROPN
ma-173	318	55	.	.	PUNCT
ma-173	319	1	anal	anal	PROPN
ma-173	319	2	.	.	PUNCT
ma-173	320	1	16	16	NUM
ma-173	320	2	(	(	PUNCT
ma-173	320	3	1979	1979	NUM
ma-173	320	4	)	)	PUNCT
ma-173	320	5	1–10.[10	1–10.[10	NOUN
ma-173	320	6	]	]	X
ma-173	320	7	p.p	p.p	PROPN
ma-173	320	8	.	.	PROPN
ma-173	320	9	zabrejko	zabrejko	PROPN
ma-173	320	10	,	,	PUNCT
ma-173	320	11	d.f	d.f	PROPN
ma-173	320	12	.	.	PROPN
ma-173	320	13	nguen	nguen	PROPN
ma-173	320	14	,	,	PUNCT
ma-173	320	15	the	the	DET
ma-173	320	16	majorant	majorant	NOUN
ma-173	320	17	method	method	NOUN
ma-173	320	18	in	in	ADP
ma-173	320	19	the	the	DET
ma-173	320	20	theory	theory	NOUN
ma-173	320	21	of	of	ADP
ma-173	320	22	newton	newton	PROPN
ma-173	320	23	-	-	PUNCT
ma-173	320	24	kantorovich	kantorovich	PROPN
ma-173	320	25	approximations	approximation	NOUN
ma-173	320	26	and	and	CCONJ
ma-173	320	27	the	the	DET
ma-173	320	28	ptakerror	ptakerror	NOUN
ma-173	320	29	estimates	estimate	NOUN
ma-173	320	30	,	,	PUNCT
ma-173	320	31	numer	numer	PROPN
ma-173	320	32	.	.	PUNCT
ma-173	321	1	funct	funct	PROPN
ma-173	321	2	.	.	PUNCT
ma-173	322	1	anal	anal	PROPN
ma-173	322	2	.	.	PUNCT
ma-173	323	1	optim	optim	PROPN
ma-173	323	2	.	.	PUNCT
ma-173	324	1	9	9	NUM
ma-173	324	2	(	(	PUNCT
ma-173	324	3	1987	1987	NUM
ma-173	324	4	)	)	PUNCT
ma-173	325	1	671–684[11	671–684[11	NUM
ma-173	325	2	]	]	PUNCT
ma-173	325	3	w.c	w.c	PROPN
ma-173	325	4	.	.	PROPN
ma-173	325	5	rheinboldt	rheinboldt	PROPN
ma-173	325	6	,	,	PUNCT
ma-173	325	7	an	an	DET
ma-173	325	8	adaptive	adaptive	ADJ
ma-173	325	9	continuation	continuation	NOUN
ma-173	325	10	process	process	NOUN
ma-173	325	11	for	for	ADP
ma-173	325	12	solving	solve	VERB
ma-173	325	13	systems	system	NOUN
ma-173	325	14	of	of	ADP
ma-173	325	15	nonlinear	nonlinear	ADJ
ma-173	325	16	equations	equation	NOUN
ma-173	325	17	,	,	PUNCT
ma-173	325	18	banach	banach	NOUN
ma-173	325	19	cent	cent	NOUN
ma-173	325	20	.	.	PUNCT
ma-173	326	1	publ.3	publ.3	NOUN
ma-173	326	2	(	(	PUNCT
ma-173	326	3	1978	1978	NUM
ma-173	326	4	)	)	PUNCT
ma-173	326	5	129–142.[12	129–142.[12	NUM
ma-173	326	6	]	]	X
ma-173	326	7	s.m	s.m	PROPN
ma-173	326	8	.	.	PROPN
ma-173	326	9	shakhno	shakhno	PROPN
ma-173	326	10	,	,	PUNCT
ma-173	326	11	convergence	convergence	NOUN
ma-173	326	12	of	of	ADP
ma-173	326	13	the	the	DET
ma-173	326	14	two	two	NUM
ma-173	326	15	-	-	PUNCT
ma-173	326	16	step	step	NOUN
ma-173	326	17	combined	combine	VERB
ma-173	326	18	method	method	NOUN
ma-173	326	19	and	and	CCONJ
ma-173	326	20	uniqueness	uniqueness	NOUN
ma-173	326	21	of	of	ADP
ma-173	326	22	the	the	DET
ma-173	326	23	solution	solution	NOUN
ma-173	326	24	of	of	ADP
ma-173	326	25	nonlinear	nonlinear	ADJ
ma-173	326	26	operatorequations	operatorequation	NOUN
ma-173	326	27	.	.	PUNCT
ma-173	327	1	j.	j.	PROPN
ma-173	327	2	comp	comp	PROPN
ma-173	327	3	.	.	PUNCT
ma-173	328	1	appl	appl	PROPN
ma-173	328	2	.	.	PROPN
ma-173	328	3	math	math	NOUN
ma-173	328	4	.	.	PUNCT
ma-173	329	1	261	261	NUM
ma-173	329	2	(	(	PUNCT
ma-173	329	3	2014	2014	NUM
ma-173	329	4	)	)	PUNCT
ma-173	330	1	378–386	378–386	NUM
ma-173	330	2	.	.	PUNCT
ma-173	331	1	https://doi.org/10.28924/ada/ma.3.26	https://doi.org/10.28924/ada/ma.3.26	ADJ
ma-173	331	2	eur	eur	PROPN
ma-173	331	3	.	.	PUNCT
ma-173	332	1	j.	j.	PROPN
ma-173	332	2	math	math	PROPN
ma-173	332	3	.	.	PUNCT
ma-173	333	1	anal	anal	PROPN
ma-173	333	2	.	.	PUNCT
ma-173	334	1	10.28924	10.28924	NUM
ma-173	334	2	/	/	SYM
ma-173	334	3	ada	ada	NOUN
ma-173	334	4	/	/	SYM
ma-173	334	5	ma.3.26	ma.3.26	NOUN
ma-173	334	6	12	12	NUM
ma-173	335	1	[	[	SYM
ma-173	335	2	13	13	NUM
ma-173	335	3	]	]	SYM
ma-173	335	4	s.m	s.m	PROPN
ma-173	335	5	.	.	PROPN
ma-173	335	6	shakhno	shakhno	PROPN
ma-173	335	7	,	,	PUNCT
ma-173	335	8	on	on	ADP
ma-173	335	9	an	an	DET
ma-173	335	10	iterative	iterative	ADJ
ma-173	335	11	algorithm	algorithm	NOUN
ma-173	335	12	with	with	ADP
ma-173	335	13	superquadratic	superquadratic	ADJ
ma-173	335	14	convergence	convergence	NOUN
ma-173	335	15	for	for	ADP
ma-173	335	16	solving	solve	VERB
ma-173	335	17	nonlinear	nonlinear	ADJ
ma-173	335	18	operator	operator	NOUN
ma-173	335	19	equations.j	equations.j	PROPN
ma-173	335	20	.	.	PUNCT
ma-173	336	1	comp	comp	PROPN
ma-173	336	2	.	.	PUNCT
ma-173	337	1	appl	appl	PROPN
ma-173	337	2	.	.	PROPN
ma-173	337	3	math	math	NOUN
ma-173	337	4	.	.	PUNCT
ma-173	338	1	231	231	NUM
ma-173	338	2	(	(	PUNCT
ma-173	338	3	2009	2009	NUM
ma-173	338	4	)	)	PUNCT
ma-173	338	5	222–235.[14	222–235.[14	PROPN
ma-173	338	6	]	]	X
ma-173	338	7	j.r	j.r	PROPN
ma-173	338	8	.	.	PROPN
ma-173	338	9	sharma	sharma	PROPN
ma-173	338	10	,	,	PUNCT
ma-173	338	11	h.	h.	PROPN
ma-173	338	12	arora	arora	PROPN
ma-173	338	13	,	,	PUNCT
ma-173	338	14	a	a	DET
ma-173	338	15	novel	novel	ADJ
ma-173	338	16	derivative	derivative	ADJ
ma-173	338	17	free	free	ADJ
ma-173	338	18	algorithm	algorithm	NOUN
ma-173	338	19	with	with	ADP
ma-173	338	20	seventh	seventh	ADJ
ma-173	338	21	order	order	NOUN
ma-173	338	22	convergence	convergence	NOUN
ma-173	338	23	for	for	ADP
ma-173	338	24	solving	solve	VERB
ma-173	338	25	systems	system	NOUN
ma-173	338	26	ofnonlinear	ofnonlinear	NOUN
ma-173	338	27	equations	equation	NOUN
ma-173	338	28	,	,	PUNCT
ma-173	338	29	numer	numer	PROPN
ma-173	338	30	.	.	PROPN
ma-173	338	31	algor	algor	PROPN
ma-173	338	32	.	.	PUNCT
ma-173	339	1	67	67	NUM
ma-173	339	2	(	(	PUNCT
ma-173	339	3	2014	2014	NUM
ma-173	339	4	)	)	PUNCT
ma-173	339	5	917–933.[15	917–933.[15	PROPN
ma-173	339	6	]	]	X
ma-173	339	7	j.f	j.f	PROPN
ma-173	339	8	.	.	PROPN
ma-173	339	9	traub	traub	PROPN
ma-173	339	10	,	,	PUNCT
ma-173	339	11	prentice	prentice	NOUN
ma-173	339	12	-	-	PUNCT
ma-173	339	13	hall	hall	NOUN
ma-173	339	14	,	,	PUNCT
ma-173	339	15	iterative	iterative	ADJ
ma-173	339	16	methods	method	NOUN
ma-173	339	17	for	for	ADP
ma-173	339	18	the	the	DET
ma-173	339	19	solution	solution	NOUN
ma-173	339	20	of	of	ADP
ma-173	339	21	equations	equation	NOUN
ma-173	339	22	,	,	PUNCT
ma-173	339	23	prentice	prentice	NOUN
ma-173	339	24	-	-	PUNCT
ma-173	339	25	hall	hall	NOUN
ma-173	339	26	,	,	PUNCT
ma-173	339	27	englewood	englewood	PROPN
ma-173	339	28	cliffs	cliffs	PROPN
ma-173	339	29	,	,	PUNCT
ma-173	339	30	newjersey	newjersey	NOUN
ma-173	339	31	,	,	PUNCT
ma-173	339	32	(	(	PUNCT
ma-173	339	33	1964).[16	1964).[16	NUM
ma-173	339	34	]	]	PUNCT
ma-173	339	35	t.	t.	PROPN
ma-173	339	36	yamamoto	yamamoto	PROPN
ma-173	339	37	,	,	PUNCT
ma-173	339	38	a	a	DET
ma-173	339	39	convergence	convergence	NOUN
ma-173	339	40	theorem	theorem	NOUN
ma-173	339	41	for	for	ADP
ma-173	339	42	newton	newton	PROPN
ma-173	339	43	-	-	PUNCT
ma-173	339	44	like	like	ADJ
ma-173	339	45	methods	method	NOUN
ma-173	339	46	in	in	ADP
ma-173	339	47	banach	banach	NOUN
ma-173	339	48	spaces	space	NOUN
ma-173	339	49	,	,	PUNCT
ma-173	339	50	numer	numer	PROPN
ma-173	339	51	.	.	PROPN
ma-173	339	52	math	math	NOUN
ma-173	339	53	.	.	PUNCT
ma-173	340	1	51	51	NUM
ma-173	340	2	(	(	PUNCT
ma-173	340	3	1987	1987	NUM
ma-173	340	4	)	)	PUNCT
ma-173	341	1	545–557	545–557	NUM
ma-173	341	2	.	.	PUNCT
ma-173	342	1	https://doi.org/10.28924/ada/ma.3.26	https://doi.org/10.28924/ada/ma.3.26	DET
ma-173	342	2	1	1	X
ma-173	342	3	.	.	X
ma-173	342	4	introduction	introduction	NOUN
ma-173	342	5	2	2	NUM
ma-173	342	6	.	.	PUNCT
ma-173	343	1	convergence	convergence	NOUN
ma-173	343	2	i	i	PRON
ma-173	343	3	:	:	PUNCT
ma-173	343	4	local	local	ADJ
ma-173	343	5	3	3	X
ma-173	343	6	.	.	PUNCT
ma-173	343	7	convergence	convergence	PROPN
ma-173	343	8	ii	ii	PROPN
ma-173	343	9	:	:	PUNCT
ma-173	343	10	semi	semi	ADJ
ma-173	343	11	-	-	ADJ
ma-173	343	12	local	local	ADJ
ma-173	343	13	4	4	NUM
ma-173	343	14	.	.	PUNCT
ma-173	343	15	numerical	numerical	ADJ
ma-173	343	16	examples	example	NOUN
ma-173	343	17	5	5	NUM
ma-173	343	18	.	.	PUNCT
ma-173	344	1	conclusion	conclusion	NOUN
ma-173	344	2	references	reference	NOUN