id	sid	tid	token	lemma	pos
ma-172	1	1	2023	2023	NUM
ma-172	1	2	ada	ada	PROPN
ma-172	1	3	academica	academica	PROPN
ma-172	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-172	1	5	.	.	PUNCT
ma-172	2	1	j.	j.	PROPN
ma-172	2	2	math	math	PROPN
ma-172	2	3	.	.	PUNCT
ma-172	3	1	anal	anal	ADJ
ma-172	3	2	.	.	PUNCT
ma-172	4	1	3	3	NUM
ma-172	4	2	(	(	PUNCT
ma-172	4	3	2023	2023	NUM
ma-172	4	4	)	)	PUNCT
ma-172	4	5	19doi	19doi	NOUN
ma-172	4	6	:	:	PUNCT
ma-172	4	7	10.28924	10.28924	NUM
ma-172	4	8	/	/	SYM
ma-172	4	9	ada	ada	PROPN
ma-172	4	10	/	/	SYM
ma-172	4	11	ma.3.19	ma.3.19	PROPN
ma-172	4	12	efficient	efficient	ADJ
ma-172	4	13	derivative	derivative	ADJ
ma-172	4	14	-	-	PUNCT
ma-172	4	15	free	free	ADJ
ma-172	4	16	class	class	NOUN
ma-172	4	17	of	of	ADP
ma-172	4	18	seventh	seventh	ADJ
ma-172	4	19	order	order	NOUN
ma-172	4	20	method	method	NOUN
ma-172	4	21	for	for	ADP
ma-172	4	22	non	non	ADJ
ma-172	4	23	-	-	ADJ
ma-172	4	24	differentiable	differentiable	ADJ
ma-172	4	25	equations	equation	NOUN
ma-172	4	26	ioannis	ioannis	PROPN
ma-172	4	27	k.	k.	PROPN
ma-172	4	28	argyros1,∗	argyros1,∗	PROPN
ma-172	4	29	,	,	PUNCT
ma-172	4	30	samundra	samundra	NOUN
ma-172	4	31	regmi2	regmi2	PROPN
ma-172	4	32	,	,	PUNCT
ma-172	4	33	jinny	jinny	PROPN
ma-172	4	34	ann	ann	PROPN
ma-172	5	1	john3	john3	PROPN
ma-172	5	2	,	,	PUNCT
ma-172	5	3	jayakumar	jayakumar	NOUN
ma-172	5	4	jayaraman3	jayaraman3	PROPN
ma-172	5	5	1department	1department	NUM
ma-172	5	6	of	of	ADP
ma-172	5	7	computing	computing	NOUN
ma-172	5	8	and	and	CCONJ
ma-172	5	9	mathematical	mathematical	ADJ
ma-172	5	10	sciences	sciences	PROPN
ma-172	5	11	,	,	PUNCT
ma-172	5	12	cameron	cameron	PROPN
ma-172	5	13	university	university	PROPN
ma-172	5	14	,	,	PUNCT
ma-172	5	15	lawton	lawton	PROPN
ma-172	5	16	,	,	PUNCT
ma-172	5	17	73505	73505	NUM
ma-172	5	18	,	,	PUNCT
ma-172	5	19	ok	ok	INTJ
ma-172	5	20	,	,	PUNCT
ma-172	5	21	usa	usa	PROPN
ma-172	5	22	iargyros@cameron.edu	iargyros@cameron.edu	PROPN
ma-172	6	1	2department	2department	NUM
ma-172	6	2	of	of	ADP
ma-172	6	3	mathematics	mathematic	NOUN
ma-172	6	4	,	,	PUNCT
ma-172	6	5	university	university	PROPN
ma-172	6	6	of	of	ADP
ma-172	6	7	houston	houston	PROPN
ma-172	6	8	,	,	PUNCT
ma-172	6	9	houston	houston	PROPN
ma-172	6	10	,	,	PUNCT
ma-172	6	11	77204	77204	NUM
ma-172	6	12	,	,	PUNCT
ma-172	6	13	tx	tx	PROPN
ma-172	6	14	,	,	PUNCT
ma-172	6	15	usa	usa	PROPN
ma-172	6	16	sregmi5@uh.edu	sregmi5@uh.edu	PROPN
ma-172	6	17	3department	3department	NUM
ma-172	6	18	of	of	ADP
ma-172	6	19	mathematics	mathematic	NOUN
ma-172	6	20	,	,	PUNCT
ma-172	6	21	puducherry	puducherry	PROPN
ma-172	6	22	technological	technological	ADJ
ma-172	6	23	university	university	NOUN
ma-172	6	24	,	,	PUNCT
ma-172	6	25	pondicherry	pondicherry	NOUN
ma-172	6	26	605014	605014	NUM
ma-172	6	27	,	,	PUNCT
ma-172	6	28	india	india	PROPN
ma-172	6	29	jinny3@pec.edu	jinny3@pec.edu	PROPN
ma-172	6	30	,	,	PUNCT
ma-172	6	31	jjayakumar@ptuniv.edu.in	jjayakumar@ptuniv.edu.in	NOUN
ma-172	6	32	∗correspondence	∗correspondence	NOUN
ma-172	6	33	:	:	PUNCT
ma-172	6	34	iargyros@cameron.edu	iargyros@cameron.edu	X
ma-172	7	1	abstract	abstract	ADJ
ma-172	7	2	.	.	PUNCT
ma-172	8	1	many	many	ADJ
ma-172	8	2	applications	application	NOUN
ma-172	8	3	from	from	ADP
ma-172	8	4	a	a	DET
ma-172	8	5	wide	wide	ADJ
ma-172	8	6	variety	variety	NOUN
ma-172	8	7	of	of	ADP
ma-172	8	8	disciplines	discipline	NOUN
ma-172	8	9	in	in	ADP
ma-172	8	10	the	the	DET
ma-172	8	11	natural	natural	ADJ
ma-172	8	12	sciences	science	NOUN
ma-172	8	13	and	and	CCONJ
ma-172	8	14	also	also	ADV
ma-172	8	15	inengineering	inengineere	VERB
ma-172	8	16	are	be	AUX
ma-172	8	17	reduced	reduce	VERB
ma-172	8	18	to	to	ADP
ma-172	8	19	solving	solve	VERB
ma-172	8	20	of	of	ADP
ma-172	8	21	an	an	DET
ma-172	8	22	equation	equation	NOUN
ma-172	8	23	or	or	CCONJ
ma-172	8	24	a	a	DET
ma-172	8	25	system	system	NOUN
ma-172	8	26	of	of	ADP
ma-172	8	27	equations	equation	NOUN
ma-172	8	28	in	in	ADP
ma-172	8	29	a	a	DET
ma-172	8	30	correspondinglychosen	correspondinglychosen	ADJ
ma-172	8	31	abstract	abstract	ADJ
ma-172	8	32	area	area	NOUN
ma-172	8	33	.	.	PUNCT
ma-172	9	1	for	for	ADP
ma-172	9	2	most	most	ADJ
ma-172	9	3	of	of	ADP
ma-172	9	4	these	these	DET
ma-172	9	5	problems	problem	NOUN
ma-172	9	6	,	,	PUNCT
ma-172	9	7	the	the	DET
ma-172	9	8	solutions	solution	NOUN
ma-172	9	9	are	be	AUX
ma-172	9	10	found	find	VERB
ma-172	9	11	iterative	iterative	NOUN
ma-172	9	12	,	,	PUNCT
ma-172	9	13	because	because	SCONJ
ma-172	9	14	theiranalytic	theiranalytic	ADJ
ma-172	9	15	versions	version	NOUN
ma-172	9	16	are	be	AUX
ma-172	9	17	difficult	difficult	ADJ
ma-172	9	18	to	to	PART
ma-172	9	19	find	find	VERB
ma-172	9	20	or	or	CCONJ
ma-172	9	21	impossible	impossible	ADJ
ma-172	9	22	.	.	PUNCT
ma-172	10	1	this	this	DET
ma-172	10	2	article	article	NOUN
ma-172	10	3	encompasses	encompass	VERB
ma-172	10	4	efficient	efficient	ADJ
ma-172	10	5	,	,	PUNCT
ma-172	10	6	derivatives	derivative	NOUN
ma-172	10	7	-	-	PUNCT
ma-172	10	8	free	free	ADJ
ma-172	10	9	,	,	PUNCT
ma-172	10	10	high	high	ADJ
ma-172	10	11	-	-	PUNCT
ma-172	10	12	convergence	convergence	NOUN
ma-172	10	13	iterative	iterative	NOUN
ma-172	10	14	methods	method	NOUN
ma-172	10	15	.	.	PUNCT
ma-172	11	1	convergence	convergence	NOUN
ma-172	11	2	of	of	ADP
ma-172	11	3	two	two	NUM
ma-172	11	4	types	type	NOUN
ma-172	11	5	:	:	PUNCT
ma-172	11	6	local	local	ADJ
ma-172	11	7	and	and	CCONJ
ma-172	11	8	semi	semi	ADJ
ma-172	11	9	-	-	ADJ
ma-172	11	10	local	local	ADJ
ma-172	11	11	areas	area	NOUN
ma-172	11	12	will	will	AUX
ma-172	11	13	beinvestigated	beinvestigate	VERB
ma-172	11	14	under	under	ADP
ma-172	11	15	the	the	DET
ma-172	11	16	conditions	condition	NOUN
ma-172	11	17	of	of	ADP
ma-172	11	18	the	the	DET
ma-172	11	19	ϕ,ψ	ϕ,ψ	NOUN
ma-172	11	20	-	-	PUNCT
ma-172	11	21	continuity	continuity	NOUN
ma-172	11	22	utilizing	utilize	VERB
ma-172	11	23	operators	operator	NOUN
ma-172	11	24	on	on	ADP
ma-172	11	25	the	the	DET
ma-172	11	26	method	method	NOUN
ma-172	11	27	.	.	PUNCT
ma-172	12	1	the	the	DET
ma-172	12	2	newmethod	newmethod	NOUN
ma-172	12	3	can	can	AUX
ma-172	12	4	also	also	ADV
ma-172	12	5	be	be	AUX
ma-172	12	6	applied	apply	VERB
ma-172	12	7	to	to	ADP
ma-172	12	8	other	other	ADJ
ma-172	12	9	methods	method	NOUN
ma-172	12	10	,	,	PUNCT
ma-172	12	11	using	use	VERB
ma-172	12	12	inverses	inverse	NOUN
ma-172	12	13	of	of	ADP
ma-172	12	14	the	the	DET
ma-172	12	15	linear	linear	ADJ
ma-172	12	16	operator	operator	NOUN
ma-172	12	17	or	or	CCONJ
ma-172	12	18	the	the	DET
ma-172	12	19	matrix	matrix	NOUN
ma-172	12	20	.	.	PUNCT
ma-172	13	1	1	1	X
ma-172	13	2	.	.	X
ma-172	13	3	introduction	introduction	NOUN
ma-172	13	4	in	in	ADP
ma-172	13	5	the	the	DET
ma-172	13	6	area	area	NOUN
ma-172	13	7	of	of	ADP
ma-172	13	8	applied	apply	VERB
ma-172	13	9	science	science	NOUN
ma-172	13	10	and	and	CCONJ
ma-172	13	11	technology	technology	NOUN
ma-172	13	12	,	,	PUNCT
ma-172	13	13	a	a	DET
ma-172	13	14	great	great	ADJ
ma-172	13	15	number	number	NOUN
ma-172	13	16	of	of	ADP
ma-172	13	17	problems	problem	NOUN
ma-172	13	18	can	can	AUX
ma-172	13	19	be	be	AUX
ma-172	13	20	resolved	resolve	VERB
ma-172	13	21	byconverting	byconverte	VERB
ma-172	13	22	them	they	PRON
ma-172	13	23	into	into	ADP
ma-172	13	24	nonlinear	nonlinear	ADJ
ma-172	13	25	form	form	NOUN
ma-172	13	26	equation	equation	NOUN
ma-172	13	27	g(x	g(x	NOUN
ma-172	13	28	)	)	PUNCT
ma-172	14	1	=	=	SYM
ma-172	14	2	0	0	PUNCT
ma-172	14	3	(	(	PUNCT
ma-172	14	4	1	1	NUM
ma-172	14	5	)	)	PUNCT
ma-172	14	6	where	where	SCONJ
ma-172	14	7	g	g	NOUN
ma-172	14	8	:	:	PUNCT
ma-172	14	9	b	b	PROPN
ma-172	14	10	⊂	⊂	PROPN
ma-172	14	11	u	u	PROPN
ma-172	14	12	→	→	SYM
ma-172	14	13	u	u	PROPN
ma-172	14	14	is	be	AUX
ma-172	14	15	differentiable	differentiable	ADJ
ma-172	14	16	as	as	ADP
ma-172	14	17	per	per	ADP
ma-172	14	18	fréchet	fréchet	NOUN
ma-172	14	19	,	,	PUNCT
ma-172	14	20	u	u	PROPN
ma-172	14	21	denotes	denote	NOUN
ma-172	14	22	complete	complete	VERB
ma-172	14	23	normed	normed	PROPN
ma-172	14	24	linear	linear	PROPN
ma-172	14	25	spaceand	spaceand	PROPN
ma-172	15	1	b	b	PROPN
ma-172	15	2	is	be	AUX
ma-172	15	3	a	a	DET
ma-172	15	4	non	non	ADJ
ma-172	15	5	-	-	ADJ
ma-172	15	6	empty	empty	ADJ
ma-172	15	7	,	,	PUNCT
ma-172	15	8	open	open	ADJ
ma-172	15	9	and	and	CCONJ
ma-172	15	10	convex	convex	VERB
ma-172	15	11	set.normally	set.normally	ADV
ma-172	15	12	,	,	PUNCT
ma-172	15	13	the	the	DET
ma-172	15	14	solutions	solution	NOUN
ma-172	15	15	to	to	ADP
ma-172	15	16	these	these	DET
ma-172	15	17	non	non	ADJ
ma-172	15	18	-	-	ADJ
ma-172	15	19	linear	linear	ADJ
ma-172	15	20	equations	equation	NOUN
ma-172	15	21	can	can	AUX
ma-172	15	22	not	not	PART
ma-172	15	23	be	be	AUX
ma-172	15	24	obtained	obtain	VERB
ma-172	15	25	in	in	ADP
ma-172	15	26	a	a	DET
ma-172	15	27	closed-form.therefore	closed-form.therefore	NOUN
ma-172	15	28	,	,	PUNCT
ma-172	15	29	the	the	DET
ma-172	15	30	most	most	ADV
ma-172	15	31	frequently	frequently	ADV
ma-172	15	32	used	use	VERB
ma-172	15	33	solving	solving	NOUN
ma-172	15	34	techniques	technique	NOUN
ma-172	15	35	are	be	AUX
ma-172	15	36	of	of	ADP
ma-172	15	37	iterative	iterative	ADJ
ma-172	15	38	nature	nature	NOUN
ma-172	15	39	.	.	PUNCT
ma-172	16	1	newton	newton	PROPN
ma-172	16	2	’s	’s	PART
ma-172	16	3	methodis	methodi	NOUN
ma-172	16	4	a	a	DET
ma-172	16	5	well	well	ADV
ma-172	16	6	-	-	PUNCT
ma-172	16	7	known	know	VERB
ma-172	16	8	iterative	iterative	NOUN
ma-172	16	9	method	method	NOUN
ma-172	16	10	for	for	ADP
ma-172	16	11	handling	handle	VERB
ma-172	16	12	non	non	ADJ
ma-172	16	13	-	-	ADJ
ma-172	16	14	linear	linear	ADJ
ma-172	16	15	equations	equation	NOUN
ma-172	16	16	.	.	PUNCT
ma-172	17	1	recently	recently	ADV
ma-172	17	2	,	,	PUNCT
ma-172	17	3	with	with	ADP
ma-172	17	4	advances	advance	NOUN
ma-172	17	5	inscience	inscience	NOUN
ma-172	17	6	and	and	CCONJ
ma-172	17	7	mathematics	mathematic	NOUN
ma-172	17	8	many	many	ADJ
ma-172	17	9	new	new	ADJ
ma-172	17	10	iterative	iterative	NOUN
ma-172	17	11	methods	method	NOUN
ma-172	17	12	of	of	ADP
ma-172	17	13	higher	high	ADJ
ma-172	17	14	order	order	NOUN
ma-172	17	15	have	have	AUX
ma-172	17	16	been	be	AUX
ma-172	17	17	discovered	discover	VERB
ma-172	17	18	for	for	ADP
ma-172	17	19	thehandling	thehandling	NOUN
ma-172	17	20	of	of	ADP
ma-172	17	21	non	non	ADJ
ma-172	17	22	-	-	ADJ
ma-172	17	23	linear	linear	ADJ
ma-172	17	24	equations	equation	NOUN
ma-172	17	25	and	and	CCONJ
ma-172	17	26	are	be	AUX
ma-172	17	27	currently	currently	ADV
ma-172	17	28	being	be	AUX
ma-172	17	29	used	use	VERB
ma-172	17	30	[	[	PUNCT
ma-172	17	31	1	1	NUM
ma-172	17	32	,	,	PUNCT
ma-172	17	33	2	2	NUM
ma-172	17	34	,	,	PUNCT
ma-172	17	35	4–8	4–8	NOUN
ma-172	17	36	,	,	PUNCT
ma-172	17	37	10–22	10–22	NUM
ma-172	17	38	]	]	PUNCT
ma-172	17	39	.	.	PUNCT
ma-172	18	1	the	the	DET
ma-172	18	2	computationof	computationof	NOUN
ma-172	18	3	derivatives	derivative	NOUN
ma-172	18	4	of	of	ADP
ma-172	18	5	second	second	ADJ
ma-172	18	6	and	and	CCONJ
ma-172	18	7	higher	high	ADJ
ma-172	18	8	order	order	NOUN
ma-172	18	9	is	be	AUX
ma-172	18	10	a	a	DET
ma-172	18	11	great	great	ADJ
ma-172	18	12	disadvantage	disadvantage	NOUN
ma-172	18	13	for	for	ADP
ma-172	18	14	the	the	DET
ma-172	18	15	iterative	iterative	NOUN
ma-172	18	16	systems	system	NOUN
ma-172	18	17	of	of	ADP
ma-172	18	18	higherorder	higherorder	NOUN
ma-172	18	19	and	and	CCONJ
ma-172	18	20	is	be	AUX
ma-172	18	21	not	not	PART
ma-172	18	22	suitable	suitable	ADJ
ma-172	18	23	for	for	ADP
ma-172	18	24	the	the	DET
ma-172	18	25	practical	practical	ADJ
ma-172	18	26	application	application	NOUN
ma-172	18	27	.	.	PUNCT
ma-172	19	1	because	because	SCONJ
ma-172	19	2	of	of	ADP
ma-172	19	3	the	the	DET
ma-172	19	4	computation	computation	NOUN
ma-172	19	5	of	of	ADP
ma-172	19	6	g	g	PROPN
ma-172	19	7	′′	′′	PROPN
ma-172	19	8	,	,	PUNCT
ma-172	19	9	the	the	DET
ma-172	19	10	received	received	NOUN
ma-172	19	11	:	:	PUNCT
ma-172	19	12	3	3	NUM
ma-172	19	13	may	may	PROPN
ma-172	19	14	2023	2023	NUM
ma-172	19	15	.	.	PUNCT
ma-172	20	1	key	key	ADJ
ma-172	20	2	words	word	NOUN
ma-172	20	3	and	and	CCONJ
ma-172	20	4	phrases	phrase	NOUN
ma-172	20	5	.	.	PUNCT
ma-172	21	1	steffensen	steffensen	NOUN
ma-172	21	2	-	-	PUNCT
ma-172	21	3	like	like	ADJ
ma-172	21	4	methods	method	NOUN
ma-172	21	5	;	;	PUNCT
ma-172	21	6	convergence	convergence	NOUN
ma-172	21	7	;	;	PUNCT
ma-172	21	8	banach	banach	NOUN
ma-172	21	9	space	space	NOUN
ma-172	21	10	;	;	PUNCT
ma-172	21	11	divided	divide	VERB
ma-172	21	12	difference.1	difference.1	PROPN
ma-172	21	13	https://adac.ee	https://adac.ee	PROPN
ma-172	21	14	https://doi.org/10.28924/ada/ma.3.19	https://doi.org/10.28924/ada/ma.3.19	NOUN
ma-172	21	15	eur	eur	NOUN
ma-172	21	16	.	.	PUNCT
ma-172	22	1	j.	j.	PROPN
ma-172	22	2	math	math	PROPN
ma-172	22	3	.	.	PUNCT
ma-172	23	1	anal	anal	PROPN
ma-172	23	2	.	.	PUNCT
ma-172	24	1	10.28924	10.28924	NUM
ma-172	24	2	/	/	SYM
ma-172	24	3	ada	ada	PROPN
ma-172	24	4	/	/	SYM
ma-172	24	5	ma.3.19	ma.3.19	PROPN
ma-172	24	6	2cubically	2cubically	ADV
ma-172	24	7	converging	converge	VERB
ma-172	24	8	classical	classical	ADJ
ma-172	24	9	schemas	schema	NOUN
ma-172	24	10	are	be	AUX
ma-172	24	11	not	not	PART
ma-172	24	12	appropriate	appropriate	ADJ
ma-172	24	13	with	with	ADP
ma-172	24	14	respect	respect	NOUN
ma-172	24	15	to	to	ADP
ma-172	24	16	the	the	DET
ma-172	24	17	cost	cost	NOUN
ma-172	24	18	of	of	ADP
ma-172	24	19	calculations.we	calculations.we	NUM
ma-172	24	20	found	find	VERB
ma-172	24	21	that	that	SCONJ
ma-172	24	22	many	many	ADJ
ma-172	24	23	such	such	ADJ
ma-172	24	24	methods	method	NOUN
ma-172	24	25	rely	rely	VERB
ma-172	24	26	on	on	ADP
ma-172	24	27	taylor	taylor	PROPN
ma-172	24	28	series	series	PROPN
ma-172	24	29	extensions	extension	NOUN
ma-172	24	30	to	to	PART
ma-172	24	31	prove	prove	VERB
ma-172	24	32	convergence	convergence	NOUN
ma-172	24	33	resultsand	resultsand	NOUN
ma-172	24	34	require	require	VERB
ma-172	24	35	the	the	DET
ma-172	24	36	existence	existence	NOUN
ma-172	24	37	of	of	ADP
ma-172	24	38	derivative	derivative	NOUN
ma-172	24	39	with	with	ADP
ma-172	24	40	at	at	ADV
ma-172	24	41	least	least	ADJ
ma-172	24	42	an	an	DET
ma-172	24	43	order	order	NOUN
ma-172	24	44	of	of	ADP
ma-172	24	45	magnitude	magnitude	NOUN
ma-172	24	46	greater	great	ADJ
ma-172	24	47	than	than	ADP
ma-172	24	48	that	that	DET
ma-172	24	49	ofthe	ofthe	ADJ
ma-172	24	50	methodology	methodology	NOUN
ma-172	25	1	[	[	X
ma-172	25	2	1	1	NUM
ma-172	25	3	,	,	PUNCT
ma-172	25	4	2	2	NUM
ma-172	25	5	,	,	PUNCT
ma-172	25	6	4	4	NUM
ma-172	25	7	,	,	PUNCT
ma-172	25	8	10–19	10–19	NUM
ma-172	25	9	,	,	PUNCT
ma-172	25	10	21	21	NUM
ma-172	25	11	,	,	PUNCT
ma-172	25	12	22	22	NUM
ma-172	25	13	]	]	PUNCT
ma-172	25	14	.	.	PUNCT
ma-172	26	1	here	here	ADV
ma-172	26	2	we	we	PRON
ma-172	26	3	consider	consider	VERB
ma-172	26	4	,	,	PUNCT
ma-172	26	5	for	for	ADP
ma-172	26	6	example	example	NOUN
ma-172	26	7	,	,	PUNCT
ma-172	26	8	a	a	DET
ma-172	26	9	three	three	NUM
ma-172	26	10	-	-	PUNCT
ma-172	26	11	step	step	NOUN
ma-172	26	12	two	two	NUM
ma-172	26	13	-	-	PUNCT
ma-172	26	14	parameterfamily	parameterfamily	ADV
ma-172	26	15	of	of	ADP
ma-172	26	16	derivative	derivative	ADJ
ma-172	26	17	free	free	ADJ
ma-172	26	18	methods	method	NOUN
ma-172	26	19	with	with	ADP
ma-172	26	20	seventh	seventh	ADJ
ma-172	26	21	-	-	PUNCT
ma-172	26	22	order	order	NOUN
ma-172	26	23	of	of	ADP
ma-172	26	24	convergence	convergence	NOUN
ma-172	26	25	for	for	ADP
ma-172	26	26	solving	solve	VERB
ma-172	26	27	systems	system	NOUN
ma-172	26	28	of	of	ADP
ma-172	26	29	nonlinearequations	nonlinearequation	NOUN
ma-172	26	30	proposed	propose	VERB
ma-172	26	31	in	in	ADP
ma-172	26	32	[	[	X
ma-172	26	33	18	18	NUM
ma-172	26	34	]	]	PUNCT
ma-172	26	35	and	and	CCONJ
ma-172	26	36	which	which	PRON
ma-172	26	37	may	may	AUX
ma-172	26	38	be	be	AUX
ma-172	26	39	expressed	express	VERB
ma-172	26	40	in	in	ADP
ma-172	26	41	the	the	DET
ma-172	26	42	following	follow	VERB
ma-172	26	43	formulation	formulation	NOUN
ma-172	26	44	:	:	PUNCT
ma-172	26	45	for	for	ADP
ma-172	26	46	x0	x0	PROPN
ma-172	26	47	∈	∈	PROPN
ma-172	26	48	b	b	PROPN
ma-172	26	49	and	and	CCONJ
ma-172	26	50	each	each	DET
ma-172	26	51	n	n	NOUN
ma-172	26	52	=	=	SYM
ma-172	26	53	0	0	NUM
ma-172	26	54	,	,	PUNCT
ma-172	26	55	1	1	NUM
ma-172	26	56	,	,	PUNCT
ma-172	26	57	2	2	NUM
ma-172	26	58	,	,	PUNCT
ma-172	26	59	.	.	PUNCT
ma-172	26	60	.	.	PUNCT
ma-172	26	61	.	.	PUNCT
ma-172	27	1	wn	wn	PROPN
ma-172	27	2	=	=	PUNCT
ma-172	27	3	xn	xn	PROPN
ma-172	28	1	+	+	NUM
ma-172	28	2	ag(xn	ag(xn	NOUN
ma-172	28	3	)	)	PUNCT
ma-172	28	4	,	,	PUNCT
ma-172	29	1	sn	sn	PROPN
ma-172	29	2	=	=	SYM
ma-172	29	3	xn	xn	PROPN
ma-172	30	1	−	−	NUM
ma-172	30	2	ag(xn	ag(xn	NOUN
ma-172	30	3	)	)	PUNCT
ma-172	30	4	,	,	PUNCT
ma-172	30	5	an	an	DET
ma-172	30	6	=	=	X
ma-172	30	7	[	[	X
ma-172	30	8	wn	wn	X
ma-172	30	9	,	,	PUNCT
ma-172	30	10	sn;g	sn;g	PROPN
ma-172	30	11	]	]	PUNCT
ma-172	30	12	,	,	PUNCT
ma-172	30	13	yn	yn	PROPN
ma-172	30	14	=	=	PUNCT
ma-172	30	15	xn	xn	PROPN
ma-172	31	1	−	−	NOUN
ma-172	31	2	a−1n	a−1n	ADV
ma-172	31	3	g(xn	g(xn	NOUN
ma-172	31	4	)	)	PUNCT
ma-172	31	5	,	,	PUNCT
ma-172	31	6	zn	zn	PROPN
ma-172	31	7	=	=	SYM
ma-172	31	8	yn	yn	PROPN
ma-172	31	9	−	−	NOUN
ma-172	31	10	a−1n	a−1n	NOUN
ma-172	31	11	g(yn	g(yn	PROPN
ma-172	31	12	)	)	PUNCT
ma-172	31	13	,	,	PUNCT
ma-172	31	14	un	un	PROPN
ma-172	32	1	=	=	SYM
ma-172	32	2	zn	zn	PROPN
ma-172	32	3	+	+	NUM
ma-172	32	4	bg(zn	bg(zn	PROPN
ma-172	32	5	)	)	PUNCT
ma-172	32	6	,	,	PUNCT
ma-172	32	7	vn	vn	PROPN
ma-172	32	8	=	=	SYM
ma-172	32	9	zn	zn	PROPN
ma-172	32	10	−	−	PROPN
ma-172	32	11	bg(zn	bg(zn	PROPN
ma-172	32	12	)	)	PUNCT
ma-172	32	13	,	,	PUNCT
ma-172	33	1	qn	qn	NOUN
ma-172	33	2	=	=	X
ma-172	34	1	[	[	X
ma-172	34	2	un	un	NOUN
ma-172	34	3	,	,	PUNCT
ma-172	34	4	vn;g	vn;g	PROPN
ma-172	34	5	]	]	PUNCT
ma-172	34	6	,	,	PUNCT
ma-172	34	7	xn+1	xn+1	PROPN
ma-172	35	1	=	=	SYM
ma-172	35	2	zn	zn	PROPN
ma-172	35	3	−	−	PROPN
ma-172	36	1	(	(	PUNCT
ma-172	36	2	pi	pi	NOUN
ma-172	36	3	+	+	CCONJ
ma-172	36	4	a−1n	a−1n	ADV
ma-172	37	1	qn(qi	qn(qi	PROPN
ma-172	38	1	+	+	CCONJ
ma-172	38	2	a−1n	a−1n	ADV
ma-172	38	3	qn(r	qn(r	VERB
ma-172	38	4	i	i	NOUN
ma-172	38	5	+	+	CCONJ
ma-172	38	6	da−1n	da−1n	ADJ
ma-172	38	7	qn)))a−1n	qn)))a−1n	ADJ
ma-172	38	8	g(zn	g(zn	PROPN
ma-172	38	9	)	)	PUNCT
ma-172	38	10	,	,	PUNCT
ma-172	38	11	(	(	PUNCT
ma-172	38	12	2	2	X
ma-172	38	13	)	)	PUNCT
ma-172	38	14	where	where	SCONJ
ma-172	38	15	a	a	DET
ma-172	38	16	,	,	PUNCT
ma-172	38	17	b	b	NOUN
ma-172	38	18	,	,	PUNCT
ma-172	38	19	p	p	X
ma-172	38	20	,	,	PUNCT
ma-172	38	21	q	q	ADJ
ma-172	38	22	,	,	PUNCT
ma-172	38	23	r	r	NOUN
ma-172	38	24	,	,	PUNCT
ma-172	38	25	d	d	PROPN
ma-172	38	26	∈	∈	PROPN
ma-172	38	27	r	r	NOUN
ma-172	38	28	,	,	PUNCT
ma-172	38	29	[	[	X
ma-172	38	30	·	·	PUNCT
ma-172	38	31	,	,	PUNCT
ma-172	38	32	·	·	PUNCT
ma-172	38	33	;	;	PUNCT
ma-172	38	34	g	g	NOUN
ma-172	38	35	]	]	X
ma-172	38	36	:	:	PUNCT
ma-172	38	37	b	b	X
ma-172	38	38	×	×	PROPN
ma-172	38	39	b	b	PROPN
ma-172	38	40	→	→	SYM
ma-172	38	41	w	w	PROPN
ma-172	38	42	(	(	PUNCT
ma-172	38	43	u	u	NOUN
ma-172	38	44	)	)	PUNCT
ma-172	38	45	,	,	PUNCT
ma-172	38	46	the	the	DET
ma-172	38	47	space	space	NOUN
ma-172	38	48	of	of	ADP
ma-172	38	49	bounded	bounded	ADJ
ma-172	38	50	linear	linear	PROPN
ma-172	38	51	operators	operator	NOUN
ma-172	38	52	from	from	ADP
ma-172	38	53	u	u	NOUN
ma-172	38	54	into	into	ADP
ma-172	38	55	u	u	PRON
ma-172	38	56	.	.	PUNCT
ma-172	39	1	the	the	DET
ma-172	39	2	local	local	ADJ
ma-172	39	3	convergence	convergence	NOUN
ma-172	39	4	analysis	analysis	NOUN
ma-172	39	5	of	of	ADP
ma-172	39	6	the	the	DET
ma-172	39	7	method	method	NOUN
ma-172	39	8	(	(	PUNCT
ma-172	39	9	2	2	X
ma-172	39	10	)	)	PUNCT
ma-172	39	11	is	be	AUX
ma-172	39	12	provided	provide	VERB
ma-172	39	13	in	in	ADP
ma-172	39	14	[	[	X
ma-172	39	15	18	18	NUM
ma-172	39	16	]	]	PUNCT
ma-172	39	17	using	use	VERB
ma-172	39	18	the	the	DET
ma-172	39	19	taylorseries	taylorserie	NOUN
ma-172	39	20	expansion	expansion	NOUN
ma-172	39	21	approach	approach	NOUN
ma-172	39	22	and	and	CCONJ
ma-172	39	23	conditions	condition	NOUN
ma-172	39	24	reaching	reach	VERB
ma-172	39	25	the	the	DET
ma-172	39	26	eighth	eighth	ADJ
ma-172	39	27	derivative	derivative	NOUN
ma-172	39	28	of	of	ADP
ma-172	39	29	the	the	DET
ma-172	39	30	operator	operator	NOUN
ma-172	39	31	g.	g.	PROPN
ma-172	39	32	thesederivatives	thesederivative	NOUN
ma-172	39	33	do	do	AUX
ma-172	39	34	not	not	PART
ma-172	39	35	appear	appear	VERB
ma-172	39	36	on	on	ADP
ma-172	39	37	the	the	DET
ma-172	39	38	method	method	NOUN
ma-172	39	39	(	(	PUNCT
ma-172	39	40	2	2	NUM
ma-172	39	41	)	)	PUNCT
ma-172	39	42	.	.	PUNCT
ma-172	40	1	the	the	DET
ma-172	40	2	convergence	convergence	NOUN
ma-172	40	3	order	order	NOUN
ma-172	40	4	is	be	AUX
ma-172	40	5	shown	show	VERB
ma-172	40	6	to	to	PART
ma-172	40	7	be	be	AUX
ma-172	40	8	seven	seven	NUM
ma-172	40	9	providedthat	providedthat	NOUN
ma-172	40	10	p	p	NOUN
ma-172	40	11	=	=	SYM
ma-172	40	12	17	17	NUM
ma-172	40	13	4	4	NUM
ma-172	40	14	,	,	PUNCT
ma-172	40	15	q	q	NOUN
ma-172	40	16	=	=	PUNCT
ma-172	40	17	−274	−274	NOUN
ma-172	40	18	,	,	PUNCT
ma-172	40	19	r	r	NOUN
ma-172	40	20	=	=	SYM
ma-172	40	21	19	19	NUM
ma-172	40	22	4	4	NUM
ma-172	40	23	and	and	CCONJ
ma-172	40	24	d	d	NOUN
ma-172	40	25	=	=	SYM
ma-172	40	26	−54	−54	PROPN
ma-172	40	27	.	.	PUNCT
ma-172	41	1	the	the	DET
ma-172	41	2	conditions	condition	NOUN
ma-172	41	3	on	on	ADP
ma-172	41	4	high	high	ADJ
ma-172	41	5	order	order	NOUN
ma-172	41	6	derivatives	derivative	NOUN
ma-172	41	7	restrict	restrict	VERB
ma-172	41	8	theapplicability	theapplicability	NOUN
ma-172	41	9	of	of	ADP
ma-172	41	10	the	the	DET
ma-172	41	11	method	method	NOUN
ma-172	41	12	(	(	PUNCT
ma-172	41	13	2	2	NUM
ma-172	41	14	)	)	PUNCT
ma-172	41	15	for	for	ADP
ma-172	41	16	solving	solve	VERB
ma-172	41	17	equations	equation	NOUN
ma-172	41	18	where	where	SCONJ
ma-172	41	19	at	at	ADV
ma-172	41	20	least	least	ADJ
ma-172	41	21	g(8	g(8	PROPN
ma-172	41	22	)	)	PUNCT
ma-172	41	23	should	should	AUX
ma-172	41	24	exist	exist	VERB
ma-172	41	25	.	.	PUNCT
ma-172	42	1	although	although	SCONJ
ma-172	42	2	,	,	PUNCT
ma-172	42	3	the	the	DET
ma-172	42	4	method	method	NOUN
ma-172	42	5	may	may	AUX
ma-172	42	6	converge	converge	VERB
ma-172	42	7	.	.	PUNCT
ma-172	43	1	let	let	VERB
ma-172	43	2	us	we	PRON
ma-172	43	3	consider	consider	VERB
ma-172	43	4	the	the	DET
ma-172	43	5	toy	toy	NOUN
ma-172	43	6	example	example	NOUN
ma-172	43	7	for	for	ADP
ma-172	43	8	b	b	NOUN
ma-172	43	9	=	=	PUNCT
ma-172	44	1	[	[	X
ma-172	44	2	−1	−1	NOUN
ma-172	44	3	,	,	PUNCT
ma-172	44	4	2	2	NUM
ma-172	44	5	]	]	PUNCT
ma-172	44	6	and	and	CCONJ
ma-172	44	7	g	g	PROPN
ma-172	44	8	defined	define	VERB
ma-172	44	9	by	by	ADP
ma-172	44	10	g(t	g(t	PROPN
ma-172	44	11	)	)	PUNCT
ma-172	44	12	=	=	PRON
ma-172	44	13	{	{	PUNCT
ma-172	44	14	t4	t4	PROPN
ma-172	44	15	log	log	PROPN
ma-172	44	16	t	t	PROPN
ma-172	45	1	+	+	CCONJ
ma-172	45	2	5t7	5t7	NUM
ma-172	46	1	−	−	NOUN
ma-172	46	2	5t6	5t6	NUM
ma-172	46	3	,	,	PUNCT
ma-172	46	4	if	if	SCONJ
ma-172	46	5	t	t	PROPN
ma-172	46	6	6=	6=	ADP
ma-172	46	7	0	0	NUM
ma-172	46	8	0	0	NUM
ma-172	46	9	,	,	PUNCT
ma-172	46	10	if	if	SCONJ
ma-172	46	11	t	t	NOUN
ma-172	46	12	=	=	SYM
ma-172	46	13	0	0	NUM
ma-172	47	1	it	it	PRON
ma-172	47	2	follows	follow	VERB
ma-172	47	3	by	by	ADP
ma-172	47	4	this	this	DET
ma-172	47	5	definition	definition	NOUN
ma-172	47	6	that	that	SCONJ
ma-172	47	7	g(ξ	g(ξ	PROPN
ma-172	47	8	)	)	PUNCT
ma-172	48	1	=	=	SYM
ma-172	48	2	g(1	g(1	NOUN
ma-172	48	3	)	)	PUNCT
ma-172	48	4	=	=	SYM
ma-172	48	5	0	0	PUNCT
ma-172	48	6	but	but	CCONJ
ma-172	48	7	g(4	g(4	PROPN
ma-172	48	8	)	)	PUNCT
ma-172	48	9	is	be	AUX
ma-172	48	10	not	not	PART
ma-172	48	11	bounded	bound	VERB
ma-172	48	12	on	on	ADP
ma-172	48	13	b.	b.	PROPN
ma-172	48	14	thus	thus	ADV
ma-172	48	15	,	,	PUNCT
ma-172	48	16	the	the	DET
ma-172	48	17	resultsin	resultsin	NOUN
ma-172	48	18	[	[	X
ma-172	48	19	18	18	NUM
ma-172	48	20	]	]	PUNCT
ma-172	48	21	can	can	AUX
ma-172	48	22	not	not	PART
ma-172	48	23	assure	assure	VERB
ma-172	48	24	that	that	SCONJ
ma-172	48	25	limn→∞	limn→∞	PROPN
ma-172	48	26	xn	xn	PUNCT
ma-172	48	27	=	=	SYM
ma-172	48	28	ξ	ξ	X
ma-172	48	29	=	=	SYM
ma-172	48	30	1	1	NUM
ma-172	48	31	.	.	PUNCT
ma-172	49	1	but	but	CCONJ
ma-172	49	2	,	,	PUNCT
ma-172	49	3	the	the	DET
ma-172	49	4	method	method	NOUN
ma-172	49	5	converges	converge	VERB
ma-172	49	6	to	to	ADP
ma-172	49	7	1.therefore	1.therefore	NUM
ma-172	49	8	,	,	PUNCT
ma-172	49	9	there	there	PRON
ma-172	49	10	is	be	VERB
ma-172	49	11	a	a	DET
ma-172	49	12	need	need	NOUN
ma-172	49	13	to	to	PART
ma-172	49	14	weaken	weaken	VERB
ma-172	49	15	the	the	DET
ma-172	49	16	conditions	condition	NOUN
ma-172	49	17	.	.	PUNCT
ma-172	50	1	in	in	ADP
ma-172	50	2	this	this	DET
ma-172	50	3	article	article	NOUN
ma-172	50	4	,	,	PUNCT
ma-172	50	5	we	we	PRON
ma-172	50	6	use	use	VERB
ma-172	50	7	only	only	ADV
ma-172	50	8	conditions	condition	NOUN
ma-172	50	9	onthe	onthe	NOUN
ma-172	50	10	operators	operator	NOUN
ma-172	50	11	on	on	ADP
ma-172	50	12	the	the	DET
ma-172	50	13	method	method	NOUN
ma-172	50	14	(	(	PUNCT
ma-172	50	15	2	2	NUM
ma-172	50	16	)	)	PUNCT
ma-172	50	17	.	.	PUNCT
ma-172	51	1	therefore	therefore	ADV
ma-172	51	2	,	,	PUNCT
ma-172	51	3	the	the	DET
ma-172	51	4	method	method	NOUN
ma-172	51	5	can	can	AUX
ma-172	51	6	be	be	AUX
ma-172	51	7	utilized	utilize	VERB
ma-172	51	8	to	to	PART
ma-172	51	9	solve	solve	VERB
ma-172	51	10	non	non	ADJ
ma-172	51	11	-	-	NOUN
ma-172	51	12	differentiableequations	differentiableequation	NOUN
ma-172	51	13	.	.	PUNCT
ma-172	52	1	furthermore	furthermore	ADV
ma-172	52	2	,	,	PUNCT
ma-172	52	3	the	the	DET
ma-172	52	4	results	result	NOUN
ma-172	52	5	should	should	AUX
ma-172	52	6	also	also	ADV
ma-172	52	7	demonstrate	demonstrate	VERB
ma-172	52	8	the	the	DET
ma-172	52	9	isolation	isolation	NOUN
ma-172	52	10	of	of	ADP
ma-172	52	11	the	the	DET
ma-172	52	12	solution	solution	NOUN
ma-172	52	13	and	and	CCONJ
ma-172	52	14	thebounds	thebound	NOUN
ma-172	52	15	of	of	ADP
ma-172	52	16	error	error	NOUN
ma-172	52	17	in	in	ADP
ma-172	52	18	advance	advance	NOUN
ma-172	52	19	.	.	PUNCT
ma-172	53	1	this	this	PRON
ma-172	53	2	is	be	AUX
ma-172	53	3	what	what	PRON
ma-172	53	4	is	be	AUX
ma-172	53	5	new	new	ADJ
ma-172	53	6	and	and	CCONJ
ma-172	53	7	what	what	PRON
ma-172	53	8	motivates	motivate	VERB
ma-172	53	9	our	our	PRON
ma-172	53	10	article	article	NOUN
ma-172	53	11	.	.	PUNCT
ma-172	54	1	this	this	PRON
ma-172	54	2	meansextending	meansextende	VERB
ma-172	54	3	its	its	PRON
ma-172	54	4	applicability	applicability	NOUN
ma-172	54	5	,	,	PUNCT
ma-172	54	6	taking	take	VERB
ma-172	54	7	advantage	advantage	NOUN
ma-172	54	8	of	of	ADP
ma-172	54	9	weaker	weak	ADJ
ma-172	54	10	conditions	condition	NOUN
ma-172	54	11	for	for	ADP
ma-172	54	12	such	such	ADJ
ma-172	54	13	methods	method	NOUN
ma-172	54	14	.	.	PUNCT
ma-172	55	1	in	in	ADP
ma-172	55	2	addition	addition	NOUN
ma-172	55	3	,	,	PUNCT
ma-172	55	4	we	we	PRON
ma-172	55	5	are	be	AUX
ma-172	55	6	also	also	ADV
ma-172	55	7	discussing	discuss	VERB
ma-172	55	8	a	a	DET
ma-172	55	9	more	more	ADV
ma-172	55	10	interesting	interesting	ADJ
ma-172	55	11	case	case	NOUN
ma-172	55	12	of	of	ADP
ma-172	55	13	semi	semi	ADJ
ma-172	55	14	-	-	ADJ
ma-172	55	15	local	local	ADJ
ma-172	55	16	convergence	convergence	NOUN
ma-172	55	17	.	.	PUNCT
ma-172	56	1	it	it	PRON
ma-172	56	2	is	be	AUX
ma-172	56	3	obvious	obvious	ADJ
ma-172	56	4	that	that	SCONJ
ma-172	56	5	theaforementioned	theaforementione	VERB
ma-172	56	6	goals	goal	NOUN
ma-172	56	7	can	can	AUX
ma-172	56	8	be	be	AUX
ma-172	56	9	easily	easily	ADV
ma-172	56	10	achieved	achieve	VERB
ma-172	56	11	in	in	ADP
ma-172	56	12	a	a	DET
ma-172	56	13	similar	similar	ADJ
ma-172	56	14	way	way	NOUN
ma-172	56	15	for	for	ADP
ma-172	56	16	other	other	ADJ
ma-172	56	17	iterative	iterative	NOUN
ma-172	56	18	methods	method	NOUN
ma-172	56	19	[	[	X
ma-172	56	20	1	1	NUM
ma-172	56	21	,	,	PUNCT
ma-172	56	22	2	2	NUM
ma-172	56	23	,	,	PUNCT
ma-172	56	24	4,10–17,19,21,22	4,10–17,19,21,22	NOUN
ma-172	56	25	]	]	PUNCT
ma-172	56	26	.	.	PUNCT
ma-172	57	1	furthermore	furthermore	ADV
ma-172	57	2	,	,	PUNCT
ma-172	57	3	our	our	PRON
ma-172	57	4	bounds	bound	NOUN
ma-172	57	5	of	of	ADP
ma-172	57	6	error	error	NOUN
ma-172	57	7	is	be	AUX
ma-172	57	8	more	more	ADV
ma-172	57	9	precise	precise	ADJ
ma-172	57	10	and	and	CCONJ
ma-172	57	11	our	our	PRON
ma-172	57	12	criteria	criterion	NOUN
ma-172	57	13	for	for	ADP
ma-172	57	14	convergenceapply	convergenceapply	NOUN
ma-172	57	15	even	even	ADV
ma-172	57	16	if	if	SCONJ
ma-172	57	17	the	the	DET
ma-172	57	18	assumptions	assumption	NOUN
ma-172	57	19	referred	refer	VERB
ma-172	57	20	to	to	ADP
ma-172	57	21	in	in	ADP
ma-172	57	22	the	the	DET
ma-172	57	23	references	reference	NOUN
ma-172	57	24	above	above	ADV
ma-172	57	25	are	be	AUX
ma-172	57	26	infringed.the	infringed.the	DET
ma-172	57	27	remainder	remainder	NOUN
ma-172	57	28	of	of	ADP
ma-172	57	29	the	the	DET
ma-172	57	30	article	article	NOUN
ma-172	57	31	is	be	AUX
ma-172	57	32	organized	organize	VERB
ma-172	57	33	as	as	SCONJ
ma-172	57	34	follows	follow	VERB
ma-172	57	35	:	:	PUNCT
ma-172	57	36	analysis	analysis	NOUN
ma-172	57	37	of	of	ADP
ma-172	57	38	local	local	ADJ
ma-172	57	39	convergence	convergence	NOUN
ma-172	57	40	is	be	AUX
ma-172	57	41	provided	provide	VERB
ma-172	57	42	insection	insection	NOUN
ma-172	57	43	2	2	NUM
ma-172	57	44	.	.	PUNCT
ma-172	57	45	majorizing	majorize	VERB
ma-172	57	46	sequences	sequence	NOUN
ma-172	57	47	will	will	AUX
ma-172	57	48	be	be	AUX
ma-172	57	49	introduced	introduce	VERB
ma-172	57	50	and	and	CCONJ
ma-172	57	51	analyzed	analyze	VERB
ma-172	57	52	for	for	ADP
ma-172	57	53	the	the	DET
ma-172	57	54	semi	semi	ADJ
ma-172	57	55	-	-	ADJ
ma-172	57	56	local	local	ADJ
ma-172	57	57	convergenceanalysis	convergenceanalysis	NOUN
ma-172	57	58	of	of	ADP
ma-172	57	59	2	2	NUM
ma-172	57	60	in	in	ADP
ma-172	57	61	section	section	NOUN
ma-172	57	62	3	3	NUM
ma-172	57	63	.	.	PUNCT
ma-172	57	64	results	result	NOUN
ma-172	57	65	demonstrating	demonstrate	VERB
ma-172	57	66	isolation	isolation	NOUN
ma-172	57	67	of	of	ADP
ma-172	57	68	the	the	DET
ma-172	57	69	solution	solution	NOUN
ma-172	57	70	is	be	AUX
ma-172	57	71	discussed	discuss	VERB
ma-172	57	72	in	in	ADP
ma-172	57	73	section	section	NOUN
ma-172	57	74	https://doi.org/10.28924/ada/ma.3.19	https://doi.org/10.28924/ada/ma.3.19	NOUN
ma-172	57	75	eur	eur	PROPN
ma-172	57	76	.	.	PUNCT
ma-172	58	1	j.	j.	PROPN
ma-172	58	2	math	math	PROPN
ma-172	58	3	.	.	PUNCT
ma-172	59	1	anal	anal	PROPN
ma-172	59	2	.	.	PUNCT
ma-172	60	1	10.28924	10.28924	NUM
ma-172	60	2	/	/	SYM
ma-172	60	3	ada	ada	PROPN
ma-172	60	4	/	/	SYM
ma-172	60	5	ma.3.19	ma.3.19	PROPN
ma-172	61	1	34	34	NUM
ma-172	61	2	.	.	PUNCT
ma-172	62	1	numeric	numeric	ADJ
ma-172	62	2	experiments	experiment	NOUN
ma-172	62	3	that	that	PRON
ma-172	62	4	use	use	VERB
ma-172	62	5	convergence	convergence	NOUN
ma-172	62	6	results	result	NOUN
ma-172	62	7	from	from	ADP
ma-172	62	8	the	the	DET
ma-172	62	9	previous	previous	ADJ
ma-172	62	10	sections	section	NOUN
ma-172	62	11	are	be	AUX
ma-172	62	12	described	describe	VERB
ma-172	62	13	insection	insection	NOUN
ma-172	62	14	5	5	NUM
ma-172	62	15	.	.	PUNCT
ma-172	63	1	the	the	DET
ma-172	63	2	concluding	conclude	VERB
ma-172	63	3	remarks	remark	NOUN
ma-172	63	4	of	of	ADP
ma-172	63	5	section	section	NOUN
ma-172	63	6	6	6	NUM
ma-172	63	7	bring	bring	VERB
ma-172	63	8	this	this	DET
ma-172	63	9	article	article	NOUN
ma-172	63	10	to	to	ADP
ma-172	63	11	an	an	DET
ma-172	63	12	end	end	NOUN
ma-172	63	13	.	.	PUNCT
ma-172	64	1	2	2	X
ma-172	64	2	.	.	X
ma-172	64	3	convergence	convergence	NOUN
ma-172	64	4	1	1	NUM
ma-172	64	5	:	:	PUNCT
ma-172	64	6	local	local	ADJ
ma-172	64	7	let	let	VERB
ma-172	64	8	m	m	VERB
ma-172	64	9	=	=	PUNCT
ma-172	65	1	[	[	X
ma-172	65	2	0,+∞	0,+∞	NUM
ma-172	65	3	)	)	PUNCT
ma-172	65	4	.	.	PUNCT
ma-172	66	1	the	the	DET
ma-172	66	2	following	follow	VERB
ma-172	66	3	conditions	condition	NOUN
ma-172	66	4	are	be	AUX
ma-172	66	5	used:(c1	used:(c1	NOUN
ma-172	66	6	)	)	PUNCT
ma-172	66	7	there	there	PRON
ma-172	66	8	exist	exist	VERB
ma-172	66	9	continuous	continuous	ADJ
ma-172	66	10	and	and	CCONJ
ma-172	66	11	non	non	ADJ
ma-172	66	12	-	-	ADJ
ma-172	66	13	decreasing	decrease	VERB
ma-172	66	14	functions	function	NOUN
ma-172	66	15	(	(	PUNCT
ma-172	66	16	cnf	cnf	NOUN
ma-172	66	17	)	)	PUNCT
ma-172	66	18	ϕ0	ϕ0	NOUN
ma-172	66	19	:	:	PUNCT
ma-172	66	20	m×m	m×m	ADJ
ma-172	66	21	→	→	SYM
ma-172	66	22	m	m	ADJ
ma-172	66	23	,	,	PUNCT
ma-172	66	24	δ1	δ1	NOUN
ma-172	66	25	:	:	PUNCT
ma-172	66	26	m	m	VERB
ma-172	66	27	→	→	SYM
ma-172	66	28	m	m	ADJ
ma-172	66	29	,	,	PUNCT
ma-172	66	30	δ2	δ2	VERB
ma-172	66	31	:	:	PUNCT
ma-172	66	32	m	m	VERB
ma-172	66	33	→	→	SYM
ma-172	66	34	m	m	PROPN
ma-172	66	35	,	,	PUNCT
ma-172	66	36	a	a	DET
ma-172	66	37	solution	solution	NOUN
ma-172	66	38	ξ	ξ	PROPN
ma-172	66	39	∈	∈	PROPN
ma-172	66	40	b	b	PROPN
ma-172	66	41	of	of	ADP
ma-172	66	42	the	the	DET
ma-172	66	43	equation	equation	NOUN
ma-172	66	44	g(x	g(x	NOUN
ma-172	66	45	)	)	PUNCT
ma-172	67	1	=	=	SYM
ma-172	67	2	0	0	NUM
ma-172	67	3	and	and	CCONJ
ma-172	67	4	a	a	DET
ma-172	67	5	linear	linear	ADJ
ma-172	67	6	operator	operator	NOUN
ma-172	67	7	p	p	PRON
ma-172	67	8	such	such	ADJ
ma-172	67	9	thatfor	thatfor	NOUN
ma-172	67	10	each	each	PRON
ma-172	67	11	w	w	NOUN
ma-172	68	1	=	=	PUNCT
ma-172	68	2	x	x	X
ma-172	68	3	+	+	X
ma-172	68	4	ag(x	ag(x	NOUN
ma-172	68	5	)	)	PUNCT
ma-172	68	6	,	,	PUNCT
ma-172	68	7	s	s	VERB
ma-172	68	8	=	=	PUNCT
ma-172	68	9	x	x	SYM
ma-172	68	10	−	−	NOUN
ma-172	68	11	ag(x	ag(x	PUNCT
ma-172	68	12	)	)	PUNCT
ma-172	68	13	and	and	CCONJ
ma-172	68	14	p−1	p−1	PROPN
ma-172	68	15	∈	∈	PROPN
ma-172	68	16	w	w	PROPN
ma-172	68	17	(	(	PUNCT
ma-172	68	18	u	u	NOUN
ma-172	68	19	)	)	PUNCT
ma-172	68	20	‖p−1([w	‖p−1([w	NOUN
ma-172	68	21	,	,	PUNCT
ma-172	68	22	s;g]−p)‖	s;g]−p)‖	PROPN
ma-172	68	23	≤	≤	PROPN
ma-172	68	24	ϕ0(‖w	ϕ0(‖w	VERB
ma-172	68	25	−	−	PROPN
ma-172	68	26	ξ‖	ξ‖	PROPN
ma-172	68	27	,	,	PUNCT
ma-172	68	28	‖s	‖s	ADJ
ma-172	68	29	−	−	PROPN
ma-172	68	30	ξ‖	ξ‖	PROPN
ma-172	68	31	)	)	PUNCT
ma-172	68	32	,	,	PUNCT
ma-172	68	33	‖w	‖w	VERB
ma-172	68	34	−	−	PROPN
ma-172	68	35	ξ‖	ξ‖	ADJ
ma-172	68	36	≤	≤	PUNCT
ma-172	68	37	δ1(‖x	δ1(‖x	PROPN
ma-172	68	38	−	−	PROPN
ma-172	68	39	ξ‖)and	ξ‖)and	PROPN
ma-172	68	40	‖s	‖s	PROPN
ma-172	68	41	−	−	ADP
ma-172	68	42	ξ‖	ξ‖	PROPN
ma-172	68	43	≤	≤	PROPN
ma-172	68	44	δ2(‖x	δ2(‖x	PROPN
ma-172	68	45	−	−	PROPN
ma-172	68	46	ξ‖	ξ‖	PROPN
ma-172	68	47	)	)	PUNCT
ma-172	68	48	.	.	PUNCT
ma-172	69	1	(	(	PUNCT
ma-172	69	2	c2	c2	PROPN
ma-172	69	3	)	)	PUNCT
ma-172	69	4	the	the	DET
ma-172	69	5	equation	equation	NOUN
ma-172	69	6	ϕ0(δ1(t	ϕ0(δ1(t	PUNCT
ma-172	69	7	)	)	PUNCT
ma-172	69	8	,	,	PUNCT
ma-172	69	9	δ2(t))−	δ2(t))−	NOUN
ma-172	69	10	1	1	NUM
ma-172	69	11	=	=	SYM
ma-172	69	12	0	0	NUM
ma-172	69	13	has	have	VERB
ma-172	69	14	a	a	DET
ma-172	69	15	smallest	small	ADJ
ma-172	69	16	positive	positive	ADJ
ma-172	69	17	solution	solution	NOUN
ma-172	69	18	denoted	denote	VERB
ma-172	69	19	by	by	ADP
ma-172	69	20	ρ0	ρ0	PROPN
ma-172	69	21	.	.	PUNCT
ma-172	70	1	let	let	VERB
ma-172	70	2	m0	m0	PROPN
ma-172	70	3	=	=	PUNCT
ma-172	71	1	[	[	X
ma-172	71	2	0	0	NUM
ma-172	71	3	,	,	PUNCT
ma-172	71	4	ρ0	ρ0	PROPN
ma-172	71	5	)	)	PUNCT
ma-172	71	6	and	and	CCONJ
ma-172	71	7	b0	b0	NOUN
ma-172	71	8	=	=	SYM
ma-172	71	9	b	b	PROPN
ma-172	71	10	∩	∩	X
ma-172	71	11	s(ξ	s(ξ	PROPN
ma-172	71	12	,	,	PUNCT
ma-172	71	13	ρ0	ρ0	PROPN
ma-172	71	14	)	)	PUNCT
ma-172	71	15	.	.	PUNCT
ma-172	72	1	(	(	PUNCT
ma-172	72	2	c3	c3	NOUN
ma-172	72	3	)	)	PUNCT
ma-172	72	4	there	there	PRON
ma-172	72	5	exist	exist	VERB
ma-172	72	6	cnf	cnf	PROPN
ma-172	72	7	ϕ	ϕ	NOUN
ma-172	72	8	:	:	PUNCT
ma-172	72	9	m0	m0	PROPN
ma-172	72	10	×m0	×m0	PROPN
ma-172	72	11	×m0	×m0	PROPN
ma-172	72	12	→	→	SYM
ma-172	72	13	m	m	SYM
ma-172	72	14	,	,	PUNCT
ma-172	72	15	δ3	δ3	PROPN
ma-172	72	16	:	:	PUNCT
ma-172	72	17	m0	m0	PROPN
ma-172	72	18	→	→	SYM
ma-172	72	19	m	m	PROPN
ma-172	72	20	,	,	PUNCT
ma-172	72	21	δ4	δ4	NOUN
ma-172	72	22	:	:	PUNCT
ma-172	72	23	m0	m0	PROPN
ma-172	72	24	→	→	SYM
ma-172	72	25	m	m	NOUN
ma-172	72	26	,	,	PUNCT
ma-172	72	27	ϕ1	ϕ1	NOUN
ma-172	72	28	:	:	PUNCT
ma-172	73	1	m0	m0	PROPN
ma-172	73	2	×m0	×m0	NOUN
ma-172	73	3	×	×	NOUN
ma-172	73	4	m0×m0	m0×m0	NOUN
ma-172	73	5	→	→	SYM
ma-172	73	6	m	m	NOUN
ma-172	73	7	,	,	PUNCT
ma-172	73	8	ϕ2	ϕ2	ADV
ma-172	73	9	:	:	PUNCT
ma-172	73	10	m0	m0	PROPN
ma-172	73	11	→	→	SYM
ma-172	73	12	m	m	VERB
ma-172	73	13	such	such	ADJ
ma-172	73	14	that	that	PRON
ma-172	73	15	for	for	ADP
ma-172	73	16	each	each	DET
ma-172	73	17	x	x	NOUN
ma-172	73	18	,	,	PUNCT
ma-172	73	19	z	z	PROPN
ma-172	73	20	∈	∈	PROPN
ma-172	73	21	b0	b0	NOUN
ma-172	73	22	,	,	PUNCT
ma-172	73	23	u	u	NOUN
ma-172	73	24	=	=	PROPN
ma-172	73	25	z	z	PROPN
ma-172	73	26	+	+	NUM
ma-172	73	27	bg(z	bg(z	NUM
ma-172	73	28	)	)	PUNCT
ma-172	73	29	,	,	PUNCT
ma-172	73	30	v	v	X
ma-172	73	31	=	=	SYM
ma-172	73	32	z	z	NOUN
ma-172	73	33	−	−	NOUN
ma-172	73	34	bg(z	bg(z	NOUN
ma-172	73	35	)	)	PUNCT
ma-172	73	36	,	,	PUNCT
ma-172	73	37	‖u	‖u	PROPN
ma-172	73	38	−	−	PROPN
ma-172	73	39	ξ‖	ξ‖	ADJ
ma-172	73	40	≤	≤	PROPN
ma-172	73	41	δ3(‖z	δ3(‖z	NOUN
ma-172	73	42	−	−	PROPN
ma-172	73	43	ξ‖	ξ‖	PROPN
ma-172	73	44	)	)	PUNCT
ma-172	73	45	,	,	PUNCT
ma-172	73	46	‖v	‖v	NOUN
ma-172	73	47	−	−	PROPN
ma-172	73	48	ξ‖	ξ‖	PROPN
ma-172	73	49	≤	≤	PROPN
ma-172	73	50	δ4(‖z	δ4(‖z	ADV
ma-172	73	51	−	−	PROPN
ma-172	73	52	ξ‖	ξ‖	PROPN
ma-172	73	53	)	)	PUNCT
ma-172	73	54	,	,	PUNCT
ma-172	73	55	‖p−1([w	‖p−1([w	NOUN
ma-172	73	56	,	,	PUNCT
ma-172	73	57	s;g]−	s;g]−	VERB
ma-172	73	58	[	[	X
ma-172	73	59	x	x	NOUN
ma-172	73	60	,	,	PUNCT
ma-172	73	61	ξ;g])‖	ξ;g])‖	ADJ
ma-172	73	62	≤	≤	X
ma-172	73	63	ϕ(‖x	ϕ(‖x	PROPN
ma-172	74	1	−	−	PROPN
ma-172	74	2	ξ‖	ξ‖	ADJ
ma-172	74	3	,	,	PUNCT
ma-172	74	4	‖w	‖w	PUNCT
ma-172	74	5	−	−	PROPN
ma-172	74	6	ξ‖	ξ‖	ADJ
ma-172	74	7	,	,	PUNCT
ma-172	74	8	‖s	‖s	ADJ
ma-172	74	9	−	−	PROPN
ma-172	74	10	ξ‖	ξ‖	PROPN
ma-172	74	11	)	)	PUNCT
ma-172	74	12	,	,	PUNCT
ma-172	74	13	‖p−1([w	‖p−1([w	NOUN
ma-172	74	14	,	,	PUNCT
ma-172	74	15	s;g]−	s;g]−	VERB
ma-172	74	16	[	[	X
ma-172	74	17	u	u	NOUN
ma-172	74	18	,	,	PUNCT
ma-172	74	19	v	v	NOUN
ma-172	74	20	;	;	PUNCT
ma-172	74	21	g])‖	g])‖	ADJ
ma-172	74	22	≤	≤	PUNCT
ma-172	74	23	ϕ1(‖w	ϕ1(‖w	NOUN
ma-172	74	24	−	−	PROPN
ma-172	74	25	ξ‖	ξ‖	PROPN
ma-172	74	26	,	,	PUNCT
ma-172	74	27	‖s	‖s	ADJ
ma-172	74	28	−	−	PROPN
ma-172	74	29	ξ‖	ξ‖	PROPN
ma-172	74	30	,	,	PUNCT
ma-172	74	31	‖u	‖u	PROPN
ma-172	74	32	−	−	PROPN
ma-172	75	1	ξ‖	ξ‖	PROPN
ma-172	75	2	,	,	PUNCT
ma-172	75	3	‖v	‖v	NOUN
ma-172	75	4	−	−	PROPN
ma-172	75	5	ξ‖)and	ξ‖)and	PROPN
ma-172	75	6	‖p−1([z	‖p−1([z	NOUN
ma-172	75	7	,	,	PUNCT
ma-172	75	8	ξ;g]−p)‖	ξ;g]−p)‖	PROPN
ma-172	75	9	≤	≤	NUM
ma-172	76	1	ϕ2(‖z	ϕ2(‖z	PROPN
ma-172	76	2	−	−	PROPN
ma-172	76	3	ξ‖	ξ‖	PROPN
ma-172	76	4	)	)	PUNCT
ma-172	76	5	.	.	PUNCT
ma-172	77	1	(	(	PUNCT
ma-172	77	2	c4	c4	NOUN
ma-172	77	3	)	)	PUNCT
ma-172	77	4	the	the	DET
ma-172	77	5	equations	equation	NOUN
ma-172	77	6	hi(t)−	hi(t)−	PROPN
ma-172	77	7	1	1	NUM
ma-172	78	1	=	=	SYM
ma-172	78	2	0	0	NUM
ma-172	78	3	,	,	PUNCT
ma-172	78	4	i	i	PRON
ma-172	78	5	=	=	NOUN
ma-172	78	6	1	1	NUM
ma-172	78	7	,	,	PUNCT
ma-172	78	8	2	2	NUM
ma-172	78	9	,	,	PUNCT
ma-172	78	10	3	3	NUM
ma-172	78	11	have	have	VERB
ma-172	78	12	smallest	small	ADJ
ma-172	78	13	solutions	solution	NOUN
ma-172	78	14	ri	ri	NOUN
ma-172	78	15	∈	∈	PROPN
ma-172	78	16	m0−{0	m0−{0	PROPN
ma-172	78	17	}	}	PUNCT
ma-172	78	18	,	,	PUNCT
ma-172	78	19	respectivelywhere	respectivelywhere	VERB
ma-172	78	20	the	the	DET
ma-172	78	21	functions	function	NOUN
ma-172	78	22	hi	hi	INTJ
ma-172	78	23	:	:	PUNCT
ma-172	78	24	m0	m0	PROPN
ma-172	78	25	→	→	SYM
ma-172	78	26	m	m	NOUN
ma-172	78	27	are	be	AUX
ma-172	78	28	defined	define	VERB
ma-172	78	29	by	by	ADP
ma-172	78	30	h1(t	h1(t	NOUN
ma-172	78	31	)	)	PUNCT
ma-172	78	32	=	=	SYM
ma-172	79	1	ϕ(t	ϕ(t	PROPN
ma-172	79	2	,	,	PUNCT
ma-172	79	3	δ1(t	δ1(t	NOUN
ma-172	79	4	)	)	PUNCT
ma-172	79	5	,	,	PUNCT
ma-172	79	6	δ2(t	δ2(t	PROPN
ma-172	79	7	)	)	PUNCT
ma-172	79	8	)	)	PUNCT
ma-172	79	9	1−	1−	NUM
ma-172	79	10	ϕ0(δ1(t	ϕ0(δ1(t	NUM
ma-172	79	11	)	)	PUNCT
ma-172	79	12	,	,	PUNCT
ma-172	79	13	δ2(t	δ2(t	PROPN
ma-172	79	14	)	)	PUNCT
ma-172	79	15	)	)	PUNCT
ma-172	79	16	,	,	PUNCT
ma-172	79	17	h2(t	h2(t	X
ma-172	79	18	)	)	PUNCT
ma-172	79	19	=	=	SYM
ma-172	79	20	ϕ(h1(t)t	ϕ(h1(t)t	NOUN
ma-172	79	21	,	,	PUNCT
ma-172	79	22	δ1(t	δ1(t	NOUN
ma-172	79	23	)	)	PUNCT
ma-172	79	24	,	,	PUNCT
ma-172	79	25	δ2(t))h1(t	δ2(t))h1(t	NUM
ma-172	79	26	)	)	PUNCT
ma-172	79	27	1−	1−	NUM
ma-172	79	28	ϕ0(δ1(t	ϕ0(δ1(t	NUM
ma-172	79	29	)	)	PUNCT
ma-172	79	30	,	,	PUNCT
ma-172	79	31	δ2(t	δ2(t	PROPN
ma-172	79	32	)	)	PUNCT
ma-172	79	33	)	)	PUNCT
ma-172	79	34	ε(t	ε(t	NOUN
ma-172	79	35	)	)	PUNCT
ma-172	79	36	=	=	SYM
ma-172	79	37	ϕ1(δ1(t	ϕ1(δ1(t	PUNCT
ma-172	79	38	)	)	PUNCT
ma-172	79	39	,	,	PUNCT
ma-172	79	40	δ2(t	δ2(t	PROPN
ma-172	79	41	)	)	PUNCT
ma-172	79	42	,	,	PUNCT
ma-172	79	43	δ3(h2(t)t	δ3(h2(t)t	NOUN
ma-172	79	44	)	)	PUNCT
ma-172	79	45	,	,	PUNCT
ma-172	79	46	δ4(h2(t)t	δ4(h2(t)t	NOUN
ma-172	79	47	)	)	PUNCT
ma-172	79	48	1−	1−	NUM
ma-172	79	49	ϕ0(δ1(t	ϕ0(δ1(t	NUM
ma-172	79	50	)	)	PUNCT
ma-172	79	51	,	,	PUNCT
ma-172	79	52	δ2(t	δ2(t	PROPN
ma-172	79	53	)	)	PUNCT
ma-172	79	54	)	)	PUNCT
ma-172	79	55	,	,	PUNCT
ma-172	79	56	λ(t	λ(t	X
ma-172	79	57	)	)	PUNCT
ma-172	79	58	=	=	SYM
ma-172	79	59	|p	|p	NOUN
ma-172	79	60	+	+	PUNCT
ma-172	79	61	q	q	X
ma-172	80	1	+	+	CCONJ
ma-172	80	2	r	r	NOUN
ma-172	81	1	+	+	NOUN
ma-172	81	2	d	d	NOUN
ma-172	81	3	−	−	PROPN
ma-172	81	4	1|+	1|+	NUM
ma-172	81	5	|p	|p	NOUN
ma-172	81	6	+	+	CCONJ
ma-172	81	7	2r	2r	NUM
ma-172	82	1	+	+	CCONJ
ma-172	82	2	3d	3d	NUM
ma-172	82	3	|ε(t	|ε(t	NOUN
ma-172	82	4	)	)	PUNCT
ma-172	82	5	+	+	NUM
ma-172	82	6	|r	|r	X
ma-172	82	7	+	+	CCONJ
ma-172	82	8	3d	3d	NUM
ma-172	82	9	|ε(t)2	|ε(t)2	PROPN
ma-172	82	10	+	+	NOUN
ma-172	82	11	|d	|d	NOUN
ma-172	82	12	|ε(t)3	|ε(t)3	NOUN
ma-172	82	13	,	,	PUNCT
ma-172	82	14	h3(t	h3(t	PRON
ma-172	82	15	)	)	PUNCT
ma-172	82	16	=	=	NOUN
ma-172	82	17	[	[	PUNCT
ma-172	82	18	ϕ(h2(t)t	ϕ(h2(t)t	PROPN
ma-172	82	19	,	,	PUNCT
ma-172	82	20	δ1(t	δ1(t	NUM
ma-172	82	21	)	)	PUNCT
ma-172	82	22	,	,	PUNCT
ma-172	82	23	δ2(t	δ2(t	PROPN
ma-172	82	24	)	)	PUNCT
ma-172	82	25	)	)	PUNCT
ma-172	82	26	1−	1−	NUM
ma-172	82	27	ϕ0(δ1(t	ϕ0(δ1(t	NUM
ma-172	82	28	)	)	PUNCT
ma-172	82	29	,	,	PUNCT
ma-172	82	30	δ2(t	δ2(t	PROPN
ma-172	82	31	)	)	PUNCT
ma-172	82	32	)	)	PUNCT
ma-172	83	1	+	+	CCONJ
ma-172	83	2	λ(t)(1	λ(t)(1	PRON
ma-172	83	3	+	+	X
ma-172	83	4	ϕ2(h2(t)t	ϕ2(h2(t)t	NOUN
ma-172	83	5	)	)	PUNCT
ma-172	83	6	)	)	PUNCT
ma-172	83	7	1−	1−	NUM
ma-172	84	1	ϕ0(δ1(t	ϕ0(δ1(t	NUM
ma-172	84	2	)	)	PUNCT
ma-172	84	3	,	,	PUNCT
ma-172	84	4	δ2(t	δ2(t	PROPN
ma-172	84	5	)	)	PUNCT
ma-172	84	6	)	)	PUNCT
ma-172	85	1	]	]	PUNCT
ma-172	86	1	h2(t	h2(t	X
ma-172	86	2	)	)	PUNCT
ma-172	86	3	.	.	PUNCT
ma-172	87	1	https://doi.org/10.28924/ada/ma.3.19	https://doi.org/10.28924/ada/ma.3.19	PRON
ma-172	87	2	eur	eur	PROPN
ma-172	87	3	.	.	PUNCT
ma-172	88	1	j.	j.	PROPN
ma-172	88	2	math	math	PROPN
ma-172	88	3	.	.	PUNCT
ma-172	89	1	anal	anal	PROPN
ma-172	89	2	.	.	PUNCT
ma-172	90	1	10.28924	10.28924	NUM
ma-172	90	2	/	/	SYM
ma-172	90	3	ada	ada	PROPN
ma-172	90	4	/	/	SYM
ma-172	90	5	ma.3.19	ma.3.19	PROPN
ma-172	90	6	4set	4set	NOUN
ma-172	90	7	r	r	NOUN
ma-172	90	8	=	=	PUNCT
ma-172	90	9	min{ri	min{ri	NUM
ma-172	90	10	}	}	PUNCT
ma-172	90	11	.	.	PUNCT
ma-172	91	1	let	let	VERB
ma-172	91	2	m1	m1	PROPN
ma-172	91	3	=	=	PUNCT
ma-172	92	1	[	[	X
ma-172	92	2	0	0	NUM
ma-172	92	3	,	,	PUNCT
ma-172	92	4	r	r	NOUN
ma-172	92	5	)	)	PUNCT
ma-172	92	6	.	.	PUNCT
ma-172	93	1	it	it	PRON
ma-172	93	2	follows	follow	VERB
ma-172	93	3	by	by	ADP
ma-172	93	4	these	these	DET
ma-172	93	5	definitions	definition	NOUN
ma-172	93	6	that	that	SCONJ
ma-172	93	7	for	for	ADP
ma-172	93	8	each	each	DET
ma-172	93	9	t	t	NOUN
ma-172	93	10	∈	∈	PROPN
ma-172	93	11	m1	m1	PROPN
ma-172	93	12	0	0	NUM
ma-172	93	13	≤	≤	NUM
ma-172	93	14	ϕ0(δ1(t	ϕ0(δ1(t	NUM
ma-172	93	15	)	)	PUNCT
ma-172	93	16	,	,	PUNCT
ma-172	93	17	δ2(t	δ2(t	PROPN
ma-172	93	18	)	)	PUNCT
ma-172	93	19	)	)	PUNCT
ma-172	93	20	<	<	X
ma-172	93	21	1	1	NUM
ma-172	93	22	,	,	PUNCT
ma-172	93	23	0	0	NUM
ma-172	93	24	≤	≤	NUM
ma-172	93	25	ε(t	ε(t	NOUN
ma-172	93	26	)	)	PUNCT
ma-172	93	27	,	,	PUNCT
ma-172	93	28	0	0	NUM
ma-172	93	29	≤	≤	NUM
ma-172	94	1	λ(t)and	λ(t)and	ADP
ma-172	94	2	0	0	NUM
ma-172	94	3	≤	≤	NUM
ma-172	94	4	hi(t	hi(t	NOUN
ma-172	94	5	)	)	PUNCT
ma-172	94	6	<	<	X
ma-172	94	7	1	1	X
ma-172	94	8	.	.	X
ma-172	94	9	notice	notice	VERB
ma-172	94	10	that	that	SCONJ
ma-172	94	11	for	for	ADP
ma-172	94	12	x0	x0	PROPN
ma-172	94	13	∈	∈	PROPN
ma-172	94	14	s(ξ	s(ξ	PROPN
ma-172	94	15	,	,	PUNCT
ma-172	94	16	r)−	r)−	PROPN
ma-172	94	17	{	{	PUNCT
ma-172	94	18	ξ	ξ	NOUN
ma-172	94	19	}	}	PUNCT
ma-172	94	20	the	the	DET
ma-172	94	21	conditions	condition	NOUN
ma-172	94	22	(	(	PUNCT
ma-172	94	23	c1)-(c2	c1)-(c2	NUM
ma-172	94	24	)	)	PUNCT
ma-172	94	25	and	and	CCONJ
ma-172	94	26	(	(	PUNCT
ma-172	94	27	c4	c4	NOUN
ma-172	94	28	)	)	PUNCT
ma-172	94	29	imply	imply	VERB
ma-172	94	30	‖p−1([w0	‖p−1([w0	NOUN
ma-172	94	31	,	,	PUNCT
ma-172	94	32	s0;g]−p)‖ϕ0(‖w0	s0;g]−p)‖ϕ0(‖w0	NOUN
ma-172	94	33	−	−	PROPN
ma-172	94	34	ξ‖	ξ‖	PROPN
ma-172	94	35	,	,	PUNCT
ma-172	94	36	‖s0	‖s0	NOUN
ma-172	94	37	−	−	PROPN
ma-172	94	38	ξ‖	ξ‖	ADJ
ma-172	94	39	)	)	PUNCT
ma-172	94	40	≤	≤	NUM
ma-172	94	41	ϕ0(δ1(r	ϕ0(δ1(r	NUM
ma-172	94	42	)	)	PUNCT
ma-172	94	43	,	,	PUNCT
ma-172	94	44	δ2(r	δ2(r	NOUN
ma-172	94	45	)	)	PUNCT
ma-172	94	46	)	)	PUNCT
ma-172	94	47	<	<	X
ma-172	95	1	1	1	X
ma-172	95	2	.	.	PUNCT
ma-172	95	3	thus	thus	ADV
ma-172	95	4	a−10	a−10	PROPN
ma-172	95	5	∈	∈	PROPN
ma-172	95	6	w	w	PROPN
ma-172	95	7	(	(	PUNCT
ma-172	95	8	u	u	NOUN
ma-172	95	9	)	)	PUNCT
ma-172	95	10	by	by	ADP
ma-172	95	11	the	the	DET
ma-172	95	12	banach	banach	ADV
ma-172	95	13	lemma	lemma	PROPN
ma-172	95	14	on	on	ADP
ma-172	95	15	invertible	invertible	ADJ
ma-172	95	16	operators	operator	NOUN
ma-172	95	17	[	[	X
ma-172	95	18	3	3	NUM
ma-172	95	19	,	,	PUNCT
ma-172	95	20	9	9	NUM
ma-172	95	21	,	,	PUNCT
ma-172	95	22	10	10	NUM
ma-172	95	23	]	]	PUNCT
ma-172	95	24	and	and	CCONJ
ma-172	95	25	the	the	DET
ma-172	95	26	firstiterate	firstiterate	NOUN
ma-172	95	27	y0	y0	PROPN
ma-172	95	28	is	be	AUX
ma-172	95	29	well	well	ADV
ma-172	95	30	-	-	PUNCT
ma-172	95	31	defined	define	VERB
ma-172	95	32	by	by	ADP
ma-172	95	33	the	the	DET
ma-172	95	34	first	first	ADJ
ma-172	95	35	sub	sub	NOUN
ma-172	95	36	-	-	NOUN
ma-172	95	37	step	step	NOUN
ma-172	95	38	of	of	ADP
ma-172	95	39	the	the	DET
ma-172	95	40	method	method	NOUN
ma-172	95	41	(	(	PUNCT
ma-172	95	42	2	2	NUM
ma-172	95	43	)	)	PUNCT
ma-172	95	44	.	.	PUNCT
ma-172	96	1	(	(	PUNCT
ma-172	96	2	c5	c5	PROPN
ma-172	96	3	)	)	PUNCT
ma-172	96	4	s[ξ	s[ξ	PROPN
ma-172	96	5	,	,	PUNCT
ma-172	96	6	r	r	NOUN
ma-172	96	7	]	]	PUNCT
ma-172	96	8	⊂	⊂	X
ma-172	97	1	b.the	b.the	DET
ma-172	97	2	motivation	motivation	NOUN
ma-172	97	3	for	for	ADP
ma-172	97	4	the	the	DET
ma-172	97	5	development	development	NOUN
ma-172	97	6	of	of	ADP
ma-172	97	7	the	the	DET
ma-172	97	8	functions	function	NOUN
ma-172	97	9	hi	hi	INTJ
ma-172	97	10	follows	follow	VERB
ma-172	97	11	in	in	ADP
ma-172	97	12	turn	turn	NOUN
ma-172	97	13	by	by	ADP
ma-172	97	14	the	the	DET
ma-172	97	15	estimates	estimate	NOUN
ma-172	97	16	‖a−1n	‖a−1n	PROPN
ma-172	97	17	p‖	p‖	PROPN
ma-172	97	18	≤	≤	ADV
ma-172	97	19	1	1	NUM
ma-172	97	20	1−	1−	NUM
ma-172	97	21	ϕ0(‖wn	ϕ0(‖wn	ADP
ma-172	97	22	−	−	PROPN
ma-172	97	23	ξ‖	ξ‖	PROPN
ma-172	97	24	,	,	PUNCT
ma-172	97	25	‖sn	‖sn	PROPN
ma-172	97	26	−	−	PROPN
ma-172	97	27	ξ‖	ξ‖	ADJ
ma-172	97	28	)	)	PUNCT
ma-172	97	29	≤	≤	NUM
ma-172	97	30	1	1	NUM
ma-172	97	31	1−	1−	NUM
ma-172	97	32	ϕ0(δ1(‖xn	ϕ0(δ1(‖xn	PROPN
ma-172	97	33	−	−	PROPN
ma-172	97	34	ξ‖	ξ‖	PROPN
ma-172	97	35	)	)	PUNCT
ma-172	97	36	,	,	PUNCT
ma-172	97	37	δ2(‖xn	δ2(‖xn	PROPN
ma-172	97	38	−	−	PROPN
ma-172	97	39	ξ‖	ξ‖	PROPN
ma-172	97	40	)	)	PUNCT
ma-172	97	41	)	)	PUNCT
ma-172	97	42	,	,	PUNCT
ma-172	97	43	yn	yn	PRON
ma-172	97	44	−	−	PROPN
ma-172	97	45	ξ	ξ	X
ma-172	97	46	=	=	SYM
ma-172	97	47	a−1n	a−1n	NOUN
ma-172	97	48	(	(	PUNCT
ma-172	97	49	an	an	PRON
ma-172	97	50	−	−	PROPN
ma-172	98	1	[	[	X
ma-172	98	2	xn	xn	X
ma-172	98	3	,	,	PUNCT
ma-172	98	4	ξ;g])(xn	ξ;g])(xn	NUM
ma-172	98	5	−	−	PROPN
ma-172	98	6	ξ	ξ	X
ma-172	98	7	)	)	PUNCT
ma-172	98	8	,	,	PUNCT
ma-172	98	9	‖yn	‖yn	PROPN
ma-172	98	10	−	−	PROPN
ma-172	98	11	ξ‖	ξ‖	ADJ
ma-172	98	12	≤	≤	PROPN
ma-172	98	13	ϕ(‖xn	ϕ(‖xn	PROPN
ma-172	98	14	−	−	PROPN
ma-172	98	15	ξ‖	ξ‖	PROPN
ma-172	98	16	,	,	PUNCT
ma-172	98	17	‖wn	‖wn	PROPN
ma-172	98	18	−	−	PROPN
ma-172	98	19	ξ‖	ξ‖	PROPN
ma-172	98	20	,	,	PUNCT
ma-172	98	21	‖sn	‖sn	PROPN
ma-172	98	22	−	−	PROPN
ma-172	98	23	ξ‖)‖xn	ξ‖)‖xn	PUNCT
ma-172	98	24	−	−	PROPN
ma-172	98	25	ξ‖	ξ‖	ADJ
ma-172	98	26	1−	1−	NUM
ma-172	98	27	ϕ0(δ1(‖xn	ϕ0(δ1(‖xn	PROPN
ma-172	98	28	−	−	PROPN
ma-172	98	29	ξ‖	ξ‖	PROPN
ma-172	98	30	)	)	PUNCT
ma-172	98	31	,	,	PUNCT
ma-172	98	32	δ2(‖xn	δ2(‖xn	PROPN
ma-172	98	33	−	−	PROPN
ma-172	98	34	ξ‖	ξ‖	PROPN
ma-172	98	35	)	)	PUNCT
ma-172	98	36	)	)	PUNCT
ma-172	98	37	≤	≤	NOUN
ma-172	98	38	h1(‖xn	h1(‖xn	PUNCT
ma-172	98	39	−	−	PROPN
ma-172	98	40	ξ‖)‖xn	ξ‖)‖xn	PUNCT
ma-172	98	41	−	−	PROPN
ma-172	98	42	ξ‖	ξ‖	ADJ
ma-172	98	43	≤	≤	PUNCT
ma-172	99	1	‖xn	‖xn	PROPN
ma-172	99	2	−	−	PROPN
ma-172	100	1	ξ‖	ξ‖	NOUN
ma-172	100	2	<	<	X
ma-172	100	3	r.	r.	PROPN
ma-172	100	4	similarly	similarly	ADV
ma-172	100	5	,	,	PUNCT
ma-172	100	6	‖zn	‖zn	PROPN
ma-172	100	7	−	−	PROPN
ma-172	100	8	ξ‖	ξ‖	ADJ
ma-172	100	9	≤	≤	NOUN
ma-172	100	10	ϕ(‖yn	ϕ(‖yn	PUNCT
ma-172	100	11	−	−	PROPN
ma-172	100	12	ξ‖	ξ‖	PROPN
ma-172	100	13	,	,	PUNCT
ma-172	100	14	‖wn	‖wn	PROPN
ma-172	100	15	−	−	PROPN
ma-172	100	16	ξ‖	ξ‖	ADJ
ma-172	100	17	,	,	PUNCT
ma-172	100	18	‖sn	‖sn	PROPN
ma-172	100	19	−	−	PROPN
ma-172	100	20	ξ‖)‖yn	ξ‖)‖yn	ADP
ma-172	100	21	−	−	PROPN
ma-172	100	22	ξ‖	ξ‖	ADJ
ma-172	100	23	1−	1−	NUM
ma-172	100	24	ϕ0(δ1(‖xn	ϕ0(δ1(‖xn	PROPN
ma-172	100	25	−	−	PROPN
ma-172	100	26	ξ‖	ξ‖	PROPN
ma-172	100	27	)	)	PUNCT
ma-172	100	28	,	,	PUNCT
ma-172	100	29	δ2(‖xn	δ2(‖xn	PROPN
ma-172	100	30	−	−	PROPN
ma-172	100	31	ξ‖	ξ‖	PROPN
ma-172	100	32	)	)	PUNCT
ma-172	100	33	)	)	PUNCT
ma-172	100	34	≤	≤	NUM
ma-172	100	35	h2(‖xn	h2(‖xn	SYM
ma-172	100	36	−	−	PROPN
ma-172	100	37	ξ‖)‖xn	ξ‖)‖xn	PUNCT
ma-172	100	38	−	−	PROPN
ma-172	100	39	ξ‖	ξ‖	ADJ
ma-172	100	40	≤	≤	PUNCT
ma-172	100	41	‖xn	‖xn	PROPN
ma-172	100	42	−	−	PROPN
ma-172	100	43	ξ‖	ξ‖	PROPN
ma-172	100	44	,	,	PUNCT
ma-172	100	45	xn+1	xn+1	PROPN
ma-172	100	46	−	−	PROPN
ma-172	101	1	ξ	ξ	X
ma-172	101	2	=	=	SYM
ma-172	101	3	zn	zn	PROPN
ma-172	101	4	−	−	PROPN
ma-172	102	1	ξ	ξ	DET
ma-172	102	2	−	−	NOUN
ma-172	102	3	a−1n	a−1n	ADV
ma-172	102	4	g(zn)−	g(zn)−	NOUN
ma-172	103	1	[	[	X
ma-172	103	2	(	(	PUNCT
ma-172	103	3	p	p	X
ma-172	103	4	+	+	NOUN
ma-172	103	5	q	q	NOUN
ma-172	104	1	+	+	CCONJ
ma-172	104	2	r	r	NOUN
ma-172	105	1	+	+	NOUN
ma-172	105	2	d	d	NOUN
ma-172	105	3	−	−	PROPN
ma-172	105	4	1)i	1)i	NUM
ma-172	105	5	+	+	CCONJ
ma-172	105	6	(	(	PUNCT
ma-172	105	7	q	q	X
ma-172	106	1	+	+	NUM
ma-172	106	2	2r	2r	NUM
ma-172	106	3	+	+	SYM
ma-172	106	4	3d)(a−1n	3d)(a−1n	NUM
ma-172	106	5	qn	qn	NOUN
ma-172	106	6	−	−	PROPN
ma-172	106	7	i	i	PROPN
ma-172	106	8	)	)	PUNCT
ma-172	107	1	+	+	CCONJ
ma-172	107	2	(	(	PUNCT
ma-172	107	3	r	r	NOUN
ma-172	107	4	+	+	NUM
ma-172	107	5	3d)(a−1n	3d)(a−1n	NUM
ma-172	107	6	qn	qn	NOUN
ma-172	107	7	−	−	PROPN
ma-172	107	8	i)2	i)2	ADJ
ma-172	107	9	+	+	CCONJ
ma-172	107	10	d(a−1n	d(a−1n	NOUN
ma-172	107	11	qn	qn	NOUN
ma-172	107	12	−	−	PROPN
ma-172	107	13	i)3]a−1n	i)3]a−1n	ADJ
ma-172	107	14	g(zn	g(zn	PROPN
ma-172	107	15	)	)	PUNCT
ma-172	107	16	which	which	PRON
ma-172	107	17	can	can	AUX
ma-172	107	18	be	be	AUX
ma-172	107	19	shortened	shorten	VERB
ma-172	107	20	for	for	ADP
ma-172	107	21	dn	dn	NOUN
ma-172	107	22	=	=	PUNCT
ma-172	107	23	a−1n	a−1n	NOUN
ma-172	107	24	(	(	PUNCT
ma-172	107	25	qn	qn	INTJ
ma-172	107	26	−	−	PROPN
ma-172	107	27	an	an	NOUN
ma-172	107	28	)	)	PUNCT
ma-172	107	29	,	,	PUNCT
ma-172	107	30	tn	tn	NOUN
ma-172	108	1	=	=	SYM
ma-172	108	2	(	(	PUNCT
ma-172	108	3	p	p	X
ma-172	108	4	+	+	NOUN
ma-172	108	5	q	q	NOUN
ma-172	108	6	+	+	CCONJ
ma-172	108	7	r	r	NOUN
ma-172	108	8	+	+	NOUN
ma-172	108	9	d	d	NOUN
ma-172	108	10	−	−	PROPN
ma-172	108	11	1)i	1)i	NUM
ma-172	108	12	+	+	CCONJ
ma-172	108	13	(	(	PUNCT
ma-172	108	14	p	p	X
ma-172	108	15	+	+	NOUN
ma-172	108	16	2r	2r	NUM
ma-172	108	17	+	+	CCONJ
ma-172	108	18	3d)dn	3d)dn	NUM
ma-172	108	19	+	+	CCONJ
ma-172	108	20	(	(	PUNCT
ma-172	108	21	r	r	NOUN
ma-172	108	22	+	+	NUM
ma-172	108	23	3d)d2n	3d)d2n	NOUN
ma-172	108	24	+	+	CCONJ
ma-172	108	25	dd3n	dd3n	NOUN
ma-172	108	26	.	.	PUNCT
ma-172	109	1	thus	thus	ADV
ma-172	109	2	xn+1	xn+1	NUM
ma-172	109	3	−	−	PROPN
ma-172	109	4	ξ	ξ	X
ma-172	109	5	=	=	PRON
ma-172	109	6	a−1n	a−1n	NOUN
ma-172	109	7	(	(	PUNCT
ma-172	109	8	an	an	PRON
ma-172	109	9	−	−	PROPN
ma-172	110	1	[	[	X
ma-172	110	2	zn	zn	X
ma-172	110	3	,	,	PUNCT
ma-172	110	4	ξ;g])(zn	ξ;g])(zn	PROPN
ma-172	110	5	−	−	PROPN
ma-172	110	6	ξ)−	ξ)−	PROPN
ma-172	110	7	tna−1n	tna−1n	PROPN
ma-172	110	8	g(zn	g(zn	PROPN
ma-172	110	9	)	)	PUNCT
ma-172	110	10	.	.	PUNCT
ma-172	111	1	https://doi.org/10.28924/ada/ma.3.19	https://doi.org/10.28924/ada/ma.3.19	PRON
ma-172	111	2	eur	eur	PROPN
ma-172	111	3	.	.	PUNCT
ma-172	112	1	j.	j.	PROPN
ma-172	112	2	math	math	PROPN
ma-172	112	3	.	.	PUNCT
ma-172	113	1	anal	anal	PROPN
ma-172	113	2	.	.	PUNCT
ma-172	114	1	10.28924	10.28924	NUM
ma-172	114	2	/	/	SYM
ma-172	114	3	ada	ada	PROPN
ma-172	114	4	/	/	SYM
ma-172	114	5	ma.3.19	ma.3.19	PROPN
ma-172	114	6	5but	5but	NUM
ma-172	114	7	,	,	PUNCT
ma-172	114	8	‖dn‖	‖dn‖	ADJ
ma-172	114	9	≤	≤	PROPN
ma-172	114	10	‖a−1n	‖a−1n	PROPN
ma-172	114	11	p‖‖p−1(qn	p‖‖p−1(qn	PROPN
ma-172	114	12	−	−	PROPN
ma-172	114	13	an)‖	an)‖	NOUN
ma-172	114	14	≤	≤	X
ma-172	114	15	ϕ1(‖wn	ϕ1(‖wn	PROPN
ma-172	115	1	−	−	PROPN
ma-172	115	2	ξ‖	ξ‖	PROPN
ma-172	115	3	,	,	PUNCT
ma-172	115	4	‖sn	‖sn	PROPN
ma-172	115	5	−	−	PROPN
ma-172	115	6	ξ‖	ξ‖	PROPN
ma-172	115	7	,	,	PUNCT
ma-172	115	8	‖un	‖un	PROPN
ma-172	115	9	−	−	PROPN
ma-172	115	10	ξ‖	ξ‖	PROPN
ma-172	115	11	,	,	PUNCT
ma-172	115	12	‖vn	‖vn	PROPN
ma-172	115	13	−	−	PROPN
ma-172	115	14	ξ‖	ξ‖	PROPN
ma-172	115	15	)	)	PUNCT
ma-172	115	16	1−	1−	NUM
ma-172	115	17	ϕ0(‖wn	ϕ0(‖wn	SYM
ma-172	115	18	−	−	PROPN
ma-172	115	19	ξ‖	ξ‖	PROPN
ma-172	115	20	,	,	PUNCT
ma-172	115	21	‖sn	‖sn	PROPN
ma-172	115	22	−	−	PROPN
ma-172	115	23	ξ‖	ξ‖	PROPN
ma-172	115	24	)	)	PUNCT
ma-172	116	1	=	=	SYM
ma-172	116	2	εn	εn	ADJ
ma-172	116	3	,	,	PUNCT
ma-172	116	4	‖tn‖	‖tn‖	ADJ
ma-172	116	5	≤	≤	NOUN
ma-172	116	6	|p	|p	NOUN
ma-172	116	7	+	+	CCONJ
ma-172	116	8	q	q	X
ma-172	117	1	+	+	CCONJ
ma-172	117	2	r	r	NOUN
ma-172	118	1	+	+	NOUN
ma-172	118	2	d	d	NOUN
ma-172	118	3	−	−	PROPN
ma-172	118	4	1|+	1|+	NUM
ma-172	118	5	|p	|p	NOUN
ma-172	118	6	+	+	CCONJ
ma-172	118	7	2r	2r	NUM
ma-172	119	1	+	+	CCONJ
ma-172	119	2	3d	3d	NUM
ma-172	119	3	|εn	|εn	X
ma-172	119	4	+	+	NUM
ma-172	119	5	|r	|r	PROPN
ma-172	119	6	+	+	CCONJ
ma-172	119	7	3d	3d	PROPN
ma-172	119	8	|ε2n	|ε2n	NOUN
ma-172	119	9	+	+	CCONJ
ma-172	119	10	|d	|d	NOUN
ma-172	119	11	|ε3n	|ε3n	PROPN
ma-172	119	12	=	=	SYM
ma-172	119	13	λn	λn	NOUN
ma-172	119	14	,	,	PUNCT
ma-172	119	15	leading	lead	VERB
ma-172	119	16	to	to	ADP
ma-172	119	17	‖xn+1	‖xn+1	PROPN
ma-172	119	18	−	−	PROPN
ma-172	119	19	ξ‖	ξ‖	ADJ
ma-172	119	20	≤	≤	PROPN
ma-172	119	21	[	[	PUNCT
ma-172	119	22	ϕ(‖zn	ϕ(‖zn	NUM
ma-172	119	23	−	−	PROPN
ma-172	119	24	ξ‖	ξ‖	PROPN
ma-172	119	25	,	,	PUNCT
ma-172	119	26	‖wn	‖wn	PROPN
ma-172	119	27	−	−	PROPN
ma-172	119	28	ξ‖	ξ‖	ADJ
ma-172	119	29	,	,	PUNCT
ma-172	119	30	‖sn	‖sn	PROPN
ma-172	119	31	−	−	PROPN
ma-172	119	32	ξ‖	ξ‖	PROPN
ma-172	119	33	)	)	PUNCT
ma-172	119	34	1−	1−	NUM
ma-172	119	35	ϕ0(δ1(‖xn	ϕ0(δ1(‖xn	PROPN
ma-172	119	36	−	−	PROPN
ma-172	119	37	ξ‖	ξ‖	PROPN
ma-172	119	38	)	)	PUNCT
ma-172	119	39	,	,	PUNCT
ma-172	119	40	δ2(‖xn	δ2(‖xn	PROPN
ma-172	119	41	−	−	PROPN
ma-172	119	42	ξ‖	ξ‖	PROPN
ma-172	119	43	)	)	PUNCT
ma-172	120	1	+	+	PUNCT
ma-172	121	1	λn(1	λn(1	X
ma-172	121	2	+	+	CCONJ
ma-172	121	3	ϕ2(‖zn	ϕ2(‖zn	ADP
ma-172	121	4	−	−	NOUN
ma-172	121	5	ξ‖	ξ‖	ADJ
ma-172	121	6	)	)	PUNCT
ma-172	121	7	)	)	PUNCT
ma-172	121	8	1−	1−	NUM
ma-172	121	9	ϕ0(δ1(‖xn	ϕ0(δ1(‖xn	PROPN
ma-172	121	10	−	−	PROPN
ma-172	121	11	ξ‖	ξ‖	PROPN
ma-172	121	12	)	)	PUNCT
ma-172	121	13	,	,	PUNCT
ma-172	121	14	δ2(‖xn	δ2(‖xn	PROPN
ma-172	121	15	−	−	PROPN
ma-172	121	16	ξ‖	ξ‖	PROPN
ma-172	121	17	)	)	PUNCT
ma-172	121	18	)	)	PUNCT
ma-172	121	19	]	]	PUNCT
ma-172	122	1	‖zn	‖zn	NUM
ma-172	122	2	−	−	VERB
ma-172	122	3	ξ‖	ξ‖	ADJ
ma-172	122	4	≤	≤	NUM
ma-172	122	5	h3(‖xn	h3(‖xn	NOUN
ma-172	122	6	−	−	PROPN
ma-172	122	7	ξ‖)‖xn	ξ‖)‖xn	PUNCT
ma-172	122	8	−	−	PROPN
ma-172	122	9	ξ‖	ξ‖	NOUN
ma-172	122	10	<	<	X
ma-172	122	11	‖xn	‖xn	PROPN
ma-172	122	12	−	−	PROPN
ma-172	122	13	ξ‖.	ξ‖.	NOUN
ma-172	122	14	hence	hence	ADV
ma-172	122	15	,	,	PUNCT
ma-172	122	16	the	the	DET
ma-172	122	17	iterates	iterate	NOUN
ma-172	122	18	{	{	PUNCT
ma-172	122	19	xn	xn	NUM
ma-172	122	20	}	}	PUNCT
ma-172	122	21	,	,	PUNCT
ma-172	122	22	{	{	PUNCT
ma-172	122	23	yn	yn	X
ma-172	122	24	}	}	PUNCT
ma-172	122	25	,	,	PUNCT
ma-172	122	26	{	{	PUNCT
ma-172	122	27	zn	zn	X
ma-172	122	28	}	}	PUNCT
ma-172	122	29	⊂	⊂	PROPN
ma-172	122	30	s(ξ	s(ξ	PROPN
ma-172	122	31	,	,	PUNCT
ma-172	122	32	r	r	NOUN
ma-172	122	33	)	)	PUNCT
ma-172	122	34	and	and	CCONJ
ma-172	122	35	there	there	PRON
ma-172	122	36	exists	exist	VERB
ma-172	122	37	c	c	NOUN
ma-172	122	38	=	=	SYM
ma-172	122	39	h3(‖x0	h3(‖x0	PROPN
ma-172	122	40	−	−	PROPN
ma-172	122	41	ξ‖	ξ‖	PROPN
ma-172	122	42	)	)	PUNCT
ma-172	122	43	∈	∈	PROPN
ma-172	123	1	[	[	X
ma-172	123	2	0	0	NUM
ma-172	123	3	,	,	PUNCT
ma-172	123	4	1	1	NUM
ma-172	123	5	)	)	PUNCT
ma-172	123	6	such	such	ADJ
ma-172	123	7	that	that	SCONJ
ma-172	123	8	‖xn+1	‖xn+1	NUM
ma-172	123	9	−	−	NOUN
ma-172	123	10	ξ‖	ξ‖	ADJ
ma-172	123	11	≤	≤	PUNCT
ma-172	123	12	c‖xn	c‖xn	PROPN
ma-172	123	13	−	−	PROPN
ma-172	123	14	ξ‖	ξ‖	NOUN
ma-172	123	15	<	<	X
ma-172	123	16	r	r	X
ma-172	123	17	,	,	PUNCT
ma-172	123	18	from	from	ADP
ma-172	123	19	which	which	PRON
ma-172	123	20	it	it	PRON
ma-172	123	21	follows	follow	VERB
ma-172	124	1	that	that	SCONJ
ma-172	124	2	limn→∞	limn→∞	PROPN
ma-172	124	3	xn	xn	X
ma-172	124	4	=	=	PUNCT
ma-172	125	1	ξ.therefore	ξ.therefore	ADV
ma-172	125	2	,	,	PUNCT
ma-172	125	3	we	we	PRON
ma-172	125	4	achieve	achieve	VERB
ma-172	125	5	the	the	DET
ma-172	125	6	following	follow	VERB
ma-172	125	7	local	local	ADJ
ma-172	125	8	convergence	convergence	NOUN
ma-172	125	9	result	result	NOUN
ma-172	125	10	for	for	ADP
ma-172	125	11	the	the	DET
ma-172	125	12	method	method	NOUN
ma-172	125	13	(	(	PUNCT
ma-172	125	14	2	2	NUM
ma-172	125	15	)	)	PUNCT
ma-172	125	16	.	.	PUNCT
ma-172	126	1	theorem	theorem	VERB
ma-172	126	2	2.1	2.1	NUM
ma-172	126	3	.	.	PUNCT
ma-172	127	1	under	under	ADP
ma-172	127	2	the	the	DET
ma-172	127	3	assumptions	assumption	NOUN
ma-172	127	4	(	(	PUNCT
ma-172	127	5	c1)-(c5	c1)-(c5	NOUN
ma-172	127	6	)	)	PUNCT
ma-172	127	7	,	,	PUNCT
ma-172	127	8	{	{	PUNCT
ma-172	127	9	xn	xn	X
ma-172	127	10	}	}	PUNCT
ma-172	127	11	⊂	⊂	PROPN
ma-172	127	12	s(ξ	s(ξ	PROPN
ma-172	127	13	,	,	PUNCT
ma-172	127	14	r	r	NOUN
ma-172	127	15	)	)	PUNCT
ma-172	127	16	and	and	CCONJ
ma-172	127	17	limn→+∞	limn→+∞	ADP
ma-172	127	18	xn	xn	PROPN
ma-172	127	19	=	=	SYM
ma-172	127	20	ξ	ξ	PROPN
ma-172	127	21	provided	provide	VERB
ma-172	127	22	that	that	SCONJ
ma-172	127	23	x0	x0	PROPN
ma-172	127	24	∈	∈	PROPN
ma-172	127	25	s(ξ	s(ξ	PROPN
ma-172	127	26	,	,	PUNCT
ma-172	127	27	r)−	r)−	PROPN
ma-172	127	28	{	{	PUNCT
ma-172	127	29	ξ	ξ	NOUN
ma-172	127	30	}	}	PUNCT
ma-172	127	31	.	.	PUNCT
ma-172	128	1	remark	remark	PROPN
ma-172	128	2	2.2	2.2	NUM
ma-172	128	3	.	.	PUNCT
ma-172	129	1	the	the	DET
ma-172	129	2	functions	function	NOUN
ma-172	129	3	δj	δj	VERB
ma-172	129	4	,	,	PUNCT
ma-172	129	5	j	j	PROPN
ma-172	129	6	=	=	SYM
ma-172	129	7	1	1	NUM
ma-172	129	8	,	,	PUNCT
ma-172	129	9	2	2	NUM
ma-172	129	10	,	,	PUNCT
ma-172	129	11	3	3	NUM
ma-172	129	12	,	,	PUNCT
ma-172	129	13	4	4	NUM
ma-172	129	14	are	be	AUX
ma-172	129	15	left	leave	VERB
ma-172	129	16	uncluttered	uncluttered	ADJ
ma-172	129	17	in	in	ADP
ma-172	129	18	the	the	DET
ma-172	129	19	theorem	theorem	ADJ
ma-172	129	20	2.1	2.1	NUM
ma-172	129	21	.	.	PUNCT
ma-172	130	1	a	a	DET
ma-172	130	2	possible	possible	ADJ
ma-172	130	3	choice	choice	NOUN
ma-172	130	4	for	for	ADP
ma-172	130	5	the	the	DET
ma-172	130	6	first	first	ADJ
ma-172	130	7	function	function	NOUN
ma-172	130	8	δ1	δ1	NOUN
ma-172	130	9	is	be	AUX
ma-172	130	10	motivated	motivate	VERB
ma-172	130	11	by	by	ADP
ma-172	130	12	the	the	DET
ma-172	130	13	estimate	estimate	NOUN
ma-172	130	14	w	w	ADP
ma-172	130	15	−	−	NOUN
ma-172	131	1	ξ	ξ	X
ma-172	132	1	=	=	PUNCT
ma-172	132	2	x	x	X
ma-172	132	3	−	−	PROPN
ma-172	132	4	ξ	ξ	X
ma-172	132	5	+	+	NUM
ma-172	132	6	af	af	PROPN
ma-172	132	7	(	(	PUNCT
ma-172	132	8	x	x	NOUN
ma-172	132	9	)	)	PUNCT
ma-172	132	10	=	=	SYM
ma-172	132	11	(	(	PUNCT
ma-172	132	12	i	i	PRON
ma-172	132	13	+	+	SYM
ma-172	132	14	a[x	a[x	NOUN
ma-172	132	15	,	,	PUNCT
ma-172	132	16	ξ;f	ξ;f	NUM
ma-172	132	17	]	]	PUNCT
ma-172	132	18	)	)	PUNCT
ma-172	132	19	(	(	PUNCT
ma-172	132	20	x	x	X
ma-172	132	21	−	−	PUNCT
ma-172	132	22	ξ	ξ	X
ma-172	132	23	)	)	PUNCT
ma-172	132	24	=	=	SYM
ma-172	133	1	(	(	PUNCT
ma-172	133	2	i	i	PRON
ma-172	133	3	+	+	CCONJ
ma-172	133	4	app−1([x	app−1([x	ADJ
ma-172	133	5	,	,	PUNCT
ma-172	133	6	ξ;g]−p	ξ;g]−p	INTJ
ma-172	133	7	+	+	ADJ
ma-172	133	8	p))(x	p))(x	PROPN
ma-172	133	9	−	−	PROPN
ma-172	133	10	ξ	ξ	NOUN
ma-172	133	11	)	)	PUNCT
ma-172	133	12	,	,	PUNCT
ma-172	133	13	=	=	PUNCT
ma-172	134	1	[	[	X
ma-172	134	2	(	(	PUNCT
ma-172	134	3	i	i	PRON
ma-172	134	4	+	+	X
ma-172	134	5	ap	ap	PROPN
ma-172	134	6	)	)	PUNCT
ma-172	135	1	+	+	CCONJ
ma-172	135	2	app−1([x	app−1([x	ADJ
ma-172	135	3	,	,	PUNCT
ma-172	135	4	ξ;g]−p)](x	ξ;g]−p)](x	NOUN
ma-172	135	5	−	−	NUM
ma-172	135	6	ξ	ξ	NOUN
ma-172	135	7	)	)	PUNCT
ma-172	135	8	,	,	PUNCT
ma-172	135	9	‖w	‖w	VERB
ma-172	135	10	−	−	PROPN
ma-172	136	1	ξ‖	ξ‖	ADJ
ma-172	136	2	≤	≤	NOUN
ma-172	137	1	[	[	PUNCT
ma-172	137	2	‖i	‖i	NOUN
ma-172	137	3	+	+	CCONJ
ma-172	137	4	ap‖+	ap‖+	PROPN
ma-172	137	5	|a|‖p‖ϕ0(‖x	|a|‖p‖ϕ0(‖x	CCONJ
ma-172	137	6	−	−	PROPN
ma-172	137	7	ξ‖)]‖x	ξ‖)]‖x	NOUN
ma-172	137	8	−	−	PROPN
ma-172	137	9	ξ‖.	ξ‖.	NOUN
ma-172	137	10	thus	thus	ADV
ma-172	137	11	,	,	PUNCT
ma-172	137	12	we	we	PRON
ma-172	137	13	can	can	AUX
ma-172	137	14	choose	choose	VERB
ma-172	137	15	δ1(t	δ1(t	PART
ma-172	137	16	)	)	PUNCT
ma-172	137	17	=	=	PUNCT
ma-172	138	1	[	[	X
ma-172	138	2	‖i	‖i	NOUN
ma-172	138	3	+	+	SYM
ma-172	138	4	ap‖+	ap‖+	PROPN
ma-172	138	5	|a|‖p‖ϕ0(t)]t	|a|‖p‖ϕ0(t)]t	NUM
ma-172	138	6	.	.	PUNCT
ma-172	139	1	similarly	similarly	ADV
ma-172	139	2	,	,	PUNCT
ma-172	139	3	we	we	PRON
ma-172	139	4	can	can	AUX
ma-172	139	5	choose	choose	VERB
ma-172	139	6	δ2(t	δ2(t	X
ma-172	139	7	)	)	PUNCT
ma-172	139	8	=	=	PUNCT
ma-172	140	1	[	[	X
ma-172	140	2	‖i	‖i	NOUN
ma-172	140	3	−	−	NOUN
ma-172	140	4	ap‖+	ap‖+	NOUN
ma-172	140	5	|a|‖p‖ϕ0(t)]t	|a|‖p‖ϕ0(t)]t	NUM
ma-172	140	6	,	,	PUNCT
ma-172	140	7	δ3(t	δ3(t	PROPN
ma-172	140	8	)	)	PUNCT
ma-172	140	9	=	=	NOUN
ma-172	141	1	[	[	X
ma-172	141	2	‖i	‖i	X
ma-172	141	3	+	+	NOUN
ma-172	141	4	bp‖+	bp‖+	NOUN
ma-172	141	5	|b|‖p‖ϕ0(h2(t)t)]h2(t)t	|b|‖p‖ϕ0(h2(t)t)]h2(t)t	NOUN
ma-172	141	6	and	and	CCONJ
ma-172	141	7	δ4(t	δ4(t	NUM
ma-172	141	8	)	)	PUNCT
ma-172	141	9	=	=	NOUN
ma-172	142	1	[	[	X
ma-172	142	2	‖i	‖i	NOUN
ma-172	142	3	−	−	NOUN
ma-172	142	4	bp‖+	bp‖+	PROPN
ma-172	142	5	|b|‖p‖ϕ0(h2(t)t)]h2(t)t	|b|‖p‖ϕ0(h2(t)t)]h2(t)t	NOUN
ma-172	142	6	.	.	PUNCT
ma-172	143	1	two	two	NUM
ma-172	143	2	possible	possible	ADJ
ma-172	143	3	choices	choice	NOUN
ma-172	143	4	for	for	ADP
ma-172	143	5	the	the	DET
ma-172	143	6	linear	linear	ADJ
ma-172	143	7	operator	operator	NOUN
ma-172	143	8	p	p	NOUN
ma-172	143	9	are	be	AUX
ma-172	143	10	:	:	PUNCT
ma-172	143	11	the	the	DET
ma-172	143	12	differentiable	differentiable	ADJ
ma-172	143	13	option	option	NOUN
ma-172	143	14	:	:	PUNCT
ma-172	143	15	p	p	X
ma-172	143	16	=	=	PUNCT
ma-172	143	17	g′(ξ	g′(ξ	NOUN
ma-172	143	18	)	)	PUNCT
ma-172	143	19	and	and	CCONJ
ma-172	143	20	the	the	DET
ma-172	143	21	non	non	ADJ
ma-172	143	22	-	-	ADJ
ma-172	143	23	differentiable	differentiable	ADJ
ma-172	143	24	option	option	NOUN
ma-172	143	25	:	:	PUNCT
ma-172	143	26	p	p	X
ma-172	144	1	=	=	PUNCT
ma-172	145	1	[	[	X
ma-172	145	2	x0	x0	PROPN
ma-172	145	3	,	,	PUNCT
ma-172	145	4	x−1;g	x−1;g	PROPN
ma-172	145	5	]	]	PUNCT
ma-172	145	6	.	.	PUNCT
ma-172	146	1	other	other	ADJ
ma-172	146	2	choices	choice	NOUN
ma-172	146	3	are	be	AUX
ma-172	146	4	possible	possible	ADJ
ma-172	146	5	[	[	X
ma-172	146	6	18	18	NUM
ma-172	146	7	]	]	PUNCT
ma-172	146	8	.	.	PUNCT
ma-172	147	1	https://doi.org/10.28924/ada/ma.3.19	https://doi.org/10.28924/ada/ma.3.19	PROPN
ma-172	147	2	eur	eur	PROPN
ma-172	147	3	.	.	PUNCT
ma-172	148	1	j.	j.	PROPN
ma-172	148	2	math	math	PROPN
ma-172	148	3	.	.	PUNCT
ma-172	149	1	anal	anal	PROPN
ma-172	149	2	.	.	PUNCT
ma-172	150	1	10.28924	10.28924	NUM
ma-172	150	2	/	/	SYM
ma-172	150	3	ada	ada	PROPN
ma-172	150	4	/	/	SYM
ma-172	150	5	ma.3.19	ma.3.19	PROPN
ma-172	150	6	63	63	NUM
ma-172	150	7	.	.	PUNCT
ma-172	151	1	convergence	convergence	NOUN
ma-172	151	2	2	2	NUM
ma-172	151	3	:	:	PUNCT
ma-172	151	4	semi	semi	ADJ
ma-172	151	5	-	-	ADJ
ma-172	151	6	local	local	ADJ
ma-172	151	7	the	the	DET
ma-172	151	8	role	role	NOUN
ma-172	151	9	of	of	ADP
ma-172	151	10	ξ	ξ	PROPN
ma-172	151	11	,	,	PUNCT
ma-172	151	12	“	"	PUNCT
ma-172	151	13	ϕ	ϕ	NOUN
ma-172	151	14	”	"	PUNCT
ma-172	151	15	is	be	AUX
ma-172	151	16	replaced	replace	VERB
ma-172	151	17	by	by	ADP
ma-172	151	18	x0	x0	PROPN
ma-172	151	19	,	,	PUNCT
ma-172	151	20	“	"	PUNCT
ma-172	151	21	ψ	ψ	NOUN
ma-172	151	22	”	"	PUNCT
ma-172	151	23	as	as	SCONJ
ma-172	151	24	follows	follow	VERB
ma-172	151	25	.	.	PUNCT
ma-172	152	1	assume:(h1	assume:(h1	X
ma-172	152	2	)	)	PUNCT
ma-172	152	3	there	there	PRON
ma-172	152	4	exist	exist	VERB
ma-172	152	5	cnf	cnf	NOUN
ma-172	152	6	ψ0	ψ0	ADV
ma-172	152	7	:	:	PUNCT
ma-172	152	8	m	m	VERB
ma-172	152	9	×	×	NOUN
ma-172	152	10	m	m	INTJ
ma-172	152	11	→	→	SYM
ma-172	152	12	m	m	PROPN
ma-172	152	13	,	,	PUNCT
ma-172	152	14	x0	x0	PROPN
ma-172	152	15	∈	∈	PROPN
ma-172	152	16	b	b	PROPN
ma-172	152	17	,	,	PUNCT
ma-172	152	18	g1	g1	PROPN
ma-172	152	19	:	:	PUNCT
ma-172	152	20	m	m	VERB
ma-172	152	21	→	→	SYM
ma-172	152	22	m	m	PROPN
ma-172	152	23	,	,	PUNCT
ma-172	152	24	g2	g2	PROPN
ma-172	152	25	:	:	PUNCT
ma-172	152	26	m	m	VERB
ma-172	152	27	→	→	SYM
ma-172	152	28	m	m	PROPN
ma-172	152	29	and	and	CCONJ
ma-172	152	30	a	a	DET
ma-172	152	31	linearoperator	linearoperator	NOUN
ma-172	152	32	p	p	NOUN
ma-172	152	33	such	such	ADJ
ma-172	152	34	that	that	PRON
ma-172	152	35	for	for	ADP
ma-172	152	36	x	x	PROPN
ma-172	152	37	∈	∈	PROPN
ma-172	152	38	b	b	PROPN
ma-172	152	39	w	w	NOUN
ma-172	152	40	=	=	PUNCT
ma-172	152	41	x	x	X
ma-172	152	42	+	+	X
ma-172	152	43	ag(x	ag(x	NOUN
ma-172	152	44	)	)	PUNCT
ma-172	152	45	,	,	PUNCT
ma-172	152	46	s	s	VERB
ma-172	152	47	=	=	PUNCT
ma-172	152	48	x	x	SYM
ma-172	152	49	−	−	NOUN
ma-172	152	50	ag(x	ag(x	NUM
ma-172	152	51	)	)	PUNCT
ma-172	152	52	,	,	PUNCT
ma-172	152	53	‖w	‖w	VERB
ma-172	152	54	−	−	PROPN
ma-172	152	55	x0‖	x0‖	PROPN
ma-172	152	56	≤	≤	PROPN
ma-172	153	1	g1(‖x	g1(‖x	ADP
ma-172	153	2	−	−	PROPN
ma-172	153	3	x0‖	x0‖	PROPN
ma-172	153	4	)	)	PUNCT
ma-172	153	5	,	,	PUNCT
ma-172	153	6	‖s	‖s	ADJ
ma-172	153	7	−	−	PROPN
ma-172	153	8	x0‖	x0‖	PROPN
ma-172	153	9	≤	≤	PROPN
ma-172	153	10	g2(‖x	g2(‖x	PROPN
ma-172	153	11	−	−	PROPN
ma-172	153	12	x0‖	x0‖	PROPN
ma-172	153	13	)	)	PUNCT
ma-172	153	14	‖p−1([w	‖p−1([w	NOUN
ma-172	153	15	,	,	PUNCT
ma-172	153	16	s;g]−p)‖	s;g]−p)‖	PROPN
ma-172	153	17	≤	≤	VERB
ma-172	153	18	ψ0(‖w	ψ0(‖w	X
ma-172	153	19	−	−	PROPN
ma-172	153	20	x0‖	x0‖	PROPN
ma-172	153	21	,	,	PUNCT
ma-172	153	22	‖s	‖s	ADJ
ma-172	153	23	−	−	PROPN
ma-172	153	24	x0‖	x0‖	PROPN
ma-172	153	25	)	)	PUNCT
ma-172	153	26	.	.	PUNCT
ma-172	154	1	(	(	PUNCT
ma-172	154	2	h2	h2	NOUN
ma-172	154	3	)	)	PUNCT
ma-172	154	4	the	the	DET
ma-172	154	5	equation	equation	NOUN
ma-172	154	6	ψ0(g1(t	ψ0(g1(t	PUNCT
ma-172	154	7	)	)	PUNCT
ma-172	154	8	,	,	PUNCT
ma-172	154	9	g2(t))−	g2(t))−	NOUN
ma-172	154	10	1	1	NUM
ma-172	154	11	=	=	SYM
ma-172	154	12	0	0	NUM
ma-172	154	13	has	have	VERB
ma-172	154	14	a	a	DET
ma-172	154	15	smallest	small	ADJ
ma-172	154	16	positive	positive	ADJ
ma-172	154	17	solution	solution	NOUN
ma-172	154	18	denoted	denote	VERB
ma-172	154	19	by	by	ADP
ma-172	154	20	ρ.let	ρ.let	PROPN
ma-172	154	21	m2	m2	PROPN
ma-172	154	22	=	=	PUNCT
ma-172	155	1	[	[	X
ma-172	155	2	0	0	NUM
ma-172	155	3	,	,	PUNCT
ma-172	155	4	ρ	ρ	NOUN
ma-172	155	5	)	)	PUNCT
ma-172	155	6	and	and	CCONJ
ma-172	155	7	b1	b1	NOUN
ma-172	155	8	=	=	SYM
ma-172	155	9	b	b	PROPN
ma-172	155	10	∩	∩	X
ma-172	155	11	s(x0	s(x0	NOUN
ma-172	155	12	,	,	PUNCT
ma-172	155	13	ρ).notice	ρ).notice	PROPN
ma-172	155	14	that	that	DET
ma-172	155	15	‖p−1([w0	‖p−1([w0	NOUN
ma-172	155	16	,	,	PUNCT
ma-172	155	17	s0;g]−p)‖	s0;g]−p)‖	VERB
ma-172	155	18	≤	≤	PROPN
ma-172	156	1	ψ(0	ψ(0	PROPN
ma-172	156	2	,	,	PUNCT
ma-172	156	3	0	0	NUM
ma-172	156	4	)	)	PUNCT
ma-172	156	5	<	<	X
ma-172	156	6	1.thus	1.thus	NUM
ma-172	156	7	,	,	PUNCT
ma-172	156	8	a−10	a−10	PROPN
ma-172	156	9	∈	∈	PROPN
ma-172	156	10	w	w	PROPN
ma-172	156	11	(	(	PUNCT
ma-172	156	12	u	u	NOUN
ma-172	156	13	)	)	PUNCT
ma-172	156	14	and	and	CCONJ
ma-172	156	15	the	the	DET
ma-172	156	16	iterate	iterate	NOUN
ma-172	156	17	y0	y0	NOUN
ma-172	156	18	is	be	AUX
ma-172	156	19	well	well	ADV
ma-172	156	20	-	-	PUNCT
ma-172	156	21	defined	define	VERB
ma-172	156	22	by	by	ADP
ma-172	156	23	the	the	DET
ma-172	156	24	first	first	ADJ
ma-172	156	25	sub	sub	NOUN
ma-172	156	26	-	-	NOUN
ma-172	156	27	step	step	NOUN
ma-172	156	28	of	of	ADP
ma-172	156	29	the	the	DET
ma-172	156	30	method(2	method(2	NOUN
ma-172	156	31	)	)	PUNCT
ma-172	156	32	.	.	PUNCT
ma-172	157	1	(	(	PUNCT
ma-172	157	2	h3	h3	NOUN
ma-172	157	3	)	)	PUNCT
ma-172	157	4	there	there	PRON
ma-172	157	5	exists	exist	VERB
ma-172	157	6	cnf	cnf	PROPN
ma-172	157	7	g3	g3	PROPN
ma-172	157	8	:	:	PUNCT
ma-172	157	9	m2	m2	PROPN
ma-172	157	10	→	→	SYM
ma-172	157	11	m	m	PROPN
ma-172	157	12	,	,	PUNCT
ma-172	157	13	g4	g4	NOUN
ma-172	157	14	:	:	PUNCT
ma-172	157	15	m2	m2	PROPN
ma-172	157	16	→	→	SYM
ma-172	157	17	m	m	PROPN
ma-172	157	18	,	,	PUNCT
ma-172	157	19	ψ1	ψ1	NOUN
ma-172	157	20	,	,	PUNCT
ma-172	157	21	ψ2	ψ2	NOUN
ma-172	157	22	:	:	PUNCT
ma-172	158	1	m2	m2	PROPN
ma-172	158	2	×m2	×m2	NOUN
ma-172	158	3	×m2	×m2	NOUN
ma-172	158	4	×m2	×m2	NOUN
ma-172	158	5	→	→	SYM
ma-172	158	6	m	m	AUX
ma-172	158	7	suchthat	suchthat	ADJ
ma-172	158	8	for	for	ADP
ma-172	158	9	each	each	DET
ma-172	158	10	x	x	NOUN
ma-172	158	11	,	,	PUNCT
ma-172	158	12	y	y	PROPN
ma-172	158	13	∈	∈	PROPN
ma-172	158	14	b1	b1	PROPN
ma-172	158	15	‖u	‖u	PROPN
ma-172	158	16	−	−	PROPN
ma-172	158	17	x0‖	x0‖	PROPN
ma-172	158	18	≤	≤	PROPN
ma-172	158	19	g3(‖z	g3(‖z	PROPN
ma-172	158	20	−	−	PROPN
ma-172	158	21	x0‖	x0‖	PROPN
ma-172	158	22	,	,	PUNCT
ma-172	158	23	‖v	‖v	NOUN
ma-172	158	24	−	−	PROPN
ma-172	158	25	x0‖	x0‖	PROPN
ma-172	158	26	≤	≤	PROPN
ma-172	159	1	g4(‖z	g4(‖z	PROPN
ma-172	159	2	−	−	PROPN
ma-172	159	3	x0‖	x0‖	PROPN
ma-172	159	4	)	)	PUNCT
ma-172	159	5	‖p−1([y	‖p−1([y	NOUN
ma-172	159	6	,	,	PUNCT
ma-172	159	7	x	x	X
ma-172	159	8	;	;	PUNCT
ma-172	159	9	g]−	g]−	VERB
ma-172	159	10	[	[	X
ma-172	159	11	w	w	NOUN
ma-172	159	12	,	,	PUNCT
ma-172	159	13	s;g])‖	s;g])‖	ADJ
ma-172	159	14	≤	≤	NUM
ma-172	159	15	ψ1(‖x	ψ1(‖x	PROPN
ma-172	159	16	−	−	PROPN
ma-172	159	17	x0‖	x0‖	PROPN
ma-172	159	18	,	,	PUNCT
ma-172	159	19	‖y	‖y	PUNCT
ma-172	160	1	−	−	PROPN
ma-172	160	2	x0‖	x0‖	PROPN
ma-172	160	3	,	,	PUNCT
ma-172	160	4	‖w	‖w	VERB
ma-172	160	5	−	−	PROPN
ma-172	160	6	x0‖	x0‖	PROPN
ma-172	160	7	,	,	PUNCT
ma-172	160	8	‖s	‖s	ADJ
ma-172	160	9	−	−	PROPN
ma-172	161	1	x0‖)and	x0‖)and	NUM
ma-172	162	1	‖p−1([w	‖p−1([w	NOUN
ma-172	162	2	,	,	PUNCT
ma-172	162	3	s;g]−	s;g]−	VERB
ma-172	163	1	[	[	X
ma-172	163	2	u	u	NOUN
ma-172	163	3	,	,	PUNCT
ma-172	163	4	v	v	NOUN
ma-172	163	5	;	;	PUNCT
ma-172	163	6	g])‖	g])‖	ADJ
ma-172	163	7	≤	≤	NUM
ma-172	163	8	ψ2(‖w	ψ2(‖w	NOUN
ma-172	163	9	−	−	PROPN
ma-172	163	10	x0‖	x0‖	PROPN
ma-172	163	11	,	,	PUNCT
ma-172	163	12	‖s	‖s	ADJ
ma-172	163	13	−	−	PROPN
ma-172	163	14	x0‖	x0‖	PROPN
ma-172	163	15	,	,	PUNCT
ma-172	163	16	‖u	‖u	PROPN
ma-172	163	17	−	−	PROPN
ma-172	163	18	x0‖	x0‖	PROPN
ma-172	163	19	,	,	PUNCT
ma-172	163	20	‖v	‖v	NOUN
ma-172	163	21	−	−	PROPN
ma-172	163	22	x0‖	x0‖	PROPN
ma-172	163	23	)	)	PUNCT
ma-172	163	24	.	.	PUNCT
ma-172	164	1	define	define	VERB
ma-172	164	2	the	the	DET
ma-172	164	3	real	real	ADJ
ma-172	164	4	sequence	sequence	NOUN
ma-172	164	5	{	{	PUNCT
ma-172	164	6	αn	αn	NOUN
ma-172	164	7	}	}	PUNCT
ma-172	164	8	for	for	ADP
ma-172	164	9	α0	α0	ADJ
ma-172	164	10	=	=	SYM
ma-172	164	11	0	0	NUM
ma-172	164	12	,	,	PUNCT
ma-172	164	13	β0	β0	ADJ
ma-172	164	14	≥	≥	NOUN
ma-172	164	15	‖a−10	‖a−10	PROPN
ma-172	164	16	g(x0)‖	g(x0)‖	PROPN
ma-172	164	17	,	,	PUNCT
ma-172	164	18	and	and	CCONJ
ma-172	164	19	each	each	DET
ma-172	164	20	n	n	NOUN
ma-172	164	21	=	=	SYM
ma-172	164	22	0	0	NUM
ma-172	164	23	,	,	PUNCT
ma-172	164	24	1	1	NUM
ma-172	164	25	,	,	PUNCT
ma-172	164	26	2	2	NUM
ma-172	164	27	,	,	PUNCT
ma-172	164	28	.	.	PUNCT
ma-172	164	29	.	.	PUNCT
ma-172	164	30	.	.	PUNCT
ma-172	165	1	by	by	ADP
ma-172	165	2	γn	γn	NOUN
ma-172	165	3	=	=	PUNCT
ma-172	165	4	βn	βn	PROPN
ma-172	165	5	+	+	CCONJ
ma-172	165	6	ψ1(αn	ψ1(αn	PROPN
ma-172	165	7	,	,	PUNCT
ma-172	165	8	βn	βn	NOUN
ma-172	165	9	,	,	PUNCT
ma-172	165	10	g1(αn	g1(αn	PROPN
ma-172	165	11	)	)	PUNCT
ma-172	165	12	,	,	PUNCT
ma-172	165	13	g2(αn))(βn	g2(αn))(βn	NOUN
ma-172	165	14	−	−	NOUN
ma-172	165	15	αn	αn	NOUN
ma-172	165	16	)	)	PUNCT
ma-172	165	17	1−	1−	NUM
ma-172	165	18	ψ0(g1(αn	ψ0(g1(αn	NOUN
ma-172	165	19	)	)	PUNCT
ma-172	165	20	,	,	PUNCT
ma-172	165	21	g2(αn	g2(αn	PROPN
ma-172	165	22	)	)	PUNCT
ma-172	165	23	)	)	PUNCT
ma-172	165	24	,	,	PUNCT
ma-172	165	25	εn,1	εn,1	PROPN
ma-172	165	26	=	=	PUNCT
ma-172	165	27	ψ2(g1(αn	ψ2(g1(αn	NUM
ma-172	165	28	)	)	PUNCT
ma-172	165	29	,	,	PUNCT
ma-172	165	30	g2(αn	g2(αn	PROPN
ma-172	165	31	)	)	PUNCT
ma-172	165	32	,	,	PUNCT
ma-172	165	33	g3(γn	g3(γn	PROPN
ma-172	165	34	)	)	PUNCT
ma-172	165	35	,	,	PUNCT
ma-172	165	36	g4(γn	g4(γn	PROPN
ma-172	165	37	)	)	PUNCT
ma-172	165	38	)	)	PUNCT
ma-172	165	39	1−	1−	NUM
ma-172	165	40	ψ0(g1(αn	ψ0(g1(αn	NOUN
ma-172	165	41	)	)	PUNCT
ma-172	165	42	,	,	PUNCT
ma-172	165	43	g2(αn	g2(αn	PROPN
ma-172	165	44	)	)	PUNCT
ma-172	165	45	)	)	PUNCT
ma-172	165	46	,	,	PUNCT
ma-172	165	47	λn,1	λn,1	PROPN
ma-172	165	48	=	=	PUNCT
ma-172	165	49	|p	|p	PROPN
ma-172	165	50	+	+	PUNCT
ma-172	165	51	q	q	X
ma-172	166	1	+	+	CCONJ
ma-172	166	2	r	r	NOUN
ma-172	167	1	+	+	CCONJ
ma-172	167	2	d	d	NOUN
ma-172	167	3	|+	|+	PRON
ma-172	167	4	|p	|p	PROPN
ma-172	167	5	+	+	CCONJ
ma-172	167	6	2r	2r	NUM
ma-172	168	1	+	+	CCONJ
ma-172	168	2	3d	3d	NUM
ma-172	168	3	|εn,1	|εn,1	PROPN
ma-172	168	4	+	+	NUM
ma-172	168	5	|r	|r	PROPN
ma-172	168	6	+	+	CCONJ
ma-172	168	7	3d	3d	PROPN
ma-172	168	8	|ε2n,1	|ε2n,1	PROPN
ma-172	168	9	+	+	CCONJ
ma-172	168	10	|d	|d	NOUN
ma-172	168	11	|ε3n,1	|ε3n,1	NOUN
ma-172	168	12	,	,	PUNCT
ma-172	168	13	αn+1	αn+1	NUM
ma-172	168	14	=	=	SYM
ma-172	168	15	γn	γn	NOUN
ma-172	168	16	+	+	CCONJ
ma-172	168	17	ψ1(βn	ψ1(βn	PROPN
ma-172	168	18	,	,	PUNCT
ma-172	168	19	γn	γn	NUM
ma-172	168	20	,	,	PUNCT
ma-172	168	21	g1(αn	g1(αn	PROPN
ma-172	168	22	)	)	PUNCT
ma-172	168	23	,	,	PUNCT
ma-172	168	24	g2(αn))(γn	g2(αn))(γn	VERB
ma-172	168	25	−	−	PROPN
ma-172	168	26	βn)λn,1	βn)λn,1	NOUN
ma-172	168	27	1−	1−	NUM
ma-172	168	28	ψ0(g1(αn	ψ0(g1(αn	NOUN
ma-172	168	29	)	)	PUNCT
ma-172	168	30	,	,	PUNCT
ma-172	168	31	g2(αn	g2(αn	PROPN
ma-172	168	32	)	)	PUNCT
ma-172	168	33	,	,	PUNCT
ma-172	168	34	δn+1	δn+1	PROPN
ma-172	168	35	=	=	SYM
ma-172	168	36	ψ1(αn	ψ1(αn	PROPN
ma-172	168	37	,	,	PUNCT
ma-172	168	38	αn+1	αn+1	NUM
ma-172	168	39	,	,	PUNCT
ma-172	168	40	g1(αn	g1(αn	PROPN
ma-172	168	41	)	)	PUNCT
ma-172	168	42	,	,	PUNCT
ma-172	168	43	g2(αn))(αn+1	g2(αn))(αn+1	VERB
ma-172	168	44	−	−	NOUN
ma-172	168	45	αn	αn	NOUN
ma-172	168	46	)	)	PUNCT
ma-172	168	47	+	+	CCONJ
ma-172	168	48	(	(	PUNCT
ma-172	168	49	1	1	NUM
ma-172	168	50	+	+	NUM
ma-172	168	51	ψ0(g1(αn	ψ0(g1(αn	NOUN
ma-172	168	52	)	)	PUNCT
ma-172	168	53	,	,	PUNCT
ma-172	168	54	g2(αn))(αn+1	g2(αn))(αn+1	VERB
ma-172	168	55	−	−	NOUN
ma-172	168	56	βn	βn	NOUN
ma-172	168	57	)	)	PUNCT
ma-172	168	58	βn+1	βn+1	PUNCT
ma-172	169	1	=	=	SYM
ma-172	169	2	αn+1	αn+1	NUM
ma-172	170	1	+	+	CCONJ
ma-172	170	2	δn+1	δn+1	PROPN
ma-172	170	3	1−	1−	NUM
ma-172	170	4	ψ0(g1(αn+1	ψ0(g1(αn+1	NOUN
ma-172	170	5	,	,	PUNCT
ma-172	170	6	g2(αn+1	g2(αn+1	NOUN
ma-172	170	7	)	)	PUNCT
ma-172	170	8	.	.	PUNCT
ma-172	171	1	(	(	PUNCT
ma-172	171	2	3	3	X
ma-172	171	3	)	)	PUNCT
ma-172	171	4	a	a	DET
ma-172	171	5	convergence	convergence	NOUN
ma-172	171	6	set	set	NOUN
ma-172	171	7	of	of	ADP
ma-172	171	8	conditions	condition	NOUN
ma-172	171	9	for	for	ADP
ma-172	171	10	the	the	DET
ma-172	171	11	sequence	sequence	NOUN
ma-172	171	12	{	{	PUNCT
ma-172	171	13	αn	αn	NOUN
ma-172	171	14	}	}	PUNCT
ma-172	171	15	is	be	AUX
ma-172	171	16	given	give	VERB
ma-172	171	17	for	for	ADP
ma-172	171	18	each	each	DET
ma-172	171	19	n	n	NOUN
ma-172	171	20	=	=	SYM
ma-172	171	21	0	0	NUM
ma-172	171	22	,	,	PUNCT
ma-172	171	23	1	1	NUM
ma-172	171	24	,	,	PUNCT
ma-172	171	25	2	2	NUM
ma-172	171	26	,	,	PUNCT
ma-172	171	27	.	.	PUNCT
ma-172	171	28	.	.	PUNCT
ma-172	172	1	..	..	PUNCT
ma-172	172	2	(	(	PUNCT
ma-172	172	3	h4	h4	PROPN
ma-172	172	4	)	)	PUNCT
ma-172	172	5	ψ0(g1(αn	ψ0(g1(αn	NOUN
ma-172	172	6	)	)	PUNCT
ma-172	172	7	,	,	PUNCT
ma-172	172	8	g2(αn	g2(αn	PROPN
ma-172	172	9	)	)	PUNCT
ma-172	172	10	)	)	PUNCT
ma-172	173	1	<	<	X
ma-172	173	2	1	1	NUM
ma-172	173	3	and	and	CCONJ
ma-172	173	4	αn	αn	NOUN
ma-172	173	5	≤	≤	NOUN
ma-172	173	6	α	α	PRON
ma-172	173	7	<	<	X
ma-172	173	8	ρ.it	ρ.it	NOUN
ma-172	173	9	follows	follow	VERB
ma-172	173	10	by	by	ADP
ma-172	173	11	this	this	DET
ma-172	173	12	condition	condition	NOUN
ma-172	173	13	and	and	CCONJ
ma-172	173	14	(	(	PUNCT
ma-172	173	15	3	3	NUM
ma-172	173	16	)	)	PUNCT
ma-172	173	17	that	that	SCONJ
ma-172	173	18	0	0	NUM
ma-172	173	19	≤	≤	NUM
ma-172	173	20	αn	αn	NOUN
ma-172	173	21	≤	≤	NUM
ma-172	173	22	βn	βn	VERB
ma-172	173	23	≤	≤	NUM
ma-172	173	24	γn	γn	ADP
ma-172	173	25	≤	≤	NUM
ma-172	173	26	αn+1	αn+1	NUM
ma-172	173	27	and	and	CCONJ
ma-172	173	28	there	there	PRON
ma-172	173	29	exists	exist	VERB
ma-172	173	30	α∗	α∗	NOUN
ma-172	173	31	∈	∈	PROPN
ma-172	174	1	[	[	X
ma-172	174	2	0	0	NUM
ma-172	174	3	,	,	PUNCT
ma-172	174	4	α	α	NOUN
ma-172	174	5	]	]	PUNCT
ma-172	174	6	such	such	ADJ
ma-172	174	7	that	that	SCONJ
ma-172	174	8	limn→∞	limn→∞	ADJ
ma-172	174	9	αn	αn	NOUN
ma-172	174	10	=	=	SYM
ma-172	174	11	α∗.	α∗.	PROPN
ma-172	174	12	https://doi.org/10.28924/ada/ma.3.19	https://doi.org/10.28924/ada/ma.3.19	NOUN
ma-172	174	13	eur	eur	NOUN
ma-172	174	14	.	.	PUNCT
ma-172	175	1	j.	j.	PROPN
ma-172	175	2	math	math	PROPN
ma-172	175	3	.	.	PUNCT
ma-172	176	1	anal	anal	PROPN
ma-172	176	2	.	.	PUNCT
ma-172	177	1	10.28924	10.28924	NUM
ma-172	177	2	/	/	SYM
ma-172	177	3	ada	ada	PROPN
ma-172	177	4	/	/	SYM
ma-172	177	5	ma.3.19	ma.3.19	PROPN
ma-172	177	6	7and	7and	NUM
ma-172	177	7	(	(	PUNCT
ma-172	177	8	h5	h5	PROPN
ma-172	177	9	)	)	PUNCT
ma-172	177	10	s[x0	s[x0	NOUN
ma-172	177	11	,	,	PUNCT
ma-172	177	12	α	α	PROPN
ma-172	177	13	∗	∗	NOUN
ma-172	177	14	]	]	X
ma-172	178	1	⊂	⊂	PROPN
ma-172	178	2	b.as	b.as	PROPN
ma-172	178	3	in	in	ADP
ma-172	178	4	the	the	DET
ma-172	178	5	local	local	ADJ
ma-172	178	6	case	case	NOUN
ma-172	178	7	the	the	DET
ma-172	178	8	motivation	motivation	NOUN
ma-172	178	9	for	for	ADP
ma-172	178	10	the	the	DET
ma-172	178	11	introduction	introduction	NOUN
ma-172	178	12	of	of	ADP
ma-172	178	13	the	the	DET
ma-172	178	14	sequence	sequence	NOUN
ma-172	178	15	{	{	PUNCT
ma-172	178	16	αn	αn	NOUN
ma-172	178	17	}	}	PUNCT
ma-172	178	18	follows	follow	VERB
ma-172	178	19	in	in	ADP
ma-172	178	20	turn	turn	NOUN
ma-172	178	21	to	to	ADP
ma-172	178	22	formthe	formthe	NOUN
ma-172	178	23	estimates	estimate	NOUN
ma-172	178	24	:	:	PUNCT
ma-172	178	25	zn	zn	PROPN
ma-172	178	26	−	−	PROPN
ma-172	179	1	yn	yn	X
ma-172	179	2	=	=	PUNCT
ma-172	179	3	−a−1n	−a−1n	NUM
ma-172	179	4	g(yn),but	g(yn),but	PROPN
ma-172	179	5	g(yn	g(yn	PROPN
ma-172	179	6	)	)	PUNCT
ma-172	179	7	=	=	SYM
ma-172	180	1	g(yn)−	g(yn)−	NOUN
ma-172	180	2	g(xn)−	g(xn)−	NOUN
ma-172	180	3	an(yn	an(yn	PROPN
ma-172	180	4	−	−	PROPN
ma-172	180	5	xn	xn	X
ma-172	180	6	)	)	PUNCT
ma-172	180	7	=	=	SYM
ma-172	180	8	(	(	PUNCT
ma-172	180	9	[	[	X
ma-172	180	10	yn	yn	X
ma-172	180	11	,	,	PUNCT
ma-172	180	12	xn;g]−	xn;g]−	PUNCT
ma-172	181	1	an)(yn	an)(yn	PROPN
ma-172	181	2	−	−	PUNCT
ma-172	182	1	xn),so	xn),so	PROPN
ma-172	183	1	‖zn	‖zn	NUM
ma-172	183	2	−	−	NOUN
ma-172	183	3	yn‖	yn‖	PROPN
ma-172	183	4	≤	≤	PROPN
ma-172	183	5	ψ1(‖xn	ψ1(‖xn	PUNCT
ma-172	183	6	−	−	PROPN
ma-172	183	7	x0‖	x0‖	PROPN
ma-172	183	8	,	,	PUNCT
ma-172	183	9	‖yn	‖yn	PROPN
ma-172	183	10	−	−	PROPN
ma-172	183	11	x0‖	x0‖	PROPN
ma-172	183	12	,	,	PUNCT
ma-172	183	13	‖wn	‖wn	PRON
ma-172	183	14	−	−	PROPN
ma-172	183	15	x0‖	x0‖	PROPN
ma-172	183	16	,	,	PUNCT
ma-172	183	17	‖sn	‖sn	PROPN
ma-172	183	18	−	−	NOUN
ma-172	183	19	x0‖)‖yn	x0‖)‖yn	PUNCT
ma-172	184	1	−	−	PROPN
ma-172	184	2	xn‖	xn‖	PROPN
ma-172	184	3	1−	1−	NUM
ma-172	184	4	ψ0(‖wn	ψ0(‖wn	SYM
ma-172	184	5	−	−	PROPN
ma-172	184	6	x0‖	x0‖	PROPN
ma-172	184	7	,	,	PUNCT
ma-172	184	8	‖sn	‖sn	PROPN
ma-172	184	9	−	−	PROPN
ma-172	184	10	x0‖	x0‖	PROPN
ma-172	184	11	)	)	PUNCT
ma-172	184	12	≤	≤	NUM
ma-172	184	13	γn	γn	ADP
ma-172	184	14	−	−	PROPN
ma-172	184	15	βn	βn	NOUN
ma-172	184	16	,	,	PUNCT
ma-172	184	17	‖zn	‖zn	PROPN
ma-172	184	18	−	−	NOUN
ma-172	184	19	x0‖	x0‖	PROPN
ma-172	184	20	≤	≤	PROPN
ma-172	185	1	‖zn	‖zn	NUM
ma-172	185	2	−	−	PROPN
ma-172	185	3	yn‖+	yn‖+	PROPN
ma-172	185	4	‖yn	‖yn	PROPN
ma-172	185	5	−	−	PROPN
ma-172	185	6	x0‖	x0‖	PROPN
ma-172	185	7	≤	≤	PROPN
ma-172	185	8	γn	γn	ADP
ma-172	185	9	−	−	PROPN
ma-172	185	10	βn	βn	ADJ
ma-172	185	11	+	+	CCONJ
ma-172	185	12	βn	βn	VERB
ma-172	185	13	−	−	PROPN
ma-172	185	14	α0	α0	PROPN
ma-172	185	15	=	=	SYM
ma-172	185	16	γn	γn	NOUN
ma-172	185	17	<	<	X
ma-172	185	18	a∗	a∗	PROPN
ma-172	185	19	,	,	PUNCT
ma-172	185	20	xn+1	xn+1	NUM
ma-172	185	21	−	−	PROPN
ma-172	185	22	zn	zn	PROPN
ma-172	185	23	=	=	SYM
ma-172	185	24	−tna−1n	−tna−1n	PROPN
ma-172	185	25	g(zn	g(zn	PROPN
ma-172	185	26	)	)	PUNCT
ma-172	185	27	,	,	PUNCT
ma-172	185	28	‖xn+1	‖xn+1	NUM
ma-172	185	29	−	−	PROPN
ma-172	185	30	zn‖	zn‖	PROPN
ma-172	185	31	≤	≤	PROPN
ma-172	185	32	λn,1ψ1(‖yn	λn,1ψ1(‖yn	NOUN
ma-172	185	33	−	−	NOUN
ma-172	185	34	x0‖	x0‖	PROPN
ma-172	185	35	,	,	PUNCT
ma-172	185	36	‖zn	‖zn	PROPN
ma-172	185	37	−	−	NOUN
ma-172	185	38	x0‖	x0‖	PROPN
ma-172	185	39	,	,	PUNCT
ma-172	185	40	‖wn	‖wn	PRON
ma-172	185	41	−	−	PROPN
ma-172	185	42	x0‖	x0‖	PROPN
ma-172	185	43	,	,	PUNCT
ma-172	185	44	‖sn	‖sn	PROPN
ma-172	185	45	−	−	PROPN
ma-172	185	46	x0‖)‖zn	x0‖)‖zn	NUM
ma-172	186	1	−	−	NOUN
ma-172	186	2	yn‖	yn‖	NOUN
ma-172	186	3	1−	1−	NUM
ma-172	186	4	ψ0(‖wn	ψ0(‖wn	NOUN
ma-172	186	5	−	−	PROPN
ma-172	186	6	x0‖	x0‖	PROPN
ma-172	186	7	,	,	PUNCT
ma-172	186	8	‖sn	‖sn	PROPN
ma-172	186	9	−	−	PROPN
ma-172	186	10	x0‖	x0‖	PROPN
ma-172	186	11	)	)	PUNCT
ma-172	186	12	≤	≤	NOUN
ma-172	186	13	αn+1	αn+1	NUM
ma-172	186	14	−	−	NOUN
ma-172	186	15	γn	γn	NOUN
ma-172	186	16	,	,	PUNCT
ma-172	186	17	since	since	SCONJ
ma-172	186	18	tn,1	tn,1	PROPN
ma-172	186	19	=	=	PUNCT
ma-172	186	20	(	(	PUNCT
ma-172	186	21	p	p	X
ma-172	186	22	+	+	NOUN
ma-172	186	23	q	q	NOUN
ma-172	187	1	+	+	CCONJ
ma-172	187	2	r	r	NOUN
ma-172	187	3	+	+	NOUN
ma-172	187	4	d)i	d)i	NOUN
ma-172	188	1	+	+	CCONJ
ma-172	188	2	(	(	PUNCT
ma-172	188	3	q	q	X
ma-172	188	4	+	+	NUM
ma-172	188	5	2r	2r	NUM
ma-172	188	6	+	+	CCONJ
ma-172	188	7	3d)dn	3d)dn	NUM
ma-172	188	8	+	+	CCONJ
ma-172	188	9	(	(	PUNCT
ma-172	188	10	r	r	NOUN
ma-172	188	11	+	+	NUM
ma-172	188	12	3d)d2n	3d)d2n	NOUN
ma-172	188	13	+	+	CCONJ
ma-172	188	14	dd3n	dd3n	PROPN
ma-172	188	15	,	,	PUNCT
ma-172	188	16	‖dn‖	‖dn‖	NOUN
ma-172	188	17	≤	≤	NUM
ma-172	188	18	ψ2(‖wn	ψ2(‖wn	PROPN
ma-172	188	19	−	−	PROPN
ma-172	188	20	x0‖	x0‖	PROPN
ma-172	188	21	,	,	PUNCT
ma-172	188	22	‖sn	‖sn	PROPN
ma-172	188	23	−	−	NOUN
ma-172	188	24	x0‖	x0‖	PROPN
ma-172	188	25	,	,	PUNCT
ma-172	188	26	‖un	‖un	PROPN
ma-172	188	27	−	−	PROPN
ma-172	188	28	x0‖	x0‖	PROPN
ma-172	188	29	,	,	PUNCT
ma-172	188	30	‖vn	‖vn	PROPN
ma-172	188	31	−	−	PROPN
ma-172	188	32	x0‖	x0‖	PROPN
ma-172	188	33	)	)	PUNCT
ma-172	188	34	1−	1−	NUM
ma-172	188	35	ψ0(‖wn	ψ0(‖wn	SYM
ma-172	189	1	−	−	PROPN
ma-172	189	2	x0‖	x0‖	PROPN
ma-172	189	3	,	,	PUNCT
ma-172	189	4	‖sn	‖sn	PROPN
ma-172	189	5	−	−	PROPN
ma-172	189	6	x0‖	x0‖	PROPN
ma-172	189	7	)	)	PUNCT
ma-172	189	8	,	,	PUNCT
ma-172	189	9	‖tn,1‖	‖tn,1‖	PROPN
ma-172	189	10	≤	≤	X
ma-172	189	11	λn,1and	λn,1and	PROPN
ma-172	189	12	‖xn+1	‖xn+1	NUM
ma-172	189	13	−	−	PROPN
ma-172	189	14	x0‖	x0‖	PROPN
ma-172	189	15	≤	≤	PROPN
ma-172	189	16	‖xn+1	‖xn+1	PUNCT
ma-172	189	17	−	−	PROPN
ma-172	189	18	zn‖+	zn‖+	PROPN
ma-172	190	1	‖zn	‖zn	NUM
ma-172	190	2	−	−	PROPN
ma-172	190	3	x0‖	x0‖	PROPN
ma-172	190	4	≤	≤	NUM
ma-172	190	5	αn+1	αn+1	NUM
ma-172	190	6	−	−	NOUN
ma-172	190	7	γn	γn	NOUN
ma-172	190	8	+	+	CCONJ
ma-172	190	9	γn	γn	ADP
ma-172	190	10	−	−	NOUN
ma-172	190	11	α0	α0	ADJ
ma-172	190	12	=	=	SYM
ma-172	190	13	αn+1	αn+1	NUM
ma-172	190	14	<	<	X
ma-172	190	15	α∗.	α∗.	NOUN
ma-172	190	16	also	also	ADV
ma-172	190	17	,	,	PUNCT
ma-172	190	18	g(xn+1	g(xn+1	NOUN
ma-172	190	19	)	)	PUNCT
ma-172	191	1	=	=	SYM
ma-172	191	2	g(xn+1)−	g(xn+1)−	PROPN
ma-172	191	3	g(xn)−	g(xn)−	NOUN
ma-172	191	4	an(yn	an(yn	PROPN
ma-172	191	5	−	−	PROPN
ma-172	191	6	xn	xn	X
ma-172	191	7	)	)	PUNCT
ma-172	192	1	=	=	SYM
ma-172	192	2	g(xn+1)−	g(xn+1)−	PROPN
ma-172	192	3	g(xn)−	g(xn)−	NOUN
ma-172	192	4	an(xn+1	an(xn+1	PROPN
ma-172	192	5	−	−	PROPN
ma-172	192	6	xn	xn	PUNCT
ma-172	192	7	)	)	PUNCT
ma-172	193	1	+	+	CCONJ
ma-172	193	2	an(xn+1	an(xn+1	PROPN
ma-172	193	3	−	−	PROPN
ma-172	193	4	yn	yn	PROPN
ma-172	193	5	)	)	PUNCT
ma-172	193	6	,	,	PUNCT
ma-172	193	7	‖p−1g(xn+1)‖	‖p−1g(xn+1)‖	VERB
ma-172	193	8	≤	≤	PROPN
ma-172	193	9	ψ1(‖xn	ψ1(‖xn	PUNCT
ma-172	194	1	−	−	PROPN
ma-172	194	2	x0‖	x0‖	PROPN
ma-172	194	3	,	,	PUNCT
ma-172	194	4	‖xn+1	‖xn+1	NOUN
ma-172	194	5	−	−	PROPN
ma-172	194	6	x0‖	x0‖	PROPN
ma-172	194	7	,	,	PUNCT
ma-172	194	8	‖wn	‖wn	PRON
ma-172	194	9	−	−	PROPN
ma-172	194	10	x0‖	x0‖	PROPN
ma-172	194	11	,	,	PUNCT
ma-172	194	12	‖sn	‖sn	PROPN
ma-172	194	13	−	−	PROPN
ma-172	194	14	x0‖)‖xn+1	x0‖)‖xn+1	PROPN
ma-172	194	15	−	−	PROPN
ma-172	194	16	xn‖	xn‖	PROPN
ma-172	195	1	+	+	CCONJ
ma-172	195	2	(	(	PUNCT
ma-172	195	3	1	1	NUM
ma-172	195	4	+	+	NUM
ma-172	195	5	ψ0(‖wn	ψ0(‖wn	NOUN
ma-172	195	6	−	−	NOUN
ma-172	195	7	x0‖	x0‖	PROPN
ma-172	195	8	,	,	PUNCT
ma-172	195	9	‖sn	‖sn	PROPN
ma-172	195	10	−	−	PROPN
ma-172	195	11	x0‖))‖xn+1	x0‖))‖xn+1	PROPN
ma-172	195	12	−	−	NOUN
ma-172	195	13	yn‖	yn‖	NOUN
ma-172	195	14	=	=	PUNCT
ma-172	195	15	δ̄n+1	δ̄n+1	NOUN
ma-172	195	16	≤	≤	X
ma-172	195	17	δn+1	δn+1	PROPN
ma-172	195	18	,	,	PUNCT
ma-172	195	19	‖yn+1	‖yn+1	PUNCT
ma-172	195	20	−	−	PROPN
ma-172	195	21	xn+1‖	xn+1‖	PROPN
ma-172	195	22	≤	≤	PROPN
ma-172	195	23	‖a−1n+1p‖‖p	‖a−1n+1p‖‖p	NUM
ma-172	195	24	−1g(xn+1‖	−1g(xn+1‖	NUM
ma-172	195	25	≤	≤	NUM
ma-172	195	26	δ̄n+1	δ̄n+1	NOUN
ma-172	195	27	1−	1−	NUM
ma-172	195	28	ψ0(‖wn+1	ψ0(‖wn+1	PROPN
ma-172	195	29	−	−	PROPN
ma-172	195	30	x0‖	x0‖	PROPN
ma-172	195	31	,	,	PUNCT
ma-172	195	32	‖sn+1	‖sn+1	PUNCT
ma-172	195	33	−	−	PROPN
ma-172	195	34	x0‖	x0‖	PROPN
ma-172	195	35	)	)	PUNCT
ma-172	195	36	≤	≤	NOUN
ma-172	195	37	βn+1	βn+1	PUNCT
ma-172	196	1	−	−	NOUN
ma-172	196	2	αn+1	αn+1	NUM
ma-172	196	3	(	(	PUNCT
ma-172	196	4	4	4	X
ma-172	196	5	)	)	PUNCT
ma-172	196	6	https://doi.org/10.28924/ada/ma.3.19	https://doi.org/10.28924/ada/ma.3.19	NOUN
ma-172	196	7	eur	eur	NOUN
ma-172	196	8	.	.	PUNCT
ma-172	197	1	j.	j.	PROPN
ma-172	197	2	math	math	PROPN
ma-172	197	3	.	.	PUNCT
ma-172	198	1	anal	anal	PROPN
ma-172	198	2	.	.	PUNCT
ma-172	199	1	10.28924	10.28924	NUM
ma-172	199	2	/	/	SYM
ma-172	199	3	ada	ada	PROPN
ma-172	199	4	/	/	SYM
ma-172	199	5	ma.3.19	ma.3.19	PROPN
ma-172	200	1	8and	8and	NUM
ma-172	200	2	‖yn+1	‖yn+1	PUNCT
ma-172	200	3	−	−	PROPN
ma-172	200	4	x0‖	x0‖	PROPN
ma-172	200	5	≤	≤	PROPN
ma-172	200	6	‖yn+1	‖yn+1	PUNCT
ma-172	200	7	−	−	NOUN
ma-172	200	8	xn+1‖+	xn+1‖+	PUNCT
ma-172	200	9	‖xn+1	‖xn+1	NUM
ma-172	201	1	−	−	PROPN
ma-172	201	2	x0‖	x0‖	PROPN
ma-172	201	3	≤	≤	PROPN
ma-172	201	4	βn+1	βn+1	PUNCT
ma-172	201	5	−	−	NOUN
ma-172	201	6	αn+1	αn+1	NUM
ma-172	202	1	+	+	NUM
ma-172	202	2	αn+1	αn+1	NUM
ma-172	202	3	−	−	NOUN
ma-172	202	4	α0	α0	PROPN
ma-172	202	5	=	=	SYM
ma-172	202	6	βn+1	βn+1	PUNCT
ma-172	202	7	<	<	X
ma-172	202	8	α∗.therefore	α∗.therefore	PROPN
ma-172	202	9	,	,	PUNCT
ma-172	202	10	the	the	DET
ma-172	202	11	sequence	sequence	NOUN
ma-172	202	12	{	{	PUNCT
ma-172	202	13	xn	xn	NOUN
ma-172	202	14	}	}	PUNCT
ma-172	202	15	is	be	AUX
ma-172	202	16	complete	complete	ADJ
ma-172	202	17	in	in	ADP
ma-172	202	18	banach	banach	NOUN
ma-172	202	19	space	space	NOUN
ma-172	202	20	u	u	NOUN
ma-172	202	21	.	.	PUNCT
ma-172	203	1	hence	hence	ADV
ma-172	203	2	,	,	PUNCT
ma-172	203	3	there	there	PRON
ma-172	203	4	exists	exist	VERB
ma-172	203	5	ξ	ξ	X
ma-172	203	6	=	=	SYM
ma-172	203	7	limn→∞	limn→∞	ADJ
ma-172	203	8	xnand	xnand	X
ma-172	203	9	by	by	ADP
ma-172	203	10	(	(	PUNCT
ma-172	203	11	4	4	X
ma-172	203	12	)	)	PUNCT
ma-172	203	13	g(ξ	g(ξ	PROPN
ma-172	203	14	)	)	PUNCT
ma-172	204	1	=	=	SYM
ma-172	204	2	0.then	0.then	NUM
ma-172	204	3	,	,	PUNCT
ma-172	204	4	we	we	PRON
ma-172	204	5	achieve	achieve	VERB
ma-172	204	6	the	the	DET
ma-172	204	7	following	follow	VERB
ma-172	204	8	semi	semi	ADJ
ma-172	204	9	-	-	ADJ
ma-172	204	10	local	local	ADJ
ma-172	204	11	convergence	convergence	NOUN
ma-172	204	12	result	result	NOUN
ma-172	204	13	for	for	ADP
ma-172	204	14	the	the	DET
ma-172	204	15	method	method	NOUN
ma-172	204	16	(	(	PUNCT
ma-172	204	17	2	2	NUM
ma-172	204	18	)	)	PUNCT
ma-172	204	19	.	.	PUNCT
ma-172	205	1	theorem	theorem	VERB
ma-172	205	2	3.1	3.1	NUM
ma-172	205	3	.	.	PUNCT
ma-172	206	1	under	under	ADP
ma-172	206	2	the	the	DET
ma-172	206	3	conditions	condition	NOUN
ma-172	206	4	(	(	PUNCT
ma-172	206	5	h1)-(h5	h1)-(h5	ADJ
ma-172	206	6	)	)	PUNCT
ma-172	206	7	the	the	DET
ma-172	206	8	sequence	sequence	NOUN
ma-172	206	9	{	{	PUNCT
ma-172	206	10	xn	xn	NOUN
ma-172	206	11	}	}	PUNCT
ma-172	206	12	converges	converge	NOUN
ma-172	206	13	to	to	ADP
ma-172	206	14	a	a	DET
ma-172	206	15	solution	solution	NOUN
ma-172	206	16	ξ	ξ	X
ma-172	206	17	∈	∈	PROPN
ma-172	206	18	s[x0	s[x0	NOUN
ma-172	206	19	,	,	PUNCT
ma-172	206	20	a	a	DET
ma-172	206	21	∗	∗	NOUN
ma-172	206	22	]	]	PUNCT
ma-172	206	23	of	of	ADP
ma-172	206	24	the	the	DET
ma-172	206	25	equation	equation	NOUN
ma-172	206	26	g(x	g(x	NOUN
ma-172	206	27	)	)	PUNCT
ma-172	207	1	=	=	SYM
ma-172	207	2	0	0	X
ma-172	207	3	.	.	PUNCT
ma-172	207	4	remark	remark	PROPN
ma-172	207	5	3.2	3.2	NUM
ma-172	207	6	.	.	PUNCT
ma-172	208	1	a	a	DET
ma-172	208	2	possible	possible	ADJ
ma-172	208	3	choice	choice	NOUN
ma-172	208	4	for	for	ADP
ma-172	208	5	the	the	DET
ma-172	208	6	functions	function	NOUN
ma-172	208	7	gj	gj	PROPN
ma-172	208	8	,	,	PUNCT
ma-172	208	9	j	j	PROPN
ma-172	208	10	=	=	SYM
ma-172	208	11	1	1	NUM
ma-172	208	12	,	,	PUNCT
ma-172	208	13	2	2	NUM
ma-172	208	14	,	,	PUNCT
ma-172	208	15	3	3	NUM
ma-172	208	16	,	,	PUNCT
ma-172	208	17	4	4	NUM
ma-172	208	18	follows	follow	VERB
ma-172	208	19	as	as	ADP
ma-172	208	20	in	in	ADP
ma-172	208	21	the	the	DET
ma-172	208	22	local	local	ADJ
ma-172	208	23	case	case	NOUN
ma-172	208	24	.	.	PUNCT
ma-172	209	1	we	we	PRON
ma-172	209	2	have	have	VERB
ma-172	209	3	in	in	ADP
ma-172	209	4	turn	turn	NOUN
ma-172	209	5	w	w	ADP
ma-172	209	6	−	−	NOUN
ma-172	209	7	x0	x0	PROPN
ma-172	210	1	=	=	PUNCT
ma-172	210	2	x	x	PUNCT
ma-172	211	1	−	−	PUNCT
ma-172	211	2	x0	x0	PROPN
ma-172	211	3	+	+	CCONJ
ma-172	211	4	a(g(x)−	a(g(x)−	PROPN
ma-172	211	5	g(x0	g(x0	NOUN
ma-172	211	6	)	)	PUNCT
ma-172	211	7	+	+	CCONJ
ma-172	211	8	g(x0	g(x0	NOUN
ma-172	211	9	)	)	PUNCT
ma-172	211	10	)	)	PUNCT
ma-172	212	1	=	=	PUNCT
ma-172	213	1	[	[	X
ma-172	213	2	(	(	PUNCT
ma-172	213	3	i	i	PRON
ma-172	213	4	+	+	X
ma-172	213	5	ap	ap	PROPN
ma-172	213	6	)	)	PUNCT
ma-172	213	7	+	+	CCONJ
ma-172	213	8	app−1([x	app−1([x	ADJ
ma-172	213	9	,	,	PUNCT
ma-172	213	10	x0;g]−p)](x	x0;g]−p)](x	PROPN
ma-172	213	11	−	−	PROPN
ma-172	213	12	x0	x0	PROPN
ma-172	213	13	)	)	PUNCT
ma-172	213	14	+	+	NUM
ma-172	213	15	ag(x0	ag(x0	NOUN
ma-172	213	16	)	)	PUNCT
ma-172	213	17	,	,	PUNCT
ma-172	213	18	lead	lead	VERB
ma-172	213	19	to	to	ADP
ma-172	213	20	the	the	DET
ma-172	213	21	choice	choice	NOUN
ma-172	213	22	g1(t	g1(t	ADP
ma-172	213	23	)	)	PUNCT
ma-172	213	24	=	=	NOUN
ma-172	214	1	[	[	X
ma-172	214	2	‖i	‖i	NOUN
ma-172	214	3	+	+	NUM
ma-172	214	4	ap‖+	ap‖+	NOUN
ma-172	214	5	|a|‖p‖ψ3(t)]t	|a|‖p‖ψ3(t)]t	NOUN
ma-172	214	6	+	+	CCONJ
ma-172	214	7	|a|‖g(x0)‖	|a|‖g(x0)‖	AUX
ma-172	214	8	provided	provide	VERB
ma-172	214	9	that	that	PRON
ma-172	214	10	for	for	ADP
ma-172	214	11	some	some	DET
ma-172	214	12	cnf	cnf	PROPN
ma-172	214	13	ψ3	ψ3	NOUN
ma-172	214	14	:	:	PUNCT
ma-172	214	15	m1	m1	PROPN
ma-172	214	16	→	→	SYM
ma-172	214	17	m	m	PROPN
ma-172	214	18	,	,	PUNCT
ma-172	214	19	x	x	PUNCT
ma-172	214	20	∈	∈	PROPN
ma-172	214	21	b	b	PROPN
ma-172	214	22	‖p−1([x	‖p−1([x	NOUN
ma-172	214	23	,	,	PUNCT
ma-172	214	24	x0;g]−p)‖	x0;g]−p)‖	PROPN
ma-172	214	25	≤	≤	PROPN
ma-172	214	26	ψ3(‖x	ψ3(‖x	PROPN
ma-172	214	27	−	−	PROPN
ma-172	214	28	x0‖	x0‖	PROPN
ma-172	214	29	)	)	PUNCT
ma-172	214	30	.	.	PUNCT
ma-172	215	1	similarly	similarly	ADV
ma-172	215	2	,	,	PUNCT
ma-172	215	3	we	we	PRON
ma-172	215	4	define	define	VERB
ma-172	215	5	g2(t	g2(t	NOUN
ma-172	215	6	)	)	PUNCT
ma-172	215	7	=	=	NOUN
ma-172	216	1	[	[	X
ma-172	216	2	‖i	‖i	NOUN
ma-172	216	3	−	−	NOUN
ma-172	216	4	ap‖+	ap‖+	NOUN
ma-172	216	5	|a|‖p‖ψ3(t)]t	|a|‖p‖ψ3(t)]t	NOUN
ma-172	216	6	+	+	CCONJ
ma-172	216	7	|a|‖g(x0)‖	|a|‖g(x0)‖	NOUN
ma-172	216	8	,	,	PUNCT
ma-172	216	9	g3(t	g3(t	NUM
ma-172	216	10	)	)	PUNCT
ma-172	216	11	=	=	NOUN
ma-172	217	1	[	[	X
ma-172	217	2	‖i	‖i	NOUN
ma-172	217	3	+	+	NOUN
ma-172	217	4	bp‖+	bp‖+	NOUN
ma-172	217	5	|a|‖p‖ψ3(t)]t	|a|‖p‖ψ3(t)]t	NOUN
ma-172	217	6	+	+	CCONJ
ma-172	217	7	|b|‖g(x0)‖	|b|‖g(x0)‖	ADJ
ma-172	217	8	,	,	PUNCT
ma-172	217	9	and	and	CCONJ
ma-172	217	10	g4(t	g4(t	ADJ
ma-172	217	11	)	)	PUNCT
ma-172	217	12	=	=	NOUN
ma-172	218	1	[	[	X
ma-172	218	2	‖i	‖i	NOUN
ma-172	218	3	−	−	NOUN
ma-172	218	4	bp‖+	bp‖+	NOUN
ma-172	218	5	|b|‖p‖ψ3(t)]t	|b|‖p‖ψ3(t)]t	NOUN
ma-172	218	6	+	+	CCONJ
ma-172	218	7	|b|‖g(x0)‖.	|b|‖g(x0)‖.	VERB
ma-172	218	8	the	the	DET
ma-172	218	9	options	option	NOUN
ma-172	218	10	for	for	ADP
ma-172	218	11	p	p	NOUN
ma-172	218	12	are	be	AUX
ma-172	218	13	:	:	PUNCT
ma-172	218	14	p	p	X
ma-172	218	15	=	=	PROPN
ma-172	218	16	g′(x0	g′(x0	NOUN
ma-172	218	17	)	)	PUNCT
ma-172	218	18	or	or	CCONJ
ma-172	218	19	p	p	NOUN
ma-172	218	20	=	=	PUNCT
ma-172	219	1	[	[	X
ma-172	219	2	x0	x0	PROPN
ma-172	219	3	,	,	PUNCT
ma-172	219	4	x−1;g	x−1;g	PROPN
ma-172	219	5	]	]	PUNCT
ma-172	219	6	.	.	PUNCT
ma-172	220	1	other	other	ADJ
ma-172	220	2	options	option	NOUN
ma-172	220	3	exist	exist	VERB
ma-172	220	4	[	[	X
ma-172	220	5	10	10	NUM
ma-172	220	6	]	]	PUNCT
ma-172	220	7	.	.	PUNCT
ma-172	221	1	4	4	X
ma-172	221	2	.	.	X
ma-172	221	3	isolation	isolation	NOUN
ma-172	221	4	of	of	ADP
ma-172	221	5	a	a	DET
ma-172	221	6	solution	solution	NOUN
ma-172	221	7	we	we	PRON
ma-172	221	8	first	first	ADV
ma-172	221	9	present	present	VERB
ma-172	221	10	the	the	DET
ma-172	221	11	uniqueness	uniqueness	NOUN
ma-172	221	12	result	result	NOUN
ma-172	221	13	for	for	ADP
ma-172	221	14	the	the	DET
ma-172	221	15	local	local	ADJ
ma-172	221	16	convergence	convergence	NOUN
ma-172	221	17	case	case	NOUN
ma-172	221	18	.	.	PUNCT
ma-172	222	1	proposition	proposition	NOUN
ma-172	222	2	4.1	4.1	NUM
ma-172	222	3	.	.	PUNCT
ma-172	223	1	there	there	PRON
ma-172	223	2	exists	exist	VERB
ma-172	223	3	a	a	DET
ma-172	223	4	solution	solution	NOUN
ma-172	223	5	v∗	v∗	PROPN
ma-172	223	6	∈	∈	PROPN
ma-172	223	7	s(ξ	s(ξ	PROPN
ma-172	223	8	,	,	PUNCT
ma-172	223	9	ρ2	ρ2	NOUN
ma-172	223	10	)	)	PUNCT
ma-172	223	11	of	of	ADP
ma-172	223	12	the	the	DET
ma-172	223	13	equation	equation	NOUN
ma-172	223	14	g(x	g(x	NOUN
ma-172	223	15	)	)	PUNCT
ma-172	224	1	=	=	SYM
ma-172	224	2	0	0	NUM
ma-172	225	1	for	for	ADP
ma-172	225	2	some	some	DET
ma-172	225	3	ρ2	ρ2	NOUN
ma-172	225	4	>	>	X
ma-172	225	5	0	0	NUM
ma-172	225	6	;	;	PUNCT
ma-172	225	7	the	the	DET
ma-172	225	8	last	last	ADJ
ma-172	225	9	condition	condition	NOUN
ma-172	225	10	in	in	ADP
ma-172	225	11	(	(	PUNCT
ma-172	225	12	c3	c3	PROPN
ma-172	225	13	)	)	PUNCT
ma-172	225	14	holds	hold	VERB
ma-172	225	15	in	in	ADP
ma-172	225	16	the	the	DET
ma-172	225	17	ball	ball	NOUN
ma-172	225	18	s(ξ	s(ξ	PROPN
ma-172	225	19	,	,	PUNCT
ma-172	225	20	ρ2	ρ2	NOUN
ma-172	225	21	)	)	PUNCT
ma-172	225	22	and	and	CCONJ
ma-172	225	23	there	there	PRON
ma-172	225	24	exists	exist	VERB
ma-172	225	25	ρ3	ρ3	NOUN
ma-172	225	26	≥	≥	NUM
ma-172	225	27	ρ2	ρ2	VERB
ma-172	225	28	such	such	ADJ
ma-172	225	29	that	that	DET
ma-172	225	30	ψ2(ρ3	ψ2(ρ3	NOUN
ma-172	225	31	)	)	PUNCT
ma-172	225	32	<	<	X
ma-172	225	33	1	1	NUM
ma-172	225	34	.	.	PUNCT
ma-172	226	1	(	(	PUNCT
ma-172	226	2	5	5	X
ma-172	226	3	)	)	PUNCT
ma-172	226	4	https://doi.org/10.28924/ada/ma.3.19	https://doi.org/10.28924/ada/ma.3.19	NOUN
ma-172	226	5	eur	eur	NOUN
ma-172	226	6	.	.	PUNCT
ma-172	227	1	j.	j.	PROPN
ma-172	227	2	math	math	PROPN
ma-172	227	3	.	.	PUNCT
ma-172	228	1	anal	anal	PROPN
ma-172	228	2	.	.	PUNCT
ma-172	229	1	10.28924	10.28924	NUM
ma-172	229	2	/	/	SYM
ma-172	229	3	ada	ada	PROPN
ma-172	229	4	/	/	SYM
ma-172	229	5	ma.3.19	ma.3.19	PROPN
ma-172	229	6	9	9	NUM
ma-172	229	7	set	set	NOUN
ma-172	229	8	b3	b3	PROPN
ma-172	229	9	=	=	SYM
ma-172	229	10	b	b	PROPN
ma-172	229	11	∩	∩	ADJ
ma-172	229	12	s[ξ	s[ξ	NOUN
ma-172	229	13	,	,	PUNCT
ma-172	229	14	ρ3	ρ3	NOUN
ma-172	229	15	]	]	PUNCT
ma-172	229	16	.	.	PUNCT
ma-172	230	1	then	then	ADV
ma-172	230	2	,	,	PUNCT
ma-172	230	3	ξ	ξ	PROPN
ma-172	230	4	is	be	AUX
ma-172	230	5	the	the	DET
ma-172	230	6	only	only	ADJ
ma-172	230	7	solution	solution	NOUN
ma-172	230	8	of	of	ADP
ma-172	230	9	the	the	DET
ma-172	230	10	equation	equation	NOUN
ma-172	230	11	g(x)=0	g(x)=0	NOUN
ma-172	230	12	in	in	ADP
ma-172	230	13	the	the	DET
ma-172	230	14	set	set	NOUN
ma-172	230	15	b3	b3	PROPN
ma-172	230	16	.	.	PUNCT
ma-172	231	1	proof	proof	NOUN
ma-172	231	2	.	.	PUNCT
ma-172	232	1	let	let	VERB
ma-172	232	2	v∗	v∗	PROPN
ma-172	232	3	6=	6=	SYM
ma-172	232	4	ξ	ξ	PROPN
ma-172	232	5	.	.	PUNCT
ma-172	233	1	then	then	ADV
ma-172	233	2	,	,	PUNCT
ma-172	233	3	the	the	DET
ma-172	233	4	divided	divided	ADJ
ma-172	233	5	difference	difference	NOUN
ma-172	233	6	v	v	ADP
ma-172	233	7	=	=	PUNCT
ma-172	234	1	[	[	X
ma-172	234	2	ξ	ξ	X
ma-172	234	3	,	,	PUNCT
ma-172	234	4	v∗;g	v∗;g	PRON
ma-172	234	5	]	]	PUNCT
ma-172	234	6	is	be	AUX
ma-172	234	7	well	well	ADV
ma-172	234	8	-	-	PUNCT
ma-172	234	9	defined	define	VERB
ma-172	234	10	.	.	PUNCT
ma-172	235	1	using	use	VERB
ma-172	235	2	the	the	DET
ma-172	235	3	lastcondition	lastcondition	NOUN
ma-172	235	4	in	in	ADP
ma-172	235	5	(	(	PUNCT
ma-172	235	6	c3	c3	PROPN
ma-172	235	7	)	)	PUNCT
ma-172	235	8	and	and	CCONJ
ma-172	235	9	(	(	PUNCT
ma-172	235	10	5	5	NUM
ma-172	235	11	)	)	PUNCT
ma-172	235	12	,	,	PUNCT
ma-172	235	13	we	we	PRON
ma-172	235	14	obtain	obtain	VERB
ma-172	235	15	in	in	ADP
ma-172	235	16	turn	turn	NOUN
ma-172	235	17	that	that	SCONJ
ma-172	235	18	‖p−1(v	‖p−1(v	PROPN
ma-172	236	1	−p)‖	−p)‖	ADV
ma-172	236	2	≤	≤	ADJ
ma-172	237	1	ψ2(‖v∗	ψ2(‖v∗	PROPN
ma-172	237	2	−	−	PROPN
ma-172	237	3	ξ‖	ξ‖	PROPN
ma-172	237	4	)	)	PUNCT
ma-172	237	5	≤	≤	NUM
ma-172	237	6	ψ2(ρ3	ψ2(ρ3	NOUN
ma-172	237	7	)	)	PUNCT
ma-172	237	8	<	<	X
ma-172	237	9	1	1	NUM
ma-172	237	10	,	,	PUNCT
ma-172	237	11	so	so	ADV
ma-172	237	12	,	,	PUNCT
ma-172	237	13	v	v	PART
ma-172	237	14	−1	−1	NOUN
ma-172	237	15	∈	∈	PROPN
ma-172	237	16	w	w	PROPN
ma-172	237	17	(	(	PUNCT
ma-172	237	18	u	u	NOUN
ma-172	237	19	)	)	PUNCT
ma-172	237	20	and	and	CCONJ
ma-172	237	21	from	from	ADP
ma-172	237	22	the	the	DET
ma-172	237	23	approximation	approximation	NOUN
ma-172	237	24	v∗	v∗	NOUN
ma-172	237	25	−	−	PROPN
ma-172	237	26	ξ	ξ	X
ma-172	237	27	=	=	SYM
ma-172	237	28	v	v	ADP
ma-172	237	29	−1(g(v∗)−	−1(g(v∗)−	VERB
ma-172	237	30	g(ξ	g(ξ	PROPN
ma-172	237	31	)	)	PUNCT
ma-172	237	32	)	)	PUNCT
ma-172	237	33	=	=	PUNCT
ma-172	238	1	v	v	NUM
ma-172	238	2	−1(0	−1(0	NOUN
ma-172	238	3	)	)	PUNCT
ma-172	239	1	=	=	SYM
ma-172	239	2	0	0	NUM
ma-172	239	3	,	,	PUNCT
ma-172	239	4	we	we	PRON
ma-172	239	5	deduce	deduce	VERB
ma-172	239	6	v∗	v∗	PROPN
ma-172	239	7	=	=	SYM
ma-172	239	8	ξ	ξ	PROPN
ma-172	239	9	.	.	PUNCT
ma-172	239	10	�	�	PROPN
ma-172	239	11	proposition	proposition	NOUN
ma-172	239	12	4.2	4.2	NUM
ma-172	239	13	.	.	PUNCT
ma-172	240	1	assume	assume	VERB
ma-172	240	2	:	:	PUNCT
ma-172	240	3	there	there	PRON
ma-172	240	4	exists	exist	VERB
ma-172	240	5	a	a	DET
ma-172	240	6	solution	solution	NOUN
ma-172	240	7	v∗	v∗	PROPN
ma-172	240	8	∈	∈	PROPN
ma-172	240	9	s(x0	s(x0	NOUN
ma-172	240	10	,	,	PUNCT
ma-172	240	11	ρ4	ρ4	ADV
ma-172	240	12	)	)	PUNCT
ma-172	240	13	of	of	ADP
ma-172	240	14	the	the	DET
ma-172	240	15	equation	equation	NOUN
ma-172	240	16	g(x	g(x	NOUN
ma-172	240	17	)	)	PUNCT
ma-172	241	1	=	=	SYM
ma-172	241	2	0	0	NUM
ma-172	242	1	for	for	ADP
ma-172	242	2	some	some	PRON
ma-172	242	3	ρ4	ρ4	ADJ
ma-172	242	4	>	>	ADP
ma-172	242	5	0	0	NUM
ma-172	242	6	;	;	PUNCT
ma-172	242	7	the	the	DET
ma-172	242	8	condition	condition	NOUN
ma-172	242	9	(	(	PUNCT
ma-172	242	10	h1	h1	PROPN
ma-172	242	11	)	)	PUNCT
ma-172	242	12	holds	hold	VERB
ma-172	242	13	on	on	ADP
ma-172	242	14	the	the	DET
ma-172	242	15	ball	ball	NOUN
ma-172	242	16	s(x0	s(x0	NOUN
ma-172	242	17	,	,	PUNCT
ma-172	242	18	ρ4	ρ4	ADV
ma-172	242	19	)	)	PUNCT
ma-172	242	20	and	and	CCONJ
ma-172	242	21	there	there	PRON
ma-172	242	22	exist	exist	VERB
ma-172	242	23	ρ5	ρ5	PROPN
ma-172	242	24	≥	≥	NOUN
ma-172	242	25	ρ4	ρ4	ADV
ma-172	242	26	such	such	ADJ
ma-172	242	27	that	that	SCONJ
ma-172	242	28	ϕ0(ρ4	ϕ0(ρ4	PROPN
ma-172	242	29	,	,	PUNCT
ma-172	242	30	ρ5	ρ5	PROPN
ma-172	242	31	)	)	PUNCT
ma-172	242	32	<	<	X
ma-172	242	33	1	1	X
ma-172	242	34	.	.	PUNCT
ma-172	243	1	(	(	PUNCT
ma-172	243	2	6	6	X
ma-172	243	3	)	)	PUNCT
ma-172	243	4	set	set	VERB
ma-172	243	5	b4	b4	NOUN
ma-172	243	6	=	=	SYM
ma-172	243	7	b	b	PROPN
ma-172	243	8	∩	∩	NOUN
ma-172	243	9	s[x0	s[x0	NOUN
ma-172	243	10	,	,	PUNCT
ma-172	243	11	ρ5	ρ5	PROPN
ma-172	243	12	]	]	PUNCT
ma-172	243	13	.	.	PUNCT
ma-172	244	1	then	then	ADV
ma-172	244	2	,	,	PUNCT
ma-172	244	3	v∗	v∗	PROPN
ma-172	244	4	is	be	AUX
ma-172	244	5	the	the	DET
ma-172	244	6	only	only	ADJ
ma-172	244	7	solution	solution	NOUN
ma-172	244	8	of	of	ADP
ma-172	244	9	the	the	DET
ma-172	244	10	equation	equation	NOUN
ma-172	244	11	g(x	g(x	NOUN
ma-172	244	12	)	)	PUNCT
ma-172	245	1	=	=	SYM
ma-172	245	2	0	0	NUM
ma-172	245	3	in	in	ADP
ma-172	245	4	the	the	DET
ma-172	245	5	set	set	NOUN
ma-172	245	6	b4	b4	NOUN
ma-172	245	7	.	.	PUNCT
ma-172	246	1	proof	proof	NOUN
ma-172	246	2	.	.	PUNCT
ma-172	247	1	let	let	VERB
ma-172	247	2	z∗	z∗	PROPN
ma-172	247	3	∈	∈	PROPN
ma-172	247	4	b4	b4	NOUN
ma-172	247	5	with	with	ADP
ma-172	247	6	g(z∗	g(z∗	NOUN
ma-172	247	7	)	)	PUNCT
ma-172	247	8	=	=	SYM
ma-172	247	9	0	0	NUM
ma-172	247	10	and	and	CCONJ
ma-172	247	11	z∗	z∗	PROPN
ma-172	247	12	6=	6=	PROPN
ma-172	247	13	v∗.	v∗.	NOUN
ma-172	247	14	define	define	VERB
ma-172	247	15	the	the	DET
ma-172	247	16	linear	linear	ADJ
ma-172	247	17	operator	operator	NOUN
ma-172	248	1	f	f	NOUN
ma-172	248	2	=	=	PUNCT
ma-172	249	1	[	[	X
ma-172	249	2	v∗	v∗	ADJ
ma-172	249	3	,	,	PUNCT
ma-172	249	4	z∗;g	z∗;g	PROPN
ma-172	249	5	]	]	PUNCT
ma-172	249	6	.	.	PUNCT
ma-172	250	1	then	then	ADV
ma-172	250	2	,	,	PUNCT
ma-172	250	3	by	by	ADP
ma-172	250	4	the	the	DET
ma-172	250	5	condition	condition	NOUN
ma-172	250	6	(	(	PUNCT
ma-172	250	7	h1	h1	PROPN
ma-172	250	8	)	)	PUNCT
ma-172	250	9	and	and	CCONJ
ma-172	250	10	(	(	PUNCT
ma-172	250	11	6	6	X
ma-172	250	12	)	)	PUNCT
ma-172	250	13	‖p−1(f	‖p−1(f	PROPN
ma-172	251	1	−p)‖	−p)‖	ADP
ma-172	251	2	≤	≤	X
ma-172	252	1	ϕ0(‖v∗	ϕ0(‖v∗	INTJ
ma-172	252	2	−	−	NOUN
ma-172	252	3	x0‖	x0‖	PROPN
ma-172	252	4	,	,	PUNCT
ma-172	252	5	‖z∗	‖z∗	NUM
ma-172	252	6	−	−	PROPN
ma-172	252	7	x0‖	x0‖	PROPN
ma-172	252	8	)	)	PUNCT
ma-172	252	9	≤	≤	PUNCT
ma-172	253	1	ϕ0(ρ4	ϕ0(ρ4	ADP
ma-172	253	2	,	,	PUNCT
ma-172	253	3	ρ5	ρ5	PROPN
ma-172	253	4	)	)	PUNCT
ma-172	253	5	<	<	X
ma-172	253	6	1	1	NUM
ma-172	253	7	,	,	PUNCT
ma-172	253	8	thus	thus	ADV
ma-172	253	9	,	,	PUNCT
ma-172	253	10	again	again	ADV
ma-172	253	11	v∗	v∗	PROPN
ma-172	253	12	=	=	SYM
ma-172	253	13	z∗.	z∗.	PROPN
ma-172	253	14	�	�	PROPN
ma-172	253	15	remark	remark	VERB
ma-172	253	16	4.3	4.3	NUM
ma-172	253	17	.	.	PUNCT
ma-172	254	1	(	(	PUNCT
ma-172	254	2	i	i	NOUN
ma-172	254	3	)	)	PUNCT
ma-172	254	4	the	the	DET
ma-172	254	5	limit	limit	NOUN
ma-172	254	6	point	point	NOUN
ma-172	254	7	α∗	α∗	NOUN
ma-172	254	8	can	can	AUX
ma-172	254	9	be	be	AUX
ma-172	254	10	replaced	replace	VERB
ma-172	254	11	by	by	ADP
ma-172	254	12	ρ	ρ	PROPN
ma-172	254	13	in	in	ADP
ma-172	254	14	the	the	DET
ma-172	254	15	condition	condition	NOUN
ma-172	254	16	(	(	PUNCT
ma-172	254	17	h5).(ii	h5).(ii	ADJ
ma-172	254	18	)	)	PUNCT
ma-172	254	19	under	under	ADP
ma-172	254	20	all	all	DET
ma-172	254	21	the	the	DET
ma-172	254	22	assumptions	assumption	NOUN
ma-172	254	23	(	(	PUNCT
ma-172	254	24	h1)-(h5	h1)-(h5	ADJ
ma-172	254	25	)	)	PUNCT
ma-172	254	26	,	,	PUNCT
ma-172	254	27	let	let	VERB
ma-172	254	28	v∗	v∗	PROPN
ma-172	254	29	=	=	SYM
ma-172	254	30	ξ	ξ	PROPN
ma-172	254	31	and	and	CCONJ
ma-172	254	32	ρ4	ρ4	ADV
ma-172	254	33	=	=	VERB
ma-172	254	34	α∗	α∗	NOUN
ma-172	254	35	in	in	ADP
ma-172	254	36	proposition	proposition	NOUN
ma-172	254	37	4.2	4.2	NUM
ma-172	254	38	.	.	PUNCT
ma-172	255	1	5	5	NUM
ma-172	255	2	.	.	X
ma-172	255	3	experiments	experiment	NOUN
ma-172	255	4	example	example	VERB
ma-172	255	5	5.1	5.1	NUM
ma-172	255	6	.	.	PUNCT
ma-172	256	1	consider	consider	VERB
ma-172	256	2	the	the	DET
ma-172	256	3	system	system	NOUN
ma-172	256	4	of	of	ADP
ma-172	256	5	differential	differential	ADJ
ma-172	256	6	equations	equation	NOUN
ma-172	256	7	with	with	ADP
ma-172	256	8	g′1(w1	g′1(w1	PROPN
ma-172	256	9	)	)	PUNCT
ma-172	256	10	=	=	SYM
ma-172	256	11	ew1	ew1	NOUN
ma-172	256	12	,	,	PUNCT
ma-172	256	13	g′2(w2	g′2(w2	NOUN
ma-172	256	14	)	)	PUNCT
ma-172	256	15	=	=	PUNCT
ma-172	257	1	(	(	PUNCT
ma-172	257	2	e	e	X
ma-172	257	3	−	−	PROPN
ma-172	257	4	1)w2	1)w2	PROPN
ma-172	257	5	+	+	CCONJ
ma-172	257	6	1	1	NUM
ma-172	257	7	,	,	PUNCT
ma-172	257	8	g′3(w3	g′3(w3	PROPN
ma-172	257	9	)	)	PUNCT
ma-172	257	10	=	=	SYM
ma-172	257	11	1	1	NUM
ma-172	257	12	subject	subject	NOUN
ma-172	257	13	to	to	ADP
ma-172	257	14	g1(0	g1(0	NOUN
ma-172	257	15	)	)	PUNCT
ma-172	258	1	=	=	SYM
ma-172	258	2	g2(0	g2(0	NOUN
ma-172	258	3	)	)	PUNCT
ma-172	258	4	=	=	SYM
ma-172	258	5	g3(0	g3(0	PROPN
ma-172	258	6	)	)	PUNCT
ma-172	258	7	=	=	SYM
ma-172	259	1	0	0	X
ma-172	259	2	.	.	PUNCT
ma-172	260	1	let	let	VERB
ma-172	260	2	g	g	PROPN
ma-172	260	3	=	=	SYM
ma-172	260	4	(	(	PUNCT
ma-172	260	5	g1	g1	PROPN
ma-172	260	6	,	,	PUNCT
ma-172	260	7	g2	g2	PROPN
ma-172	260	8	,	,	PUNCT
ma-172	260	9	g3	g3	PROPN
ma-172	260	10	)	)	PUNCT
ma-172	260	11	.	.	PUNCT
ma-172	261	1	let	let	VERB
ma-172	261	2	u	u	PRON
ma-172	261	3	=	=	PROPN
ma-172	261	4	r3	r3	PROPN
ma-172	261	5	and	and	CCONJ
ma-172	261	6	b	b	NOUN
ma-172	261	7	=	=	SYM
ma-172	261	8	u[0	u[0	PROPN
ma-172	261	9	,	,	PUNCT
ma-172	261	10	1	1	NUM
ma-172	261	11	]	]	PUNCT
ma-172	261	12	.	.	PUNCT
ma-172	262	1	then	then	ADV
ma-172	262	2	ξ	ξ	X
ma-172	262	3	=	=	SYM
ma-172	262	4	(	(	PUNCT
ma-172	262	5	0	0	NUM
ma-172	262	6	,	,	PUNCT
ma-172	262	7	0	0	NUM
ma-172	262	8	,	,	PUNCT
ma-172	262	9	0)t	0)t	X
ma-172	262	10	is	be	AUX
ma-172	262	11	a	a	DET
ma-172	262	12	root	root	NOUN
ma-172	262	13	.	.	PUNCT
ma-172	263	1	let	let	AUX
ma-172	263	2	function	function	VERB
ma-172	263	3	g	g	NOUN
ma-172	263	4	on	on	ADP
ma-172	263	5	b	b	NOUN
ma-172	263	6	for	for	ADP
ma-172	263	7	w	w	NOUN
ma-172	263	8	=	=	SYM
ma-172	263	9	(	(	PUNCT
ma-172	263	10	w1	w1	NOUN
ma-172	263	11	,	,	PUNCT
ma-172	263	12	w2	w2	NOUN
ma-172	263	13	,	,	PUNCT
ma-172	263	14	w3	w3	PROPN
ma-172	263	15	)	)	PUNCT
ma-172	263	16	t	t	PROPN
ma-172	263	17	be	be	AUX
ma-172	263	18	g(w	g(w	ADJ
ma-172	263	19	)	)	PUNCT
ma-172	264	1	=	=	SYM
ma-172	264	2	(	(	PUNCT
ma-172	264	3	ew1	ew1	PROPN
ma-172	264	4	−	−	NUM
ma-172	264	5	1	1	NUM
ma-172	264	6	,	,	PUNCT
ma-172	264	7	e	e	NOUN
ma-172	264	8	−	−	PROPN
ma-172	264	9	1	1	NUM
ma-172	264	10	2	2	NUM
ma-172	264	11	w22	w22	NOUN
ma-172	264	12	+	+	X
ma-172	264	13	w2	w2	NOUN
ma-172	264	14	,	,	PUNCT
ma-172	264	15	w3	w3	PROPN
ma-172	264	16	)	)	PUNCT
ma-172	264	17	t	t	PROPN
ma-172	264	18	.	.	PUNCT
ma-172	265	1	this	this	DET
ma-172	265	2	definition	definition	NOUN
ma-172	265	3	gives	give	VERB
ma-172	265	4	g′(w	g′(w	NOUN
ma-172	265	5	)	)	PUNCT
ma-172	265	6	=	=	PUNCT
ma-172	266	1	e	e	PROPN
ma-172	266	2	w1	w1	NOUN
ma-172	266	3	0	0	NUM
ma-172	266	4	0	0	NUM
ma-172	266	5	0	0	NUM
ma-172	267	1	(	(	PUNCT
ma-172	267	2	e	e	X
ma-172	267	3	−	−	PROPN
ma-172	267	4	1)w2	1)w2	PROPN
ma-172	268	1	+	+	CCONJ
ma-172	268	2	1	1	NUM
ma-172	268	3	0	0	NUM
ma-172	268	4	0	0	NUM
ma-172	268	5	0	0	NUM
ma-172	268	6	1	1	NUM
ma-172	268	7			NOUN
ma-172	268	8	https://doi.org/10.28924/ada/ma.3.19	https://doi.org/10.28924/ada/ma.3.19	NOUN
ma-172	268	9	eur	eur	NOUN
ma-172	268	10	.	.	PUNCT
ma-172	269	1	j.	j.	PROPN
ma-172	269	2	math	math	PROPN
ma-172	269	3	.	.	PUNCT
ma-172	270	1	anal	anal	PROPN
ma-172	270	2	.	.	PUNCT
ma-172	271	1	10.28924	10.28924	NUM
ma-172	271	2	/	/	SYM
ma-172	271	3	ada	ada	PROPN
ma-172	271	4	/	/	SYM
ma-172	271	5	ma.3.19	ma.3.19	PROPN
ma-172	271	6	10	10	NUM
ma-172	271	7	thus	thus	ADV
ma-172	271	8	,	,	PUNCT
ma-172	271	9	by	by	ADP
ma-172	271	10	the	the	DET
ma-172	271	11	definition	definition	NOUN
ma-172	271	12	of	of	ADP
ma-172	271	13	g	g	PROPN
ma-172	271	14	it	it	PRON
ma-172	271	15	follows	follow	VERB
ma-172	271	16	that	that	PRON
ma-172	271	17	g′(ξ	g′(ξ	VERB
ma-172	271	18	)	)	PUNCT
ma-172	272	1	=	=	SYM
ma-172	272	2	1	1	X
ma-172	272	3	.	.	PUNCT
ma-172	272	4	let	let	VERB
ma-172	272	5	p	p	PROPN
ma-172	272	6	=	=	PROPN
ma-172	272	7	g′(ξ	g′(ξ	NOUN
ma-172	272	8	)	)	PUNCT
ma-172	272	9	and	and	CCONJ
ma-172	272	10	[	[	X
ma-172	272	11	x	x	X
ma-172	272	12	,	,	PUNCT
ma-172	272	13	y	y	PROPN
ma-172	272	14	;	;	PUNCT
ma-172	272	15	g	g	NOUN
ma-172	272	16	]	]	X
ma-172	272	17	=	=	SYM
ma-172	272	18	∫	∫	PROPN
ma-172	273	1	1	1	NUM
ma-172	273	2	0	0	NUM
ma-172	273	3	g	g	NOUN
ma-172	273	4	′(x	′(x	NOUN
ma-172	273	5	+	+	CCONJ
ma-172	273	6	θ(y	θ(y	NOUN
ma-172	273	7	−	−	PROPN
ma-172	274	1	x))dθ	x))dθ	AUX
ma-172	274	2	.	.	PUNCT
ma-172	275	1	then	then	ADV
ma-172	275	2	,	,	PUNCT
ma-172	275	3	for	for	ADP
ma-172	275	4	a	a	DET
ma-172	275	5	=	=	SYM
ma-172	275	6	b	b	NOUN
ma-172	275	7	=	=	SYM
ma-172	275	8	1	1	NUM
ma-172	275	9	,	,	PUNCT
ma-172	275	10	the	the	DET
ma-172	275	11	conditions	condition	NOUN
ma-172	275	12	(	(	PUNCT
ma-172	275	13	c1)-(c5	c1)-(c5	NOUN
ma-172	275	14	)	)	PUNCT
ma-172	275	15	are	be	AUX
ma-172	275	16	validated	validate	VERB
ma-172	275	17	by	by	ADP
ma-172	275	18	remark	remark	NOUN
ma-172	275	19	2.2	2.2	NUM
ma-172	275	20	provided	provide	VERB
ma-172	275	21	that	that	SCONJ
ma-172	275	22	δ1(t	δ1(t	ADV
ma-172	275	23	)	)	PUNCT
ma-172	275	24	=	=	SYM
ma-172	275	25	(	(	PUNCT
ma-172	275	26	2	2	NUM
ma-172	275	27	+	+	CCONJ
ma-172	275	28	1	1	NUM
ma-172	275	29	2	2	NUM
ma-172	275	30	(	(	PUNCT
ma-172	275	31	e	e	NOUN
ma-172	275	32	−	−	PROPN
ma-172	275	33	1)t)t	1)t)t	NUM
ma-172	275	34	,	,	PUNCT
ma-172	275	35	δ2(t	δ2(t	PROPN
ma-172	275	36	)	)	PUNCT
ma-172	275	37	=	=	SYM
ma-172	275	38	1	1	NUM
ma-172	275	39	2	2	NUM
ma-172	275	40	(	(	PUNCT
ma-172	275	41	e	e	X
ma-172	275	42	−	−	PROPN
ma-172	275	43	1)t2	1)t2	PROPN
ma-172	275	44	,	,	PUNCT
ma-172	275	45	ϕ0(t1	ϕ0(t1	PROPN
ma-172	275	46	,	,	PUNCT
ma-172	275	47	t2	t2	NOUN
ma-172	275	48	)	)	PUNCT
ma-172	275	49	=	=	SYM
ma-172	275	50	1	1	NUM
ma-172	275	51	2	2	NUM
ma-172	275	52	(	(	PUNCT
ma-172	275	53	e	e	NOUN
ma-172	275	54	−	−	PROPN
ma-172	275	55	1)(δ1(t1	1)(δ1(t1	NUM
ma-172	275	56	)	)	PUNCT
ma-172	275	57	+	+	X
ma-172	275	58	δ2(t2	δ2(t2	ADJ
ma-172	275	59	)	)	PUNCT
ma-172	275	60	)	)	PUNCT
ma-172	276	1	δ3(t	δ3(t	X
ma-172	276	2	)	)	PUNCT
ma-172	276	3	=	=	NOUN
ma-172	276	4	(	(	PUNCT
ma-172	276	5	2	2	NUM
ma-172	276	6	+	+	CCONJ
ma-172	276	7	1	1	NUM
ma-172	276	8	2	2	NUM
ma-172	276	9	(	(	PUNCT
ma-172	276	10	e	e	NOUN
ma-172	276	11	−	−	PROPN
ma-172	276	12	1)h2(t))h2(t)t	1)h2(t))h2(t)t	NUM
ma-172	276	13	,	,	PUNCT
ma-172	276	14	δ4(t	δ4(t	PROPN
ma-172	276	15	)	)	PUNCT
ma-172	276	16	=	=	SYM
ma-172	276	17	1	1	NUM
ma-172	276	18	2	2	NUM
ma-172	276	19	(	(	PUNCT
ma-172	276	20	e	e	NOUN
ma-172	276	21	−	−	PROPN
ma-172	276	22	1)h2(t	1)h2(t	NUM
ma-172	276	23	)	)	PUNCT
ma-172	276	24	2t2	2t2	NUM
ma-172	276	25	,	,	PUNCT
ma-172	276	26	ϕ(t1	ϕ(t1	NOUN
ma-172	276	27	,	,	PUNCT
ma-172	276	28	t2	t2	PROPN
ma-172	276	29	,	,	PUNCT
ma-172	276	30	t3	t3	PROPN
ma-172	276	31	)	)	PUNCT
ma-172	276	32	=	=	SYM
ma-172	276	33	1	1	NUM
ma-172	276	34	2	2	NUM
ma-172	276	35	(	(	PUNCT
ma-172	276	36	e	e	NOUN
ma-172	276	37	−	−	PROPN
ma-172	276	38	1)(t1	1)(t1	NUM
ma-172	276	39	+	+	PUNCT
ma-172	276	40	δ1(t2	δ1(t2	NUM
ma-172	276	41	)	)	PUNCT
ma-172	276	42	+	+	CCONJ
ma-172	276	43	δ2(t3	δ2(t3	VERB
ma-172	276	44	)	)	PUNCT
ma-172	276	45	)	)	PUNCT
ma-172	277	1	ϕ1(t1	ϕ1(t1	PROPN
ma-172	277	2	,	,	PUNCT
ma-172	277	3	t2	t2	NOUN
ma-172	277	4	,	,	PUNCT
ma-172	277	5	t3	t3	PROPN
ma-172	277	6	,	,	PUNCT
ma-172	277	7	t4	t4	PROPN
ma-172	277	8	)	)	PUNCT
ma-172	277	9	=	=	SYM
ma-172	277	10	1	1	NUM
ma-172	277	11	2	2	NUM
ma-172	277	12	(	(	PUNCT
ma-172	277	13	e	e	NOUN
ma-172	277	14	−	−	PROPN
ma-172	277	15	1)[δ1(t1	1)[δ1(t1	NUM
ma-172	277	16	)	)	PUNCT
ma-172	277	17	+	+	PUNCT
ma-172	277	18	δ2(t2	δ2(t2	ADJ
ma-172	277	19	)	)	PUNCT
ma-172	277	20	+	+	CCONJ
ma-172	277	21	δ3(t3	δ3(t3	X
ma-172	277	22	)	)	PUNCT
ma-172	277	23	+	+	NUM
ma-172	277	24	δ4(t4	δ4(t4	NOUN
ma-172	277	25	)	)	PUNCT
ma-172	277	26	]	]	PUNCT
ma-172	277	27	and	and	CCONJ
ma-172	277	28	ϕ2(t	ϕ2(t	NUM
ma-172	277	29	)	)	PUNCT
ma-172	277	30	=	=	SYM
ma-172	277	31	1	1	NUM
ma-172	277	32	2	2	NUM
ma-172	277	33	(	(	PUNCT
ma-172	277	34	e	e	NOUN
ma-172	277	35	−	−	PROPN
ma-172	277	36	1)t	1)t	PROPN
ma-172	277	37	.	.	PUNCT
ma-172	278	1	by	by	ADP
ma-172	278	2	solving	solve	VERB
ma-172	278	3	,	,	PUNCT
ma-172	278	4	we	we	PRON
ma-172	278	5	get	get	VERB
ma-172	278	6	ρ0	ρ0	PROPN
ma-172	278	7	=	=	SYM
ma-172	278	8	0.426037	0.426037	NUM
ma-172	278	9	and	and	CCONJ
ma-172	278	10	hence	hence	ADV
ma-172	278	11	m0	m0	NOUN
ma-172	278	12	=	=	PUNCT
ma-172	279	1	[	[	X
ma-172	279	2	0	0	NUM
ma-172	279	3	,	,	PUNCT
ma-172	279	4	ρ0	ρ0	PROPN
ma-172	279	5	)	)	PUNCT
ma-172	279	6	.	.	PUNCT
ma-172	280	1	the	the	DET
ma-172	280	2	radii	radius	NOUN
ma-172	280	3	are	be	AUX
ma-172	280	4	obtained	obtain	VERB
ma-172	280	5	as	as	ADP
ma-172	280	6	r1	r1	PROPN
ma-172	280	7	=	=	SYM
ma-172	280	8	0.204146	0.204146	NUM
ma-172	280	9	,	,	PUNCT
ma-172	280	10	r2	r2	PROPN
ma-172	280	11	=	=	PUNCT
ma-172	280	12	0.134409	0.134409	NUM
ma-172	280	13	and	and	CCONJ
ma-172	280	14	r3	r3	PROPN
ma-172	280	15	=	=	SYM
ma-172	280	16	0.126891	0.126891	NUM
ma-172	280	17	.	.	PUNCT
ma-172	281	1	therefore	therefore	ADV
ma-172	281	2	,	,	PUNCT
ma-172	281	3	by	by	ADP
ma-172	281	4	the	the	DET
ma-172	281	5	definition	definition	NOUN
ma-172	281	6	r	r	NOUN
ma-172	281	7	=	=	PUNCT
ma-172	281	8	min{ri	min{ri	NUM
ma-172	281	9	}	}	PUNCT
ma-172	281	10	,	,	PUNCT
ma-172	281	11	we	we	PRON
ma-172	281	12	get	get	VERB
ma-172	281	13	the	the	DET
ma-172	281	14	radius	radius	NOUN
ma-172	281	15	of	of	ADP
ma-172	281	16	convergence	convergence	NOUN
ma-172	281	17	,	,	PUNCT
ma-172	281	18	r	r	NOUN
ma-172	281	19	=	=	SYM
ma-172	281	20	0.126891	0.126891	NUM
ma-172	281	21	.	.	PUNCT
ma-172	282	1	remark	remark	NOUN
ma-172	282	2	5.2	5.2	NUM
ma-172	282	3	.	.	PUNCT
ma-172	283	1	a	a	DET
ma-172	283	2	non	non	ADJ
ma-172	283	3	-	-	ADJ
ma-172	283	4	differentiable	differentiable	ADJ
ma-172	283	5	non	non	ADJ
ma-172	283	6	-	-	ADJ
ma-172	283	7	linear	linear	ADJ
ma-172	283	8	system	system	NOUN
ma-172	283	9	is	be	AUX
ma-172	283	10	solved	solve	VERB
ma-172	283	11	using	use	VERB
ma-172	283	12	the	the	DET
ma-172	283	13	method	method	NOUN
ma-172	283	14	(	(	PUNCT
ma-172	283	15	2	2	NUM
ma-172	283	16	)	)	PUNCT
ma-172	283	17	,	,	PUNCT
ma-172	283	18	where	where	SCONJ
ma-172	283	19	the	the	DET
ma-172	283	20	divided	divided	ADJ
ma-172	283	21	difference	difference	NOUN
ma-172	283	22	is	be	AUX
ma-172	283	23	defined	define	VERB
ma-172	283	24	by	by	ADP
ma-172	283	25	the	the	DET
ma-172	283	26	2×2	2×2	NUM
ma-172	283	27	matrix	matrix	NOUN
ma-172	283	28	given	give	VERB
ma-172	283	29	for	for	ADP
ma-172	283	30	t̄	t̄	NOUN
ma-172	283	31	=	=	SYM
ma-172	283	32	(	(	PUNCT
ma-172	283	33	t1	t1	NOUN
ma-172	283	34	,	,	PUNCT
ma-172	283	35	t2	t2	NOUN
ma-172	283	36	)	)	PUNCT
ma-172	283	37	∈	∈	PROPN
ma-172	283	38	r×r	r×r	PROPN
ma-172	283	39	,	,	PUNCT
ma-172	283	40	t̃	t̃	PROPN
ma-172	283	41	=	=	SYM
ma-172	283	42	(	(	PUNCT
ma-172	283	43	t3	t3	PROPN
ma-172	283	44	,	,	PUNCT
ma-172	283	45	t4	t4	PROPN
ma-172	283	46	)	)	PUNCT
ma-172	283	47	∈	∈	PROPN
ma-172	283	48	r×r	r×r	PROPN
ma-172	283	49	and	and	CCONJ
ma-172	283	50	g	g	NOUN
ma-172	283	51	=	=	SYM
ma-172	283	52	(	(	PUNCT
ma-172	283	53	g1	g1	PROPN
ma-172	283	54	,	,	PUNCT
ma-172	283	55	g2	g2	PROPN
ma-172	283	56	)	)	PUNCT
ma-172	283	57	by	by	ADP
ma-172	283	58	[	[	X
ma-172	283	59	t̄	t̄	NOUN
ma-172	283	60	,	,	PUNCT
ma-172	283	61	t̃;g]i	t̃;g]i	VERB
ma-172	283	62	,	,	PUNCT
ma-172	283	63	1	1	NUM
ma-172	283	64	=	=	SYM
ma-172	283	65	gi(t3	gi(t3	X
ma-172	283	66	,	,	PUNCT
ma-172	283	67	t4)−	t4)−	NOUN
ma-172	283	68	gi(t1	gi(t1	PROPN
ma-172	283	69	,	,	PUNCT
ma-172	284	1	t4	t4	PROPN
ma-172	284	2	)	)	PUNCT
ma-172	284	3	t3	t3	PROPN
ma-172	284	4	−	−	PROPN
ma-172	284	5	t1	t1	NOUN
ma-172	284	6	,	,	PUNCT
ma-172	284	7	t3	t3	PROPN
ma-172	284	8	6=	6=	PROPN
ma-172	284	9	t1	t1	NOUN
ma-172	284	10	and	and	CCONJ
ma-172	284	11	[	[	X
ma-172	284	12	t̄	t̄	NOUN
ma-172	284	13	,	,	PUNCT
ma-172	284	14	t̃;g]i	t̃;g]i	VERB
ma-172	284	15	,	,	PUNCT
ma-172	284	16	2	2	NUM
ma-172	284	17	=	=	SYM
ma-172	284	18	gi(t1	gi(t1	X
ma-172	284	19	,	,	PUNCT
ma-172	284	20	t4)−	t4)−	NOUN
ma-172	284	21	gi(t1	gi(t1	NOUN
ma-172	284	22	,	,	PUNCT
ma-172	284	23	t2	t2	NOUN
ma-172	284	24	)	)	PUNCT
ma-172	285	1	t4	t4	PROPN
ma-172	285	2	−	−	PROPN
ma-172	285	3	t2	t2	PROPN
ma-172	285	4	,	,	PUNCT
ma-172	285	5	t4	t4	PROPN
ma-172	285	6	6=	6=	PROPN
ma-172	285	7	t2	t2	PROPN
ma-172	285	8	.	.	PUNCT
ma-172	286	1	otherwise	otherwise	ADV
ma-172	286	2	,	,	PUNCT
ma-172	286	3	we	we	PRON
ma-172	286	4	set	set	VERB
ma-172	286	5	[	[	X
ma-172	286	6	·	·	PUNCT
ma-172	286	7	,	,	PUNCT
ma-172	286	8	·	·	PUNCT
ma-172	286	9	;	;	PUNCT
ma-172	286	10	g	g	NOUN
ma-172	286	11	]	]	X
ma-172	286	12	=	=	PUNCT
ma-172	287	1	0	0	X
ma-172	287	2	.	.	PUNCT
ma-172	288	1	the	the	DET
ma-172	288	2	actual	actual	ADJ
ma-172	288	3	example	example	NOUN
ma-172	288	4	is	be	AUX
ma-172	288	5	given	give	VERB
ma-172	288	6	below	below	ADP
ma-172	288	7	example	example	NOUN
ma-172	288	8	5.3	5.3	NUM
ma-172	288	9	.	.	PUNCT
ma-172	289	1	let	let	VERB
ma-172	289	2	us	we	PRON
ma-172	289	3	solve	solve	VERB
ma-172	289	4	the	the	DET
ma-172	289	5	non	non	ADJ
ma-172	289	6	-	-	ADJ
ma-172	289	7	linear	linear	ADJ
ma-172	289	8	and	and	CCONJ
ma-172	289	9	non	non	ADJ
ma-172	289	10	-	-	ADJ
ma-172	289	11	differentiable	differentiable	ADJ
ma-172	289	12	system	system	NOUN
ma-172	289	13	given	give	VERB
ma-172	289	14	as	as	ADP
ma-172	289	15	3t21	3t21	NUM
ma-172	289	16	t2	t2	NOUN
ma-172	289	17	+	+	CCONJ
ma-172	289	18	t22	t22	PROPN
ma-172	289	19	−	−	PROPN
ma-172	289	20	1	1	NUM
ma-172	289	21	+	+	CCONJ
ma-172	289	22	|t1	|t1	NOUN
ma-172	289	23	−	−	PROPN
ma-172	289	24	1|	1|	NUM
ma-172	290	1	=	=	SYM
ma-172	290	2	0	0	NUM
ma-172	290	3	t41	t41	PROPN
ma-172	291	1	+	+	CCONJ
ma-172	291	2	t1	t1	PROPN
ma-172	291	3	t	t	NOUN
ma-172	291	4	3	3	NUM
ma-172	291	5	2	2	NUM
ma-172	291	6	−	−	NUM
ma-172	291	7	1	1	NUM
ma-172	291	8	+	+	NOUN
ma-172	291	9	|t2|	|t2|	NOUN
ma-172	291	10	=	=	SYM
ma-172	291	11	0	0	X
ma-172	291	12	.	.	X
ma-172	291	13	https://doi.org/10.28924/ada/ma.3.19	https://doi.org/10.28924/ada/ma.3.19	PROPN
ma-172	291	14	eur	eur	PROPN
ma-172	291	15	.	.	PUNCT
ma-172	292	1	j.	j.	PROPN
ma-172	292	2	math	math	PROPN
ma-172	292	3	.	.	PUNCT
ma-172	293	1	anal	anal	PROPN
ma-172	293	2	.	.	PUNCT
ma-172	294	1	10.28924	10.28924	NUM
ma-172	294	2	/	/	SYM
ma-172	294	3	ada	ada	PROPN
ma-172	294	4	/	/	SYM
ma-172	294	5	ma.3.19	ma.3.19	PROPN
ma-172	294	6	11	11	NUM
ma-172	294	7	then	then	ADV
ma-172	294	8	,	,	PUNCT
ma-172	294	9	we	we	PRON
ma-172	294	10	set	set	VERB
ma-172	294	11	g	g	PROPN
ma-172	294	12	=	=	SYM
ma-172	294	13	(	(	PUNCT
ma-172	294	14	g1	g1	PROPN
ma-172	294	15	,	,	PUNCT
ma-172	294	16	g2	g2	PROPN
ma-172	294	17	)	)	PUNCT
ma-172	294	18	,	,	PUNCT
ma-172	294	19	where	where	SCONJ
ma-172	294	20	g1(t1	g1(t1	NOUN
ma-172	294	21	,	,	PUNCT
ma-172	294	22	t2	t2	NOUN
ma-172	294	23	)	)	PUNCT
ma-172	294	24	=	=	SYM
ma-172	294	25	3t21	3t21	NUM
ma-172	294	26	t2	t2	NOUN
ma-172	294	27	+	+	CCONJ
ma-172	294	28	t22	t22	PROPN
ma-172	294	29	−	−	PROPN
ma-172	294	30	1	1	NUM
ma-172	294	31	+	+	CCONJ
ma-172	294	32	|t1	|t1	NOUN
ma-172	294	33	−	−	PROPN
ma-172	294	34	1|	1|	NUM
ma-172	294	35	g2(t1	g2(t1	NOUN
ma-172	294	36	,	,	PUNCT
ma-172	294	37	t2	t2	NOUN
ma-172	294	38	)	)	PUNCT
ma-172	294	39	=	=	SYM
ma-172	294	40	t41	t41	PROPN
ma-172	295	1	+	+	CCONJ
ma-172	295	2	t1	t1	PROPN
ma-172	295	3	t	t	NOUN
ma-172	295	4	3	3	NUM
ma-172	295	5	2	2	NUM
ma-172	295	6	−	−	NUM
ma-172	295	7	1	1	NUM
ma-172	295	8	+	+	NOUN
ma-172	295	9	|t2|	|t2|	NOUN
ma-172	295	10	choose	choose	VERB
ma-172	295	11	the	the	DET
ma-172	295	12	initial	initial	ADJ
ma-172	295	13	points	point	NOUN
ma-172	295	14	(	(	PUNCT
ma-172	295	15	5	5	NUM
ma-172	295	16	,	,	PUNCT
ma-172	295	17	5	5	NUM
ma-172	295	18	)	)	PUNCT
ma-172	295	19	and	and	CCONJ
ma-172	295	20	(	(	PUNCT
ma-172	295	21	1	1	NUM
ma-172	295	22	,	,	PUNCT
ma-172	295	23	0	0	NUM
ma-172	295	24	)	)	PUNCT
ma-172	295	25	.	.	PUNCT
ma-172	296	1	then	then	ADV
ma-172	296	2	,	,	PUNCT
ma-172	296	3	using	use	VERB
ma-172	296	4	the	the	DET
ma-172	296	5	aforementioned	aforementioned	ADJ
ma-172	296	6	divided	divide	VERB
ma-172	296	7	difference	difference	NOUN
ma-172	296	8	and	and	CCONJ
ma-172	296	9	the	the	DET
ma-172	296	10	method	method	NOUN
ma-172	296	11	(	(	PUNCT
ma-172	296	12	2	2	NUM
ma-172	296	13	)	)	PUNCT
ma-172	296	14	,	,	PUNCT
ma-172	296	15	we	we	PRON
ma-172	296	16	obtain	obtain	VERB
ma-172	296	17	the	the	DET
ma-172	296	18	solution	solution	NOUN
ma-172	296	19	ξ	ξ	X
ma-172	296	20	=	=	PUNCT
ma-172	296	21	(	(	PUNCT
ma-172	296	22	x∗1	x∗1	ADJ
ma-172	296	23	,	,	PUNCT
ma-172	296	24	x	x	X
ma-172	296	25	∗	∗	NOUN
ma-172	296	26	2	2	NUM
ma-172	296	27	)	)	PUNCT
ma-172	296	28	after	after	ADP
ma-172	296	29	three	three	NUM
ma-172	296	30	iterations	iteration	NOUN
ma-172	296	31	with	with	ADP
ma-172	296	32	x∗1	x∗1	ADJ
ma-172	296	33	=	=	SYM
ma-172	296	34	0.894655074977661	0.894655074977661	NUM
ma-172	296	35	and	and	CCONJ
ma-172	296	36	x∗2	x∗2	PROPN
ma-172	296	37	=	=	NOUN
ma-172	296	38	0.327826643198819	0.327826643198819	NUM
ma-172	296	39	.	.	PUNCT
ma-172	296	40	example	example	NOUN
ma-172	297	1	5.4	5.4	NUM
ma-172	297	2	.	.	PUNCT
ma-172	298	1	we	we	PRON
ma-172	298	2	consider	consider	VERB
ma-172	298	3	the	the	DET
ma-172	298	4	system	system	NOUN
ma-172	298	5	of	of	ADP
ma-172	298	6	25	25	NUM
ma-172	298	7	equations	equation	NOUN
ma-172	298	8	25∑	25∑	NUM
ma-172	298	9	j=1,j	j=1,j	NOUN
ma-172	298	10	6	6	NUM
ma-172	298	11	=	=	NOUN
ma-172	298	12	i	i	NUM
ma-172	298	13	xj	xj	PROPN
ma-172	298	14	−	−	PROPN
ma-172	298	15	e−xi	e−xi	PROPN
ma-172	299	1	=	=	SYM
ma-172	299	2	0	0	PROPN
ma-172	299	3	,	,	PUNCT
ma-172	299	4	1	1	NUM
ma-172	299	5	≤	≤	NUM
ma-172	299	6	i	i	X
ma-172	299	7	≤	≤	NOUN
ma-172	299	8	25	25	NUM
ma-172	299	9	,	,	PUNCT
ma-172	299	10	with	with	ADP
ma-172	299	11	initial	initial	ADJ
ma-172	299	12	point	point	NOUN
ma-172	299	13	x0	x0	PROPN
ma-172	299	14	=	=	PUNCT
ma-172	299	15	{	{	PUNCT
ma-172	299	16	1.5	1.5	NUM
ma-172	299	17	,	,	PUNCT
ma-172	299	18	1.5	1.5	NUM
ma-172	299	19	,	,	PUNCT
ma-172	299	20	.	.	PUNCT
ma-172	299	21	.	.	PUNCT
ma-172	300	1	.	.	PUNCT
ma-172	301	1	,	,	PUNCT
ma-172	301	2	1.5}t	1.5}t	NUM
ma-172	301	3	.	.	PUNCT
ma-172	302	1	then	then	ADV
ma-172	302	2	,	,	PUNCT
ma-172	302	3	applying	apply	VERB
ma-172	302	4	method	method	NOUN
ma-172	302	5	(	(	PUNCT
ma-172	302	6	2	2	X
ma-172	302	7	)	)	PUNCT
ma-172	302	8	we	we	PRON
ma-172	302	9	get	get	VERB
ma-172	302	10	the	the	DET
ma-172	302	11	solution	solution	NOUN
ma-172	302	12	ξ	ξ	X
ma-172	302	13	=	=	SYM
ma-172	302	14	{	{	PUNCT
ma-172	302	15	0.04003162719010837	0.04003162719010837	NUM
ma-172	302	16	·	·	PUNCT
ma-172	302	17	·	·	PUNCT
ma-172	302	18	·	·	PUNCT
ma-172	302	19	,	,	PUNCT
ma-172	302	20	0.04003162719010837	0.04003162719010837	NUM
ma-172	302	21	·	·	PUNCT
ma-172	302	22	·	·	PUNCT
ma-172	302	23	·	·	PUNCT
ma-172	302	24	,	,	PUNCT
ma-172	302	25	.	.	PUNCT
ma-172	302	26	.	.	PUNCT
ma-172	303	1	.	.	PUNCT
ma-172	304	1	,	,	PUNCT
ma-172	304	2	0.04003162719010837	0.04003162719010837	NUM
ma-172	304	3	·	·	PUNCT
ma-172	304	4	·	·	PUNCT
ma-172	304	5	·	·	PUNCT
ma-172	304	6	}	}	PUNCT
ma-172	304	7	t	t	NOUN
ma-172	304	8	after	after	ADP
ma-172	304	9	4	4	NUM
ma-172	304	10	iterations	iteration	NOUN
ma-172	304	11	.	.	PUNCT
ma-172	305	1	6	6	NUM
ma-172	305	2	.	.	X
ma-172	305	3	conclusion	conclusion	NOUN
ma-172	305	4	a	a	DET
ma-172	305	5	new	new	ADJ
ma-172	305	6	procedure	procedure	NOUN
ma-172	305	7	has	have	AUX
ma-172	305	8	been	be	AUX
ma-172	305	9	developed	develop	VERB
ma-172	305	10	to	to	PART
ma-172	305	11	demonstrate	demonstrate	VERB
ma-172	305	12	both	both	DET
ma-172	305	13	local	local	ADJ
ma-172	305	14	and	and	CCONJ
ma-172	305	15	semi	semi	ADJ
ma-172	305	16	-	-	ADJ
ma-172	305	17	local	local	ADJ
ma-172	305	18	convergenceanalysis	convergenceanalysis	NOUN
ma-172	305	19	of	of	ADP
ma-172	305	20	high	high	ADJ
ma-172	305	21	-	-	PUNCT
ma-172	305	22	order	order	NOUN
ma-172	305	23	convergence	convergence	NOUN
ma-172	305	24	methods	method	NOUN
ma-172	305	25	,	,	PUNCT
ma-172	305	26	using	use	VERB
ma-172	305	27	only	only	ADJ
ma-172	305	28	derivatives	derivative	NOUN
ma-172	305	29	that	that	PRON
ma-172	305	30	appear	appear	VERB
ma-172	305	31	on	on	ADP
ma-172	305	32	the	the	DET
ma-172	305	33	methodology.previous	methodology.previous	PROPN
ma-172	305	34	works	work	NOUN
ma-172	305	35	have	have	AUX
ma-172	305	36	proven	prove	VERB
ma-172	305	37	convergence	convergence	NOUN
ma-172	305	38	based	base	VERB
ma-172	305	39	on	on	ADP
ma-172	305	40	the	the	DET
ma-172	305	41	existence	existence	NOUN
ma-172	305	42	of	of	ADP
ma-172	305	43	high	high	ADJ
ma-172	305	44	-	-	PUNCT
ma-172	305	45	order	order	NOUN
ma-172	305	46	derivatives	derivative	NOUN
ma-172	305	47	that	that	PRON
ma-172	305	48	maynot	maynot	AUX
ma-172	305	49	be	be	AUX
ma-172	305	50	present	present	ADJ
ma-172	305	51	in	in	ADP
ma-172	305	52	the	the	DET
ma-172	305	53	methodology	methodology	NOUN
ma-172	305	54	.	.	PUNCT
ma-172	306	1	hence	hence	ADV
ma-172	306	2	,	,	PUNCT
ma-172	306	3	it	it	PRON
ma-172	306	4	has	have	AUX
ma-172	306	5	been	be	AUX
ma-172	306	6	a	a	DET
ma-172	306	7	limitation	limitation	NOUN
ma-172	306	8	of	of	ADP
ma-172	306	9	their	their	PRON
ma-172	306	10	applicability	applicability	NOUN
ma-172	306	11	.	.	PUNCT
ma-172	307	1	thisprocedure	thisprocedure	NOUN
ma-172	307	2	also	also	ADV
ma-172	307	3	offers	offer	VERB
ma-172	307	4	error	error	NOUN
ma-172	307	5	limits	limit	NOUN
ma-172	307	6	and	and	CCONJ
ma-172	307	7	uniqueness	uniqueness	NOUN
ma-172	307	8	results	result	NOUN
ma-172	307	9	that	that	PRON
ma-172	307	10	were	be	AUX
ma-172	307	11	not	not	PART
ma-172	307	12	available	available	ADJ
ma-172	307	13	before	before	ADV
ma-172	307	14	.	.	PUNCT
ma-172	308	1	moreover	moreover	ADV
ma-172	308	2	,	,	PUNCT
ma-172	308	3	this	this	DET
ma-172	308	4	procedure	procedure	NOUN
ma-172	308	5	is	be	AUX
ma-172	308	6	general	general	ADJ
ma-172	308	7	in	in	ADP
ma-172	308	8	the	the	DET
ma-172	308	9	sense	sense	NOUN
ma-172	308	10	that	that	SCONJ
ma-172	308	11	it	it	PRON
ma-172	308	12	is	be	AUX
ma-172	308	13	not	not	PART
ma-172	308	14	dependent	dependent	ADJ
ma-172	308	15	on	on	ADP
ma-172	308	16	the	the	DET
ma-172	308	17	method	method	NOUN
ma-172	308	18	itself	itself	PRON
ma-172	308	19	.	.	PUNCT
ma-172	309	1	this	this	PRON
ma-172	309	2	is	be	AUX
ma-172	309	3	thereason	thereason	NOUN
ma-172	309	4	why	why	SCONJ
ma-172	309	5	it	it	PRON
ma-172	309	6	may	may	AUX
ma-172	309	7	be	be	AUX
ma-172	309	8	used	use	VERB
ma-172	309	9	in	in	ADP
ma-172	309	10	the	the	DET
ma-172	309	11	same	same	ADJ
ma-172	309	12	way	way	NOUN
ma-172	309	13	to	to	PART
ma-172	309	14	broaden	broaden	VERB
ma-172	309	15	the	the	DET
ma-172	309	16	scope	scope	NOUN
ma-172	309	17	of	of	ADP
ma-172	309	18	other	other	ADJ
ma-172	309	19	methods	method	NOUN
ma-172	309	20	of	of	ADP
ma-172	309	21	higher	high	ADJ
ma-172	309	22	order	order	NOUN
ma-172	309	23	,	,	PUNCT
ma-172	309	24	such	such	ADJ
ma-172	309	25	as	as	ADP
ma-172	309	26	single	single	ADJ
ma-172	309	27	and	and	CCONJ
ma-172	309	28	multi	multi	ADJ
ma-172	309	29	-	-	ADJ
ma-172	309	30	step	step	ADJ
ma-172	309	31	methods	method	NOUN
ma-172	309	32	[	[	X
ma-172	309	33	1	1	NUM
ma-172	309	34	,	,	PUNCT
ma-172	309	35	2	2	NUM
ma-172	309	36	,	,	PUNCT
ma-172	309	37	4	4	NUM
ma-172	309	38	,	,	PUNCT
ma-172	309	39	10–17,19,21,22	10–17,19,21,22	NUM
ma-172	309	40	]	]	PUNCT
ma-172	309	41	.	.	PUNCT
ma-172	310	1	references	reference	NOUN
ma-172	310	2	[	[	X
ma-172	310	3	1	1	NUM
ma-172	310	4	]	]	PUNCT
ma-172	310	5	a.	a.	NOUN
ma-172	310	6	cordero	cordero	PROPN
ma-172	310	7	,	,	PUNCT
ma-172	310	8	j.	j.	PROPN
ma-172	310	9	l.	l.	PROPN
ma-172	310	10	hueso	hueso	PROPN
ma-172	310	11	,	,	PUNCT
ma-172	310	12	e.	e.	PROPN
ma-172	310	13	martínez	martínez	PROPN
ma-172	310	14	,	,	PUNCT
ma-172	310	15	j.	j.	PROPN
ma-172	310	16	r.	r.	PROPN
ma-172	310	17	torregrosa	torregrosa	PROPN
ma-172	310	18	,	,	PUNCT
ma-172	310	19	a	a	DET
ma-172	310	20	modified	modify	VERB
ma-172	310	21	newton	newton	PROPN
ma-172	310	22	-	-	PUNCT
ma-172	310	23	jarratt	jarratt	PROPN
ma-172	310	24	’s	’s	PART
ma-172	310	25	composition	composition	NOUN
ma-172	310	26	,	,	PUNCT
ma-172	310	27	numer	numer	NOUN
ma-172	310	28	.	.	PUNCT
ma-172	311	1	algorithms55	algorithms55	PROPN
ma-172	311	2	(	(	PUNCT
ma-172	311	3	2010	2010	NUM
ma-172	311	4	)	)	PUNCT
ma-172	311	5	87	87	NUM
ma-172	311	6	-	-	SYM
ma-172	311	7	99	99	NUM
ma-172	311	8	.	.	PUNCT
ma-172	311	9	https://doi.org/10.1007/s11075-009-9359-z.[2	https://doi.org/10.1007/s11075-009-9359-z.[2	ADV
ma-172	311	10	]	]	PUNCT
ma-172	311	11	a.	a.	NOUN
ma-172	311	12	m.	m.	PROPN
ma-172	311	13	ostrowski	ostrowski	PROPN
ma-172	311	14	,	,	PUNCT
ma-172	311	15	solutions	solution	NOUN
ma-172	311	16	of	of	ADP
ma-172	311	17	equations	equation	NOUN
ma-172	311	18	and	and	CCONJ
ma-172	311	19	system	system	NOUN
ma-172	311	20	of	of	ADP
ma-172	311	21	equations	equation	NOUN
ma-172	311	22	,	,	PUNCT
ma-172	311	23	academic	academic	ADJ
ma-172	311	24	press	press	NOUN
ma-172	311	25	(	(	PUNCT
ma-172	311	26	1960	1960	NUM
ma-172	311	27	)	)	PUNCT
ma-172	311	28	new	new	ADJ
ma-172	311	29	york.[3	york.[3	NOUN
ma-172	311	30	]	]	X
ma-172	311	31	f.	f.	PROPN
ma-172	311	32	a.	a.	PROPN
ma-172	311	33	potra	potra	PROPN
ma-172	311	34	,	,	PUNCT
ma-172	311	35	v.	v.	PROPN
ma-172	311	36	ptak	ptak	PROPN
ma-172	311	37	,	,	PUNCT
ma-172	311	38	nondiscrete	nondiscrete	ADJ
ma-172	311	39	induction	induction	NOUN
ma-172	311	40	and	and	CCONJ
ma-172	311	41	iterarive	iterarive	ADJ
ma-172	311	42	processes	process	NOUN
ma-172	311	43	.	.	PUNCT
ma-172	312	1	pitman	pitman	NOUN
ma-172	312	2	publishing	publishing	PROPN
ma-172	312	3	(	(	PUNCT
ma-172	312	4	1984	1984	NUM
ma-172	312	5	)	)	PUNCT
ma-172	312	6	boston.[4	boston.[4	PROPN
ma-172	312	7	]	]	X
ma-172	312	8	h.	h.	PROPN
ma-172	312	9	ren	ren	PROPN
ma-172	312	10	,	,	PUNCT
ma-172	312	11	q.	q.	PROPN
ma-172	312	12	wu	wu	PROPN
ma-172	312	13	,	,	PUNCT
ma-172	312	14	w.	w.	PROPN
ma-172	312	15	bi	bi	PROPN
ma-172	312	16	,	,	PUNCT
ma-172	312	17	a	a	DET
ma-172	312	18	class	class	NOUN
ma-172	312	19	of	of	ADP
ma-172	312	20	two	two	NUM
ma-172	312	21	-	-	PUNCT
ma-172	312	22	step	step	NOUN
ma-172	312	23	steffensen	steffensen	NOUN
ma-172	312	24	type	type	NOUN
ma-172	312	25	methods	method	NOUN
ma-172	312	26	with	with	ADP
ma-172	312	27	fourth	fourth	ADJ
ma-172	312	28	-	-	PUNCT
ma-172	312	29	order	order	NOUN
ma-172	312	30	convergence	convergence	NOUN
ma-172	312	31	,	,	PUNCT
ma-172	312	32	appl	appl	NOUN
ma-172	312	33	.	.	PUNCT
ma-172	313	1	math.comput	math.comput	NOUN
ma-172	313	2	.	.	PUNCT
ma-172	314	1	209	209	NUM
ma-172	314	2	(	(	PUNCT
ma-172	314	3	2009	2009	NUM
ma-172	314	4	)	)	PUNCT
ma-172	315	1	206–210	206–210	NUM
ma-172	315	2	.	.	PUNCT
ma-172	316	1	https://doi.org/10.1016/j.amc.2008.12.039.[5	https://doi.org/10.1016/j.amc.2008.12.039.[5	X
ma-172	316	2	]	]	PUNCT
ma-172	317	1	i.	i.	PROPN
ma-172	317	2	k.	k.	PROPN
ma-172	317	3	argyros	argyros	PROPN
ma-172	317	4	,	,	PUNCT
ma-172	317	5	j.	j.	PROPN
ma-172	317	6	a.	a.	PROPN
ma-172	317	7	john	john	PROPN
ma-172	317	8	,	,	PUNCT
ma-172	317	9	j.	j.	PROPN
ma-172	317	10	jayaraman	jayaraman	PROPN
ma-172	317	11	,	,	PUNCT
ma-172	317	12	on	on	ADP
ma-172	317	13	the	the	DET
ma-172	317	14	semi	semi	ADJ
ma-172	317	15	-	-	ADJ
ma-172	317	16	local	local	ADJ
ma-172	317	17	convergence	convergence	NOUN
ma-172	317	18	of	of	ADP
ma-172	317	19	a	a	DET
ma-172	317	20	sixth	sixth	ADJ
ma-172	317	21	order	order	NOUN
ma-172	317	22	method	method	NOUN
ma-172	317	23	in	in	ADP
ma-172	317	24	banach	banach	NOUN
ma-172	317	25	space	space	NOUN
ma-172	317	26	,	,	PUNCT
ma-172	317	27	j.numer	j.numer	NOUN
ma-172	317	28	.	.	PUNCT
ma-172	318	1	anal	anal	PROPN
ma-172	318	2	.	.	PUNCT
ma-172	319	1	approx	approx	PROPN
ma-172	319	2	.	.	PUNCT
ma-172	320	1	theory	theory	NOUN
ma-172	320	2	51	51	NUM
ma-172	320	3	(	(	PUNCT
ma-172	320	4	2022	2022	NUM
ma-172	320	5	)	)	PUNCT
ma-172	320	6	144–154	144–154	NUM
ma-172	320	7	.	.	PUNCT
ma-172	321	1	https://doi.org/10.33993/jnaat512-1284.[6	https://doi.org/10.33993/jnaat512-1284.[6	X
ma-172	321	2	]	]	X
ma-172	321	3	i.	i.	PROPN
ma-172	321	4	k.	k.	PROPN
ma-172	321	5	argyros	argyros	PROPN
ma-172	321	6	,	,	PUNCT
ma-172	321	7	j.	j.	PROPN
ma-172	321	8	a.	a.	PROPN
ma-172	321	9	john	john	PROPN
ma-172	321	10	,	,	PUNCT
ma-172	321	11	j.	j.	PROPN
ma-172	321	12	jayaraman	jayaraman	PROPN
ma-172	321	13	,	,	PUNCT
ma-172	321	14	s.	s.	PROPN
ma-172	321	15	regmi	regmi	PROPN
ma-172	321	16	,	,	PUNCT
ma-172	321	17	extended	extend	VERB
ma-172	321	18	local	local	ADJ
ma-172	321	19	convergence	convergence	NOUN
ma-172	321	20	for	for	ADP
ma-172	321	21	the	the	DET
ma-172	321	22	chebyshev	chebyshev	NOUN
ma-172	321	23	method	method	NOUN
ma-172	321	24	under	under	ADP
ma-172	321	25	themajorant	themajorant	ADJ
ma-172	321	26	condition	condition	NOUN
ma-172	321	27	,	,	PUNCT
ma-172	321	28	asian	asian	ADJ
ma-172	321	29	res	re	NOUN
ma-172	321	30	.	.	PUNCT
ma-172	322	1	j.	j.	PROPN
ma-172	322	2	math	math	PROPN
ma-172	322	3	.	.	PUNCT
ma-172	323	1	18	18	NUM
ma-172	323	2	(	(	PUNCT
ma-172	323	3	2022	2022	NUM
ma-172	323	4	)	)	PUNCT
ma-172	324	1	102–109	102–109	NUM
ma-172	324	2	.	.	PUNCT
ma-172	325	1	https://doi.org/10.9734/arjom/2022/v18i12629	https://doi.org/10.9734/arjom/2022/v18i12629	PROPN
ma-172	325	2	.	.	PUNCT
ma-172	326	1	https://doi.org/10.28924/ada/ma.3.19	https://doi.org/10.28924/ada/ma.3.19	PROPN
ma-172	326	2	https://doi.org/10.1007/s11075-009-9359-z	https://doi.org/10.1007/s11075-009-9359-z	PROPN
ma-172	326	3	https://doi.org/10.1016/j.amc.2008.12.039	https://doi.org/10.1016/j.amc.2008.12.039	NOUN
ma-172	326	4	https://doi.org/10.33993/jnaat512-1284	https://doi.org/10.33993/jnaat512-1284	VERB
ma-172	326	5	https://doi.org/10.9734/arjom/2022/v18i12629	https://doi.org/10.9734/arjom/2022/v18i12629	PROPN
ma-172	326	6	eur	eur	PROPN
ma-172	326	7	.	.	PUNCT
ma-172	327	1	j.	j.	PROPN
ma-172	327	2	math	math	PROPN
ma-172	327	3	.	.	PUNCT
ma-172	328	1	anal	anal	PROPN
ma-172	328	2	.	.	PUNCT
ma-172	329	1	10.28924	10.28924	NUM
ma-172	329	2	/	/	SYM
ma-172	329	3	ada	ada	PROPN
ma-172	329	4	/	/	SYM
ma-172	329	5	ma.3.19	ma.3.19	PROPN
ma-172	329	6	12	12	NUM
ma-172	330	1	[	[	X
ma-172	330	2	7	7	NUM
ma-172	330	3	]	]	ADJ
ma-172	330	4	i.	i.	PROPN
ma-172	330	5	k.	k.	PROPN
ma-172	330	6	argyros	argyros	PROPN
ma-172	330	7	,	,	PUNCT
ma-172	330	8	s.	s.	PROPN
ma-172	330	9	regmi	regmi	PROPN
ma-172	330	10	,	,	PUNCT
ma-172	330	11	j.	j.	PROPN
ma-172	330	12	a.	a.	PROPN
ma-172	330	13	john	john	PROPN
ma-172	330	14	,	,	PUNCT
ma-172	330	15	j.	j.	PROPN
ma-172	330	16	jayaraman	jayaraman	PROPN
ma-172	330	17	,	,	PUNCT
ma-172	330	18	extended	extended	ADJ
ma-172	330	19	convergence	convergence	NOUN
ma-172	330	20	for	for	ADP
ma-172	330	21	two	two	NUM
ma-172	330	22	sixth	sixth	ADJ
ma-172	330	23	order	order	NOUN
ma-172	330	24	methods	method	NOUN
ma-172	330	25	under	under	ADP
ma-172	330	26	the	the	DET
ma-172	330	27	sameweak	sameweak	NOUN
ma-172	330	28	conditions	condition	NOUN
ma-172	330	29	,	,	PUNCT
ma-172	330	30	foundations	foundation	NOUN
ma-172	330	31	3	3	NUM
ma-172	330	32	(	(	PUNCT
ma-172	330	33	2023	2023	NUM
ma-172	330	34	)	)	PUNCT
ma-172	330	35	127–139	127–139	NUM
ma-172	330	36	.	.	PUNCT
ma-172	331	1	https://doi.org/10.3390/foundations3010012.[8	https://doi.org/10.3390/foundations3010012.[8	PROPN
ma-172	331	2	]	]	PUNCT
ma-172	331	3	j.	j.	PROPN
ma-172	331	4	a.	a.	PROPN
ma-172	331	5	john	john	PROPN
ma-172	331	6	,	,	PUNCT
ma-172	331	7	j.	j.	PROPN
ma-172	331	8	jayaraman	jayaraman	PROPN
ma-172	331	9	,	,	PUNCT
ma-172	331	10	i.	i.	PROPN
ma-172	331	11	k.	k.	PROPN
ma-172	332	1	argyros	argyros	PROPN
ma-172	332	2	,	,	PUNCT
ma-172	332	3	local	local	ADJ
ma-172	332	4	convergence	convergence	NOUN
ma-172	332	5	of	of	ADP
ma-172	332	6	an	an	DET
ma-172	332	7	optimal	optimal	ADJ
ma-172	332	8	method	method	NOUN
ma-172	332	9	of	of	ADP
ma-172	332	10	order	order	NOUN
ma-172	332	11	four	four	NUM
ma-172	332	12	for	for	ADP
ma-172	332	13	solving	solve	VERB
ma-172	332	14	non	non	ADJ
ma-172	332	15	-	-	NOUN
ma-172	332	16	linearsystem	linearsystem	ADJ
ma-172	332	17	,	,	PUNCT
ma-172	332	18	int	int	NOUN
ma-172	332	19	.	.	PUNCT
ma-172	333	1	j.	j.	PROPN
ma-172	333	2	appl	appl	PROPN
ma-172	333	3	.	.	PUNCT
ma-172	334	1	comput	comput	PROPN
ma-172	334	2	.	.	PUNCT
ma-172	335	1	math	math	NOUN
ma-172	335	2	.	.	PUNCT
ma-172	336	1	8	8	NUM
ma-172	336	2	(	(	PUNCT
ma-172	336	3	2022	2022	NUM
ma-172	336	4	)	)	PUNCT
ma-172	336	5	194	194	NUM
ma-172	336	6	.	.	PUNCT
ma-172	337	1	https://doi.org/10.1007/s40819-022-01404-3.[9	https://doi.org/10.1007/s40819-022-01404-3.[9	PROPN
ma-172	337	2	]	]	PUNCT
ma-172	337	3	j.	j.	PROPN
ma-172	337	4	f.	f.	PROPN
ma-172	337	5	steffensen	steffensen	PROPN
ma-172	337	6	,	,	PUNCT
ma-172	337	7	remarks	remark	VERB
ma-172	337	8	on	on	ADP
ma-172	337	9	iteration	iteration	NOUN
ma-172	337	10	,	,	PUNCT
ma-172	337	11	scand	scand	PROPN
ma-172	337	12	.	.	PUNCT
ma-172	337	13	actuar	actuar	PROPN
ma-172	337	14	.	.	PUNCT
ma-172	338	1	j.	j.	PROPN
ma-172	338	2	16	16	NUM
ma-172	338	3	(	(	PUNCT
ma-172	338	4	1933	1933	NUM
ma-172	338	5	)	)	PUNCT
ma-172	338	6	64–72	64–72	NUM
ma-172	338	7	.	.	PUNCT
ma-172	339	1	https://doi.org/10.1080/03461238	https://doi.org/10.1080/03461238	NOUN
ma-172	339	2	.	.	PUNCT
ma-172	340	1	1933.10419209.[10	1933.10419209.[10	NUM
ma-172	340	2	]	]	PUNCT
ma-172	340	3	j.	j.	PROPN
ma-172	340	4	f.	f.	PROPN
ma-172	340	5	traub	traub	PROPN
ma-172	340	6	,	,	PUNCT
ma-172	340	7	iterative	iterative	NOUN
ma-172	340	8	methods	method	NOUN
ma-172	340	9	for	for	ADP
ma-172	340	10	the	the	DET
ma-172	340	11	solution	solution	NOUN
ma-172	340	12	of	of	ADP
ma-172	340	13	equations	equation	NOUN
ma-172	340	14	,	,	PUNCT
ma-172	340	15	prentice	prentice	NOUN
ma-172	340	16	-	-	PUNCT
ma-172	340	17	hall	hall	NOUN
ma-172	340	18	,	,	PUNCT
ma-172	340	19	new	new	PROPN
ma-172	340	20	jersey	jersey	PROPN
ma-172	340	21	(	(	PUNCT
ma-172	340	22	1964).[11	1964).[11	PROPN
ma-172	340	23	]	]	PUNCT
ma-172	340	24	j.	j.	PROPN
ma-172	340	25	m	m	PROPN
ma-172	340	26	ortega	ortega	PROPN
ma-172	340	27	,	,	PUNCT
ma-172	340	28	w.	w.	PROPN
ma-172	340	29	c	c	PROPN
ma-172	340	30	rheinboldt	rheinboldt	PROPN
ma-172	340	31	,	,	PUNCT
ma-172	340	32	iterative	iterative	ADJ
ma-172	340	33	solution	solution	NOUN
ma-172	340	34	of	of	ADP
ma-172	340	35	nonlinear	nonlinear	ADJ
ma-172	340	36	equations	equation	NOUN
ma-172	340	37	in	in	ADP
ma-172	340	38	several	several	ADJ
ma-172	340	39	variables	variable	NOUN
ma-172	340	40	,	,	PUNCT
ma-172	340	41	academic	academic	ADJ
ma-172	340	42	press	press	NOUN
ma-172	340	43	,	,	PUNCT
ma-172	340	44	newyork	newyork	NOUN
ma-172	340	45	,	,	PUNCT
ma-172	340	46	(	(	PUNCT
ma-172	340	47	1970	1970	NUM
ma-172	340	48	)	)	PUNCT
ma-172	340	49	.	.	PUNCT
ma-172	341	1	https://doi.org/10.1137/1.9780898719468.fm.[12	https://doi.org/10.1137/1.9780898719468.fm.[12	PROPN
ma-172	341	2	]	]	X
ma-172	341	3	j.	j.	PROPN
ma-172	341	4	r.	r.	PROPN
ma-172	341	5	sharma	sharma	PROPN
ma-172	341	6	,	,	PUNCT
ma-172	341	7	h.	h.	PROPN
ma-172	341	8	arora	arora	PROPN
ma-172	341	9	,	,	PUNCT
ma-172	341	10	an	an	DET
ma-172	341	11	efficient	efficient	ADJ
ma-172	341	12	derivative	derivative	ADJ
ma-172	341	13	free	free	ADJ
ma-172	341	14	iterative	iterative	NOUN
ma-172	341	15	method	method	NOUN
ma-172	341	16	for	for	ADP
ma-172	341	17	solving	solve	VERB
ma-172	341	18	systems	system	NOUN
ma-172	341	19	of	of	ADP
ma-172	341	20	nonlinear	nonlinear	ADJ
ma-172	341	21	equations	equation	NOUN
ma-172	341	22	,	,	PUNCT
ma-172	341	23	appl.anal	appl.anal	NUM
ma-172	341	24	.	.	PUNCT
ma-172	341	25	discrete	discrete	ADJ
ma-172	341	26	math	math	NOUN
ma-172	341	27	.	.	PUNCT
ma-172	342	1	7	7	NUM
ma-172	342	2	(	(	PUNCT
ma-172	342	3	2013	2013	NUM
ma-172	342	4	)	)	PUNCT
ma-172	342	5	390–403	390–403	NUM
ma-172	342	6	.	.	PUNCT
ma-172	343	1	https://doi.org/10.2298/aadm130725016s.[13	https://doi.org/10.2298/aadm130725016s.[13	PROPN
ma-172	343	2	]	]	X
ma-172	343	3	j.	j.	PROPN
ma-172	343	4	r.	r.	PROPN
ma-172	343	5	sharma	sharma	PROPN
ma-172	343	6	,	,	PUNCT
ma-172	343	7	h.	h.	PROPN
ma-172	343	8	arora	arora	PROPN
ma-172	343	9	,	,	PUNCT
ma-172	343	10	a	a	DET
ma-172	343	11	novel	novel	ADJ
ma-172	343	12	derivative	derivative	ADJ
ma-172	343	13	free	free	ADJ
ma-172	343	14	algorithm	algorithm	NOUN
ma-172	343	15	with	with	ADP
ma-172	343	16	seventh	seventh	ADJ
ma-172	343	17	order	order	NOUN
ma-172	343	18	convergence	convergence	NOUN
ma-172	343	19	for	for	ADP
ma-172	343	20	solving	solve	VERB
ma-172	343	21	systems	system	NOUN
ma-172	343	22	ofnonlinear	ofnonlinear	NOUN
ma-172	343	23	equations	equation	NOUN
ma-172	343	24	,	,	PUNCT
ma-172	343	25	numer	numer	NOUN
ma-172	343	26	.	.	PUNCT
ma-172	344	1	algorithms	algorithms	PROPN
ma-172	344	2	4	4	NUM
ma-172	344	3	(	(	PUNCT
ma-172	344	4	2014	2014	NUM
ma-172	344	5	)	)	PUNCT
ma-172	344	6	917–933	917–933	NUM
ma-172	344	7	.	.	PUNCT
ma-172	345	1	https://doi.org/10.1007/s11075-014-9832-1.[14	https://doi.org/10.1007/s11075-014-9832-1.[14	PROPN
ma-172	345	2	]	]	PUNCT
ma-172	345	3	j.	j.	PROPN
ma-172	345	4	r.	r.	PROPN
ma-172	345	5	sharma	sharma	PROPN
ma-172	345	6	,	,	PUNCT
ma-172	345	7	h.	h.	PROPN
ma-172	345	8	arora	arora	PROPN
ma-172	345	9	,	,	PUNCT
ma-172	345	10	efficient	efficient	ADJ
ma-172	345	11	derivative	derivative	ADJ
ma-172	345	12	-	-	PUNCT
ma-172	345	13	free	free	ADJ
ma-172	345	14	numerical	numerical	ADJ
ma-172	345	15	methods	method	NOUN
ma-172	345	16	for	for	ADP
ma-172	345	17	solving	solve	VERB
ma-172	345	18	systems	system	NOUN
ma-172	345	19	of	of	ADP
ma-172	345	20	nonlinear	nonlinear	ADJ
ma-172	345	21	equations	equation	NOUN
ma-172	345	22	,	,	PUNCT
ma-172	345	23	comput	comput	NOUN
ma-172	345	24	.	.	PUNCT
ma-172	346	1	appl	appl	PROPN
ma-172	346	2	.	.	PROPN
ma-172	346	3	math	math	PROPN
ma-172	346	4	.	.	PUNCT
ma-172	347	1	35	35	NUM
ma-172	347	2	(	(	PUNCT
ma-172	347	3	2016	2016	NUM
ma-172	347	4	)	)	PUNCT
ma-172	348	1	269–284	269–284	NUM
ma-172	348	2	.	.	PUNCT
ma-172	349	1	https://doi.org/10.1007/s40314-014-0193-0.[15	https://doi.org/10.1007/s40314-014-0193-0.[15	PROPN
ma-172	349	2	]	]	PUNCT
ma-172	349	3	j.	j.	PROPN
ma-172	349	4	r.	r.	PROPN
ma-172	349	5	sharma	sharma	PROPN
ma-172	349	6	,	,	PUNCT
ma-172	349	7	p.	p.	PROPN
ma-172	349	8	gupta	gupta	PROPN
ma-172	349	9	,	,	PUNCT
ma-172	349	10	efficient	efficient	ADJ
ma-172	349	11	family	family	NOUN
ma-172	349	12	of	of	ADP
ma-172	349	13	traub	traub	PROPN
ma-172	349	14	-	-	PUNCT
ma-172	349	15	steffensen	steffensen	NOUN
ma-172	349	16	-	-	PUNCT
ma-172	349	17	type	type	NOUN
ma-172	349	18	methods	method	NOUN
ma-172	349	19	for	for	ADP
ma-172	349	20	solving	solve	VERB
ma-172	349	21	systems	system	NOUN
ma-172	349	22	of	of	ADP
ma-172	349	23	nonlinear	nonlinear	PROPN
ma-172	349	24	equations.adv	equations.adv	PROPN
ma-172	349	25	.	.	PUNCT
ma-172	350	1	numer	numer	PROPN
ma-172	350	2	.	.	PUNCT
ma-172	351	1	anal	anal	PROPN
ma-172	351	2	.	.	PUNCT
ma-172	352	1	2014	2014	NUM
ma-172	352	2	(	(	PUNCT
ma-172	352	3	2014	2014	NUM
ma-172	352	4	)	)	PUNCT
ma-172	352	5	152187	152187	NUM
ma-172	352	6	.	.	PUNCT
ma-172	353	1	https://doi.org/10.1155/2014/152187.[16	https://doi.org/10.1155/2014/152187.[16	PROPN
ma-172	353	2	]	]	PUNCT
ma-172	353	3	m.	m.	PROPN
ma-172	353	4	grau	grau	PROPN
ma-172	353	5	-	-	PUNCT
ma-172	353	6	sánchez	sánchez	PROPN
ma-172	353	7	,	,	PUNCT
ma-172	353	8	à	à	X
ma-172	353	9	.	.	PUNCT
ma-172	353	10	grau	grau	PROPN
ma-172	353	11	,	,	PUNCT
ma-172	353	12	m.	m.	NOUN
ma-172	353	13	noguera	noguera	NOUN
ma-172	353	14	,	,	PUNCT
ma-172	353	15	frozen	freeze	VERB
ma-172	353	16	divided	divide	VERB
ma-172	353	17	difference	difference	NOUN
ma-172	353	18	scheme	scheme	NOUN
ma-172	353	19	for	for	ADP
ma-172	353	20	solving	solve	VERB
ma-172	353	21	systems	system	NOUN
ma-172	353	22	of	of	ADP
ma-172	353	23	nonlinear	nonlinear	ADJ
ma-172	353	24	equations	equation	NOUN
ma-172	353	25	,	,	PUNCT
ma-172	353	26	j.	j.	PROPN
ma-172	353	27	comput	comput	PROPN
ma-172	353	28	.	.	PUNCT
ma-172	354	1	appl	appl	PROPN
ma-172	354	2	.	.	PUNCT
ma-172	354	3	math	math	PROPN
ma-172	354	4	.	.	PUNCT
ma-172	355	1	235	235	NUM
ma-172	355	2	(	(	PUNCT
ma-172	355	3	2011	2011	NUM
ma-172	355	4	)	)	PUNCT
ma-172	355	5	1739	1739	NUM
ma-172	355	6	-	-	SYM
ma-172	355	7	1743	1743	NUM
ma-172	355	8	.	.	PUNCT
ma-172	356	1	https://doi.org/10.1016/j.cam.2010.09.019.[17	https://doi.org/10.1016/j.cam.2010.09.019.[17	PROPN
ma-172	356	2	]	]	PUNCT
ma-172	356	3	m.	m.	NOUN
ma-172	356	4	grau	grau	PROPN
ma-172	356	5	-	-	PUNCT
ma-172	356	6	sánchez	sánchez	PROPN
ma-172	356	7	,	,	PUNCT
ma-172	356	8	m.	m.	NOUN
ma-172	356	9	noguera	noguera	PROPN
ma-172	356	10	,	,	PUNCT
ma-172	356	11	s.	s.	PROPN
ma-172	356	12	amat	amat	PROPN
ma-172	356	13	,	,	PUNCT
ma-172	356	14	on	on	ADP
ma-172	356	15	the	the	DET
ma-172	356	16	approximation	approximation	NOUN
ma-172	356	17	of	of	ADP
ma-172	356	18	derivatives	derivative	NOUN
ma-172	356	19	using	use	VERB
ma-172	356	20	divided	divided	ADJ
ma-172	356	21	difference	difference	NOUN
ma-172	356	22	operatorspreserving	operatorspreserve	VERB
ma-172	356	23	the	the	DET
ma-172	356	24	local	local	ADJ
ma-172	356	25	convergence	convergence	NOUN
ma-172	356	26	order	order	NOUN
ma-172	356	27	of	of	ADP
ma-172	356	28	iterative	iterative	ADJ
ma-172	356	29	methods	method	NOUN
ma-172	356	30	,	,	PUNCT
ma-172	356	31	j.	j.	PROPN
ma-172	356	32	comput	comput	PROPN
ma-172	356	33	.	.	PUNCT
ma-172	357	1	appl	appl	PROPN
ma-172	357	2	.	.	PROPN
ma-172	357	3	math	math	NOUN
ma-172	357	4	.	.	PUNCT
ma-172	358	1	237	237	NUM
ma-172	358	2	(	(	PUNCT
ma-172	358	3	2013	2013	NUM
ma-172	358	4	)	)	PUNCT
ma-172	358	5	363	363	NUM
ma-172	358	6	-	-	SYM
ma-172	358	7	372	372	NUM
ma-172	358	8	.	.	PUNCT
ma-172	358	9	https	https	NOUN
ma-172	358	10	:	:	PUNCT
ma-172	359	1	//doi.org/10.1016	//doi.org/10.1016	PROPN
ma-172	359	2	/	/	SYM
ma-172	359	3	j.cam.2012.06.005.[18	j.cam.2012.06.005.[18	NUM
ma-172	359	4	]	]	PUNCT
ma-172	359	5	m.	m.	PROPN
ma-172	359	6	narang	narang	PROPN
ma-172	359	7	,	,	PUNCT
ma-172	359	8	s.	s.	PROPN
ma-172	359	9	bhatia	bhatia	PROPN
ma-172	359	10	,	,	PUNCT
ma-172	359	11	v.	v.	PROPN
ma-172	359	12	kanwar	kanwar	PROPN
ma-172	359	13	,	,	PUNCT
ma-172	359	14	new	new	ADJ
ma-172	359	15	efficient	efficient	ADJ
ma-172	359	16	derivative	derivative	ADJ
ma-172	359	17	free	free	ADJ
ma-172	359	18	family	family	NOUN
ma-172	359	19	of	of	ADP
ma-172	359	20	seventh	seventh	ADJ
ma-172	359	21	-	-	PUNCT
ma-172	359	22	order	order	NOUN
ma-172	359	23	methods	method	NOUN
ma-172	359	24	for	for	ADP
ma-172	359	25	solving	solve	VERB
ma-172	359	26	systemsof	systemsof	PROPN
ma-172	359	27	nonlinear	nonlinear	ADJ
ma-172	359	28	equations	equation	NOUN
ma-172	359	29	,	,	PUNCT
ma-172	359	30	numer	numer	NOUN
ma-172	359	31	.	.	PUNCT
ma-172	360	1	algorithms	algorithms	PROPN
ma-172	360	2	76	76	NUM
ma-172	360	3	(	(	PUNCT
ma-172	360	4	2017	2017	NUM
ma-172	360	5	)	)	PUNCT
ma-172	360	6	283	283	NUM
ma-172	360	7	-	-	SYM
ma-172	360	8	307	307	NUM
ma-172	360	9	.	.	PUNCT
ma-172	361	1	https://doi.org/10.1007/s11075-016-0254-0.[19	https://doi.org/10.1007/s11075-016-0254-0.[19	PROPN
ma-172	361	2	]	]	PUNCT
ma-172	361	3	q.	q.	PROPN
ma-172	361	4	zheng	zheng	PROPN
ma-172	361	5	,	,	PUNCT
ma-172	361	6	p.	p.	PROPN
ma-172	361	7	zhao	zhao	PROPN
ma-172	361	8	,	,	PUNCT
ma-172	361	9	f.	f.	PROPN
ma-172	361	10	huang	huang	PROPN
ma-172	361	11	,	,	PUNCT
ma-172	361	12	a	a	DET
ma-172	361	13	family	family	NOUN
ma-172	361	14	of	of	ADP
ma-172	361	15	fourth	fourth	ADJ
ma-172	361	16	-	-	PUNCT
ma-172	361	17	order	order	NOUN
ma-172	361	18	steffensen	steffensen	NOUN
ma-172	361	19	-	-	PUNCT
ma-172	361	20	type	type	NOUN
ma-172	361	21	methods	method	NOUN
ma-172	361	22	with	with	ADP
ma-172	361	23	the	the	DET
ma-172	361	24	applications	application	NOUN
ma-172	361	25	on	on	ADP
ma-172	361	26	solvingnonlinear	solvingnonlinear	ADJ
ma-172	361	27	odes	ode	NOUN
ma-172	361	28	,	,	PUNCT
ma-172	361	29	appl	appl	PROPN
ma-172	361	30	.	.	PROPN
ma-172	361	31	math	math	NOUN
ma-172	361	32	.	.	PUNCT
ma-172	362	1	comput	comput	NOUN
ma-172	362	2	.	.	PUNCT
ma-172	363	1	217	217	NUM
ma-172	363	2	(	(	PUNCT
ma-172	363	3	2011	2011	NUM
ma-172	363	4	)	)	PUNCT
ma-172	363	5	8196–8203	8196–8203	NUM
ma-172	363	6	.	.	PUNCT
ma-172	364	1	https://doi.org/10.1016/j.amc.2011.01.095.[20	https://doi.org/10.1016/j.amc.2011.01.095.[20	PROPN
ma-172	364	2	]	]	PUNCT
ma-172	364	3	s.	s.	PROPN
ma-172	364	4	regmi	regmi	PROPN
ma-172	364	5	,	,	PUNCT
ma-172	364	6	i.	i.	PROPN
ma-172	364	7	k.	k.	PROPN
ma-172	365	1	argyros	argyros	PROPN
ma-172	365	2	,	,	PUNCT
ma-172	365	3	j.	j.	PROPN
ma-172	365	4	a.	a.	PROPN
ma-172	365	5	john	john	PROPN
ma-172	365	6	,	,	PUNCT
ma-172	365	7	j.	j.	PROPN
ma-172	365	8	jayaraman	jayaraman	PROPN
ma-172	365	9	,	,	PUNCT
ma-172	365	10	extended	extended	ADJ
ma-172	365	11	convergence	convergence	NOUN
ma-172	365	12	of	of	ADP
ma-172	365	13	two	two	NUM
ma-172	365	14	multi	multi	ADJ
ma-172	365	15	-	-	ADJ
ma-172	365	16	step	step	ADJ
ma-172	365	17	iterative	iterative	NOUN
ma-172	365	18	methods	method	NOUN
ma-172	365	19	,	,	PUNCT
ma-172	365	20	foun	foun	PROPN
ma-172	365	21	-	-	PUNCT
ma-172	365	22	dations	dation	NOUN
ma-172	365	23	3	3	NUM
ma-172	365	24	(	(	PUNCT
ma-172	365	25	2023	2023	NUM
ma-172	365	26	)	)	PUNCT
ma-172	365	27	140–153	140–153	NUM
ma-172	365	28	.	.	PUNCT
ma-172	366	1	https://doi.org/10.3390/foundations3010013.[21	https://doi.org/10.3390/foundations3010013.[21	X
ma-172	366	2	]	]	X
ma-172	366	3	x.	x.	PROPN
ma-172	366	4	wang	wang	PROPN
ma-172	366	5	,	,	PUNCT
ma-172	366	6	t.	t.	PROPN
ma-172	366	7	zhang	zhang	PROPN
ma-172	366	8	,	,	PUNCT
ma-172	366	9	a	a	DET
ma-172	366	10	family	family	NOUN
ma-172	366	11	of	of	ADP
ma-172	366	12	steffensen	steffensen	NOUN
ma-172	366	13	type	type	NOUN
ma-172	366	14	methods	method	NOUN
ma-172	366	15	with	with	ADP
ma-172	366	16	seventh	seventh	ADJ
ma-172	366	17	-	-	PUNCT
ma-172	366	18	order	order	NOUN
ma-172	366	19	convergence	convergence	NOUN
ma-172	366	20	,	,	PUNCT
ma-172	366	21	numer	numer	NOUN
ma-172	366	22	.	.	PUNCT
ma-172	366	23	algorithms	algorithms	PROPN
ma-172	366	24	62(2013	62(2013	NUM
ma-172	366	25	)	)	PUNCT
ma-172	366	26	429–444	429–444	NUM
ma-172	366	27	.	.	PUNCT
ma-172	367	1	https://doi.org/10.1007/s11075-012-9597-3.[22	https://doi.org/10.1007/s11075-012-9597-3.[22	NOUN
ma-172	367	2	]	]	PUNCT
ma-172	368	1	z.	z.	PROPN
ma-172	368	2	liu	liu	PROPN
ma-172	368	3	,	,	PUNCT
ma-172	368	4	q	q	X
ma-172	368	5	,	,	PUNCT
ma-172	368	6	zheng	zheng	PROPN
ma-172	368	7	,	,	PUNCT
ma-172	368	8	p.	p.	PROPN
ma-172	368	9	zhao	zhao	PROPN
ma-172	368	10	,	,	PUNCT
ma-172	368	11	a	a	DET
ma-172	368	12	variant	variant	NOUN
ma-172	368	13	of	of	ADP
ma-172	368	14	steffensen	steffensen	NOUN
ma-172	368	15	’s	’s	PART
ma-172	368	16	method	method	NOUN
ma-172	368	17	of	of	ADP
ma-172	368	18	fourth	fourth	ADJ
ma-172	368	19	-	-	PUNCT
ma-172	368	20	order	order	NOUN
ma-172	368	21	convergence	convergence	NOUN
ma-172	368	22	and	and	CCONJ
ma-172	368	23	its	its	PRON
ma-172	368	24	applications	application	NOUN
ma-172	368	25	,	,	PUNCT
ma-172	368	26	appl.math	appl.math	PROPN
ma-172	368	27	.	.	PUNCT
ma-172	368	28	comput	comput	NOUN
ma-172	368	29	.	.	PUNCT
ma-172	369	1	216	216	NUM
ma-172	369	2	(	(	PUNCT
ma-172	369	3	2010	2010	NUM
ma-172	369	4	)	)	PUNCT
ma-172	369	5	1978	1978	NUM
ma-172	369	6	-	-	SYM
ma-172	369	7	1983	1983	NUM
ma-172	369	8	.	.	PUNCT
ma-172	370	1	https://doi.org/10.1016/j.amc.2010.03.028	https://doi.org/10.1016/j.amc.2010.03.028	PROPN
ma-172	370	2	.	.	PUNCT
ma-172	371	1	https://doi.org/10.28924/ada/ma.3.19	https://doi.org/10.28924/ada/ma.3.19	NOUN
ma-172	371	2	https://doi.org/10.3390/foundations3010012	https://doi.org/10.3390/foundations3010012	NOUN
ma-172	372	1	https://doi.org/10.1007/s40819-022-01404-3	https://doi.org/10.1007/s40819-022-01404-3	PROPN
ma-172	372	2	https://doi.org/10.1080/03461238.1933.10419209	https://doi.org/10.1080/03461238.1933.10419209	AUX
ma-172	372	3	https://doi.org/10.1080/03461238.1933.10419209	https://doi.org/10.1080/03461238.1933.10419209	VERB
ma-172	372	4	https://doi.org/10.1137/1.9780898719468.fm	https://doi.org/10.1137/1.9780898719468.fm	PUNCT
ma-172	373	1	https://doi.org/10.2298/aadm130725016s	https://doi.org/10.2298/aadm130725016s	PROPN
ma-172	373	2	https://doi.org/10.1007/s11075-014-9832-1	https://doi.org/10.1007/s11075-014-9832-1	PROPN
ma-172	373	3	https://doi.org/10.1007/s40314-014-0193-0	https://doi.org/10.1007/s40314-014-0193-0	PROPN
ma-172	373	4	https://doi.org/10.1155/2014/152187	https://doi.org/10.1155/2014/152187	PROPN
ma-172	373	5	https://doi.org/10.1016/j.cam.2010.09.019	https://doi.org/10.1016/j.cam.2010.09.019	PROPN
ma-172	373	6	https://doi.org/10.1016/j.cam.2012.06.005	https://doi.org/10.1016/j.cam.2012.06.005	PROPN
ma-172	373	7	https://doi.org/10.1016/j.cam.2012.06.005	https://doi.org/10.1016/j.cam.2012.06.005	VERB
ma-172	373	8	https://doi.org/10.1007/s11075-016-0254-0	https://doi.org/10.1007/s11075-016-0254-0	NUM
ma-172	373	9	https://doi.org/10.1016/j.amc.2011.01.095	https://doi.org/10.1016/j.amc.2011.01.095	PROPN
ma-172	373	10	https://doi.org/10.3390/foundations3010013	https://doi.org/10.3390/foundations3010013	PROPN
ma-172	373	11	https://doi.org/10.1007/s11075-012-9597-3	https://doi.org/10.1007/s11075-012-9597-3	PROPN
ma-172	373	12	https://doi.org/10.1016/j.amc.2010.03.028	https://doi.org/10.1016/j.amc.2010.03.028	NOUN
ma-172	373	13	1	1	NUM
ma-172	373	14	.	.	PUNCT
ma-172	373	15	introduction	introduction	NOUN
ma-172	373	16	2	2	NUM
ma-172	373	17	.	.	PUNCT
ma-172	373	18	convergence	convergence	NOUN
ma-172	373	19	1	1	NUM
ma-172	373	20	:	:	PUNCT
ma-172	373	21	local	local	ADJ
ma-172	373	22	3	3	NUM
ma-172	373	23	.	.	PUNCT
ma-172	373	24	convergence	convergence	NOUN
ma-172	373	25	2	2	NUM
ma-172	373	26	:	:	PUNCT
ma-172	373	27	semi	semi	ADJ
ma-172	373	28	-	-	ADJ
ma-172	373	29	local	local	ADJ
ma-172	373	30	4	4	NUM
ma-172	373	31	.	.	PUNCT
ma-172	373	32	isolation	isolation	NOUN
ma-172	373	33	of	of	ADP
ma-172	373	34	a	a	DET
ma-172	373	35	solution	solution	NOUN
ma-172	373	36	5	5	NUM
ma-172	373	37	.	.	PUNCT
ma-172	373	38	experiments	experiment	NOUN
ma-172	373	39	6	6	NUM
ma-172	373	40	.	.	PUNCT
ma-172	374	1	conclusion	conclusion	NOUN
ma-172	374	2	references	reference	NOUN