id	sid	tid	token	lemma	pos
ma-294	1	1	2025	2025	NUM
ma-294	1	2	ada	ada	PROPN
ma-294	1	3	academica	academica	PROPN
ma-294	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-294	1	5	.	.	PUNCT
ma-294	2	1	j.	j.	PROPN
ma-294	2	2	math	math	PROPN
ma-294	2	3	.	.	PUNCT
ma-294	3	1	anal	anal	ADJ
ma-294	3	2	.	.	PUNCT
ma-294	4	1	5	5	NUM
ma-294	4	2	(	(	PUNCT
ma-294	4	3	2025	2025	NUM
ma-294	4	4	)	)	PUNCT
ma-294	4	5	9doi	9doi	NOUN
ma-294	4	6	:	:	PUNCT
ma-294	4	7	10.28924	10.28924	NUM
ma-294	4	8	/	/	SYM
ma-294	4	9	ada	ada	PROPN
ma-294	4	10	/	/	SYM
ma-294	4	11	ma.5.9	ma.5.9	PROPN
ma-294	4	12	numerical	numerical	ADJ
ma-294	4	13	results	result	NOUN
ma-294	4	14	for	for	ADP
ma-294	4	15	gauss	gauss	ADJ
ma-294	4	16	-	-	PUNCT
ma-294	4	17	seidel	seidel	PROPN
ma-294	4	18	iterative	iterative	NOUN
ma-294	4	19	algorithm	algorithm	NOUN
ma-294	4	20	based	base	VERB
ma-294	4	21	on	on	ADP
ma-294	4	22	newton	newton	PROPN
ma-294	4	23	methods	method	NOUN
ma-294	4	24	for	for	ADP
ma-294	4	25	unconstrained	unconstrained	ADJ
ma-294	4	26	optimization	optimization	NOUN
ma-294	4	27	problems	problem	NOUN
ma-294	4	28	nguyen	nguyen	PROPN
ma-294	4	29	dinh	dinh	PROPN
ma-294	4	30	dung	dung	PROPN
ma-294	4	31	tnu	tnu	PROPN
ma-294	4	32	-	-	NOUN
ma-294	4	33	university	university	NOUN
ma-294	4	34	of	of	ADP
ma-294	4	35	information	information	NOUN
ma-294	4	36	and	and	CCONJ
ma-294	4	37	communication	communication	NOUN
ma-294	4	38	technology	technology	NOUN
ma-294	4	39	,	,	PUNCT
ma-294	4	40	thai	thai	PROPN
ma-294	4	41	nguyen	nguyen	PROPN
ma-294	4	42	,	,	PUNCT
ma-294	4	43	vietnam	vietnam	PROPN
ma-294	4	44	nddung@ictu.edu.vn	nddung@ictu.edu.vn	ADJ
ma-294	4	45	abstract	abstract	NOUN
ma-294	4	46	.	.	PUNCT
ma-294	5	1	optimization	optimization	NOUN
ma-294	5	2	problems	problem	NOUN
ma-294	5	3	play	play	VERB
ma-294	5	4	a	a	DET
ma-294	5	5	crucial	crucial	ADJ
ma-294	5	6	role	role	NOUN
ma-294	5	7	in	in	ADP
ma-294	5	8	various	various	ADJ
ma-294	5	9	fields	field	NOUN
ma-294	5	10	such	such	ADJ
ma-294	5	11	as	as	ADP
ma-294	5	12	economics	economic	NOUN
ma-294	5	13	,	,	PUNCT
ma-294	5	14	engineering	engineering	NOUN
ma-294	5	15	,	,	PUNCT
ma-294	5	16	and	and	CCONJ
ma-294	5	17	computer	computer	NOUN
ma-294	5	18	science	science	NOUN
ma-294	5	19	.	.	PUNCT
ma-294	6	1	they	they	PRON
ma-294	6	2	involve	involve	VERB
ma-294	6	3	finding	find	VERB
ma-294	6	4	the	the	DET
ma-294	6	5	best	good	ADJ
ma-294	6	6	value	value	NOUN
ma-294	6	7	(	(	PUNCT
ma-294	6	8	maximum	maximum	ADJ
ma-294	6	9	or	or	CCONJ
ma-294	6	10	minimum	minimum	NOUN
ma-294	6	11	)	)	PUNCT
ma-294	6	12	of	of	ADP
ma-294	6	13	an	an	DET
ma-294	6	14	objectivefunction	objectivefunction	NOUN
ma-294	6	15	.	.	PUNCT
ma-294	7	1	in	in	ADP
ma-294	7	2	unconstrained	unconstrained	ADJ
ma-294	7	3	optimization	optimization	NOUN
ma-294	7	4	problems	problem	NOUN
ma-294	7	5	,	,	PUNCT
ma-294	7	6	the	the	DET
ma-294	7	7	goal	goal	NOUN
ma-294	7	8	is	be	AUX
ma-294	7	9	to	to	PART
ma-294	7	10	find	find	VERB
ma-294	7	11	a	a	DET
ma-294	7	12	point	point	NOUN
ma-294	7	13	where	where	SCONJ
ma-294	7	14	the	the	DET
ma-294	7	15	function’svalue	function’svalue	NOUN
ma-294	7	16	reaches	reach	VERB
ma-294	7	17	a	a	DET
ma-294	7	18	maximum	maximum	ADJ
ma-294	7	19	or	or	CCONJ
ma-294	7	20	minimum	minimum	NOUN
ma-294	7	21	without	without	ADP
ma-294	7	22	being	be	AUX
ma-294	7	23	restricted	restrict	VERB
ma-294	7	24	by	by	ADP
ma-294	7	25	any	any	DET
ma-294	7	26	conditions	condition	NOUN
ma-294	7	27	.	.	PUNCT
ma-294	8	1	currently	currently	ADV
ma-294	8	2	,	,	PUNCT
ma-294	8	3	thereare	thereare	VERB
ma-294	8	4	many	many	ADJ
ma-294	8	5	different	different	ADJ
ma-294	8	6	methods	method	NOUN
ma-294	8	7	to	to	PART
ma-294	8	8	solve	solve	VERB
ma-294	8	9	unconstrained	unconstrained	ADJ
ma-294	8	10	optimization	optimization	NOUN
ma-294	8	11	problems	problem	NOUN
ma-294	8	12	,	,	PUNCT
ma-294	8	13	one	one	NUM
ma-294	8	14	of	of	ADP
ma-294	8	15	which	which	PRON
ma-294	8	16	is	be	AUX
ma-294	8	17	the	the	DET
ma-294	8	18	newtonmethod	newtonmethod	NOUN
ma-294	8	19	.	.	PUNCT
ma-294	9	1	this	this	DET
ma-294	9	2	method	method	NOUN
ma-294	9	3	is	be	AUX
ma-294	9	4	based	base	VERB
ma-294	9	5	on	on	ADP
ma-294	9	6	using	use	VERB
ma-294	9	7	a	a	DET
ma-294	9	8	second	second	ADJ
ma-294	9	9	-	-	PUNCT
ma-294	9	10	order	order	NOUN
ma-294	9	11	taylor	taylor	PROPN
ma-294	9	12	series	series	PROPN
ma-294	9	13	expansion	expansion	NOUN
ma-294	9	14	to	to	PART
ma-294	9	15	approximate	approximate	VERB
ma-294	9	16	theobjective	theobjective	NOUN
ma-294	9	17	function	function	NOUN
ma-294	9	18	.	.	PUNCT
ma-294	10	1	by	by	ADP
ma-294	10	2	calculating	calculate	VERB
ma-294	10	3	the	the	DET
ma-294	10	4	first	first	ADJ
ma-294	10	5	derivative	derivative	ADJ
ma-294	10	6	(	(	PUNCT
ma-294	10	7	gradient	gradient	NOUN
ma-294	10	8	)	)	PUNCT
ma-294	10	9	and	and	CCONJ
ma-294	10	10	second	second	ADJ
ma-294	10	11	derivative	derivative	ADJ
ma-294	10	12	(	(	PUNCT
ma-294	10	13	hessian	hessian	NOUN
ma-294	10	14	matrix)of	matrix)of	ADV
ma-294	10	15	the	the	DET
ma-294	10	16	function	function	NOUN
ma-294	10	17	,	,	PUNCT
ma-294	10	18	the	the	DET
ma-294	10	19	newton	newton	PROPN
ma-294	10	20	method	method	NOUN
ma-294	10	21	determines	determine	VERB
ma-294	10	22	the	the	DET
ma-294	10	23	direction	direction	NOUN
ma-294	10	24	and	and	CCONJ
ma-294	10	25	step	step	NOUN
ma-294	10	26	size	size	NOUN
ma-294	10	27	to	to	PART
ma-294	10	28	find	find	VERB
ma-294	10	29	the	the	DET
ma-294	10	30	extrema	extrema	NOUN
ma-294	10	31	.	.	PUNCT
ma-294	11	1	thismethod	thismethod	NOUN
ma-294	11	2	has	have	VERB
ma-294	11	3	a	a	DET
ma-294	11	4	very	very	ADV
ma-294	11	5	fast	fast	ADJ
ma-294	11	6	convergence	convergence	NOUN
ma-294	11	7	rate	rate	NOUN
ma-294	11	8	when	when	SCONJ
ma-294	11	9	near	near	ADP
ma-294	11	10	the	the	DET
ma-294	11	11	solution	solution	NOUN
ma-294	11	12	and	and	CCONJ
ma-294	11	13	is	be	AUX
ma-294	11	14	particularly	particularly	ADV
ma-294	11	15	effective	effective	ADJ
ma-294	11	16	forproblems	forproblem	NOUN
ma-294	11	17	with	with	ADP
ma-294	11	18	complex	complex	ADJ
ma-294	11	19	mathematical	mathematical	ADJ
ma-294	11	20	structures	structure	NOUN
ma-294	11	21	.	.	PUNCT
ma-294	12	1	in	in	ADP
ma-294	12	2	this	this	DET
ma-294	12	3	paper	paper	NOUN
ma-294	12	4	,	,	PUNCT
ma-294	12	5	we	we	PRON
ma-294	12	6	introduce	introduce	VERB
ma-294	12	7	a	a	DET
ma-294	12	8	gauss	gauss	ADJ
ma-294	12	9	-	-	PUNCT
ma-294	12	10	seidel	seidel	NOUN
ma-294	12	11	-	-	PUNCT
ma-294	12	12	typealgorithm	typealgorithm	PROPN
ma-294	12	13	implemented	implement	VERB
ma-294	12	14	for	for	ADP
ma-294	12	15	the	the	DET
ma-294	12	16	newton	newton	PROPN
ma-294	12	17	and	and	CCONJ
ma-294	12	18	quasi	quasi	PROPN
ma-294	12	19	-	-	PROPN
ma-294	12	20	newton	newton	PROPN
ma-294	12	21	methods	method	NOUN
ma-294	12	22	,	,	PUNCT
ma-294	12	23	which	which	PRON
ma-294	12	24	is	be	AUX
ma-294	12	25	an	an	DET
ma-294	12	26	efficient	efficient	ADJ
ma-294	12	27	approachfor	approachfor	NOUN
ma-294	12	28	finding	find	VERB
ma-294	12	29	solutions	solution	NOUN
ma-294	12	30	to	to	ADP
ma-294	12	31	optimization	optimization	NOUN
ma-294	12	32	problems	problem	NOUN
ma-294	12	33	when	when	SCONJ
ma-294	12	34	the	the	DET
ma-294	12	35	objective	objective	ADJ
ma-294	12	36	function	function	NOUN
ma-294	12	37	is	be	AUX
ma-294	12	38	a	a	DET
ma-294	12	39	convex	convex	ADJ
ma-294	12	40	functional	functional	ADJ
ma-294	12	41	.	.	PUNCT
ma-294	13	1	wealso	wealso	PROPN
ma-294	13	2	present	present	VERB
ma-294	13	3	some	some	DET
ma-294	13	4	computational	computational	ADJ
ma-294	13	5	results	result	NOUN
ma-294	13	6	for	for	ADP
ma-294	13	7	the	the	DET
ma-294	13	8	algorithm	algorithm	NOUN
ma-294	13	9	to	to	PART
ma-294	13	10	illustrate	illustrate	VERB
ma-294	13	11	the	the	DET
ma-294	13	12	convergence	convergence	NOUN
ma-294	13	13	of	of	ADP
ma-294	13	14	the	the	DET
ma-294	13	15	method	method	NOUN
ma-294	13	16	.	.	PUNCT
ma-294	14	1	1	1	X
ma-294	14	2	.	.	X
ma-294	14	3	introduction	introduction	NOUN
ma-294	14	4	in	in	ADP
ma-294	14	5	this	this	DET
ma-294	14	6	paper	paper	NOUN
ma-294	14	7	,	,	PUNCT
ma-294	14	8	we	we	PRON
ma-294	14	9	focus	focus	VERB
ma-294	14	10	on	on	ADP
ma-294	14	11	solving	solve	VERB
ma-294	14	12	the	the	DET
ma-294	14	13	unconstrained	unconstrained	ADJ
ma-294	14	14	nonlinear	nonlinear	ADJ
ma-294	14	15	optimization	optimization	NOUN
ma-294	14	16	problem	problem	NOUN
ma-294	14	17	min	min	PROPN
ma-294	14	18	x∈rn	x∈rn	PROPN
ma-294	14	19	f	f	PROPN
ma-294	14	20	(	(	PUNCT
ma-294	14	21	x	x	X
ma-294	14	22	)	)	PUNCT
ma-294	14	23	(	(	PUNCT
ma-294	14	24	1	1	X
ma-294	14	25	)	)	PUNCT
ma-294	14	26	where	where	SCONJ
ma-294	14	27	f	f	PROPN
ma-294	14	28	(	(	PUNCT
ma-294	14	29	x	x	X
ma-294	14	30	)	)	PUNCT
ma-294	14	31	is	be	AUX
ma-294	14	32	a	a	DET
ma-294	14	33	convex	convex	NOUN
ma-294	14	34	functional	functional	ADJ
ma-294	14	35	with	with	ADP
ma-294	14	36	second	second	ADJ
ma-294	14	37	derivative	derivative	NOUN
ma-294	14	38	on	on	ADP
ma-294	14	39	rn	rn	PROPN
ma-294	14	40	.	.	PUNCT
ma-294	14	41	optimization	optimization	NOUN
ma-294	14	42	problem	problem	NOUN
ma-294	14	43	(	(	PUNCT
ma-294	14	44	1	1	X
ma-294	14	45	)	)	PUNCT
ma-294	14	46	is	be	AUX
ma-294	14	47	alsoa	alsoa	ADJ
ma-294	14	48	problem	problem	NOUN
ma-294	14	49	derived	derive	VERB
ma-294	14	50	from	from	ADP
ma-294	14	51	many	many	ADJ
ma-294	14	52	problems	problem	NOUN
ma-294	14	53	in	in	ADP
ma-294	14	54	different	different	ADJ
ma-294	14	55	fields	field	NOUN
ma-294	14	56	in	in	ADP
ma-294	14	57	economics	economic	NOUN
ma-294	14	58	and	and	CCONJ
ma-294	14	59	engineering	engineering	NOUN
ma-294	14	60	.	.	PUNCT
ma-294	15	1	solvingproblem	solvingproblem	NOUN
ma-294	15	2	(	(	PUNCT
ma-294	15	3	1	1	X
ma-294	15	4	)	)	PUNCT
ma-294	15	5	can	can	AUX
ma-294	15	6	lead	lead	VERB
ma-294	15	7	to	to	ADP
ma-294	15	8	solving	solve	VERB
ma-294	15	9	a	a	DET
ma-294	15	10	system	system	NOUN
ma-294	15	11	of	of	ADP
ma-294	15	12	nonlinear	nonlinear	ADJ
ma-294	15	13	equations	equation	NOUN
ma-294	15	14	and	and	CCONJ
ma-294	15	15	has	have	VERB
ma-294	15	16	many	many	ADJ
ma-294	15	17	different	different	ADJ
ma-294	15	18	appli	appli	NOUN
ma-294	15	19	-	-	PUNCT
ma-294	15	20	cations	cation	NOUN
ma-294	15	21	,	,	PUNCT
ma-294	15	22	for	for	ADP
ma-294	15	23	example	example	NOUN
ma-294	15	24	in	in	ADP
ma-294	15	25	solving	solve	VERB
ma-294	15	26	the	the	DET
ma-294	15	27	`	`	PUNCT
ma-294	15	28	1	1	NUM
ma-294	15	29	-	-	PUNCT
ma-294	15	30	norm	norm	NOUN
ma-294	15	31	problem	problem	NOUN
ma-294	15	32	arising	arise	VERB
ma-294	15	33	from	from	ADP
ma-294	15	34	compressing	compress	VERB
ma-294	15	35	sensing	sense	VERB
ma-294	15	36	[	[	X
ma-294	15	37	1][4	1][4	NUM
ma-294	15	38	]	]	X
ma-294	15	39	,	,	PUNCT
ma-294	15	40	invariational	invariational	ADJ
ma-294	15	41	inequalities	inequality	NOUN
ma-294	15	42	problems	problem	NOUN
ma-294	15	43	[	[	X
ma-294	15	44	5][6	5][6	NUM
ma-294	15	45	]	]	PUNCT
ma-294	15	46	,	,	PUNCT
ma-294	15	47	and	and	CCONJ
ma-294	15	48	optimal	optimal	ADJ
ma-294	15	49	power	power	NOUN
ma-294	15	50	flow	flow	NOUN
ma-294	15	51	equations	equation	NOUN
ma-294	16	1	[	[	X
ma-294	16	2	7	7	X
ma-294	16	3	]	]	PUNCT
ma-294	16	4	among	among	ADP
ma-294	16	5	others	other	NOUN
ma-294	16	6	.	.	PUNCT
ma-294	17	1	ina	ina	PROPN
ma-294	17	2	broader	broad	ADJ
ma-294	17	3	sense	sense	NOUN
ma-294	17	4	,	,	PUNCT
ma-294	17	5	optimization	optimization	NOUN
ma-294	17	6	should	should	AUX
ma-294	17	7	be	be	AUX
ma-294	17	8	understood	understand	VERB
ma-294	17	9	as	as	ADP
ma-294	17	10	the	the	DET
ma-294	17	11	activities	activity	NOUN
ma-294	17	12	aimed	aim	VERB
ma-294	17	13	at	at	ADP
ma-294	17	14	obtaining	obtain	VERB
ma-294	17	15	the	the	DET
ma-294	17	16	bestresult	bestresult	NOUN
ma-294	17	17	under	under	ADP
ma-294	17	18	certain	certain	ADJ
ma-294	17	19	conditions	condition	NOUN
ma-294	17	20	(	(	PUNCT
ma-294	17	21	maximizing	maximize	VERB
ma-294	17	22	profit	profit	NOUN
ma-294	17	23	,	,	PUNCT
ma-294	17	24	minimizing	minimize	VERB
ma-294	17	25	costs	cost	NOUN
ma-294	17	26	)	)	PUNCT
ma-294	17	27	.	.	PUNCT
ma-294	18	1	the	the	DET
ma-294	18	2	theory	theory	NOUN
ma-294	18	3	of	of	ADP
ma-294	18	4	optimizationmethods	optimizationmethod	NOUN
ma-294	18	5	is	be	AUX
ma-294	18	6	not	not	PART
ma-294	18	7	new	new	ADJ
ma-294	18	8	,	,	PUNCT
ma-294	18	9	there	there	PRON
ma-294	18	10	are	be	VERB
ma-294	18	11	a	a	DET
ma-294	18	12	huge	huge	ADJ
ma-294	18	13	number	number	NOUN
ma-294	18	14	of	of	ADP
ma-294	18	15	optimization	optimization	NOUN
ma-294	18	16	methods	method	NOUN
ma-294	18	17	:	:	PUNCT
ma-294	18	18	methods	method	NOUN
ma-294	18	19	based	base	VERB
ma-294	18	20	on	on	ADP
ma-294	18	21	the	the	DET
ma-294	18	22	use	use	NOUN
ma-294	18	23	received	receive	VERB
ma-294	18	24	:	:	PUNCT
ma-294	18	25	27	27	NUM
ma-294	18	26	oct	oct	NOUN
ma-294	18	27	2024	2024	NUM
ma-294	18	28	.	.	PUNCT
ma-294	19	1	key	key	ADJ
ma-294	19	2	words	word	NOUN
ma-294	19	3	and	and	CCONJ
ma-294	19	4	phrases	phrase	NOUN
ma-294	19	5	.	.	PUNCT
ma-294	20	1	convex	convex	PROPN
ma-294	20	2	optimization	optimization	NOUN
ma-294	20	3	;	;	PUNCT
ma-294	20	4	newton	newton	PROPN
ma-294	20	5	;	;	PUNCT
ma-294	20	6	quasi	quasi	NOUN
ma-294	20	7	-	-	PROPN
ma-294	20	8	newton	newton	PROPN
ma-294	20	9	;	;	PUNCT
ma-294	20	10	hessen	hessen	NOUN
ma-294	20	11	matrix	matrix	NOUN
ma-294	20	12	;	;	PUNCT
ma-294	20	13	gauss	gauss	NUM
ma-294	20	14	–	–	PUNCT
ma-294	20	15	seidel.1	seidel.1	ADV
ma-294	20	16	https://adac.ee	https://adac.ee	PROPN
ma-294	20	17	https://doi.org/10.28924/ada/ma.5.9	https://doi.org/10.28924/ada/ma.5.9	PROPN
ma-294	20	18	eur	eur	NOUN
ma-294	20	19	.	.	PUNCT
ma-294	21	1	j.	j.	PROPN
ma-294	21	2	math	math	PROPN
ma-294	21	3	.	.	PUNCT
ma-294	22	1	anal	anal	PROPN
ma-294	22	2	.	.	PUNCT
ma-294	23	1	10.28924	10.28924	NUM
ma-294	23	2	/	/	SYM
ma-294	23	3	ada	ada	PROPN
ma-294	23	4	/	/	SYM
ma-294	23	5	ma.5.9	ma.5.9	PROPN
ma-294	23	6	2of	2of	PROPN
ma-294	23	7	lagrange	lagrange	PROPN
ma-294	23	8	multipliers	multiplier	NOUN
ma-294	23	9	,	,	PUNCT
ma-294	23	10	methods	method	NOUN
ma-294	23	11	of	of	ADP
ma-294	23	12	dynamic	dynamic	ADJ
ma-294	23	13	programming	programming	NOUN
ma-294	23	14	,	,	PUNCT
ma-294	23	15	and	and	CCONJ
ma-294	23	16	methods	method	NOUN
ma-294	23	17	of	of	ADP
ma-294	23	18	the	the	DET
ma-294	23	19	calculus	calculus	NOUN
ma-294	23	20	of	of	ADP
ma-294	23	21	vari	vari	NOUN
ma-294	23	22	-	-	PUNCT
ma-294	23	23	ations	ation	NOUN
ma-294	23	24	,	,	PUNCT
ma-294	23	25	linear	linear	ADJ
ma-294	23	26	and	and	CCONJ
ma-294	23	27	nonlinear	nonlinear	ADJ
ma-294	23	28	programming	programming	NOUN
ma-294	23	29	methods	method	NOUN
ma-294	23	30	,	,	PUNCT
ma-294	23	31	there	there	PRON
ma-294	23	32	are	be	VERB
ma-294	23	33	currently	currently	ADV
ma-294	23	34	many	many	ADJ
ma-294	23	35	different	different	ADJ
ma-294	23	36	solutionsdepending	solutionsdepende	VERB
ma-294	23	37	on	on	ADP
ma-294	23	38	the	the	DET
ma-294	23	39	objective	objective	ADJ
ma-294	23	40	function	function	NOUN
ma-294	23	41	.	.	PUNCT
ma-294	24	1	one	one	NUM
ma-294	24	2	of	of	ADP
ma-294	24	3	the	the	DET
ma-294	24	4	simplest	simple	ADJ
ma-294	24	5	methods	method	NOUN
ma-294	24	6	is	be	AUX
ma-294	24	7	the	the	DET
ma-294	24	8	steepest	steep	ADJ
ma-294	24	9	descent	descent	NOUN
ma-294	24	10	methodor	methodor	ADV
ma-294	24	11	also	also	ADV
ma-294	24	12	known	know	VERB
ma-294	24	13	as	as	ADP
ma-294	24	14	the	the	DET
ma-294	24	15	gradient	gradient	ADJ
ma-294	24	16	descent	descent	NOUN
ma-294	24	17	method	method	NOUN
ma-294	24	18	[	[	X
ma-294	24	19	2	2	NUM
ma-294	24	20	]	]	PUNCT
ma-294	24	21	,	,	PUNCT
ma-294	24	22	[	[	X
ma-294	24	23	8	8	NUM
ma-294	24	24	]	]	PUNCT
ma-294	24	25	,	,	PUNCT
ma-294	24	26	this	this	DET
ma-294	24	27	method	method	NOUN
ma-294	24	28	is	be	AUX
ma-294	24	29	simple	simple	ADJ
ma-294	24	30	and	and	CCONJ
ma-294	24	31	applicable	applicable	ADJ
ma-294	24	32	to	to	ADP
ma-294	24	33	afairly	afairly	ADV
ma-294	24	34	wide	wide	ADJ
ma-294	24	35	class	class	NOUN
ma-294	24	36	of	of	ADP
ma-294	24	37	objective	objective	ADJ
ma-294	24	38	functions	function	NOUN
ma-294	24	39	,	,	PUNCT
ma-294	24	40	the	the	DET
ma-294	24	41	content	content	NOUN
ma-294	24	42	of	of	ADP
ma-294	24	43	the	the	DET
ma-294	24	44	method	method	NOUN
ma-294	24	45	is	be	AUX
ma-294	24	46	to	to	PART
ma-294	24	47	give	give	VERB
ma-294	24	48	a	a	DET
ma-294	24	49	sequence	sequence	NOUN
ma-294	24	50	of	of	ADP
ma-294	24	51	iter	iter	NOUN
ma-294	24	52	-	-	PUNCT
ma-294	24	53	ations	ation	NOUN
ma-294	24	54	x	x	SYM
ma-294	24	55	(	(	PUNCT
ma-294	24	56	k+1	k+1	NOUN
ma-294	24	57	)	)	PUNCT
ma-294	24	58	=	=	SYM
ma-294	24	59	x	x	SYM
ma-294	24	60	(	(	PUNCT
ma-294	24	61	k	k	NOUN
ma-294	24	62	)	)	PUNCT
ma-294	25	1	−	−	PROPN
ma-294	25	2	αk∇f	αk∇f	PROPN
ma-294	25	3	(	(	PUNCT
ma-294	25	4	xk	xk	PROPN
ma-294	25	5	)	)	PUNCT
ma-294	25	6	,	,	PUNCT
ma-294	25	7	αk	αk	AUX
ma-294	25	8	>	>	X
ma-294	25	9	0	0	NUM
ma-294	25	10	,	,	PUNCT
ma-294	25	11	where	where	SCONJ
ma-294	25	12	αk	αk	NOUN
ma-294	25	13	is	be	AUX
ma-294	25	14	the	the	DET
ma-294	25	15	step	step	NOUN
ma-294	25	16	length	length	NOUN
ma-294	25	17	determined	determine	VERB
ma-294	25	18	by	by	ADP
ma-294	25	19	armijo’srule	armijo’srule	NOUN
ma-294	25	20	after	after	ADP
ma-294	25	21	the	the	DET
ma-294	25	22	exact	exact	ADJ
ma-294	25	23	or	or	CCONJ
ma-294	25	24	inexact	inexact	ADJ
ma-294	25	25	line	line	NOUN
ma-294	25	26	search	search	NOUN
ma-294	25	27	,	,	PUNCT
ma-294	25	28	this	this	DET
ma-294	25	29	method	method	NOUN
ma-294	25	30	has	have	VERB
ma-294	25	31	the	the	DET
ma-294	25	32	disadvantage	disadvantage	NOUN
ma-294	25	33	of	of	ADP
ma-294	25	34	linear	linear	ADJ
ma-294	25	35	convergencerate	convergencerate	NOUN
ma-294	25	36	.	.	PUNCT
ma-294	26	1	we	we	PRON
ma-294	26	2	want	want	VERB
ma-294	26	3	to	to	PART
ma-294	26	4	improve	improve	VERB
ma-294	26	5	the	the	DET
ma-294	26	6	efficiency	efficiency	NOUN
ma-294	26	7	of	of	ADP
ma-294	26	8	the	the	DET
ma-294	26	9	algorithm	algorithm	NOUN
ma-294	26	10	’s	’s	PART
ma-294	26	11	convergence	convergence	NOUN
ma-294	26	12	,	,	PUNCT
ma-294	26	13	the	the	DET
ma-294	26	14	newton	newton	PROPN
ma-294	26	15	method	method	NOUN
ma-294	26	16	is	be	AUX
ma-294	26	17	agood	agood	ADJ
ma-294	26	18	choice	choice	NOUN
ma-294	26	19	[	[	X
ma-294	26	20	9][12	9][12	NOUN
ma-294	26	21	]	]	X
ma-294	26	22	,	,	PUNCT
ma-294	26	23	newton	newton	PROPN
ma-294	26	24	’s	’s	PART
ma-294	26	25	method	method	NOUN
ma-294	26	26	was	be	AUX
ma-294	26	27	first	first	ADV
ma-294	26	28	proposed	propose	VERB
ma-294	26	29	by	by	ADP
ma-294	26	30	isaac	isaac	PROPN
ma-294	26	31	newton	newton	PROPN
ma-294	26	32	in	in	ADP
ma-294	26	33	1964	1964	NUM
ma-294	26	34	when	when	SCONJ
ma-294	26	35	findingsolutions	findingsolution	NOUN
ma-294	26	36	to	to	ADP
ma-294	26	37	nonlinear	nonlinear	ADJ
ma-294	26	38	equations	equation	NOUN
ma-294	26	39	.	.	PUNCT
ma-294	27	1	to	to	ADP
ma-294	27	2	date	date	NOUN
ma-294	27	3	,	,	PUNCT
ma-294	27	4	newton	newton	PROPN
ma-294	27	5	’s	’s	PART
ma-294	27	6	methods	method	NOUN
ma-294	27	7	have	have	AUX
ma-294	27	8	widely	widely	ADV
ma-294	27	9	been	be	AUX
ma-294	27	10	used	use	VERB
ma-294	27	11	for	for	ADP
ma-294	27	12	solvingthe	solvingthe	PROPN
ma-294	27	13	unconstrained	unconstrained	ADJ
ma-294	27	14	nonlinear	nonlinear	ADJ
ma-294	27	15	optimization	optimization	NOUN
ma-294	27	16	problem	problem	NOUN
ma-294	27	17	.	.	PUNCT
ma-294	28	1	as	as	ADP
ma-294	28	2	a	a	DET
ma-294	28	3	result	result	NOUN
ma-294	28	4	,	,	PUNCT
ma-294	28	5	studies	study	NOUN
ma-294	28	6	of	of	ADP
ma-294	28	7	newton	newton	PROPN
ma-294	28	8	’s	’s	PART
ma-294	28	9	method	method	PROPN
ma-294	28	10	forman	forman	PROPN
ma-294	28	11	extremely	extremely	ADV
ma-294	28	12	active	active	ADJ
ma-294	28	13	area	area	NOUN
ma-294	28	14	of	of	ADP
ma-294	28	15	research	research	NOUN
ma-294	28	16	,	,	PUNCT
ma-294	28	17	with	with	SCONJ
ma-294	28	18	new	new	ADJ
ma-294	28	19	variants	variant	NOUN
ma-294	28	20	being	be	AUX
ma-294	28	21	constantly	constantly	ADV
ma-294	28	22	developed	develop	VERB
ma-294	28	23	and	and	CCONJ
ma-294	28	24	tested.basic	tested.basic	ADJ
ma-294	28	25	results	result	NOUN
ma-294	28	26	on	on	ADP
ma-294	28	27	newton	newton	PROPN
ma-294	28	28	’s	’s	PART
ma-294	28	29	method	method	NOUN
ma-294	28	30	and	and	CCONJ
ma-294	28	31	comprehensive	comprehensive	ADJ
ma-294	28	32	lists	list	NOUN
ma-294	28	33	of	of	ADP
ma-294	28	34	references	reference	NOUN
ma-294	28	35	can	can	AUX
ma-294	28	36	be	be	AUX
ma-294	28	37	found	find	VERB
ma-294	28	38	,	,	PUNCT
ma-294	28	39	e.g.	e.g.	ADV
ma-294	28	40	,	,	PUNCT
ma-294	28	41	in	in	ADP
ma-294	28	42	thebooks	thebook	NOUN
ma-294	28	43	by	by	ADP
ma-294	28	44	dennis	dennis	PROPN
ma-294	28	45	and	and	CCONJ
ma-294	28	46	schnabel	schnabel	PROPN
ma-294	29	1	[	[	X
ma-294	29	2	13	13	NUM
ma-294	29	3	]	]	PUNCT
ma-294	29	4	,	,	PUNCT
ma-294	29	5	ostrowski	ostrowski	VERB
ma-294	30	1	[	[	X
ma-294	30	2	14	14	NUM
ma-294	30	3	]	]	PUNCT
ma-294	30	4	,	,	PUNCT
ma-294	30	5	ortega	ortega	PROPN
ma-294	30	6	and	and	CCONJ
ma-294	30	7	rheinboldt	rheinboldt	ADJ
ma-294	31	1	[	[	X
ma-294	31	2	15	15	NUM
ma-294	31	3	]	]	PUNCT
ma-294	31	4	,	,	PUNCT
ma-294	31	5	deuflhard	deuflhard	NOUN
ma-294	31	6	[	[	X
ma-294	31	7	16	16	NUM
ma-294	31	8	]	]	X
ma-294	31	9	andcorless	andcorless	NOUN
ma-294	31	10	and	and	CCONJ
ma-294	31	11	fillion	fillion	NOUN
ma-294	32	1	[	[	X
ma-294	32	2	17	17	NUM
ma-294	32	3	]	]	PUNCT
ma-294	32	4	,	,	PUNCT
ma-294	32	5	survey	survey	NOUN
ma-294	32	6	of	of	ADP
ma-294	32	7	newton	newton	PROPN
ma-294	32	8	’s	’s	PART
ma-294	32	9	method	method	NOUN
ma-294	32	10	in	in	ADP
ma-294	32	11	[	[	X
ma-294	32	12	18	18	NUM
ma-294	32	13	]	]	PUNCT
ma-294	32	14	.	.	PUNCT
ma-294	33	1	the	the	DET
ma-294	33	2	general	general	ADJ
ma-294	33	3	iterative	iterative	NOUN
ma-294	33	4	rule	rule	NOUN
ma-294	33	5	for	for	ADP
ma-294	33	6	solving	solve	VERB
ma-294	33	7	(	(	PUNCT
ma-294	33	8	1)starts	1)starts	NUM
ma-294	33	9	from	from	ADP
ma-294	33	10	an	an	DET
ma-294	33	11	initial	initial	ADJ
ma-294	33	12	approximation	approximation	NOUN
ma-294	33	13	and	and	CCONJ
ma-294	33	14	generates	generate	VERB
ma-294	33	15	a	a	DET
ma-294	33	16	sequence	sequence	NOUN
ma-294	33	17	using	use	VERB
ma-294	33	18	the	the	DET
ma-294	33	19	general	general	ADJ
ma-294	33	20	iterative	iterative	NOUN
ma-294	33	21	scheme	scheme	NOUN
ma-294	33	22	x(k+1	x(k+1	NUM
ma-294	33	23	)	)	PUNCT
ma-294	33	24	=	=	PUNCT
ma-294	33	25	x(k	x(k	PROPN
ma-294	33	26	)	)	PUNCT
ma-294	33	27	+	+	CCONJ
ma-294	33	28	αkdk	αkdk	NOUN
ma-294	33	29	.	.	PUNCT
ma-294	34	1	(	(	PUNCT
ma-294	34	2	2	2	X
ma-294	34	3	)	)	PUNCT
ma-294	34	4	where	where	SCONJ
ma-294	34	5	dk	dk	PROPN
ma-294	34	6	is	be	AUX
ma-294	34	7	an	an	DET
ma-294	34	8	appropriate	appropriate	ADJ
ma-294	34	9	search	search	NOUN
ma-294	34	10	direction	direction	NOUN
ma-294	34	11	.	.	PUNCT
ma-294	35	1	general	general	ADJ
ma-294	35	2	class	class	NOUN
ma-294	35	3	of	of	ADP
ma-294	35	4	algorithms	algorithm	NOUN
ma-294	35	5	of	of	ADP
ma-294	35	6	the	the	DET
ma-294	35	7	form	form	NOUN
ma-294	35	8	(	(	PUNCT
ma-294	35	9	2	2	X
ma-294	35	10	)	)	PUNCT
ma-294	35	11	is	be	AUX
ma-294	35	12	knownas	knowna	NOUN
ma-294	35	13	the	the	DET
ma-294	35	14	line	line	NOUN
ma-294	35	15	search	search	NOUN
ma-294	35	16	algorithms	algorithm	NOUN
ma-294	35	17	.	.	PUNCT
ma-294	36	1	the	the	DET
ma-294	36	2	method	method	NOUN
ma-294	36	3	has	have	VERB
ma-294	36	4	a	a	DET
ma-294	36	5	local	local	ADJ
ma-294	36	6	quadratic	quadratic	ADJ
ma-294	36	7	convergence	convergence	NOUN
ma-294	36	8	,	,	PUNCT
ma-294	36	9	thus	thus	ADV
ma-294	36	10	convergingextremely	convergingextremely	ADV
ma-294	36	11	fast	fast	VERB
ma-294	36	12	in	in	ADP
ma-294	36	13	a	a	DET
ma-294	36	14	neighbourhood	neighbourhood	NOUN
ma-294	36	15	of	of	ADP
ma-294	36	16	the	the	DET
ma-294	36	17	solution	solution	NOUN
ma-294	36	18	[	[	X
ma-294	36	19	19	19	NUM
ma-294	36	20	]	]	PUNCT
ma-294	36	21	.	.	PUNCT
ma-294	37	1	nowadays	nowadays	ADV
ma-294	37	2	,	,	PUNCT
ma-294	37	3	this	this	DET
ma-294	37	4	method	method	NOUN
ma-294	37	5	is	be	AUX
ma-294	37	6	extended	extend	VERB
ma-294	37	7	tofind	tofind	ADJ
ma-294	37	8	optimal	optimal	ADJ
ma-294	37	9	solutions	solution	NOUN
ma-294	37	10	for	for	ADP
ma-294	37	11	multivariable	multivariable	ADJ
ma-294	37	12	functions	function	NOUN
ma-294	37	13	based	base	VERB
ma-294	37	14	on	on	ADP
ma-294	37	15	taylor	taylor	PROPN
ma-294	37	16	expansion	expansion	NOUN
ma-294	37	17	,	,	PUNCT
ma-294	37	18	the	the	DET
ma-294	37	19	solution	solution	NOUN
ma-294	37	20	of	of	ADP
ma-294	37	21	theoptimization	theoptimization	NOUN
ma-294	37	22	problem	problem	NOUN
ma-294	37	23	is	be	AUX
ma-294	37	24	performed	perform	VERB
ma-294	37	25	in	in	ADP
ma-294	37	26	an	an	DET
ma-294	37	27	iterative	iterative	NOUN
ma-294	37	28	sequence	sequence	NOUN
ma-294	37	29	x(k+1	x(k+1	PUNCT
ma-294	37	30	)	)	PUNCT
ma-294	38	1	=	=	SYM
ma-294	38	2	x(k)−	x(k)−	PROPN
ma-294	38	3	[	[	PUNCT
ma-294	38	4	∇2f	∇2f	PROPN
ma-294	38	5	(	(	PUNCT
ma-294	38	6	x(k	x(k	PROPN
ma-294	38	7	)	)	PUNCT
ma-294	38	8	)	)	PUNCT
ma-294	39	1	]	]	PUNCT
ma-294	39	2	−1∇f	−1∇f	NOUN
ma-294	39	3	(	(	PUNCT
ma-294	39	4	x(k)),if	x(k)),if	ADP
ma-294	39	5	the	the	DET
ma-294	39	6	objective	objective	ADJ
ma-294	39	7	function	function	NOUN
ma-294	39	8	is	be	AUX
ma-294	39	9	not	not	PART
ma-294	39	10	quadratic	quadratic	ADJ
ma-294	39	11	,	,	PUNCT
ma-294	39	12	the	the	DET
ma-294	39	13	above	above	ADJ
ma-294	39	14	iteration	iteration	NOUN
ma-294	39	15	sequence	sequence	NOUN
ma-294	39	16	may	may	AUX
ma-294	39	17	diverge	diverge	VERB
ma-294	39	18	or	or	CCONJ
ma-294	39	19	converge	converge	VERB
ma-294	39	20	to	to	ADP
ma-294	39	21	alocal	alocal	ADJ
ma-294	39	22	minimum	minimum	NOUN
ma-294	39	23	or	or	CCONJ
ma-294	39	24	converge	converge	VERB
ma-294	39	25	to	to	ADP
ma-294	39	26	a	a	DET
ma-294	39	27	saddle	saddle	NOUN
ma-294	39	28	point	point	NOUN
ma-294	39	29	.	.	PUNCT
ma-294	40	1	a	a	DET
ma-294	40	2	variant	variant	NOUN
ma-294	40	3	of	of	ADP
ma-294	40	4	newton	newton	PROPN
ma-294	40	5	’s	’s	PART
ma-294	40	6	method	method	NOUN
ma-294	40	7	introduced	introduce	VERB
ma-294	40	8	in	in	ADP
ma-294	40	9	[	[	X
ma-294	40	10	20	20	NUM
ma-294	40	11	]	]	PUNCT
ma-294	40	12	is	be	AUX
ma-294	40	13	thegeneralized	thegeneralize	VERB
ma-294	40	14	newton	newton	PROPN
ma-294	40	15	’s	’s	PART
ma-294	40	16	method	method	NOUN
ma-294	40	17	,	,	PUNCT
ma-294	40	18	in	in	ADP
ma-294	40	19	which	which	PRON
ma-294	40	20	the	the	DET
ma-294	40	21	solution	solution	NOUN
ma-294	40	22	to	to	ADP
ma-294	40	23	the	the	DET
ma-294	40	24	optimization	optimization	NOUN
ma-294	40	25	problem	problem	NOUN
ma-294	40	26	is	be	AUX
ma-294	40	27	computed	compute	VERB
ma-294	40	28	by	by	ADP
ma-294	40	29	theiteration	theiteration	NOUN
ma-294	40	30	sequence	sequence	NOUN
ma-294	40	31	x(k+1	x(k+1	PUNCT
ma-294	40	32	)	)	PUNCT
ma-294	40	33	=	=	SYM
ma-294	41	1	x(k	x(k	PROPN
ma-294	41	2	)	)	PUNCT
ma-294	42	1	−	−	PROPN
ma-294	43	1	αk	αk	INTJ
ma-294	43	2	[	[	PUNCT
ma-294	43	3	∇2f	∇2f	PROPN
ma-294	43	4	(	(	PUNCT
ma-294	43	5	x(k	x(k	PROPN
ma-294	43	6	)	)	PUNCT
ma-294	43	7	)	)	PUNCT
ma-294	43	8	]	]	X
ma-294	44	1	−1∇f	−1∇f	NOUN
ma-294	44	2	(	(	PUNCT
ma-294	44	3	x(k	x(k	PROPN
ma-294	44	4	)	)	PUNCT
ma-294	44	5	)	)	PUNCT
ma-294	44	6	,	,	PUNCT
ma-294	44	7	where	where	SCONJ
ma-294	44	8	αk	αk	NOUN
ma-294	44	9	is	be	AUX
ma-294	44	10	called	call	VERB
ma-294	44	11	the	the	DET
ma-294	44	12	step	step	NOUN
ma-294	44	13	lengthand	lengthand	NOUN
ma-294	44	14	is	be	AUX
ma-294	44	15	determined	determine	VERB
ma-294	44	16	by	by	ADP
ma-294	44	17	one	one	NUM
ma-294	44	18	-	-	PUNCT
ma-294	44	19	dimensional	dimensional	ADJ
ma-294	44	20	search	search	NOUN
ma-294	44	21	methods	method	NOUN
ma-294	44	22	in	in	ADP
ma-294	44	23	the	the	DET
ma-294	44	24	direction	direction	NOUN
ma-294	44	25	−	−	PROPN
ma-294	45	1	[	[	X
ma-294	45	2	∇2f	∇2f	X
ma-294	45	3	(	(	PUNCT
ma-294	45	4	x(k))]−1∇f	x(k))]−1∇f	PROPN
ma-294	45	5	(	(	PUNCT
ma-294	45	6	x(k	x(k	PROPN
ma-294	45	7	)	)	PUNCT
ma-294	45	8	)	)	PUNCT
ma-294	45	9	.	.	PUNCT
ma-294	46	1	however	however	ADV
ma-294	46	2	,	,	PUNCT
ma-294	46	3	in	in	ADP
ma-294	46	4	some	some	DET
ma-294	46	5	practical	practical	ADJ
ma-294	46	6	problems	problem	NOUN
ma-294	46	7	when	when	SCONJ
ma-294	46	8	leading	lead	VERB
ma-294	46	9	to	to	ADP
ma-294	46	10	optimization	optimization	NOUN
ma-294	46	11	problems	problem	NOUN
ma-294	46	12	where	where	SCONJ
ma-294	46	13	the	the	DET
ma-294	46	14	objectivefunction	objectivefunction	NOUN
ma-294	46	15	does	do	AUX
ma-294	46	16	not	not	PART
ma-294	46	17	have	have	VERB
ma-294	46	18	a	a	DET
ma-294	46	19	second	second	ADJ
ma-294	46	20	derivative	derivative	NOUN
ma-294	46	21	,	,	PUNCT
ma-294	46	22	applying	apply	VERB
ma-294	46	23	newton	newton	PROPN
ma-294	46	24	’s	’s	PART
ma-294	46	25	method	method	NOUN
ma-294	46	26	is	be	AUX
ma-294	46	27	not	not	PART
ma-294	46	28	feasible	feasible	ADJ
ma-294	46	29	.	.	PUNCT
ma-294	47	1	to	to	ADP
ma-294	47	2	overcomethis	overcomethis	PRON
ma-294	47	3	limitation	limitation	NOUN
ma-294	47	4	,	,	PUNCT
ma-294	47	5	recently	recently	ADV
ma-294	47	6	some	some	DET
ma-294	47	7	results	result	NOUN
ma-294	47	8	in	in	ADP
ma-294	47	9	[	[	X
ma-294	47	10	21	21	NUM
ma-294	47	11	]	]	PUNCT
ma-294	47	12	and	and	CCONJ
ma-294	47	13	[	[	X
ma-294	47	14	22	22	NUM
ma-294	47	15	]	]	PUNCT
ma-294	47	16	have	have	AUX
ma-294	47	17	proposed	propose	VERB
ma-294	47	18	a	a	DET
ma-294	47	19	quasi	quasi	PROPN
ma-294	47	20	newton	newton	PROPN
ma-294	47	21	algorithm	algorithm	PROPN
ma-294	47	22	forfinding	forfinde	VERB
ma-294	47	23	solutions	solution	NOUN
ma-294	47	24	to	to	ADP
ma-294	47	25	nonlinear	nonlinear	ADJ
ma-294	47	26	optimization	optimization	NOUN
ma-294	47	27	problems	problem	NOUN
ma-294	47	28	,	,	PUNCT
ma-294	47	29	showing	show	VERB
ma-294	47	30	the	the	DET
ma-294	47	31	effectiveness	effectiveness	NOUN
ma-294	47	32	of	of	ADP
ma-294	47	33	the	the	DET
ma-294	47	34	method.the	method.the	DET
ma-294	47	35	numerical	numerical	ADJ
ma-294	47	36	results	result	NOUN
ma-294	47	37	in	in	ADP
ma-294	47	38	the	the	DET
ma-294	47	39	papers	paper	NOUN
ma-294	47	40	all	all	PRON
ma-294	47	41	use	use	VERB
ma-294	47	42	jacobi	jacobi	PROPN
ma-294	47	43	iteration	iteration	NOUN
ma-294	47	44	,	,	PUNCT
ma-294	47	45	so	so	SCONJ
ma-294	47	46	we	we	PRON
ma-294	47	47	hope	hope	VERB
ma-294	47	48	to	to	PART
ma-294	47	49	improve	improve	VERB
ma-294	47	50	the	the	DET
ma-294	47	51	conver	conver	NOUN
ma-294	47	52	-	-	PUNCT
ma-294	47	53	gence	gence	NOUN
ma-294	47	54	of	of	ADP
ma-294	47	55	the	the	DET
ma-294	47	56	algorithm	algorithm	NOUN
ma-294	47	57	by	by	ADP
ma-294	47	58	applying	apply	VERB
ma-294	47	59	the	the	DET
ma-294	47	60	idea	idea	NOUN
ma-294	47	61	of	of	ADP
ma-294	47	62	gauss	gauss	ADJ
ma-294	47	63	-	-	PUNCT
ma-294	47	64	seidel	seidel	PROPN
ma-294	47	65	iteration	iteration	NOUN
ma-294	47	66	to	to	ADP
ma-294	47	67	the	the	DET
ma-294	47	68	implementation	implementation	NOUN
ma-294	47	69	ofnewton	ofnewton	NOUN
ma-294	47	70	and	and	CCONJ
ma-294	47	71	quansi	quansi	PROPN
ma-294	47	72	-	-	PUNCT
ma-294	47	73	newton	newton	PROPN
ma-294	47	74	methods	method	NOUN
ma-294	47	75	.	.	PUNCT
ma-294	48	1	so	so	ADV
ma-294	48	2	,	,	PUNCT
ma-294	48	3	in	in	ADP
ma-294	48	4	this	this	DET
ma-294	48	5	paper	paper	NOUN
ma-294	48	6	,	,	PUNCT
ma-294	48	7	we	we	PRON
ma-294	48	8	propose	propose	VERB
ma-294	48	9	gauss	gauss	PROPN
ma-294	48	10	–	–	PUNCT
ma-294	48	11	seidel	seidel	PROPN
ma-294	48	12	algorithmsimplemented	algorithmsimplemente	VERB
ma-294	48	13	for	for	ADP
ma-294	48	14	the	the	DET
ma-294	48	15	newton	newton	PROPN
ma-294	48	16	and	and	CCONJ
ma-294	48	17	quasi	quasi	PROPN
ma-294	48	18	-	-	PROPN
ma-294	48	19	newton	newton	PROPN
ma-294	48	20	method	method	NOUN
ma-294	48	21	for	for	ADP
ma-294	48	22	finding	find	VERB
ma-294	48	23	solutions	solution	NOUN
ma-294	48	24	at	at	ADP
ma-294	48	25	each	each	DET
ma-294	48	26	iterationstep	iterationstep	NOUN
ma-294	48	27	,	,	PUNCT
ma-294	48	28	in	in	ADP
ma-294	48	29	which	which	PRON
ma-294	48	30	we	we	PRON
ma-294	48	31	inherit	inherit	VERB
ma-294	48	32	the	the	DET
ma-294	48	33	information	information	NOUN
ma-294	48	34	of	of	ADP
ma-294	48	35	the	the	DET
ma-294	48	36	component	component	NOUN
ma-294	48	37	solutions	solution	NOUN
ma-294	48	38	calculated	calculate	VERB
ma-294	48	39	in	in	ADP
ma-294	48	40	the	the	DET
ma-294	48	41	current	current	ADJ
ma-294	48	42	https://doi.org/10.28924/ada/ma.5.9	https://doi.org/10.28924/ada/ma.5.9	PROPN
ma-294	48	43	eur	eur	NOUN
ma-294	48	44	.	.	PUNCT
ma-294	49	1	j.	j.	PROPN
ma-294	49	2	math	math	PROPN
ma-294	49	3	.	.	PUNCT
ma-294	50	1	anal	anal	PROPN
ma-294	50	2	.	.	PUNCT
ma-294	51	1	10.28924	10.28924	NUM
ma-294	51	2	/	/	SYM
ma-294	51	3	ada	ada	PROPN
ma-294	51	4	/	/	SYM
ma-294	51	5	ma.5.9	ma.5.9	PROPN
ma-294	51	6	3iteration	3iteration	PROPN
ma-294	51	7	instead	instead	ADV
ma-294	51	8	of	of	ADP
ma-294	51	9	using	use	VERB
ma-294	51	10	the	the	DET
ma-294	51	11	solutions	solution	NOUN
ma-294	51	12	calculated	calculate	VERB
ma-294	51	13	in	in	ADP
ma-294	51	14	the	the	DET
ma-294	51	15	previous	previous	ADJ
ma-294	51	16	iteration	iteration	NOUN
ma-294	51	17	.	.	PUNCT
ma-294	52	1	the	the	DET
ma-294	52	2	computationalresults	computationalresult	NOUN
ma-294	52	3	illustrating	illustrate	VERB
ma-294	52	4	the	the	DET
ma-294	52	5	algorithm	algorithm	NOUN
ma-294	52	6	are	be	AUX
ma-294	52	7	given	give	VERB
ma-294	52	8	to	to	PART
ma-294	52	9	confirm	confirm	VERB
ma-294	52	10	the	the	DET
ma-294	52	11	convergence	convergence	NOUN
ma-294	52	12	of	of	ADP
ma-294	52	13	the	the	DET
ma-294	52	14	algorithm	algorithm	NOUN
ma-294	52	15	.	.	PUNCT
ma-294	53	1	thepaper	thepaper	NOUN
ma-294	53	2	is	be	AUX
ma-294	53	3	organized	organize	VERB
ma-294	53	4	as	as	SCONJ
ma-294	53	5	follows	follow	VERB
ma-294	53	6	.	.	PUNCT
ma-294	54	1	section	section	NOUN
ma-294	54	2	2	2	NUM
ma-294	54	3	presents	present	VERB
ma-294	54	4	the	the	DET
ma-294	54	5	newton	newton	PROPN
ma-294	54	6	’s	’s	PART
ma-294	54	7	method	method	NOUN
ma-294	54	8	and	and	CCONJ
ma-294	54	9	implementation	implementation	NOUN
ma-294	54	10	ofthe	ofthe	ADJ
ma-294	54	11	gauss	gauss	ADJ
ma-294	54	12	-	-	PUNCT
ma-294	54	13	seidel	seidel	PROPN
ma-294	54	14	iterative	iterative	NOUN
ma-294	54	15	algorithm	algorithm	NOUN
ma-294	54	16	based	base	VERB
ma-294	54	17	on	on	ADP
ma-294	54	18	newton	newton	PROPN
ma-294	54	19	and	and	CCONJ
ma-294	54	20	quasi	quasi	PROPN
ma-294	54	21	-	-	PROPN
ma-294	54	22	newton	newton	PROPN
ma-294	54	23	methods	method	NOUN
ma-294	54	24	.	.	PUNCT
ma-294	55	1	experimentalresults	experimentalresult	NOUN
ma-294	55	2	illustrating	illustrate	VERB
ma-294	55	3	the	the	DET
ma-294	55	4	convergence	convergence	NOUN
ma-294	55	5	are	be	AUX
ma-294	55	6	presented	present	VERB
ma-294	55	7	in	in	ADP
ma-294	55	8	section	section	NOUN
ma-294	55	9	3	3	NUM
ma-294	55	10	.	.	PUNCT
ma-294	56	1	finally	finally	ADV
ma-294	56	2	,	,	PUNCT
ma-294	56	3	there	there	PRON
ma-294	56	4	are	be	VERB
ma-294	56	5	conclusions	conclusion	NOUN
ma-294	56	6	andreferences	andreference	NOUN
ma-294	56	7	.	.	PUNCT
ma-294	57	1	2	2	X
ma-294	57	2	.	.	NUM
ma-294	57	3	proposed	propose	VERB
ma-294	57	4	method	method	NOUN
ma-294	57	5	2.1	2.1	NUM
ma-294	57	6	.	.	PUNCT
ma-294	58	1	newton	newton	PROPN
ma-294	58	2	’s	’s	PART
ma-294	58	3	method.let	method.let	PROPN
ma-294	58	4	x∗	x∗	PROPN
ma-294	58	5	is	be	AUX
ma-294	58	6	the	the	DET
ma-294	58	7	minimum	minimum	ADJ
ma-294	58	8	point	point	NOUN
ma-294	58	9	of	of	ADP
ma-294	58	10	the	the	DET
ma-294	58	11	functional	functional	ADJ
ma-294	58	12	,	,	PUNCT
ma-294	58	13	then	then	ADV
ma-294	58	14	the	the	DET
ma-294	58	15	necessary	necessary	ADJ
ma-294	58	16	condition	condition	NOUN
ma-294	58	17	is	be	AUX
ma-294	58	18	∂f	∂f	PROPN
ma-294	58	19	∂xi	∂xi	NOUN
ma-294	58	20	(	(	PUNCT
ma-294	58	21	x∗	x∗	PROPN
ma-294	58	22	)	)	PUNCT
ma-294	58	23	=	=	SYM
ma-294	58	24	0	0	X
ma-294	58	25	.	.	X
ma-294	58	26	inorder	inorder	NOUN
ma-294	58	27	to	to	PART
ma-294	58	28	determine	determine	VERB
ma-294	58	29	the	the	DET
ma-294	58	30	iterative	iterative	NOUN
ma-294	58	31	sequence	sequence	NOUN
ma-294	58	32	,	,	PUNCT
ma-294	58	33	we	we	PRON
ma-294	58	34	use	use	VERB
ma-294	58	35	the	the	DET
ma-294	58	36	taylor	taylor	PROPN
ma-294	58	37	expansion	expansion	NOUN
ma-294	58	38	for	for	ADP
ma-294	58	39	f	f	PROPN
ma-294	58	40	(	(	PUNCT
ma-294	58	41	x	x	NOUN
ma-294	58	42	)	)	PUNCT
ma-294	58	43	,	,	PUNCT
ma-294	58	44	we	we	PRON
ma-294	58	45	have	have	VERB
ma-294	58	46	f	f	PROPN
ma-294	58	47	(	(	PUNCT
ma-294	58	48	x	x	NOUN
ma-294	58	49	)	)	PUNCT
ma-294	58	50	=	=	SYM
ma-294	58	51	f	f	PROPN
ma-294	58	52	(	(	PUNCT
ma-294	58	53	x(k	x(k	PROPN
ma-294	58	54	)	)	PUNCT
ma-294	58	55	)	)	PUNCT
ma-294	59	1	+	+	VERB
ma-294	59	2	∇fk(x−	∇fk(x−	PROPN
ma-294	59	3	x(k	x(k	NUM
ma-294	59	4	)	)	PUNCT
ma-294	59	5	)	)	PUNCT
ma-294	60	1	+	+	CCONJ
ma-294	60	2	1	1	NUM
ma-294	60	3	2	2	NUM
ma-294	60	4	(	(	PUNCT
ma-294	60	5	x−	x−	PROPN
ma-294	60	6	x(k))2jk	x(k))2jk	PROPN
ma-294	60	7	,	,	PUNCT
ma-294	60	8	(	(	PUNCT
ma-294	60	9	3	3	X
ma-294	60	10	)	)	PUNCT
ma-294	60	11	where	where	SCONJ
ma-294	60	12	∇f	∇f	PROPN
ma-294	60	13	(	(	PUNCT
ma-294	60	14	x	x	NOUN
ma-294	60	15	)	)	PUNCT
ma-294	60	16	=	=	SYM
ma-294	60	17	(	(	PUNCT
ma-294	60	18	∂f∂x1	∂f∂x1	PROPN
ma-294	60	19	,	,	PUNCT
ma-294	60	20	∂f∂x2	∂f∂x2	NOUN
ma-294	60	21	,	,	PUNCT
ma-294	60	22	...	...	PUNCT
ma-294	60	23	,	,	PUNCT
ma-294	60	24	∂f∂xn	∂f∂xn	PROPN
ma-294	60	25	)	)	PUNCT
ma-294	60	26	,	,	PUNCT
ma-294	60	27	jk	jk	PROPN
ma-294	60	28	is	be	AUX
ma-294	60	29	the	the	DET
ma-294	60	30	hessen	hessen	NOUN
ma-294	60	31	matrix	matrix	NOUN
ma-294	60	32	and	and	CCONJ
ma-294	60	33	is	be	AUX
ma-294	60	34	defined	define	VERB
ma-294	60	35	as	as	ADP
ma-294	60	36	∇2f	∇2f	PROPN
ma-294	60	37	(	(	PUNCT
ma-294	60	38	x	x	NOUN
ma-294	60	39	)	)	PUNCT
ma-294	60	40	=	=	SYM
ma-294	60	41			NOUN
ma-294	60	42	∂2f	∂2f	VERB
ma-294	60	43	∂x21	∂x21	PROPN
ma-294	60	44	∂2f	∂2f	VERB
ma-294	60	45	∂x1∂x2	∂x1∂x2	NOUN
ma-294	60	46	...	...	PUNCT
ma-294	60	47	∂2f	∂2f	VERB
ma-294	60	48	∂x1∂xn	∂x1∂xn	VERB
ma-294	60	49	∂2f	∂2f	VERB
ma-294	60	50	∂x2∂x1	∂x2∂x1	NOUN
ma-294	60	51	∂2f	∂2f	VERB
ma-294	60	52	∂x22	∂x22	PROPN
ma-294	60	53	...	...	PUNCT
ma-294	60	54	∂2f	∂2f	VERB
ma-294	60	55	∂x2∂xn	∂x2∂xn	X
ma-294	60	56	..........................................	..........................................	PUNCT
ma-294	60	57	∂2f	∂2f	VERB
ma-294	60	58	∂xn∂x1	∂xn∂x1	NOUN
ma-294	60	59	∂2f	∂2f	VERB
ma-294	60	60	∂xn∂x2	∂xn∂x2	NOUN
ma-294	60	61	...	...	PUNCT
ma-294	60	62	∂2f	∂2f	VERB
ma-294	60	63	∂x2n	∂x2n	NOUN
ma-294	60	64			PROPN
ma-294	60	65	.	.	PUNCT
ma-294	61	1	since	since	SCONJ
ma-294	61	2	2	2	NUM
ma-294	61	3	,	,	PUNCT
ma-294	61	4	we	we	PRON
ma-294	61	5	have	have	VERB
ma-294	61	6	∇f	∇f	NOUN
ma-294	61	7	=	=	SYM
ma-294	61	8	∇fk	∇fk	NOUN
ma-294	61	9	+	+	CCONJ
ma-294	61	10	(	(	PUNCT
ma-294	61	11	x	x	X
ma-294	61	12	−	−	NOUN
ma-294	61	13	x	x	SYM
ma-294	61	14	(	(	PUNCT
ma-294	61	15	k))jk	k))jk	PROPN
ma-294	61	16	.	.	PUNCT
ma-294	62	1	(	(	PUNCT
ma-294	62	2	4	4	X
ma-294	62	3	)	)	PUNCT
ma-294	62	4	so	so	ADV
ma-294	62	5	,	,	PUNCT
ma-294	62	6	we	we	PRON
ma-294	62	7	have	have	VERB
ma-294	62	8	the	the	DET
ma-294	62	9	iterative	iterative	NOUN
ma-294	62	10	process	process	NOUN
ma-294	62	11	.	.	PUNCT
ma-294	63	1	x(k+1	x(k+1	PUNCT
ma-294	63	2	)	)	PUNCT
ma-294	64	1	=	=	SYM
ma-294	64	2	x(k	x(k	PROPN
ma-294	64	3	)	)	PUNCT
ma-294	64	4	−	−	PROPN
ma-294	65	1	(	(	PUNCT
ma-294	65	2	jk)−1∇fk	jk)−1∇fk	ADV
ma-294	65	3	,	,	PUNCT
ma-294	65	4	k	k	PROPN
ma-294	65	5	=	=	SYM
ma-294	65	6	1	1	NUM
ma-294	65	7	,	,	PUNCT
ma-294	65	8	2	2	NUM
ma-294	65	9	,	,	PUNCT
ma-294	65	10	3	3	NUM
ma-294	65	11	,	,	PUNCT
ma-294	65	12	...	...	PUNCT
ma-294	65	13	,	,	PUNCT
ma-294	65	14	n.	n.	NOUN
ma-294	65	15	(	(	PUNCT
ma-294	65	16	5	5	NUM
ma-294	65	17	)	)	PUNCT
ma-294	65	18	formula	formula	NOUN
ma-294	65	19	(	(	PUNCT
ma-294	65	20	4	4	NUM
ma-294	65	21	)	)	PUNCT
ma-294	65	22	is	be	AUX
ma-294	65	23	called	call	VERB
ma-294	65	24	newton	newton	PROPN
ma-294	65	25	’s	’s	PART
ma-294	65	26	iteration	iteration	NOUN
ma-294	65	27	formula	formula	NOUN
ma-294	65	28	with	with	ADP
ma-294	65	29	second	second	ADJ
ma-294	65	30	-	-	PUNCT
ma-294	65	31	order	order	NOUN
ma-294	65	32	convergence	convergence	NOUN
ma-294	65	33	rate	rate	NOUN
ma-294	65	34	.	.	PUNCT
ma-294	66	1	the	the	DET
ma-294	66	2	algo	algo	PROPN
ma-294	66	3	-	-	PUNCT
ma-294	66	4	rithm	rithm	PROPN
ma-294	66	5	is	be	AUX
ma-294	66	6	implemented	implement	VERB
ma-294	66	7	as	as	SCONJ
ma-294	66	8	follows	follow	VERB
ma-294	66	9	:	:	PUNCT
ma-294	66	10	algorithm	algorithm	NOUN
ma-294	66	11	1	1	NUM
ma-294	66	12	:	:	PUNCT
ma-294	66	13	function	function	NOUN
ma-294	66	14	x	x	NOUN
ma-294	66	15	=	=	NOUN
ma-294	66	16	newton(x(1),ε	newton(x(1),ε	NUM
ma-294	66	17	)	)	PUNCT
ma-294	66	18	;	;	PUNCT
ma-294	67	1	k=1	k=1	X
ma-294	67	2	;	;	PUNCT
ma-294	67	3	while(‖∇fk‖	while(‖∇fk‖	PROPN
ma-294	67	4	>	>	SYM
ma-294	67	5	ε	ε	PROPN
ma-294	67	6	)	)	PUNCT
ma-294	67	7	d(k	d(k	PROPN
ma-294	67	8	)	)	PUNCT
ma-294	67	9	=	=	PUNCT
ma-294	67	10	−(jk)−1∇fk	−(jk)−1∇fk	NOUN
ma-294	67	11	;	;	PUNCT
ma-294	67	12	x(k+1	x(k+1	NUM
ma-294	67	13	)	)	PUNCT
ma-294	67	14	=	=	SYM
ma-294	68	1	x(k	x(k	PROPN
ma-294	68	2	)	)	PUNCT
ma-294	68	3	+	+	CCONJ
ma-294	68	4	d(k	d(k	PROPN
ma-294	68	5	)	)	PUNCT
ma-294	68	6	;	;	PUNCT
ma-294	68	7	k	k	X
ma-294	68	8	=	=	SYM
ma-294	68	9	k+1	k+1	X
ma-294	68	10	;	;	PUNCT
ma-294	68	11	end	end	NOUN
ma-294	68	12	;	;	PUNCT
ma-294	68	13	x	x	SYM
ma-294	68	14	=	=	SYM
ma-294	68	15	x(k	x(k	PROPN
ma-294	68	16	)	)	PUNCT
ma-294	68	17	;	;	PUNCT
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ma-294	68	19	eur	eur	PROPN
ma-294	68	20	.	.	PUNCT
ma-294	69	1	j.	j.	PROPN
ma-294	69	2	math	math	PROPN
ma-294	69	3	.	.	PUNCT
ma-294	70	1	anal	anal	PROPN
ma-294	70	2	.	.	PUNCT
ma-294	71	1	10.28924	10.28924	NUM
ma-294	71	2	/	/	SYM
ma-294	71	3	ada	ada	PROPN
ma-294	71	4	/	/	PROPN
ma-294	71	5	ma.5.9	ma.5.9	PROPN
ma-294	71	6	4	4	NUM
ma-294	71	7	according	accord	VERB
ma-294	71	8	to	to	ADP
ma-294	71	9	this	this	DET
ma-294	71	10	algorithm	algorithm	NOUN
ma-294	71	11	,	,	PUNCT
ma-294	71	12	at	at	ADP
ma-294	71	13	the	the	DET
ma-294	71	14	step	step	NOUN
ma-294	71	15	k	k	NOUN
ma-294	71	16	:	:	PUNCT
ma-294	71	17	d(k	d(k	PROPN
ma-294	71	18	)	)	PUNCT
ma-294	72	1	=	=	PUNCT
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ma-294	72	3	,	,	PUNCT
ma-294	72	4	x	x	X
ma-294	72	5	(	(	PUNCT
ma-294	72	6	k+1	k+1	NOUN
ma-294	72	7	)	)	PUNCT
ma-294	72	8	=	=	SYM
ma-294	72	9	x	x	X
ma-294	72	10	(	(	PUNCT
ma-294	72	11	k)+	k)+	NOUN
ma-294	72	12	d	d	X
ma-294	72	13	(	(	PUNCT
ma-294	72	14	k	k	NOUN
ma-294	72	15	)	)	PUNCT
ma-294	72	16	,	,	PUNCT
ma-294	72	17	we	we	PRON
ma-294	72	18	implementcomponent	implementcomponent	ADJ
ma-294	72	19	inheritance	inheritance	NOUN
ma-294	72	20	x(k+1)i	x(k+1)i	PROPN
ma-294	72	21	calculated	calculate	VERB
ma-294	72	22	to	to	PART
ma-294	72	23	calculate	calculate	VERB
ma-294	72	24	x	x	PUNCT
ma-294	72	25	(	(	PUNCT
ma-294	72	26	k+1)j	k+1)j	PROPN
ma-294	72	27	,	,	PUNCT
ma-294	72	28	j	j	X
ma-294	72	29	=	=	PUNCT
ma-294	72	30	i	i	PRON
ma-294	72	31	+	+	NOUN
ma-294	72	32	1	1	NUM
ma-294	72	33	,	,	PUNCT
ma-294	72	34	...	...	PUNCT
ma-294	72	35	,	,	PUNCT
ma-294	72	36	n	n	CCONJ
ma-294	72	37	,	,	PUNCT
ma-294	72	38	so	so	CCONJ
ma-294	72	39	(	(	PUNCT
ma-294	72	40	5	5	X
ma-294	72	41	)	)	PUNCT
ma-294	72	42	is	be	AUX
ma-294	72	43	replaced	replace	VERB
ma-294	72	44	by	by	ADP
ma-294	72	45	x	x	X
ma-294	72	46	(	(	PUNCT
ma-294	72	47	k+1	k+1	NOUN
ma-294	72	48	)	)	PUNCT
ma-294	72	49	i	i	NOUN
ma-294	72	50	=	=	PUNCT
ma-294	73	1	x	x	X
ma-294	73	2	(	(	PUNCT
ma-294	73	3	k	k	NOUN
ma-294	73	4	)	)	PUNCT
ma-294	73	5	i	i	PRON
ma-294	73	6	+	+	NUM
ma-294	74	1	d	d	X
ma-294	74	2	(	(	PUNCT
ma-294	74	3	k	k	NOUN
ma-294	74	4	)	)	PUNCT
ma-294	74	5	i	i	PRON
ma-294	74	6	,	,	PUNCT
ma-294	74	7	(	(	PUNCT
ma-294	74	8	6	6	NUM
ma-294	74	9	)	)	PUNCT
ma-294	74	10	where	where	SCONJ
ma-294	74	11	d	d	NOUN
ma-294	74	12	(	(	PUNCT
ma-294	74	13	k	k	NOUN
ma-294	74	14	)	)	PUNCT
ma-294	74	15	1	1	NUM
ma-294	75	1	=	=	SYM
ma-294	75	2	−	−	PROPN
ma-294	75	3	n∑	n∑	NOUN
ma-294	75	4	j=1	j=1	NOUN
ma-294	75	5	[	[	PUNCT
ma-294	75	6	(	(	PUNCT
ma-294	75	7	jk	jk	NOUN
ma-294	75	8	)	)	PUNCT
ma-294	75	9	−1]∇f	−1]∇f	PROPN
ma-294	75	10	(	(	PUNCT
ma-294	75	11	x	x	X
ma-294	75	12	(	(	PUNCT
ma-294	75	13	k)j	k)j	NOUN
ma-294	75	14	)	)	PUNCT
ma-294	76	1	d	d	NOUN
ma-294	76	2	(	(	PUNCT
ma-294	76	3	k	k	NOUN
ma-294	76	4	)	)	PUNCT
ma-294	76	5	i	i	PRON
ma-294	76	6	=	=	PUNCT
ma-294	77	1	−	−	PROPN
ma-294	77	2	i−1∑	i−1∑	NUM
ma-294	77	3	j=1	j=1	NOUN
ma-294	77	4	[	[	PUNCT
ma-294	77	5	(	(	PUNCT
ma-294	77	6	jk	jk	NOUN
ma-294	77	7	)	)	PUNCT
ma-294	77	8	−1]∇f	−1]∇f	PROPN
ma-294	77	9	(	(	PUNCT
ma-294	77	10	x	x	X
ma-294	77	11	(	(	PUNCT
ma-294	77	12	k+1)j	k+1)j	PROPN
ma-294	77	13	)	)	PUNCT
ma-294	77	14	−	−	PROPN
ma-294	78	1	n∑	n∑	PROPN
ma-294	78	2	j	j	PROPN
ma-294	79	1	=	=	NOUN
ma-294	79	2	i+1	i+1	X
ma-294	79	3	[	[	PUNCT
ma-294	79	4	(	(	PUNCT
ma-294	79	5	jk	jk	NOUN
ma-294	79	6	)	)	PUNCT
ma-294	79	7	−1]∇f	−1]∇f	PROPN
ma-294	79	8	(	(	PUNCT
ma-294	79	9	x	x	X
ma-294	79	10	(	(	PUNCT
ma-294	79	11	k)j	k)j	NOUN
ma-294	79	12	)	)	PUNCT
ma-294	79	13	,	,	PUNCT
ma-294	79	14	i	i	PRON
ma-294	79	15	=	=	NOUN
ma-294	79	16	2	2	NUM
ma-294	79	17	,	,	PUNCT
ma-294	79	18	...	...	PUNCT
ma-294	79	19	,	,	PUNCT
ma-294	79	20	n	n	PROPN
ma-294	79	21	so	so	ADV
ma-294	79	22	,	,	PUNCT
ma-294	79	23	newton	newton	PROPN
ma-294	79	24	’s	’s	PART
ma-294	79	25	algorithm	algorithm	NOUN
ma-294	79	26	is	be	AUX
ma-294	79	27	updated	update	VERB
ma-294	79	28	as	as	SCONJ
ma-294	79	29	follows	follow	VERB
ma-294	79	30	:	:	PUNCT
ma-294	79	31	algorithm	algorithm	NOUN
ma-294	79	32	2	2	NUM
ma-294	79	33	:	:	PUNCT
ma-294	79	34	function	function	NOUN
ma-294	79	35	x	x	NOUN
ma-294	79	36	=	=	NOUN
ma-294	79	37	newton(x(1),ε	newton(x(1),ε	NUM
ma-294	79	38	)	)	PUNCT
ma-294	79	39	;	;	PUNCT
ma-294	80	1	k=1	k=1	X
ma-294	80	2	;	;	PUNCT
ma-294	80	3	n	n	CCONJ
ma-294	80	4	=	=	PROPN
ma-294	80	5	length(x(0	length(x(0	PROPN
ma-294	80	6	)	)	PUNCT
ma-294	80	7	)	)	PUNCT
ma-294	80	8	;	;	PUNCT
ma-294	80	9	while(‖∇fk‖	while(‖∇fk‖	PROPN
ma-294	80	10	>	>	SYM
ma-294	80	11	ε	ε	PROPN
ma-294	80	12	)	)	PUNCT
ma-294	80	13	d(k	d(k	PROPN
ma-294	80	14	)	)	PUNCT
ma-294	80	15	=	=	PUNCT
ma-294	80	16	0	0	NUM
ma-294	80	17	;	;	PUNCT
ma-294	80	18	for	for	ADP
ma-294	80	19	j=1	j=1	NOUN
ma-294	80	20	:	:	PUNCT
ma-294	80	21	n	n	PROPN
ma-294	80	22	d	d	PROPN
ma-294	80	23	(	(	PUNCT
ma-294	80	24	k	k	NOUN
ma-294	80	25	)	)	PUNCT
ma-294	80	26	1	1	NUM
ma-294	80	27	=	=	SYM
ma-294	80	28	d	d	X
ma-294	80	29	(	(	PUNCT
ma-294	80	30	k	k	NOUN
ma-294	80	31	)	)	PUNCT
ma-294	80	32	1	1	NUM
ma-294	80	33	−	−	NOUN
ma-294	80	34	[	[	PUNCT
ma-294	80	35	(	(	PUNCT
ma-294	80	36	jk)−1	jk)−1	NOUN
ma-294	80	37	]	]	X
ma-294	80	38	∇f	∇f	NOUN
ma-294	80	39	(	(	PUNCT
ma-294	80	40	x	x	INTJ
ma-294	80	41	(	(	PUNCT
ma-294	80	42	k)j	k)j	NOUN
ma-294	80	43	)	)	PUNCT
ma-294	80	44	end	end	NOUN
ma-294	80	45	;	;	PUNCT
ma-294	80	46	x	x	X
ma-294	80	47	(	(	PUNCT
ma-294	80	48	k+1	k+1	NOUN
ma-294	80	49	)	)	PUNCT
ma-294	81	1	1	1	NUM
ma-294	81	2	=	=	SYM
ma-294	81	3	x	x	X
ma-294	81	4	(	(	PUNCT
ma-294	81	5	k	k	NOUN
ma-294	81	6	)	)	PUNCT
ma-294	81	7	1	1	NUM
ma-294	82	1	+	+	CCONJ
ma-294	82	2	d	d	X
ma-294	82	3	(	(	PUNCT
ma-294	82	4	k	k	NOUN
ma-294	82	5	)	)	PUNCT
ma-294	82	6	1	1	NUM
ma-294	82	7	for	for	ADP
ma-294	82	8	i=2	i=2	PROPN
ma-294	82	9	:	:	PUNCT
ma-294	82	10	n	n	PROPN
ma-294	82	11	for	for	ADP
ma-294	82	12	j=1	j=1	NOUN
ma-294	82	13	:	:	PUNCT
ma-294	82	14	i-1	i-1	ADJ
ma-294	82	15	d	d	PROPN
ma-294	82	16	(	(	PUNCT
ma-294	82	17	k	k	NOUN
ma-294	82	18	)	)	PUNCT
ma-294	82	19	i	i	NOUN
ma-294	82	20	=	=	SYM
ma-294	83	1	d	d	X
ma-294	83	2	(	(	PUNCT
ma-294	83	3	k	k	NOUN
ma-294	83	4	)	)	PUNCT
ma-294	84	1	i	i	PRON
ma-294	84	2	−	−	X
ma-294	85	1	[	[	PUNCT
ma-294	85	2	(	(	PUNCT
ma-294	85	3	jk)−1	jk)−1	NOUN
ma-294	85	4	]	]	X
ma-294	85	5	∇f	∇f	NOUN
ma-294	85	6	(	(	PUNCT
ma-294	85	7	x	x	X
ma-294	85	8	(	(	PUNCT
ma-294	85	9	k+1)j	k+1)j	PROPN
ma-294	85	10	)	)	PUNCT
ma-294	85	11	end	end	NOUN
ma-294	85	12	;	;	PUNCT
ma-294	85	13	for	for	ADP
ma-294	85	14	j	j	PROPN
ma-294	85	15	=	=	VERB
ma-294	85	16	i	i	PROPN
ma-294	85	17	:	:	PUNCT
ma-294	85	18	n	n	PROPN
ma-294	85	19	d	d	X
ma-294	85	20	(	(	PUNCT
ma-294	85	21	k	k	NOUN
ma-294	85	22	)	)	PUNCT
ma-294	85	23	i	i	NOUN
ma-294	86	1	=	=	SYM
ma-294	87	1	d	d	X
ma-294	87	2	(	(	PUNCT
ma-294	87	3	k	k	NOUN
ma-294	87	4	)	)	PUNCT
ma-294	88	1	i	i	PRON
ma-294	88	2	−	−	X
ma-294	89	1	[	[	PUNCT
ma-294	89	2	(	(	PUNCT
ma-294	89	3	jk)−1	jk)−1	NOUN
ma-294	89	4	]	]	X
ma-294	89	5	∇f	∇f	NOUN
ma-294	89	6	(	(	PUNCT
ma-294	89	7	x	x	INTJ
ma-294	89	8	(	(	PUNCT
ma-294	89	9	k)j	k)j	NOUN
ma-294	89	10	)	)	PUNCT
ma-294	89	11	end	end	NOUN
ma-294	89	12	;	;	PUNCT
ma-294	89	13	x	x	X
ma-294	89	14	(	(	PUNCT
ma-294	89	15	k+1	k+1	NOUN
ma-294	89	16	)	)	PUNCT
ma-294	89	17	i	i	NOUN
ma-294	89	18	=	=	PUNCT
ma-294	89	19	x	x	X
ma-294	89	20	(	(	PUNCT
ma-294	89	21	k	k	NOUN
ma-294	89	22	)	)	PUNCT
ma-294	90	1	i	i	PRON
ma-294	91	1	+	+	NUM
ma-294	92	1	d	d	X
ma-294	92	2	(	(	PUNCT
ma-294	92	3	k	k	NOUN
ma-294	92	4	)	)	PUNCT
ma-294	92	5	i	i	PRON
ma-294	92	6	end	end	VERB
ma-294	92	7	;	;	PUNCT
ma-294	92	8	k	k	X
ma-294	92	9	=	=	SYM
ma-294	92	10	k+1	k+1	X
ma-294	92	11	;	;	PUNCT
ma-294	92	12	end	end	NOUN
ma-294	92	13	;	;	PUNCT
ma-294	92	14	x	x	SYM
ma-294	92	15	=	=	PUNCT
ma-294	92	16	x(k+1)in	x(k+1)in	PROPN
ma-294	92	17	case	case	NOUN
ma-294	92	18	the	the	DET
ma-294	92	19	objective	objective	ADJ
ma-294	92	20	function	function	NOUN
ma-294	92	21	is	be	AUX
ma-294	92	22	not	not	PART
ma-294	92	23	second	second	ADJ
ma-294	92	24	-	-	PUNCT
ma-294	92	25	order	order	NOUN
ma-294	92	26	differentiable	differentiable	NOUN
ma-294	92	27	,	,	PUNCT
ma-294	92	28	then	then	ADV
ma-294	92	29	instead	instead	ADV
ma-294	92	30	of	of	ADP
ma-294	92	31	using	use	VERB
ma-294	92	32	newton’smethod	newton’smethod	NOUN
ma-294	92	33	,	,	PUNCT
ma-294	92	34	we	we	PRON
ma-294	92	35	will	will	AUX
ma-294	92	36	use	use	VERB
ma-294	92	37	the	the	DET
ma-294	92	38	quasi	quasi	ADJ
ma-294	92	39	-	-	ADJ
ma-294	92	40	newtonian	newtonian	ADJ
ma-294	92	41	method	method	NOUN
ma-294	92	42	.	.	PUNCT
ma-294	93	1	2.2	2.2	NUM
ma-294	93	2	.	.	PUNCT
ma-294	94	1	quasi	quasi	PROPN
ma-294	94	2	-	-	PROPN
ma-294	94	3	newton	newton	PROPN
ma-294	94	4	method.the	method.the	DET
ma-294	94	5	idea	idea	NOUN
ma-294	94	6	of	of	ADP
ma-294	94	7	the	the	DET
ma-294	94	8	quasi	quasi	PROPN
ma-294	94	9	-	-	PROPN
ma-294	94	10	newton	newton	PROPN
ma-294	94	11	method	method	NOUN
ma-294	94	12	[	[	X
ma-294	94	13	22	22	NUM
ma-294	94	14	]	]	PUNCT
ma-294	94	15	is	be	AUX
ma-294	94	16	derived	derive	VERB
ma-294	94	17	from	from	ADP
ma-294	94	18	formula	formula	NOUN
ma-294	94	19	(	(	PUNCT
ma-294	94	20	5	5	NUM
ma-294	94	21	)	)	PUNCT
ma-294	95	1	,	,	PUNCT
ma-294	95	2	we	we	PRON
ma-294	95	3	approximate	approximate	VERB
ma-294	95	4	the	the	DET
ma-294	95	5	hessen	hessen	NOUN
ma-294	95	6	https://doi.org/10.28924/ada/ma.5.9	https://doi.org/10.28924/ada/ma.5.9	PROPN
ma-294	95	7	eur	eur	PROPN
ma-294	95	8	.	.	PUNCT
ma-294	96	1	j.	j.	PROPN
ma-294	96	2	math	math	PROPN
ma-294	96	3	.	.	PUNCT
ma-294	97	1	anal	anal	PROPN
ma-294	97	2	.	.	PUNCT
ma-294	98	1	10.28924	10.28924	NUM
ma-294	98	2	/	/	SYM
ma-294	98	3	ada	ada	PROPN
ma-294	98	4	/	/	SYM
ma-294	98	5	ma.5.9	ma.5.9	PROPN
ma-294	98	6	5matrix	5matrix	NUM
ma-294	98	7	jk	jk	NOUN
ma-294	98	8	by	by	ADP
ma-294	98	9	matrix	matrix	NOUN
ma-294	98	10	bk	bk	PUNCT
ma-294	98	11	so	so	ADV
ma-294	98	12	,	,	PUNCT
ma-294	98	13	since	since	SCONJ
ma-294	98	14	(	(	PUNCT
ma-294	98	15	3	3	NUM
ma-294	98	16	)	)	PUNCT
ma-294	98	17	,	,	PUNCT
ma-294	98	18	we	we	PRON
ma-294	98	19	have	have	VERB
ma-294	98	20	the	the	DET
ma-294	98	21	following	follow	VERB
ma-294	98	22	iteration	iteration	NOUN
ma-294	98	23	process	process	NOUN
ma-294	98	24	:	:	PUNCT
ma-294	98	25	x(k+1	x(k+1	X
ma-294	98	26	)	)	PUNCT
ma-294	98	27	=	=	SYM
ma-294	99	1	x(k	x(k	PROPN
ma-294	99	2	)	)	PUNCT
ma-294	100	1	−	−	PRON
ma-294	101	1	αk	αk	NOUN
ma-294	102	1	[	[	X
ma-294	102	2	bk	bk	X
ma-294	102	3	]	]	SYM
ma-294	102	4	−1∇fk	−1∇fk	NOUN
ma-294	102	5	,	,	PUNCT
ma-294	102	6	k	k	PROPN
ma-294	102	7	=	=	SYM
ma-294	102	8	1	1	NUM
ma-294	102	9	..	..	PUNCT
ma-294	102	10	n	n	CCONJ
ma-294	102	11	,	,	PUNCT
ma-294	102	12	(	(	PUNCT
ma-294	102	13	7	7	NUM
ma-294	102	14	)	)	PUNCT
ma-294	102	15	where	where	SCONJ
ma-294	102	16	,	,	PUNCT
ma-294	102	17	αk	αk	PRON
ma-294	102	18	is	be	AUX
ma-294	102	19	the	the	DET
ma-294	102	20	step	step	NOUN
ma-294	102	21	length	length	NOUN
ma-294	102	22	determined	determine	VERB
ma-294	102	23	in	in	ADP
ma-294	102	24	the	the	DET
ma-294	102	25	direction	direction	NOUN
ma-294	102	26	sk	sk	VERB
ma-294	102	27	=	=	PUNCT
ma-294	102	28	−	−	PROPN
ma-294	103	1	[	[	X
ma-294	103	2	bk	bk	X
ma-294	103	3	]	]	SYM
ma-294	103	4	−1∇fk	−1∇fk	NOUN
ma-294	103	5	,	,	PUNCT
ma-294	103	6	it	it	PRON
ma-294	103	7	can	can	AUX
ma-294	103	8	change	change	VERB
ma-294	103	9	at	at	ADP
ma-294	103	10	eachiteration	eachiteration	NOUN
ma-294	103	11	and	and	CCONJ
ma-294	103	12	satisfy	satisfy	VERB
ma-294	103	13	the	the	DET
ma-294	103	14	wolfe	wolfe	PROPN
ma-294	103	15	condition	condition	NOUN
ma-294	104	1	[	[	X
ma-294	104	2	22	22	NUM
ma-294	104	3	]	]	PUNCT
ma-294	104	4	.	.	PUNCT
ma-294	105	1	f	f	PROPN
ma-294	105	2	(	(	PUNCT
ma-294	105	3	x(k	x(k	PROPN
ma-294	105	4	)	)	PUNCT
ma-294	105	5	+	+	NUM
ma-294	105	6	αksk	αksk	ADJ
ma-294	105	7	)	)	PUNCT
ma-294	105	8	≤	≤	NUM
ma-294	105	9	f	f	X
ma-294	105	10	(	(	PUNCT
ma-294	105	11	x(k	x(k	PROPN
ma-294	105	12	)	)	PUNCT
ma-294	105	13	)	)	PUNCT
ma-294	106	1	+	+	CCONJ
ma-294	106	2	c1αkstk	c1αkstk	PROPN
ma-294	106	3	∇f	∇f	PROPN
ma-294	106	4	(	(	PUNCT
ma-294	106	5	x(k	x(k	PROPN
ma-294	106	6	)	)	PUNCT
ma-294	106	7	)	)	PUNCT
ma-294	106	8	−stk	−stk	PUNCT
ma-294	107	1	∇f	∇f	PROPN
ma-294	107	2	(	(	PUNCT
ma-294	107	3	x(k	x(k	PROPN
ma-294	107	4	)	)	PUNCT
ma-294	107	5	+	+	NUM
ma-294	107	6	αksk	αksk	ADJ
ma-294	107	7	)	)	PUNCT
ma-294	107	8	≤	≤	NOUN
ma-294	107	9	−c2stk	−c2stk	PROPN
ma-294	107	10	∇f	∇f	PROPN
ma-294	107	11	(	(	PUNCT
ma-294	107	12	x(k	x(k	PROPN
ma-294	107	13	)	)	PUNCT
ma-294	107	14	)	)	PUNCT
ma-294	107	15	0	0	PUNCT
ma-294	107	16	<	<	X
ma-294	107	17	c1	c1	PROPN
ma-294	107	18	<	<	X
ma-294	107	19	c2	c2	PROPN
ma-294	107	20	<	<	X
ma-294	107	21	1	1	NUM
ma-294	107	22	(	(	PUNCT
ma-294	107	23	8)	8)	NUM
ma-294	107	24	αk	αk	NOUN
ma-294	107	25	is	be	AUX
ma-294	107	26	determined	determine	VERB
ma-294	107	27	by	by	ADP
ma-294	107	28	algorithm	algorithm	NOUN
ma-294	107	29	3	3	NUM
ma-294	107	30	algorithm	algorithm	NOUN
ma-294	107	31	3	3	NUM
ma-294	107	32	:	:	PUNCT
ma-294	107	33	function	function	VERB
ma-294	107	34	αk	αk	NOUN
ma-294	107	35	=	=	SYM
ma-294	107	36	linesearch(f	linesearch(f	NOUN
ma-294	107	37	,	,	PUNCT
ma-294	107	38	xk	xk	X
ma-294	107	39	,	,	PUNCT
ma-294	107	40	sk	sk	INTJ
ma-294	107	41	)	)	PUNCT
ma-294	107	42	;	;	PUNCT
ma-294	107	43	initialize	initialize	VERB
ma-294	107	44	constants	constant	NOUN
ma-294	107	45	c1	c1	PROPN
ma-294	107	46	,	,	PUNCT
ma-294	107	47	c2	c2	PROPN
ma-294	107	48	,	,	PUNCT
ma-294	107	49	β	β	X
ma-294	107	50	satisfy	satisfy	NOUN
ma-294	107	51	0	0	PUNCT
ma-294	107	52	<	<	X
ma-294	107	53	c1	c1	PROPN
ma-294	107	54	<	<	X
ma-294	107	55	c2	c2	PROPN
ma-294	107	56	<	<	X
ma-294	107	57	1	1	NUM
ma-294	107	58	;	;	PUNCT
ma-294	107	59	0	0	NUM
ma-294	107	60	<	<	X
ma-294	107	61	β	β	X
ma-294	107	62	<	<	X
ma-294	107	63	1	1	NUM
ma-294	107	64	α	α	NOUN
ma-294	107	65	=	=	SYM
ma-294	107	66	α0	α0	PROPN
ma-294	107	67	while(f	while(f	PROPN
ma-294	107	68	(	(	PUNCT
ma-294	107	69	x	x	PROPN
ma-294	107	70	(	(	PUNCT
ma-294	107	71	k	k	NOUN
ma-294	107	72	)	)	PUNCT
ma-294	107	73	+	+	NUM
ma-294	107	74	αsk	αsk	NOUN
ma-294	107	75	)	)	PUNCT
ma-294	107	76	>	>	X
ma-294	108	1	f	f	X
ma-294	108	2	(	(	PUNCT
ma-294	108	3	x	x	X
ma-294	108	4	(	(	PUNCT
ma-294	108	5	k	k	NOUN
ma-294	108	6	)	)	PUNCT
ma-294	108	7	)	)	PUNCT
ma-294	109	1	+	+	CCONJ
ma-294	109	2	c1αs	c1αs	X
ma-294	109	3	t	t	X
ma-294	109	4	k	k	PROPN
ma-294	109	5	∇f	∇f	PROPN
ma-294	109	6	(	(	PUNCT
ma-294	109	7	x	x	INTJ
ma-294	109	8	(	(	PUNCT
ma-294	109	9	k	k	NOUN
ma-294	109	10	)	)	PUNCT
ma-294	109	11	)	)	PUNCT
ma-294	109	12	or	or	CCONJ
ma-294	109	13	−stk	−stk	NOUN
ma-294	109	14	∇f	∇f	PROPN
ma-294	109	15	(	(	PUNCT
ma-294	109	16	x	x	SYM
ma-294	109	17	(	(	PUNCT
ma-294	109	18	k	k	NOUN
ma-294	109	19	)	)	PUNCT
ma-294	109	20	+	+	NUM
ma-294	109	21	αsk	αsk	NOUN
ma-294	109	22	)	)	PUNCT
ma-294	109	23	>	>	X
ma-294	109	24	−c2stk	−c2stk	PROPN
ma-294	109	25	∇f	∇f	PROPN
ma-294	109	26	(	(	PUNCT
ma-294	109	27	x	x	X
ma-294	109	28	(	(	PUNCT
ma-294	109	29	k	k	NOUN
ma-294	109	30	)	)	PUNCT
ma-294	109	31	)	)	PUNCT
ma-294	109	32	)	)	PUNCT
ma-294	110	1	α	α	X
ma-294	110	2	=	=	PUNCT
ma-294	110	3	βα	βα	PROPN
ma-294	110	4	;	;	PUNCT
ma-294	110	5	end	end	NOUN
ma-294	110	6	;	;	PUNCT
ma-294	110	7	αk	αk	ADP
ma-294	110	8	=	=	SYM
ma-294	110	9	α;in	α;in	ADJ
ma-294	110	10	case	case	NOUN
ma-294	110	11	the	the	DET
ma-294	110	12	objective	objective	ADJ
ma-294	110	13	function	function	NOUN
ma-294	110	14	is	be	AUX
ma-294	110	15	a	a	DET
ma-294	110	16	convex	convex	NOUN
ma-294	110	17	function	function	NOUN
ma-294	110	18	,	,	PUNCT
ma-294	110	19	the	the	DET
ma-294	110	20	obtained	obtain	VERB
ma-294	110	21	optimal	optimal	ADJ
ma-294	110	22	point	point	NOUN
ma-294	110	23	is	be	AUX
ma-294	110	24	the	the	DET
ma-294	110	25	global	global	ADJ
ma-294	110	26	optimalsolution	optimalsolution	NOUN
ma-294	110	27	of	of	ADP
ma-294	110	28	problem	problem	NOUN
ma-294	110	29	(	(	PUNCT
ma-294	110	30	1	1	NUM
ma-294	110	31	)	)	PUNCT
ma-294	110	32	.	.	PUNCT
ma-294	111	1	it	it	PRON
ma-294	111	2	is	be	AUX
ma-294	111	3	easy	easy	ADJ
ma-294	111	4	to	to	PART
ma-294	111	5	see	see	VERB
ma-294	111	6	in	in	ADP
ma-294	111	7	[	[	X
ma-294	111	8	13	13	NUM
ma-294	111	9	]	]	PUNCT
ma-294	111	10	,	,	PUNCT
ma-294	111	11	if	if	SCONJ
ma-294	111	12	bk	bk	ADV
ma-294	111	13	=	=	VERB
ma-294	112	1	i	i	PRON
ma-294	112	2	then	then	ADV
ma-294	112	3	the	the	DET
ma-294	112	4	iterative	iterative	NOUN
ma-294	112	5	formula	formula	NOUN
ma-294	112	6	(	(	PUNCT
ma-294	112	7	7	7	X
ma-294	112	8	)	)	PUNCT
ma-294	112	9	is	be	AUX
ma-294	112	10	thesteepest	thesteepest	NOUN
ma-294	112	11	descent	descent	NOUN
ma-294	112	12	method	method	NOUN
ma-294	112	13	published	publish	VERB
ma-294	112	14	in	in	ADP
ma-294	112	15	[	[	X
ma-294	112	16	23	23	NUM
ma-294	112	17	]	]	PUNCT
ma-294	112	18	.	.	PUNCT
ma-294	113	1	bk	bk	PRON
ma-294	113	2	is	be	AUX
ma-294	113	3	an	an	DET
ma-294	113	4	approximation	approximation	NOUN
ma-294	113	5	matrix	matrix	NOUN
ma-294	113	6	for	for	ADP
ma-294	113	7	the	the	DET
ma-294	113	8	hessen	hessen	PROPN
ma-294	113	9	matrixand	matrixand	PROPN
ma-294	113	10	satisfies	satisfy	VERB
ma-294	113	11	the	the	DET
ma-294	113	12	condition	condition	NOUN
ma-294	113	13	∇f	∇f	PROPN
ma-294	113	14	(	(	PUNCT
ma-294	113	15	x(k	x(k	PROPN
ma-294	113	16	)	)	PUNCT
ma-294	113	17	)	)	PUNCT
ma-294	114	1	=	=	SYM
ma-294	114	2	∇f	∇f	NOUN
ma-294	114	3	(	(	PUNCT
ma-294	114	4	x(k−1))−	x(k−1))−	PROPN
ma-294	114	5	bk(x(k	bk(x(k	NOUN
ma-294	114	6	)	)	PUNCT
ma-294	114	7	−	−	PROPN
ma-294	114	8	x(k−1	x(k−1	PROPN
ma-294	114	9	)	)	PUNCT
ma-294	114	10	)	)	PUNCT
ma-294	114	11	.	.	PUNCT
ma-294	115	1	(	(	PUNCT
ma-294	115	2	9	9	X
ma-294	115	3	)	)	PUNCT
ma-294	115	4	at	at	ADP
ma-294	115	5	x	x	X
ma-294	115	6	(	(	PUNCT
ma-294	115	7	k+1	k+1	NOUN
ma-294	115	8	)	)	PUNCT
ma-294	115	9	,	,	PUNCT
ma-294	115	10	we	we	PRON
ma-294	115	11	have	have	VERB
ma-294	115	12	∇f	∇f	PROPN
ma-294	115	13	(	(	PUNCT
ma-294	115	14	x(k+1	x(k+1	ADJ
ma-294	115	15	)	)	PUNCT
ma-294	115	16	)	)	PUNCT
ma-294	116	1	=	=	SYM
ma-294	116	2	∇f	∇f	PROPN
ma-294	116	3	(	(	PUNCT
ma-294	116	4	x(k))−	x(k))−	NOUN
ma-294	116	5	bk+1(x(k+1	bk+1(x(k+1	PROPN
ma-294	116	6	)	)	PUNCT
ma-294	116	7	−	−	PROPN
ma-294	116	8	x(k	x(k	NOUN
ma-294	116	9	)	)	PUNCT
ma-294	116	10	)	)	PUNCT
ma-294	116	11	(	(	PUNCT
ma-294	116	12	10	10	NUM
ma-294	116	13	)	)	PUNCT
ma-294	116	14	or	or	CCONJ
ma-294	116	15	can	can	AUX
ma-294	116	16	write	write	VERB
ma-294	116	17	bk+1dk	bk+1dk	PROPN
ma-294	116	18	=	=	PROPN
ma-294	116	19	gk	gk	PROPN
ma-294	116	20	,	,	PUNCT
ma-294	116	21	(	(	PUNCT
ma-294	116	22	11	11	NUM
ma-294	116	23	)	)	PUNCT
ma-294	116	24	where	where	SCONJ
ma-294	116	25	,	,	PUNCT
ma-294	116	26	dk	dk	PROPN
ma-294	116	27	=	=	PUNCT
ma-294	116	28	x	x	X
ma-294	116	29	(	(	PUNCT
ma-294	116	30	k+1	k+1	NOUN
ma-294	116	31	)	)	PUNCT
ma-294	116	32	−	−	NOUN
ma-294	116	33	x	x	SYM
ma-294	116	34	(	(	PUNCT
ma-294	116	35	k	k	NOUN
ma-294	116	36	)	)	PUNCT
ma-294	116	37	,	,	PUNCT
ma-294	116	38	gk	gk	PROPN
ma-294	116	39	=	=	PUNCT
ma-294	116	40	∇fk+1	∇fk+1	PROPN
ma-294	116	41	−∇fkformula	−∇fkformula	NOUN
ma-294	116	42	(	(	PUNCT
ma-294	116	43	11	11	NUM
ma-294	116	44	)	)	PUNCT
ma-294	116	45	can	can	AUX
ma-294	116	46	be	be	AUX
ma-294	116	47	rewritten	rewrite	VERB
ma-294	116	48	as	as	SCONJ
ma-294	116	49	follows	follow	VERB
ma-294	116	50	:	:	PUNCT
ma-294	116	51	dk	dk	X
ma-294	116	52	=	=	PUNCT
ma-294	117	1	[	[	X
ma-294	117	2	bk+1]−1	bk+1]−1	NOUN
ma-294	117	3	gk	gk	PROPN
ma-294	117	4	,	,	PUNCT
ma-294	117	5	(	(	PUNCT
ma-294	117	6	12	12	NUM
ma-294	117	7	)	)	PUNCT
ma-294	117	8	where	where	SCONJ
ma-294	117	9	,	,	PUNCT
ma-294	117	10	bk+1	bk+1	NOUN
ma-294	117	11	is	be	AUX
ma-294	117	12	a	a	DET
ma-294	117	13	positive	positive	ADJ
ma-294	117	14	definite	definite	ADJ
ma-294	117	15	symmetric	symmetric	ADJ
ma-294	117	16	matrix	matrix	NOUN
ma-294	117	17	and	and	CCONJ
ma-294	117	18	is	be	AUX
ma-294	117	19	updated	update	VERB
ma-294	117	20	according	accord	VERB
ma-294	117	21	to	to	ADP
ma-294	117	22	the	the	DET
ma-294	117	23	formula	formula	NOUN
ma-294	117	24	bk+1	bk+1	NOUN
ma-294	117	25	=	=	PUNCT
ma-294	117	26	bk	bk	PROPN
ma-294	117	27	+	+	NOUN
ma-294	117	28	czzt	czzt	ADJ
ma-294	117	29	.	.	PUNCT
ma-294	118	1	(	(	PUNCT
ma-294	118	2	13	13	NUM
ma-294	118	3	)	)	PUNCT
ma-294	118	4	https://doi.org/10.28924/ada/ma.5.9	https://doi.org/10.28924/ada/ma.5.9	NOUN
ma-294	118	5	eur	eur	NOUN
ma-294	118	6	.	.	PUNCT
ma-294	119	1	j.	j.	PROPN
ma-294	119	2	math	math	PROPN
ma-294	119	3	.	.	PUNCT
ma-294	120	1	anal	anal	PROPN
ma-294	120	2	.	.	PUNCT
ma-294	121	1	10.28924	10.28924	NUM
ma-294	121	2	/	/	SYM
ma-294	121	3	ada	ada	PROPN
ma-294	121	4	/	/	SYM
ma-294	121	5	ma.5.9	ma.5.9	PROPN
ma-294	121	6	6	6	NUM
ma-294	121	7	since	since	SCONJ
ma-294	121	8	(	(	PUNCT
ma-294	121	9	11	11	NUM
ma-294	121	10	)	)	PUNCT
ma-294	121	11	,	,	PUNCT
ma-294	121	12	we	we	PRON
ma-294	121	13	have	have	VERB
ma-294	121	14	(	(	PUNCT
ma-294	121	15	bk	bk	NOUN
ma-294	121	16	+	+	NUM
ma-294	121	17	czzt	czzt	ADJ
ma-294	121	18	)	)	PUNCT
ma-294	122	1	dk	dk	X
ma-294	122	2	=	=	PUNCT
ma-294	122	3	gk	gk	PROPN
ma-294	122	4	.	.	PUNCT
ma-294	123	1	so	so	ADV
ma-294	123	2	,	,	PUNCT
ma-294	123	3	cz	cz	NOUN
ma-294	123	4	=	=	SYM
ma-294	123	5	gk−[bk	gk−[bk	PROPN
ma-294	123	6	]	]	X
ma-294	123	7	dk	dk	PROPN
ma-294	123	8	zt	zt	PROPN
ma-294	123	9	dk	dk	PROPN
ma-294	123	10	.	.	PUNCT
ma-294	124	1	let	let	VERB
ma-294	124	2	z	z	NOUN
ma-294	124	3	=	=	SYM
ma-294	124	4	gk	gk	NOUN
ma-294	124	5	−	−	PROPN
ma-294	125	1	[	[	X
ma-294	125	2	bk	bk	X
ma-294	125	3	]	]	X
ma-294	125	4	dk	dk	INTJ
ma-294	125	5	,	,	PUNCT
ma-294	125	6	then	then	ADV
ma-294	125	7	c	c	NOUN
ma-294	125	8	=	=	SYM
ma-294	125	9	1	1	NUM
ma-294	125	10	zt	zt	PROPN
ma-294	125	11	dk	dk	PROPN
ma-294	125	12	and	and	CCONJ
ma-294	125	13	bk+1	bk+1	NOUN
ma-294	125	14	=	=	PUNCT
ma-294	125	15	bk	bk	PROPN
ma-294	125	16	+	+	PROPN
ma-294	125	17	(	(	PUNCT
ma-294	125	18	gk	gk	PROPN
ma-294	125	19	−	−	PROPN
ma-294	125	20	bkdk	bkdk	PROPN
ma-294	125	21	)	)	PUNCT
ma-294	125	22	(	(	PUNCT
ma-294	125	23	gk	gk	PROPN
ma-294	125	24	−	−	PROPN
ma-294	125	25	bkdk)t	bkdk)t	X
ma-294	125	26	(	(	PUNCT
ma-294	125	27	gk	gk	PROPN
ma-294	125	28	−	−	PROPN
ma-294	125	29	bkdk)t	bkdk)t	PROPN
ma-294	125	30	dk	dk	X
ma-294	125	31	.	.	PUNCT
ma-294	126	1	(	(	PUNCT
ma-294	126	2	14	14	NUM
ma-294	126	3	)	)	PUNCT
ma-294	126	4	we	we	PRON
ma-294	126	5	can	can	AUX
ma-294	126	6	also	also	ADV
ma-294	126	7	use	use	VERB
ma-294	126	8	the	the	DET
ma-294	126	9	following	follow	VERB
ma-294	126	10	calculation	calculation	NOUN
ma-294	126	11	:	:	PUNCT
ma-294	126	12	bk+1	bk+1	NOUN
ma-294	126	13	=	=	PUNCT
ma-294	126	14	bk	bk	NOUN
ma-294	126	15	+	+	PUNCT
ma-294	126	16	c1z1zt1	c1z1zt1	X
ma-294	127	1	+	+	CCONJ
ma-294	127	2	c2z2zt2	c2z2zt2	PROPN
ma-294	127	3	,	,	PUNCT
ma-294	127	4	dk	dk	NOUN
ma-294	127	5	=	=	NOUN
ma-294	127	6	bkgk	bkgk	NOUN
ma-294	127	7	+	+	CCONJ
ma-294	127	8	c1z1(zt1	c1z1(zt1	CCONJ
ma-294	127	9	gk	gk	PROPN
ma-294	127	10	)	)	PUNCT
ma-294	127	11	+	+	CCONJ
ma-294	127	12	c2z2(zt2	c2z2(zt2	ADJ
ma-294	127	13	gk	gk	PROPN
ma-294	127	14	)	)	PUNCT
ma-294	127	15	.	.	PUNCT
ma-294	128	1	let	let	VERB
ma-294	128	2	z1	z1	NOUN
ma-294	128	3	=	=	PUNCT
ma-294	128	4	dk	dk	PROPN
ma-294	128	5	and	and	CCONJ
ma-294	128	6	z2	z2	PROPN
ma-294	128	7	=	=	SYM
ma-294	128	8	bkgk	bkgk	NOUN
ma-294	128	9	,	,	PUNCT
ma-294	128	10	similar	similar	ADJ
ma-294	128	11	to	to	ADP
ma-294	128	12	formula	formula	NOUN
ma-294	128	13	(	(	PUNCT
ma-294	128	14	15	15	NUM
ma-294	128	15	)	)	PUNCT
ma-294	128	16	,	,	PUNCT
ma-294	128	17	we	we	PRON
ma-294	128	18	have	have	VERB
ma-294	128	19	bk+1	bk+1	NOUN
ma-294	128	20	=	=	PUNCT
ma-294	128	21	bk	bk	PROPN
ma-294	128	22	+	+	NOUN
ma-294	128	23	gkgtk	gkgtk	NOUN
ma-294	128	24	gtk	gtk	NOUN
ma-294	128	25	dk	dk	PROPN
ma-294	128	26	−	−	PROPN
ma-294	129	1	(	(	PUNCT
ma-294	129	2	bkdk	bkdk	PROPN
ma-294	129	3	)	)	PUNCT
ma-294	129	4	(	(	PUNCT
ma-294	129	5	bkdk)t	bkdk)t	X
ma-294	129	6	dtk	dtk	PROPN
ma-294	129	7	bkdk	bkdk	PROPN
ma-294	129	8	(	(	PUNCT
ma-294	129	9	15	15	NUM
ma-294	129	10	)	)	PUNCT
ma-294	129	11	thus	thus	ADV
ma-294	129	12	,	,	PUNCT
ma-294	129	13	the	the	DET
ma-294	129	14	algorithm	algorithm	NOUN
ma-294	129	15	to	to	PART
ma-294	129	16	find	find	VERB
ma-294	129	17	the	the	DET
ma-294	129	18	solution	solution	NOUN
ma-294	129	19	of	of	ADP
ma-294	129	20	problem	problem	NOUN
ma-294	129	21	(	(	PUNCT
ma-294	129	22	1	1	X
ma-294	129	23	)	)	PUNCT
ma-294	129	24	is	be	AUX
ma-294	129	25	implemented	implement	VERB
ma-294	129	26	as	as	SCONJ
ma-294	129	27	follows	follow	VERB
ma-294	129	28	:	:	PUNCT
ma-294	129	29	algorithm	algorithm	NOUN
ma-294	129	30	4	4	NUM
ma-294	129	31	:	:	PUNCT
ma-294	129	32	function	function	NOUN
ma-294	129	33	x	x	NOUN
ma-294	129	34	=	=	NOUN
ma-294	129	35	qnewton(x(1	qnewton(x(1	X
ma-294	129	36	)	)	PUNCT
ma-294	129	37	,	,	PUNCT
ma-294	129	38	ε	ε	PROPN
ma-294	129	39	)	)	PUNCT
ma-294	129	40	;	;	PUNCT
ma-294	130	1	k=1	k=1	X
ma-294	130	2	bk	bk	VERB
ma-294	130	3	=	=	PUNCT
ma-294	131	1	i	i	NOUN
ma-294	131	2	;	;	PUNCT
ma-294	131	3	while(‖∇fk‖	while(‖∇fk‖	PROPN
ma-294	131	4	>	>	SYM
ma-294	131	5	ε	ε	PROPN
ma-294	131	6	)	)	PUNCT
ma-294	131	7	sk	sk	PROPN
ma-294	131	8	=	=	PUNCT
ma-294	131	9	−	−	PROPN
ma-294	132	1	[	[	X
ma-294	132	2	bk	bk	X
ma-294	132	3	]	]	SYM
ma-294	132	4	−1∇fk	−1∇fk	NOUN
ma-294	132	5	;	;	PUNCT
ma-294	132	6	αk=	αk=	PROPN
ma-294	132	7	linesearch(f	linesearch(f	VERB
ma-294	132	8	,	,	PUNCT
ma-294	132	9	x	x	PROPN
ma-294	132	10	(	(	PUNCT
ma-294	132	11	k),sk	k),sk	PROPN
ma-294	132	12	)	)	PUNCT
ma-294	132	13	;	;	PUNCT
ma-294	132	14	x(k+1	x(k+1	X
ma-294	132	15	)	)	PUNCT
ma-294	132	16	=	=	SYM
ma-294	133	1	x(k	x(k	PROPN
ma-294	133	2	)	)	PUNCT
ma-294	134	1	+	+	CCONJ
ma-294	134	2	αksk	αksk	ADJ
ma-294	134	3	;	;	PUNCT
ma-294	134	4	dk	dk	X
ma-294	134	5	=	=	PUNCT
ma-294	134	6	x(k+1	x(k+1	PROPN
ma-294	134	7	)	)	PUNCT
ma-294	134	8	−	−	PUNCT
ma-294	135	1	x(k	x(k	PROPN
ma-294	135	2	)	)	PUNCT
ma-294	135	3	;	;	PUNCT
ma-294	135	4	gk	gk	PROPN
ma-294	135	5	=	=	PUNCT
ma-294	135	6	∇fk+1	∇fk+1	PROPN
ma-294	135	7	−∇fk	−∇fk	NOUN
ma-294	135	8	;	;	PUNCT
ma-294	135	9	update	update	NOUN
ma-294	135	10	bk+1	bk+1	NOUN
ma-294	135	11	according	accord	VERB
ma-294	135	12	to	to	ADP
ma-294	135	13	(	(	PUNCT
ma-294	135	14	14	14	NUM
ma-294	135	15	)	)	PUNCT
ma-294	135	16	or	or	CCONJ
ma-294	135	17	(	(	PUNCT
ma-294	135	18	15	15	NUM
ma-294	135	19	)	)	PUNCT
ma-294	135	20	;	;	PUNCT
ma-294	135	21	k	k	X
ma-294	135	22	=	=	SYM
ma-294	135	23	k+1	k+1	X
ma-294	135	24	;	;	PUNCT
ma-294	135	25	end	end	NOUN
ma-294	135	26	;	;	PUNCT
ma-294	135	27	x	x	SYM
ma-294	136	1	=	=	SYM
ma-294	136	2	x(k+1);according	x(k+1);accorde	VERB
ma-294	136	3	to	to	ADP
ma-294	136	4	this	this	DET
ma-294	136	5	algorithm	algorithm	NOUN
ma-294	136	6	,	,	PUNCT
ma-294	136	7	starting	start	VERB
ma-294	136	8	from	from	ADP
ma-294	136	9	point	point	NOUN
ma-294	136	10	x(1	x(1	PROPN
ma-294	136	11	)	)	PUNCT
ma-294	136	12	,	,	PUNCT
ma-294	136	13	the	the	DET
ma-294	136	14	iteration	iteration	NOUN
ma-294	136	15	sequence	sequence	NOUN
ma-294	136	16	(	(	PUNCT
ma-294	136	17	15	15	NUM
ma-294	136	18	)	)	PUNCT
ma-294	136	19	converges	converge	NOUN
ma-294	136	20	to	to	ADP
ma-294	136	21	thelocal	thelocal	ADJ
ma-294	136	22	optimum	optimum	ADJ
ma-294	136	23	x∗	x∗	NOUN
ma-294	136	24	and	and	CCONJ
ma-294	136	25	satisfied	satisfied	ADJ
ma-294	136	26	.	.	PUNCT
ma-294	137	1	f	f	X
ma-294	137	2	(	(	PUNCT
ma-294	137	3	x(1	x(1	PROPN
ma-294	137	4	)	)	PUNCT
ma-294	137	5	)	)	PUNCT
ma-294	138	1	≥	≥	X
ma-294	138	2	...	...	PUNCT
ma-294	139	1	≥	≥	X
ma-294	139	2	f	f	X
ma-294	139	3	(	(	PUNCT
ma-294	139	4	x(k	x(k	PROPN
ma-294	139	5	)	)	PUNCT
ma-294	139	6	)	)	PUNCT
ma-294	139	7	≥	≥	X
ma-294	139	8	...	...	PUNCT
ma-294	140	1	≥	≥	X
ma-294	140	2	f	f	X
ma-294	140	3	(	(	PUNCT
ma-294	140	4	x∗	x∗	PROPN
ma-294	140	5	)	)	PUNCT
ma-294	140	6	in	in	ADP
ma-294	140	7	case	case	NOUN
ma-294	140	8	the	the	DET
ma-294	140	9	objective	objective	ADJ
ma-294	140	10	function	function	NOUN
ma-294	140	11	is	be	AUX
ma-294	140	12	a	a	DET
ma-294	140	13	convex	convex	NOUN
ma-294	140	14	function	function	NOUN
ma-294	140	15	,	,	PUNCT
ma-294	140	16	the	the	DET
ma-294	140	17	obtained	obtain	VERB
ma-294	140	18	optimal	optimal	ADJ
ma-294	140	19	point	point	NOUN
ma-294	140	20	is	be	AUX
ma-294	140	21	the	the	DET
ma-294	140	22	global	global	ADJ
ma-294	140	23	optimalsolution	optimalsolution	NOUN
ma-294	140	24	of	of	ADP
ma-294	140	25	problem	problem	NOUN
ma-294	140	26	(	(	PUNCT
ma-294	140	27	1	1	NUM
ma-294	140	28	)	)	PUNCT
ma-294	140	29	.	.	PUNCT
ma-294	141	1	to	to	PART
ma-294	141	2	illustrate	illustrate	VERB
ma-294	141	3	the	the	DET
ma-294	141	4	theoretical	theoretical	ADJ
ma-294	141	5	results	result	NOUN
ma-294	141	6	,	,	PUNCT
ma-294	141	7	here	here	ADV
ma-294	141	8	are	be	AUX
ma-294	141	9	some	some	DET
ma-294	141	10	experimental	experimental	ADJ
ma-294	141	11	calculationresults	calculationresult	NOUN
ma-294	141	12	of	of	ADP
ma-294	141	13	the	the	DET
ma-294	141	14	algorithm	algorithm	NOUN
ma-294	141	15	.	.	PUNCT
ma-294	142	1	3	3	X
ma-294	142	2	.	.	X
ma-294	142	3	experimental	experimental	ADJ
ma-294	142	4	results	result	NOUN
ma-294	142	5	and	and	CCONJ
ma-294	142	6	discussions	discussion	NOUN
ma-294	142	7	in	in	ADP
ma-294	142	8	this	this	DET
ma-294	142	9	section	section	NOUN
ma-294	142	10	,	,	PUNCT
ma-294	142	11	we	we	PRON
ma-294	142	12	perform	perform	VERB
ma-294	142	13	experimental	experimental	ADJ
ma-294	142	14	calculations	calculation	NOUN
ma-294	142	15	to	to	PART
ma-294	142	16	illustrate	illustrate	VERB
ma-294	142	17	the	the	DET
ma-294	142	18	convergence	convergence	NOUN
ma-294	142	19	of	of	ADP
ma-294	142	20	the	the	DET
ma-294	142	21	algorithmintroduced	algorithmintroduce	VERB
ma-294	142	22	in	in	ADP
ma-294	142	23	the	the	DET
ma-294	142	24	paper	paper	NOUN
ma-294	142	25	.	.	PUNCT
ma-294	143	1	the	the	DET
ma-294	143	2	data	datum	NOUN
ma-294	143	3	is	be	AUX
ma-294	143	4	given	give	VERB
ma-294	143	5	:	:	PUNCT
ma-294	143	6	objective	objective	ADJ
ma-294	143	7	function	function	NOUN
ma-294	143	8	f	f	PROPN
ma-294	143	9	(	(	PUNCT
ma-294	143	10	x	x	X
ma-294	143	11	)	)	PUNCT
ma-294	143	12	=	=	SYM
ma-294	144	1	10∑	10∑	NUM
ma-294	144	2	i=1	i=1	PROPN
ma-294	144	3	(	(	PUNCT
ma-294	144	4	xi	xi	ADP
ma-294	144	5	−	−	PROPN
ma-294	144	6	i)4	i)4	NOUN
ma-294	144	7	(	(	PUNCT
ma-294	144	8	16	16	NUM
ma-294	144	9	)	)	PUNCT
ma-294	144	10	https://doi.org/10.28924/ada/ma.5.9	https://doi.org/10.28924/ada/ma.5.9	PROPN
ma-294	144	11	eur	eur	NOUN
ma-294	144	12	.	.	PUNCT
ma-294	145	1	j.	j.	PROPN
ma-294	145	2	math	math	PROPN
ma-294	145	3	.	.	PUNCT
ma-294	146	1	anal	anal	PROPN
ma-294	146	2	.	.	PUNCT
ma-294	147	1	10.28924	10.28924	NUM
ma-294	147	2	/	/	SYM
ma-294	147	3	ada	ada	PROPN
ma-294	147	4	/	/	SYM
ma-294	147	5	ma.5.9	ma.5.9	PROPN
ma-294	147	6	7initial	7initial	ADJ
ma-294	147	7	approximation	approximation	NOUN
ma-294	147	8	:	:	PUNCT
ma-294	147	9	x(1	x(1	PROPN
ma-294	147	10	)	)	PUNCT
ma-294	148	1	=	=	PRON
ma-294	148	2	(	(	PUNCT
ma-294	148	3	0	0	NUM
ma-294	148	4	,	,	PUNCT
ma-294	148	5	0	0	NUM
ma-294	148	6	,	,	PUNCT
ma-294	148	7	...	...	PUNCT
ma-294	148	8	,	,	PUNCT
ma-294	148	9	0	0	NUM
ma-294	148	10	)	)	PUNCT
ma-294	148	11	.	.	PUNCT
ma-294	149	1	it	it	PRON
ma-294	149	2	is	be	AUX
ma-294	149	3	easy	easy	ADJ
ma-294	149	4	to	to	PART
ma-294	149	5	see	see	VERB
ma-294	149	6	that	that	SCONJ
ma-294	149	7	the	the	DET
ma-294	149	8	exact	exact	ADJ
ma-294	149	9	solution	solution	NOUN
ma-294	149	10	of	of	ADP
ma-294	149	11	problem	problem	NOUN
ma-294	149	12	(	(	PUNCT
ma-294	149	13	1)is	1)is	NUM
ma-294	149	14	x∗	x∗	X
ma-294	149	15	=	=	SYM
ma-294	149	16	(	(	PUNCT
ma-294	149	17	1	1	NUM
ma-294	149	18	,	,	PUNCT
ma-294	149	19	2	2	NUM
ma-294	149	20	,	,	PUNCT
ma-294	149	21	...	...	PUNCT
ma-294	149	22	,	,	PUNCT
ma-294	149	23	10	10	NUM
ma-294	149	24	)	)	PUNCT
ma-294	149	25	,	,	PUNCT
ma-294	149	26	f	f	PROPN
ma-294	149	27	(	(	PUNCT
ma-294	149	28	x∗	x∗	X
ma-294	149	29	)	)	PUNCT
ma-294	149	30	=	=	SYM
ma-294	150	1	0	0	X
ma-294	150	2	.	.	PUNCT
ma-294	151	1	the	the	DET
ma-294	151	2	objective	objective	ADJ
ma-294	151	3	function	function	NOUN
ma-294	151	4	(	(	PUNCT
ma-294	151	5	16	16	NUM
ma-294	151	6	)	)	PUNCT
ma-294	151	7	is	be	AUX
ma-294	151	8	differentiable	differentiable	ADJ
ma-294	151	9	at	at	ADP
ma-294	151	10	all	all	DET
ma-294	151	11	levels	level	NOUN
ma-294	151	12	,	,	PUNCT
ma-294	151	13	so	so	ADV
ma-294	151	14	thehessen	thehessen	ADJ
ma-294	151	15	matrix	matrix	NOUN
ma-294	151	16	exists	exist	VERB
ma-294	151	17	,	,	PUNCT
ma-294	151	18	so	so	SCONJ
ma-294	151	19	we	we	PRON
ma-294	151	20	can	can	AUX
ma-294	151	21	completely	completely	ADV
ma-294	151	22	apply	apply	VERB
ma-294	151	23	newton	newton	PROPN
ma-294	151	24	’s	’s	PART
ma-294	151	25	algorithm	algorithm	NOUN
ma-294	151	26	to	to	PART
ma-294	151	27	solve	solve	VERB
ma-294	151	28	problem	problem	NOUN
ma-294	151	29	(	(	PUNCT
ma-294	151	30	1	1	NUM
ma-294	151	31	)	)	PUNCT
ma-294	151	32	.	.	PUNCT
ma-294	152	1	let	let	VERB
ma-294	152	2	er	er	INTJ
ma-294	152	3	r	r	NOUN
ma-294	152	4	=	=	PUNCT
ma-294	152	5	∥∥x(k	∥∥x(k	PROPN
ma-294	152	6	)	)	PUNCT
ma-294	152	7	−	−	NOUN
ma-294	152	8	x∗	x∗	VERB
ma-294	152	9	∥∥	∥∥	X
ma-294	152	10	2	2	NUM
ma-294	152	11	,	,	PUNCT
ma-294	152	12	we	we	PRON
ma-294	152	13	have	have	VERB
ma-294	152	14	the	the	DET
ma-294	152	15	computational	computational	ADJ
ma-294	152	16	results	result	NOUN
ma-294	152	17	illustrating	illustrate	VERB
ma-294	152	18	the	the	DET
ma-294	152	19	convergence	convergence	NOUN
ma-294	152	20	of	of	ADP
ma-294	152	21	newton’salgorithm	newton’salgorithm	NOUN
ma-294	152	22	given	give	VERB
ma-294	152	23	in	in	ADP
ma-294	152	24	table	table	NOUN
ma-294	152	25	1	1	NUM
ma-294	152	26	:	:	PUNCT
ma-294	152	27	table	table	NOUN
ma-294	152	28	1	1	NUM
ma-294	152	29	.	.	NUM
ma-294	152	30	approximate	approximate	ADJ
ma-294	152	31	solution	solution	NOUN
ma-294	152	32	of	of	ADP
ma-294	152	33	problem	problem	NOUN
ma-294	152	34	(	(	PUNCT
ma-294	152	35	1	1	X
ma-294	152	36	)	)	PUNCT
ma-294	152	37	obtained	obtain	VERB
ma-294	152	38	from	from	ADP
ma-294	152	39	algorithm	algorithm	NOUN
ma-294	152	40	2	2	NUM
ma-294	152	41	x(k	x(k	PROPN
ma-294	152	42	)	)	PUNCT
ma-294	153	1	k	k	NOUN
ma-294	153	2	=	=	SYM
ma-294	153	3	5	5	NUM
ma-294	153	4	k	k	NOUN
ma-294	153	5	=	=	SYM
ma-294	153	6	10	10	NUM
ma-294	153	7	k	k	NOUN
ma-294	153	8	=	=	SYM
ma-294	153	9	15	15	NUM
ma-294	153	10	k	k	NOUN
ma-294	153	11	=	=	SYM
ma-294	153	12	20	20	NUM
ma-294	153	13	x	x	SYM
ma-294	153	14	(	(	PUNCT
ma-294	153	15	k	k	NOUN
ma-294	153	16	)	)	PUNCT
ma-294	153	17	1	1	NUM
ma-294	153	18	0.8025	0.8025	NUM
ma-294	153	19	0.9740	0.9740	NUM
ma-294	153	20	0.9966	0.9966	NUM
ma-294	153	21	0.9995	0.9995	NUM
ma-294	153	22	x	x	SYM
ma-294	153	23	(	(	PUNCT
ma-294	153	24	k	k	NOUN
ma-294	153	25	)	)	PUNCT
ma-294	153	26	2	2	NUM
ma-294	153	27	1.6049	1.6049	NUM
ma-294	153	28	1.9480	1.9480	NUM
ma-294	153	29	1.9931	1.9931	NUM
ma-294	153	30	1.9991	1.9991	NUM
ma-294	153	31	x	x	SYM
ma-294	153	32	(	(	PUNCT
ma-294	153	33	k	k	NOUN
ma-294	153	34	)	)	PUNCT
ma-294	153	35	3	3	NUM
ma-294	153	36	2.4074	2.4074	NUM
ma-294	153	37	2.9220	2.9220	NUM
ma-294	153	38	2.9897	2.9897	NUM
ma-294	153	39	2.9986	2.9986	NUM
ma-294	153	40	x	x	SYM
ma-294	153	41	(	(	PUNCT
ma-294	153	42	k	k	NOUN
ma-294	153	43	)	)	PUNCT
ma-294	153	44	4	4	NUM
ma-294	153	45	3.2099	3.2099	NUM
ma-294	153	46	3.8960	3.8960	NUM
ma-294	153	47	3.9863	3.9863	NUM
ma-294	153	48	3.9982	3.9982	NUM
ma-294	153	49	x	x	SYM
ma-294	153	50	(	(	PUNCT
ma-294	153	51	k	k	NOUN
ma-294	153	52	)	)	PUNCT
ma-294	153	53	5	5	NUM
ma-294	153	54	4.0123	4.0123	NUM
ma-294	153	55	4.8699	4.8699	NUM
ma-294	153	56	4.9829	4.9829	NUM
ma-294	153	57	4.9977	4.9977	NUM
ma-294	153	58	x	x	SYM
ma-294	153	59	(	(	PUNCT
ma-294	153	60	k	k	NOUN
ma-294	153	61	)	)	PUNCT
ma-294	153	62	6	6	NUM
ma-294	153	63	4.8148	4.8148	NUM
ma-294	153	64	5.8439	5.8439	NUM
ma-294	153	65	5.9794	5.9794	NUM
ma-294	153	66	5.9973	5.9973	NUM
ma-294	153	67	x	x	SYM
ma-294	153	68	(	(	PUNCT
ma-294	153	69	k	k	NOUN
ma-294	153	70	)	)	PUNCT
ma-294	153	71	7	7	NUM
ma-294	153	72	5.6173	5.6173	NUM
ma-294	153	73	6.8179	6.8179	NUM
ma-294	153	74	6.9760	6.9760	NUM
ma-294	153	75	6.9968	6.9968	NUM
ma-294	153	76	x	x	SYM
ma-294	153	77	(	(	PUNCT
ma-294	153	78	k	k	NOUN
ma-294	153	79	)	)	PUNCT
ma-294	153	80	8	8	NUM
ma-294	153	81	6.4198	6.4198	NUM
ma-294	153	82	7.7919	7.7919	NUM
ma-294	153	83	7.9726	7.9726	NUM
ma-294	153	84	7.9964	7.9964	NUM
ma-294	153	85	x	x	SYM
ma-294	153	86	(	(	PUNCT
ma-294	153	87	k	k	NOUN
ma-294	153	88	)	)	PUNCT
ma-294	153	89	9	9	NUM
ma-294	153	90	7.2222	7.2222	NUM
ma-294	153	91	8.7659	8.7659	NUM
ma-294	153	92	8.9692	8.9692	NUM
ma-294	153	93	8.9959	8.9959	NUM
ma-294	153	94	x	x	SYM
ma-294	153	95	(	(	PUNCT
ma-294	153	96	k	k	NOUN
ma-294	153	97	)	)	PUNCT
ma-294	153	98	10	10	NUM
ma-294	153	99	8.0247	8.0247	NUM
ma-294	153	100	9.7399	9.7399	NUM
ma-294	153	101	9.9657	9.9657	NUM
ma-294	153	102	9.9955	9.9955	NUM
ma-294	153	103	err	err	NOUN
ma-294	153	104	3.8758	3.8758	NUM
ma-294	153	105	0.5104	0.5104	NUM
ma-294	153	106	0.0672	0.0672	NUM
ma-294	153	107	0.0089	0.0089	NUM
ma-294	153	108	the	the	DET
ma-294	153	109	calculation	calculation	NOUN
ma-294	153	110	results	result	VERB
ma-294	153	111	in	in	ADP
ma-294	153	112	table	table	NOUN
ma-294	153	113	1	1	NUM
ma-294	153	114	show	show	VERB
ma-294	153	115	that	that	SCONJ
ma-294	153	116	the	the	DET
ma-294	153	117	approximate	approximate	ADJ
ma-294	153	118	solution	solution	NOUN
ma-294	153	119	found	find	VERB
ma-294	153	120	converges	converge	NOUN
ma-294	153	121	to	to	ADP
ma-294	153	122	the	the	DET
ma-294	153	123	exactsolution	exactsolution	NOUN
ma-294	153	124	of	of	ADP
ma-294	153	125	the	the	DET
ma-294	153	126	problem	problem	NOUN
ma-294	153	127	according	accord	VERB
ma-294	153	128	to	to	ADP
ma-294	153	129	the	the	DET
ma-294	153	130	number	number	NOUN
ma-294	153	131	of	of	ADP
ma-294	153	132	iterations	iteration	NOUN
ma-294	153	133	.	.	PUNCT
ma-294	154	1	the	the	DET
ma-294	154	2	graphs	graph	NOUN
ma-294	154	3	in	in	ADP
ma-294	154	4	figure	figure	NOUN
ma-294	154	5	1	1	NUM
ma-294	154	6	and	and	CCONJ
ma-294	154	7	figure2	figure2	NOUN
ma-294	154	8	illustrate	illustrate	VERB
ma-294	154	9	the	the	DET
ma-294	154	10	convergence	convergence	NOUN
ma-294	154	11	of	of	ADP
ma-294	154	12	the	the	DET
ma-294	154	13	algorithm	algorithm	NOUN
ma-294	154	14	.	.	PUNCT
ma-294	155	1	figure	figure	NOUN
ma-294	155	2	1	1	NUM
ma-294	155	3	.	.	NOUN
ma-294	155	4	error	error	NOUN
ma-294	155	5	graph	graph	NOUN
ma-294	155	6	according	accord	VERB
ma-294	155	7	to	to	ADP
ma-294	155	8	the	the	DET
ma-294	155	9	number	number	NOUN
ma-294	155	10	of	of	ADP
ma-294	155	11	iterations	iteration	NOUN
ma-294	155	12	with	with	ADP
ma-294	155	13	the	the	DET
ma-294	155	14	number	number	NOUN
ma-294	155	15	of	of	ADP
ma-294	155	16	iterations	iteration	NOUN
ma-294	155	17	k=1,2	k=1,2	PROPN
ma-294	155	18	,	,	PUNCT
ma-294	155	19	.	.	PUNCT
ma-294	155	20	.	.	PUNCT
ma-294	156	1	.	.	PUNCT
ma-294	157	1	,	,	PUNCT
ma-294	157	2	20	20	NUM
ma-294	157	3	obtained	obtain	VERB
ma-294	157	4	from	from	ADP
ma-294	157	5	algorithm	algorithm	NOUN
ma-294	157	6	2	2	NUM
ma-294	157	7	https://doi.org/10.28924/ada/ma.5.9	https://doi.org/10.28924/ada/ma.5.9	PROPN
ma-294	157	8	eur	eur	NOUN
ma-294	157	9	.	.	PUNCT
ma-294	158	1	j.	j.	PROPN
ma-294	158	2	math	math	PROPN
ma-294	158	3	.	.	PUNCT
ma-294	159	1	anal	anal	PROPN
ma-294	159	2	.	.	PUNCT
ma-294	160	1	10.28924	10.28924	NUM
ma-294	160	2	/	/	SYM
ma-294	160	3	ada	ada	PROPN
ma-294	160	4	/	/	SYM
ma-294	160	5	ma.5.9	ma.5.9	PROPN
ma-294	160	6	8	8	NUM
ma-294	160	7	figure	figure	NOUN
ma-294	160	8	2	2	NUM
ma-294	160	9	.	.	NOUN
ma-294	160	10	objective	objective	ADJ
ma-294	160	11	function	function	NOUN
ma-294	160	12	graph	graph	NOUN
ma-294	160	13	according	accord	VERB
ma-294	160	14	to	to	ADP
ma-294	160	15	the	the	DET
ma-294	160	16	number	number	NOUN
ma-294	160	17	of	of	ADP
ma-294	160	18	iterations	iteration	NOUN
ma-294	160	19	(	(	PUNCT
ma-294	160	20	number	number	NOUN
ma-294	160	21	of	of	ADP
ma-294	160	22	iterations	iteration	NOUN
ma-294	160	23	k=1,2	k=1,2	PROPN
ma-294	160	24	,	,	PUNCT
ma-294	160	25	.	.	PUNCT
ma-294	160	26	.	.	PUNCT
ma-294	160	27	.	.	PUNCT
ma-294	161	1	,	,	PUNCT
ma-294	161	2	20	20	NUM
ma-294	161	3	)	)	PUNCT
ma-294	161	4	obtained	obtain	VERB
ma-294	161	5	from	from	ADP
ma-294	161	6	algorithm	algorithm	NOUN
ma-294	161	7	2from	2from	NUM
ma-294	161	8	figure	figure	NOUN
ma-294	161	9	1	1	NUM
ma-294	161	10	and	and	CCONJ
ma-294	161	11	figure	figure	NOUN
ma-294	161	12	2	2	NUM
ma-294	161	13	,	,	PUNCT
ma-294	161	14	it	it	PRON
ma-294	161	15	can	can	AUX
ma-294	161	16	be	be	AUX
ma-294	161	17	seen	see	VERB
ma-294	161	18	that	that	SCONJ
ma-294	161	19	the	the	DET
ma-294	161	20	error	error	NOUN
ma-294	161	21	function	function	NOUN
ma-294	161	22	and	and	CCONJ
ma-294	161	23	the	the	DET
ma-294	161	24	objective	objective	ADJ
ma-294	161	25	function	function	NOUN
ma-294	161	26	aremonotonically	aremonotonically	ADV
ma-294	161	27	decreasing	decrease	VERB
ma-294	161	28	functions	function	NOUN
ma-294	161	29	with	with	ADP
ma-294	161	30	the	the	DET
ma-294	161	31	number	number	NOUN
ma-294	161	32	of	of	ADP
ma-294	161	33	iterations	iteration	NOUN
ma-294	161	34	,	,	PUNCT
ma-294	161	35	which	which	PRON
ma-294	161	36	shows	show	VERB
ma-294	161	37	that	that	SCONJ
ma-294	161	38	the	the	DET
ma-294	161	39	approximatesolution	approximatesolution	NOUN
ma-294	161	40	converges	converge	VERB
ma-294	161	41	to	to	ADP
ma-294	161	42	the	the	DET
ma-294	161	43	exact	exact	ADJ
ma-294	161	44	solution	solution	NOUN
ma-294	161	45	of	of	ADP
ma-294	161	46	problem	problem	NOUN
ma-294	161	47	(	(	PUNCT
ma-294	161	48	1	1	NUM
ma-294	161	49	)	)	PUNCT
ma-294	161	50	.	.	PUNCT
ma-294	162	1	now	now	ADV
ma-294	162	2	,	,	PUNCT
ma-294	162	3	let	let	VERB
ma-294	162	4	us	we	PRON
ma-294	162	5	consider	consider	VERB
ma-294	162	6	the	the	DET
ma-294	162	7	following	follow	VERB
ma-294	162	8	objectivefunction	objectivefunction	NOUN
ma-294	162	9	:	:	PUNCT
ma-294	163	1	f	f	PROPN
ma-294	163	2	(	(	PUNCT
ma-294	163	3	x	x	X
ma-294	163	4	)	)	PUNCT
ma-294	163	5	=	=	PUNCT
ma-294	163	6			PUNCT
ma-294	164	1	10∑	10∑	NUM
ma-294	164	2	i=1	i=1	PROPN
ma-294	164	3	(	(	PUNCT
ma-294	164	4	xi	xi	PROPN
ma-294	164	5	−	−	PROPN
ma-294	164	6	1i	1i	NOUN
ma-294	164	7	)	)	PUNCT
ma-294	164	8	4	4	NUM
ma-294	164	9	∃xi	∃xi	NOUN
ma-294	164	10	<	<	X
ma-294	164	11	1	1	NUM
ma-294	165	1	i	i	PRON
ma-294	165	2	10∑	10∑	NUM
ma-294	165	3	i=1	i=1	PROPN
ma-294	165	4	(	(	PUNCT
ma-294	165	5	xi	xi	PROPN
ma-294	165	6	−	−	PROPN
ma-294	165	7	1i	1i	NOUN
ma-294	165	8	)	)	PUNCT
ma-294	165	9	√	√	PROPN
ma-294	165	10	xi	xi	PUNCT
ma-294	166	1	−	−	PROPN
ma-294	166	2	1i	1i	NOUN
ma-294	166	3	∀xi	∀xi	PROPN
ma-294	166	4	≥	≥	NUM
ma-294	166	5	1	1	NUM
ma-294	166	6	i	i	NOUN
ma-294	166	7	(	(	PUNCT
ma-294	166	8	17	17	NUM
ma-294	166	9	)	)	PUNCT
ma-294	166	10	the	the	DET
ma-294	166	11	objective	objective	ADJ
ma-294	166	12	function	function	NOUN
ma-294	166	13	does	do	AUX
ma-294	166	14	not	not	PART
ma-294	166	15	have	have	VERB
ma-294	166	16	a	a	DET
ma-294	166	17	second	second	ADJ
ma-294	166	18	derivative	derivative	NOUN
ma-294	166	19	at	at	ADP
ma-294	166	20	x∗	x∗	PROPN
ma-294	166	21	=	=	SYM
ma-294	166	22	(	(	PUNCT
ma-294	166	23	1	1	NUM
ma-294	166	24	,	,	PUNCT
ma-294	166	25	12	12	NUM
ma-294	166	26	,	,	PUNCT
ma-294	166	27	...	...	PUNCT
ma-294	166	28	,	,	PUNCT
ma-294	166	29	110	110	NUM
ma-294	166	30	)	)	PUNCT
ma-294	166	31	,	,	PUNCT
ma-294	166	32	so	so	ADV
ma-294	166	33	,	,	PUNCT
ma-294	166	34	in	in	ADP
ma-294	166	35	order	order	NOUN
ma-294	166	36	to	to	ADP
ma-294	166	37	findthe	findthe	DET
ma-294	166	38	solution	solution	NOUN
ma-294	166	39	for	for	ADP
ma-294	166	40	problem	problem	NOUN
ma-294	166	41	(	(	PUNCT
ma-294	166	42	1	1	NUM
ma-294	166	43	)	)	PUNCT
ma-294	166	44	with	with	ADP
ma-294	166	45	objective	objective	ADJ
ma-294	166	46	function	function	NOUN
ma-294	166	47	(	(	PUNCT
ma-294	166	48	16	16	NUM
ma-294	166	49	)	)	PUNCT
ma-294	166	50	,	,	PUNCT
ma-294	166	51	we	we	PRON
ma-294	166	52	perform	perform	VERB
ma-294	166	53	algorithm	algorithm	NOUN
ma-294	166	54	4	4	NUM
ma-294	166	55	with	with	ADP
ma-294	166	56	the	the	DET
ma-294	166	57	hessenmatrix	hessenmatrix	NOUN
ma-294	166	58	approximation	approximation	NOUN
ma-294	166	59	.	.	PUNCT
ma-294	167	1	matrix	matrix	NOUN
ma-294	167	2	updated	update	VERB
ma-294	167	3	according	accord	VERB
ma-294	167	4	to	to	ADP
ma-294	167	5	formula	formula	NOUN
ma-294	167	6	(	(	PUNCT
ma-294	167	7	15	15	NUM
ma-294	167	8	)	)	PUNCT
ma-294	167	9	.	.	PUNCT
ma-294	168	1	the	the	DET
ma-294	168	2	calculation	calculation	NOUN
ma-294	168	3	results	result	NOUN
ma-294	168	4	are	be	AUX
ma-294	168	5	givenin	givenin	ADJ
ma-294	168	6	table	table	NOUN
ma-294	168	7	2	2	NUM
ma-294	168	8	.	.	PUNCT
ma-294	168	9	table	table	NOUN
ma-294	168	10	2	2	NUM
ma-294	168	11	.	.	NOUN
ma-294	168	12	approximate	approximate	ADJ
ma-294	168	13	solution	solution	NOUN
ma-294	168	14	of	of	ADP
ma-294	168	15	problem	problem	NOUN
ma-294	168	16	(	(	PUNCT
ma-294	168	17	1	1	X
ma-294	168	18	)	)	PUNCT
ma-294	168	19	obtained	obtain	VERB
ma-294	168	20	from	from	ADP
ma-294	168	21	algorithm	algorithm	NOUN
ma-294	168	22	4	4	NUM
ma-294	168	23	x(k	x(k	PROPN
ma-294	168	24	)	)	PUNCT
ma-294	168	25	k	k	NOUN
ma-294	169	1	=	=	SYM
ma-294	169	2	5	5	NUM
ma-294	169	3	k	k	NOUN
ma-294	169	4	=	=	SYM
ma-294	169	5	10	10	NUM
ma-294	169	6	k	k	NOUN
ma-294	169	7	=	=	SYM
ma-294	169	8	15	15	NUM
ma-294	169	9	k	k	NOUN
ma-294	169	10	=	=	SYM
ma-294	169	11	20	20	NUM
ma-294	169	12	x	x	SYM
ma-294	169	13	(	(	PUNCT
ma-294	169	14	k	k	NOUN
ma-294	169	15	)	)	PUNCT
ma-294	169	16	1	1	NUM
ma-294	169	17	0.4598	0.4598	NUM
ma-294	169	18	0.8654	0.8654	NUM
ma-294	169	19	0.9708	0.9708	NUM
ma-294	169	20	1.0128	1.0128	NUM
ma-294	169	21	x	x	SYM
ma-294	169	22	(	(	PUNCT
ma-294	169	23	k	k	NOUN
ma-294	169	24	)	)	PUNCT
ma-294	169	25	2	2	NUM
ma-294	169	26	0.5080	0.5080	NUM
ma-294	169	27	0.5079	0.5079	NUM
ma-294	169	28	0.5078	0.5078	NUM
ma-294	169	29	0.5078	0.5078	NUM
ma-294	169	30	x	x	SYM
ma-294	169	31	(	(	PUNCT
ma-294	169	32	k	k	NOUN
ma-294	169	33	)	)	PUNCT
ma-294	169	34	3	3	NUM
ma-294	169	35	0.2322	0.2322	NUM
ma-294	169	36	0.3231	0.3231	NUM
ma-294	169	37	0.3459	0.3459	NUM
ma-294	169	38	0.3548	0.3548	NUM
ma-294	169	39	x	x	SYM
ma-294	169	40	(	(	PUNCT
ma-294	169	41	k	k	NOUN
ma-294	169	42	)	)	PUNCT
ma-294	169	43	4	4	NUM
ma-294	169	44	0.1490	0.1490	NUM
ma-294	169	45	0.2424	0.2424	NUM
ma-294	169	46	0.2659	0.2659	NUM
ma-294	169	47	0.2748	0.2748	NUM
ma-294	169	48	x	x	SYM
ma-294	169	49	(	(	PUNCT
ma-294	169	50	k	k	NOUN
ma-294	169	51	)	)	PUNCT
ma-294	169	52	5	5	NUM
ma-294	169	53	0.0987	0.0987	NUM
ma-294	169	54	0.1791	0.1791	NUM
ma-294	169	55	0.1997	0.1997	NUM
ma-294	169	56	0.2078	0.2078	NUM
ma-294	169	57	x	x	SYM
ma-294	169	58	(	(	PUNCT
ma-294	169	59	k	k	NOUN
ma-294	169	60	)	)	PUNCT
ma-294	169	61	6	6	NUM
ma-294	169	62	0.0672	0.0672	NUM
ma-294	169	63	0.1341	0.1341	NUM
ma-294	169	64	0.1525	0.1525	NUM
ma-294	169	65	0.1600	0.1600	NUM
ma-294	169	66	x	x	SYM
ma-294	169	67	(	(	PUNCT
ma-294	169	68	k	k	NOUN
ma-294	169	69	)	)	PUNCT
ma-294	169	70	7	7	NUM
ma-294	169	71	0.0471	0.0471	NUM
ma-294	169	72	0.1025	0.1025	NUM
ma-294	169	73	0.1196	0.1196	NUM
ma-294	169	74	0.1271	0.1271	NUM
ma-294	169	75	x	x	SYM
ma-294	169	76	(	(	PUNCT
ma-294	169	77	k	k	NOUN
ma-294	169	78	)	)	PUNCT
ma-294	169	79	8	8	NUM
ma-294	169	80	0.0340	0.0340	NUM
ma-294	169	81	0.0798	0.0798	NUM
ma-294	169	82	0.0959	0.0959	NUM
ma-294	169	83	0.1039	0.1039	NUM
ma-294	169	84	x	x	SYM
ma-294	169	85	(	(	PUNCT
ma-294	169	86	k	k	NOUN
ma-294	169	87	)	)	PUNCT
ma-294	169	88	9	9	NUM
ma-294	169	89	0.0251	0.0251	NUM
ma-294	169	90	0.0632	0.0632	NUM
ma-294	169	91	0.0784	0.0784	NUM
ma-294	169	92	0.0866	0.0866	NUM
ma-294	169	93	x	x	SYM
ma-294	169	94	(	(	PUNCT
ma-294	169	95	k	k	NOUN
ma-294	169	96	)	)	PUNCT
ma-294	169	97	10	10	NUM
ma-294	169	98	0.0190	0.0190	NUM
ma-294	169	99	0.0508	0.0508	NUM
ma-294	169	100	0.0649	0.0649	NUM
ma-294	169	101	0.0733	0.0733	NUM
ma-294	169	102	err	err	NOUN
ma-294	169	103	0.6032	0.6032	NUM
ma-294	169	104	0.1680	0.1680	NUM
ma-294	169	105	0.0722	0.0722	NUM
ma-294	169	106	0.0584	0.0584	NUM
ma-294	169	107	https://doi.org/10.28924/ada/ma.5.9	https://doi.org/10.28924/ada/ma.5.9	PROPN
ma-294	169	108	eur	eur	NOUN
ma-294	169	109	.	.	PUNCT
ma-294	170	1	j.	j.	PROPN
ma-294	170	2	math	math	PROPN
ma-294	170	3	.	.	PUNCT
ma-294	171	1	anal	anal	PROPN
ma-294	171	2	.	.	PUNCT
ma-294	172	1	10.28924	10.28924	NUM
ma-294	172	2	/	/	SYM
ma-294	172	3	ada	ada	PROPN
ma-294	172	4	/	/	SYM
ma-294	172	5	ma.5.9	ma.5.9	PROPN
ma-294	172	6	9the	9the	DET
ma-294	172	7	calculation	calculation	NOUN
ma-294	172	8	results	result	NOUN
ma-294	172	9	in	in	ADP
ma-294	172	10	table	table	NOUN
ma-294	172	11	2	2	NUM
ma-294	172	12	show	show	VERB
ma-294	172	13	that	that	SCONJ
ma-294	172	14	the	the	DET
ma-294	172	15	approximate	approximate	ADJ
ma-294	172	16	solution	solution	NOUN
ma-294	172	17	found	find	VERB
ma-294	172	18	converges	converge	NOUN
ma-294	172	19	to	to	ADP
ma-294	172	20	the	the	DET
ma-294	172	21	exactsolution	exactsolution	NOUN
ma-294	172	22	of	of	ADP
ma-294	172	23	the	the	DET
ma-294	172	24	problem	problem	NOUN
ma-294	172	25	depending	depend	VERB
ma-294	172	26	on	on	ADP
ma-294	172	27	the	the	DET
ma-294	172	28	number	number	NOUN
ma-294	172	29	of	of	ADP
ma-294	172	30	iterations	iteration	NOUN
ma-294	172	31	.	.	PUNCT
ma-294	173	1	the	the	DET
ma-294	173	2	calculation	calculation	NOUN
ma-294	173	3	results	result	VERB
ma-294	173	4	show	show	VERB
ma-294	173	5	thatthe	thatthe	PRON
ma-294	173	6	quasi	quasi	PROPN
ma-294	173	7	-	-	PROPN
ma-294	173	8	newton	newton	PROPN
ma-294	173	9	method	method	NOUN
ma-294	173	10	has	have	VERB
ma-294	173	11	the	the	DET
ma-294	173	12	advantage	advantage	NOUN
ma-294	173	13	of	of	ADP
ma-294	173	14	not	not	PART
ma-294	173	15	requiring	require	VERB
ma-294	173	16	a	a	DET
ma-294	173	17	quadratic	quadratic	ADJ
ma-294	173	18	differentiable	differentiable	ADJ
ma-294	173	19	objectivefunction	objectivefunction	NOUN
ma-294	173	20	,	,	PUNCT
ma-294	173	21	but	but	CCONJ
ma-294	173	22	the	the	DET
ma-294	173	23	convergence	convergence	NOUN
ma-294	173	24	is	be	AUX
ma-294	173	25	quite	quite	ADV
ma-294	173	26	slow	slow	ADJ
ma-294	173	27	compared	compare	VERB
ma-294	173	28	to	to	ADP
ma-294	173	29	the	the	DET
ma-294	173	30	newton	newton	PROPN
ma-294	173	31	method	method	NOUN
ma-294	173	32	.	.	PUNCT
ma-294	174	1	the	the	DET
ma-294	174	2	error	error	NOUN
ma-294	174	3	functionand	functionand	NOUN
ma-294	174	4	the	the	DET
ma-294	174	5	objective	objective	ADJ
ma-294	174	6	function	function	NOUN
ma-294	174	7	are	be	AUX
ma-294	174	8	not	not	PART
ma-294	174	9	monotonically	monotonically	ADV
ma-294	174	10	decreasing	decrease	VERB
ma-294	174	11	functions	function	NOUN
ma-294	174	12	with	with	ADP
ma-294	174	13	the	the	DET
ma-294	174	14	number	number	NOUN
ma-294	174	15	of	of	ADP
ma-294	174	16	iterations	iteration	NOUN
ma-294	174	17	,	,	PUNCT
ma-294	174	18	but	but	CCONJ
ma-294	174	19	tend	tend	VERB
ma-294	174	20	to	to	PART
ma-294	174	21	decrease	decrease	VERB
ma-294	174	22	gradually	gradually	ADV
ma-294	174	23	,	,	PUNCT
ma-294	174	24	which	which	PRON
ma-294	174	25	also	also	ADV
ma-294	174	26	confirms	confirm	VERB
ma-294	174	27	that	that	SCONJ
ma-294	174	28	the	the	DET
ma-294	174	29	approximate	approximate	ADJ
ma-294	174	30	solution	solution	NOUN
ma-294	174	31	converges	converge	VERB
ma-294	174	32	to	to	ADP
ma-294	174	33	theexact	theexact	ADJ
ma-294	174	34	solution	solution	NOUN
ma-294	174	35	of	of	ADP
ma-294	174	36	the	the	DET
ma-294	174	37	problem	problem	NOUN
ma-294	174	38	.	.	PUNCT
ma-294	175	1	the	the	DET
ma-294	175	2	graphs	graph	NOUN
ma-294	175	3	in	in	ADP
ma-294	175	4	figure	figure	NOUN
ma-294	175	5	3	3	NUM
ma-294	175	6	and	and	CCONJ
ma-294	175	7	figure	figure	VERB
ma-294	175	8	4	4	NUM
ma-294	175	9	illustrate	illustrate	VERB
ma-294	175	10	the	the	DET
ma-294	175	11	convergence	convergence	NOUN
ma-294	175	12	ofthe	ofthe	NOUN
ma-294	175	13	algorithm	algorithm	NOUN
ma-294	175	14	.	.	PUNCT
ma-294	176	1	figure	figure	NOUN
ma-294	176	2	3	3	NUM
ma-294	176	3	.	.	NOUN
ma-294	176	4	error	error	NOUN
ma-294	176	5	graph	graph	NOUN
ma-294	176	6	depending	depend	VERB
ma-294	176	7	on	on	ADP
ma-294	176	8	the	the	DET
ma-294	176	9	number	number	NOUN
ma-294	176	10	of	of	ADP
ma-294	176	11	iterations	iteration	NOUN
ma-294	176	12	with	with	ADP
ma-294	176	13	the	the	DET
ma-294	176	14	number	number	NOUN
ma-294	176	15	of	of	ADP
ma-294	176	16	iterations	iteration	NOUN
ma-294	176	17	k=1,2	k=1,2	PROPN
ma-294	176	18	,	,	PUNCT
ma-294	176	19	.	.	PUNCT
ma-294	176	20	.	.	PUNCT
ma-294	177	1	.	.	PUNCT
ma-294	178	1	,	,	PUNCT
ma-294	178	2	20	20	NUM
ma-294	178	3	obtained	obtain	VERB
ma-294	178	4	from	from	ADP
ma-294	178	5	algorithm	algorithm	NOUN
ma-294	178	6	4	4	NUM
ma-294	178	7	figure	figure	NOUN
ma-294	178	8	4	4	NUM
ma-294	178	9	.	.	PUNCT
ma-294	178	10	graph	graph	NOUN
ma-294	178	11	of	of	ADP
ma-294	178	12	the	the	DET
ma-294	178	13	objective	objective	ADJ
ma-294	178	14	function	function	NOUN
ma-294	178	15	depending	depend	VERB
ma-294	178	16	on	on	ADP
ma-294	178	17	the	the	DET
ma-294	178	18	number	number	NOUN
ma-294	178	19	of	of	ADP
ma-294	178	20	iterations	iteration	NOUN
ma-294	178	21	(	(	PUNCT
ma-294	178	22	number	number	NOUN
ma-294	178	23	of	of	ADP
ma-294	178	24	iterations	iteration	NOUN
ma-294	178	25	k=1,2	k=1,2	PROPN
ma-294	178	26	,	,	PUNCT
ma-294	178	27	.	.	PUNCT
ma-294	178	28	.	.	PUNCT
ma-294	178	29	.	.	PUNCT
ma-294	179	1	,	,	PUNCT
ma-294	179	2	20	20	NUM
ma-294	179	3	)	)	PUNCT
ma-294	179	4	obtained	obtain	VERB
ma-294	179	5	from	from	ADP
ma-294	179	6	algorithm	algorithm	NOUN
ma-294	179	7	4	4	NUM
ma-294	179	8	https://doi.org/10.28924/ada/ma.5.9	https://doi.org/10.28924/ada/ma.5.9	PROPN
ma-294	179	9	eur	eur	ADJ
ma-294	179	10	.	.	PUNCT
ma-294	180	1	j.	j.	PROPN
ma-294	180	2	math	math	PROPN
ma-294	180	3	.	.	PUNCT
ma-294	181	1	anal	anal	PROPN
ma-294	181	2	.	.	PUNCT
ma-294	182	1	10.28924	10.28924	NUM
ma-294	182	2	/	/	SYM
ma-294	182	3	ada	ada	PROPN
ma-294	182	4	/	/	SYM
ma-294	182	5	ma.5.9	ma.5.9	PROPN
ma-294	182	6	104	104	NUM
ma-294	182	7	.	.	PUNCT
ma-294	183	1	conclusion	conclusion	NOUN
ma-294	183	2	in	in	ADP
ma-294	183	3	this	this	DET
ma-294	183	4	paper	paper	NOUN
ma-294	183	5	,	,	PUNCT
ma-294	183	6	we	we	PRON
ma-294	183	7	implement	implement	VERB
ma-294	183	8	an	an	DET
ma-294	183	9	iterative	iterative	NOUN
ma-294	183	10	algorithm	algorithm	NOUN
ma-294	183	11	to	to	PART
ma-294	183	12	solve	solve	VERB
ma-294	183	13	the	the	DET
ma-294	183	14	unconstrained	unconstrained	ADJ
ma-294	183	15	convex	convex	NOUN
ma-294	183	16	optimizationproblem	optimizationproblem	NOUN
ma-294	183	17	based	base	VERB
ma-294	183	18	on	on	ADP
ma-294	183	19	newton	newton	PROPN
ma-294	183	20	and	and	CCONJ
ma-294	183	21	quasi	quasi	PROPN
ma-294	183	22	-	-	PROPN
ma-294	183	23	newton	newton	PROPN
ma-294	183	24	iteration	iteration	NOUN
ma-294	183	25	methods	method	NOUN
ma-294	183	26	,	,	PUNCT
ma-294	183	27	in	in	ADP
ma-294	183	28	which	which	PRON
ma-294	183	29	the	the	DET
ma-294	183	30	information	information	NOUN
ma-294	183	31	of	of	ADP
ma-294	183	32	thecomponent	thecomponent	NOUN
ma-294	183	33	solutions	solution	NOUN
ma-294	183	34	calculated	calculate	VERB
ma-294	183	35	in	in	ADP
ma-294	183	36	the	the	DET
ma-294	183	37	current	current	ADJ
ma-294	183	38	iteration	iteration	NOUN
ma-294	183	39	is	be	AUX
ma-294	183	40	inherited	inherit	VERB
ma-294	183	41	instead	instead	ADV
ma-294	183	42	of	of	ADP
ma-294	183	43	using	use	VERB
ma-294	183	44	the	the	DET
ma-294	183	45	solutionscalculated	solutionscalculate	VERB
ma-294	183	46	in	in	ADP
ma-294	183	47	the	the	DET
ma-294	183	48	previous	previous	ADJ
ma-294	183	49	iteration	iteration	NOUN
ma-294	183	50	.	.	PUNCT
ma-294	184	1	the	the	DET
ma-294	184	2	computational	computational	ADJ
ma-294	184	3	results	result	NOUN
ma-294	184	4	according	accord	VERB
ma-294	184	5	to	to	ADP
ma-294	184	6	the	the	DET
ma-294	184	7	algorithm	algorithm	NOUN
ma-294	184	8	areperformed	areperforme	VERB
ma-294	184	9	on	on	ADP
ma-294	184	10	the	the	DET
ma-294	184	11	matlab	matlab	PROPN
ma-294	184	12	2014	2014	NUM
ma-294	184	13	environment	environment	NOUN
ma-294	184	14	,	,	PUNCT
ma-294	184	15	the	the	DET
ma-294	184	16	numerical	numerical	ADJ
ma-294	184	17	results	result	NOUN
ma-294	184	18	have	have	AUX
ma-294	184	19	confirmed	confirm	VERB
ma-294	184	20	the	the	DET
ma-294	184	21	convergenceof	convergenceof	NOUN
ma-294	184	22	the	the	DET
ma-294	184	23	method	method	NOUN
ma-294	184	24	and	and	CCONJ
ma-294	184	25	are	be	AUX
ma-294	184	26	consistent	consistent	ADJ
ma-294	184	27	with	with	ADP
ma-294	184	28	the	the	DET
ma-294	184	29	theory	theory	NOUN
ma-294	184	30	presented	present	VERB
ma-294	184	31	in	in	ADP
ma-294	184	32	the	the	DET
ma-294	184	33	paper	paper	NOUN
ma-294	184	34	.	.	PUNCT
ma-294	185	1	references	reference	NOUN
ma-294	185	2	[	[	X
ma-294	185	3	1	1	X
ma-294	185	4	]	]	PUNCT
ma-294	185	5	s.	s.	PROPN
ma-294	185	6	aji	aji	PROPN
ma-294	185	7	,	,	PUNCT
ma-294	185	8	p.	p.	PROPN
ma-294	185	9	kumam	kumam	PROPN
ma-294	185	10	,	,	PUNCT
ma-294	185	11	a.m.	a.m.	PROPN
ma-294	185	12	awwal	awwal	PROPN
ma-294	185	13	,	,	PUNCT
ma-294	185	14	m.m	m.m	PROPN
ma-294	185	15	.	.	PROPN
ma-294	185	16	yahaya	yahaya	PROPN
ma-294	185	17	,	,	PUNCT
ma-294	185	18	w.	w.	PROPN
ma-294	185	19	kumam	kumam	PROPN
ma-294	185	20	,	,	PUNCT
ma-294	185	21	two	two	NUM
ma-294	185	22	hybrid	hybrid	ADJ
ma-294	185	23	spectral	spectral	ADJ
ma-294	185	24	methods	method	NOUN
ma-294	185	25	with	with	ADP
ma-294	185	26	inertial	inertial	ADJ
ma-294	185	27	effect	effect	NOUN
ma-294	185	28	for	for	ADP
ma-294	185	29	solv	solv	ADJ
ma-294	185	30	-	-	ADJ
ma-294	185	31	ing	ing	ADJ
ma-294	185	32	system	system	NOUN
ma-294	185	33	of	of	ADP
ma-294	185	34	nonlinear	nonlinear	ADJ
ma-294	185	35	monotone	monotone	ADJ
ma-294	185	36	equations	equation	NOUN
ma-294	185	37	with	with	ADP
ma-294	185	38	application	application	NOUN
ma-294	185	39	in	in	ADP
ma-294	185	40	robotics	robotic	NOUN
ma-294	185	41	,	,	PUNCT
ma-294	185	42	ieee	ieee	NOUN
ma-294	185	43	access	access	NOUN
ma-294	185	44	9	9	NUM
ma-294	185	45	(	(	PUNCT
ma-294	185	46	2021	2021	NUM
ma-294	185	47	)	)	PUNCT
ma-294	185	48	30918–30928	30918–30928	NUM
ma-294	185	49	.	.	PUNCT
ma-294	186	1	https://doi.org/10.1109/access.2021.3056567.[2	https://doi.org/10.1109/access.2021.3056567.[2	NOUN
ma-294	186	2	]	]	X
ma-294	186	3	y.	y.	PROPN
ma-294	186	4	zhou	zhou	PROPN
ma-294	186	5	,	,	PUNCT
ma-294	186	6	y.	y.	PROPN
ma-294	186	7	wu	wu	PROPN
ma-294	186	8	,	,	PUNCT
ma-294	186	9	x.	x.	PROPN
ma-294	186	10	li	li	PROPN
ma-294	186	11	,	,	PUNCT
ma-294	186	12	a	a	DET
ma-294	186	13	new	new	ADJ
ma-294	186	14	hybrid	hybrid	ADJ
ma-294	186	15	prpfr	prpfr	NOUN
ma-294	186	16	conjugate	conjugate	VERB
ma-294	186	17	gradient	gradient	ADJ
ma-294	186	18	method	method	NOUN
ma-294	186	19	for	for	ADP
ma-294	186	20	solving	solve	VERB
ma-294	186	21	nonlinear	nonlinear	ADJ
ma-294	186	22	monotone	monotone	ADJ
ma-294	186	23	equationsand	equationsand	NOUN
ma-294	186	24	image	image	NOUN
ma-294	186	25	restoration	restoration	NOUN
ma-294	186	26	problems	problem	NOUN
ma-294	186	27	,	,	PUNCT
ma-294	186	28	math	math	NOUN
ma-294	186	29	.	.	PUNCT
ma-294	187	1	probl	probl	PROPN
ma-294	187	2	.	.	PUNCT
ma-294	188	1	eng	eng	PROPN
ma-294	188	2	.	.	PROPN
ma-294	188	3	2020	2020	NUM
ma-294	188	4	(	(	PUNCT
ma-294	188	5	2020	2020	NUM
ma-294	188	6	)	)	PUNCT
ma-294	188	7	6391321	6391321	NUM
ma-294	188	8	.	.	PUNCT
ma-294	189	1	https://doi.org/10.1155/2020/	https://doi.org/10.1155/2020/	ADJ
ma-294	189	2	6391321.[3	6391321.[3	NUM
ma-294	189	3	]	]	X
ma-294	189	4	m.	m.	NOUN
ma-294	189	5	eshaghnezhad	eshaghnezhad	PROPN
ma-294	189	6	,	,	PUNCT
ma-294	189	7	s.	s.	PROPN
ma-294	189	8	effati	effati	PROPN
ma-294	189	9	,	,	PUNCT
ma-294	189	10	a.	a.	NOUN
ma-294	189	11	mansoori	mansoori	PROPN
ma-294	189	12	,	,	PUNCT
ma-294	189	13	a	a	DET
ma-294	189	14	neurodynamic	neurodynamic	ADJ
ma-294	189	15	model	model	NOUN
ma-294	189	16	to	to	PART
ma-294	189	17	solve	solve	VERB
ma-294	189	18	nonlinear	nonlinear	ADJ
ma-294	189	19	pseudo	pseudo	NOUN
ma-294	189	20	-	-	ADJ
ma-294	189	21	monotone	monotone	ADJ
ma-294	189	22	projectionequation	projectionequation	NOUN
ma-294	189	23	and	and	CCONJ
ma-294	189	24	its	its	PRON
ma-294	189	25	applications	application	NOUN
ma-294	189	26	,	,	PUNCT
ma-294	189	27	ieee	ieee	NOUN
ma-294	189	28	trans	tran	NOUN
ma-294	189	29	.	.	PUNCT
ma-294	190	1	cybern	cybern	PROPN
ma-294	190	2	.	.	PUNCT
ma-294	191	1	47	47	NUM
ma-294	191	2	(	(	PUNCT
ma-294	191	3	2017	2017	NUM
ma-294	191	4	)	)	PUNCT
ma-294	191	5	3050–3062	3050–3062	NUM
ma-294	191	6	.	.	PUNCT
ma-294	192	1	https://doi.org/10.1109/tcyb	https://doi.org/10.1109/tcyb	X
ma-294	192	2	.	.	PUNCT
ma-294	193	1	2016.2611529.[4	2016.2611529.[4	NUM
ma-294	193	2	]	]	X
ma-294	193	3	s.	s.	PROPN
ma-294	193	4	crisci	crisci	PROPN
ma-294	193	5	,	,	PUNCT
ma-294	193	6	m.	m.	NOUN
ma-294	193	7	piana	piana	PROPN
ma-294	193	8	,	,	PUNCT
ma-294	193	9	v.	v.	ADP
ma-294	193	10	ruggiero	ruggiero	PROPN
ma-294	193	11	,	,	PUNCT
ma-294	193	12	m.	m.	NOUN
ma-294	193	13	scussolini	scussolini	PROPN
ma-294	193	14	,	,	PUNCT
ma-294	193	15	a	a	DET
ma-294	193	16	regularized	regularize	VERB
ma-294	193	17	affine	affine	NOUN
ma-294	193	18	-	-	PUNCT
ma-294	193	19	scaling	scale	VERB
ma-294	193	20	trust	trust	NOUN
ma-294	193	21	-	-	PUNCT
ma-294	193	22	region	region	NOUN
ma-294	193	23	method	method	NOUN
ma-294	193	24	for	for	ADP
ma-294	193	25	parametricimaging	parametricimaging	NOUN
ma-294	193	26	of	of	ADP
ma-294	193	27	dynamic	dynamic	ADJ
ma-294	193	28	pet	pet	ADJ
ma-294	193	29	data	datum	NOUN
ma-294	193	30	,	,	PUNCT
ma-294	193	31	siam	siam	PROPN
ma-294	193	32	j.	j.	PROPN
ma-294	193	33	imaging	imaging	PROPN
ma-294	193	34	sci	sci	PROPN
ma-294	193	35	.	.	PROPN
ma-294	193	36	14	14	NUM
ma-294	193	37	(	(	PUNCT
ma-294	193	38	2021	2021	NUM
ma-294	193	39	)	)	PUNCT
ma-294	193	40	418–439	418–439	NUM
ma-294	193	41	.	.	PUNCT
ma-294	194	1	https://doi.org/10.1137/20m1336370.[5	https://doi.org/10.1137/20m1336370.[5	PRON
ma-294	194	2	]	]	X
ma-294	194	3	j.k	j.k	PROPN
ma-294	194	4	.	.	PUNCT
ma-294	195	1	liu	liu	PROPN
ma-294	195	2	,	,	PUNCT
ma-294	195	3	x.l	x.l	PROPN
ma-294	195	4	.	.	PROPN
ma-294	195	5	du	du	PROPN
ma-294	195	6	,	,	PUNCT
ma-294	195	7	m.	m.	NOUN
ma-294	195	8	scussolini	scussolini	PROPN
ma-294	195	9	,	,	PUNCT
ma-294	195	10	a	a	DET
ma-294	195	11	gradient	gradient	ADJ
ma-294	195	12	projection	projection	NOUN
ma-294	195	13	method	method	NOUN
ma-294	195	14	for	for	ADP
ma-294	195	15	the	the	DET
ma-294	195	16	sparse	sparse	ADJ
ma-294	195	17	signal	signal	NOUN
ma-294	195	18	reconstruction	reconstruction	NOUN
ma-294	195	19	in	in	ADP
ma-294	195	20	compressivesensing	compressivesensing	PROPN
ma-294	195	21	,	,	PUNCT
ma-294	195	22	appl	appl	PROPN
ma-294	195	23	.	.	PROPN
ma-294	196	1	anal	anal	PROPN
ma-294	196	2	.	.	PUNCT
ma-294	197	1	97	97	NUM
ma-294	197	2	(	(	PUNCT
ma-294	197	3	2018	2018	NUM
ma-294	197	4	)	)	PUNCT
ma-294	197	5	2122–2131	2122–2131	NUM
ma-294	197	6	.	.	PUNCT
ma-294	198	1	https://doi.org/10.1080/00036811.2017.1400510.[6	https://doi.org/10.1080/00036811.2017.1400510.[6	ADP
ma-294	198	2	]	]	X
ma-294	198	3	a.m.	a.m.	PROPN
ma-294	198	4	awwal	awwal	PROPN
ma-294	198	5	,	,	PUNCT
ma-294	198	6	l.	l.	PROPN
ma-294	198	7	wang	wang	PROPN
ma-294	198	8	,	,	PUNCT
ma-294	198	9	p.	p.	PROPN
ma-294	198	10	kumam	kumam	PROPN
ma-294	198	11	,	,	PUNCT
ma-294	198	12	h.	h.	PROPN
ma-294	198	13	mohammad	mohammad	PROPN
ma-294	198	14	,	,	PUNCT
ma-294	198	15	w.	w.	PROPN
ma-294	198	16	watthayu	watthayu	PROPN
ma-294	198	17	,	,	PUNCT
ma-294	198	18	a	a	DET
ma-294	198	19	projection	projection	NOUN
ma-294	198	20	hestenes	hestene	NOUN
ma-294	198	21	–	–	PUNCT
ma-294	198	22	stiefel	stiefel	NOUN
ma-294	198	23	method	method	NOUN
ma-294	198	24	with	with	ADP
ma-294	198	25	spectralparameter	spectralparameter	NOUN
ma-294	198	26	for	for	ADP
ma-294	198	27	nonlinear	nonlinear	ADJ
ma-294	198	28	monotone	monotone	ADJ
ma-294	198	29	equations	equation	NOUN
ma-294	198	30	and	and	CCONJ
ma-294	198	31	signal	signal	NOUN
ma-294	198	32	processing	processing	NOUN
ma-294	198	33	,	,	PUNCT
ma-294	198	34	math	math	NOUN
ma-294	198	35	.	.	PUNCT
ma-294	199	1	comput	comput	PROPN
ma-294	199	2	.	.	PUNCT
ma-294	200	1	appl	appl	PROPN
ma-294	200	2	.	.	PUNCT
ma-294	201	1	25	25	NUM
ma-294	201	2	(	(	PUNCT
ma-294	201	3	2020	2020	NUM
ma-294	201	4	)	)	PUNCT
ma-294	201	5	27	27	NUM
ma-294	201	6	.	.	PUNCT
ma-294	201	7	https	https	NOUN
ma-294	201	8	:	:	PUNCT
ma-294	201	9	//doi.org/10.3390	//doi.org/10.3390	ADJ
ma-294	201	10	/	/	SYM
ma-294	201	11	mca25020027.[7	mca25020027.[7	PROPN
ma-294	201	12	]	]	PUNCT
ma-294	201	13	b.	b.	PROPN
ma-294	201	14	ghaddar	ghaddar	PROPN
ma-294	201	15	,	,	PUNCT
ma-294	201	16	j.	j.	PROPN
ma-294	201	17	marecek	marecek	PROPN
ma-294	201	18	,	,	PUNCT
ma-294	201	19	m.	m.	NOUN
ma-294	201	20	mevissen	mevissen	PROPN
ma-294	201	21	,	,	PUNCT
ma-294	201	22	optimal	optimal	ADJ
ma-294	201	23	power	power	NOUN
ma-294	201	24	flow	flow	NOUN
ma-294	201	25	as	as	ADP
ma-294	201	26	a	a	DET
ma-294	201	27	polynomial	polynomial	ADJ
ma-294	201	28	optimization	optimization	NOUN
ma-294	201	29	problem	problem	NOUN
ma-294	201	30	,	,	PUNCT
ma-294	201	31	ieee	ieee	PROPN
ma-294	201	32	trans.power	trans.power	PROPN
ma-294	201	33	syst	syst	PROPN
ma-294	201	34	.	.	PUNCT
ma-294	201	35	31	31	NUM
ma-294	201	36	(	(	PUNCT
ma-294	201	37	2016	2016	NUM
ma-294	201	38	)	)	PUNCT
ma-294	201	39	539–546	539–546	NUM
ma-294	201	40	.	.	PUNCT
ma-294	202	1	https://doi.org/10.1109/tpwrs.2015.2390037.[8	https://doi.org/10.1109/tpwrs.2015.2390037.[8	X
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ma-294	202	20	.	.	PUNCT
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ma-294	204	2	(	(	PUNCT
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ma-294	204	4	.	.	PUNCT
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ma-294	205	31	)	)	PUNCT
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ma-294	207	25	.	.	PUNCT
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ma-294	209	2	(	(	PUNCT
ma-294	209	3	2000	2000	NUM
ma-294	209	4	)	)	PUNCT
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ma-294	209	6	.	.	PUNCT
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ma-294	210	7	.	.	PROPN
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ma-294	210	11	.	.	PROPN
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ma-294	210	13	,	,	PUNCT
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ma-294	210	24	(	(	PUNCT
ma-294	210	25	2002	2002	NUM
ma-294	210	26	)	)	PUNCT
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ma-294	210	28	.	.	PUNCT
ma-294	211	1	https://doi.org/10.1137/s0036144502414942.[12	https://doi.org/10.1137/s0036144502414942.[12	PROPN
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ma-294	211	10	,	,	PUNCT
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ma-294	211	13	,	,	PUNCT
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ma-294	211	23	)	)	PUNCT
ma-294	211	24	,	,	PUNCT
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ma-294	211	26	-	-	SYM
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ma-294	211	28	]	]	X
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ma-294	211	56	(	(	PUNCT
ma-294	211	57	1996	1996	NUM
ma-294	211	58	)	)	PUNCT
ma-294	211	59	.	.	PUNCT
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ma-294	213	10	,	,	PUNCT
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ma-294	213	15	(	(	PUNCT
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ma-294	213	30	equations	equation	NOUN
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ma-294	213	34	,	,	PUNCT
ma-294	213	35	academic	academic	ADJ
ma-294	213	36	press	press	NOUN
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ma-294	213	39	(	(	PUNCT
ma-294	213	40	1970	1970	NUM
ma-294	213	41	)	)	PUNCT
ma-294	213	42	.	.	PUNCT
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ma-294	218	2	.	.	PUNCT
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ma-294	219	7	[	[	X
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ma-294	219	9	]	]	PUNCT
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ma-294	219	17	problems	problem	NOUN
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ma-294	219	31	(	(	PUNCT
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ma-294	219	33	)	)	PUNCT
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ma-294	220	2	]	]	X
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ma-294	220	14	numerical	numerical	ADJ
ma-294	220	15	methods	method	NOUN
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ma-294	220	23	,	,	PUNCT
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ma-294	220	28	(	(	PUNCT
ma-294	220	29	2013	2013	NUM
ma-294	220	30	)	)	PUNCT
ma-294	220	31	.	.	PUNCT
ma-294	221	1	https://doi.org/10.1007/978-1-4614-8453-0.[18	https://doi.org/10.1007/978-1-4614-8453-0.[18	PROPN
ma-294	221	2	]	]	PUNCT
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ma-294	222	4	,	,	PUNCT
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ma-294	222	10	use	use	NOUN
ma-294	222	11	in	in	ADP
ma-294	222	12	optimization	optimization	NOUN
ma-294	222	13	,	,	PUNCT
ma-294	222	14	eur	eur	PROPN
ma-294	222	15	.	.	PUNCT
ma-294	223	1	j.	j.	PROPN
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ma-294	224	1	res	re	NOUN
ma-294	224	2	.	.	PUNCT
ma-294	225	1	181	181	NUM
ma-294	225	2	(	(	PUNCT
ma-294	225	3	2007	2007	NUM
ma-294	225	4	)	)	PUNCT
ma-294	225	5	1086–1096	1086–1096	NUM
ma-294	225	6	.	.	PUNCT
ma-294	226	1	https	https	NOUN
ma-294	226	2	:	:	PUNCT
ma-294	226	3	//doi.org/10.1016	//doi.org/10.1016	PROPN
ma-294	226	4	/	/	SYM
ma-294	226	5	j.ejor.2005.06.076.[19	j.ejor.2005.06.076.[19	PROPN
ma-294	226	6	]	]	X
ma-294	226	7	l.v	l.v	PROPN
ma-294	226	8	.	.	PROPN
ma-294	226	9	kantorovich	kantorovich	PROPN
ma-294	226	10	,	,	PUNCT
ma-294	226	11	functional	functional	ADJ
ma-294	226	12	analysis	analysis	NOUN
ma-294	226	13	and	and	CCONJ
ma-294	226	14	applied	applied	ADJ
ma-294	226	15	mathematics	mathematic	NOUN
ma-294	226	16	,	,	PUNCT
ma-294	226	17	uspekhi	uspekhi	PROPN
ma-294	226	18	mat	mat	PROPN
ma-294	226	19	.	.	PUNCT
ma-294	227	1	nauk	nauk	NOUN
ma-294	227	2	3	3	NUM
ma-294	227	3	(	(	PUNCT
ma-294	227	4	1948	1948	NUM
ma-294	227	5	)	)	PUNCT
ma-294	227	6	89–185	89–185	PROPN
ma-294	227	7	.	.	PUNCT
ma-294	227	8	https	https	NOUN
ma-294	227	9	:	:	PUNCT
ma-294	227	10	//doi.org/10.1070	//doi.org/10.1070	X
ma-294	227	11	/	/	SYM
ma-294	227	12	rm1948v003n06abeh003995.[20	rm1948v003n06abeh003995.[20	PROPN
ma-294	227	13	]	]	PUNCT
ma-294	227	14	k.	k.	PROPN
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ma-294	228	2	,	,	PUNCT
ma-294	228	3	r.k	r.k	PROPN
ma-294	228	4	.	.	PROPN
ma-294	228	5	vasudeva	vasudeva	PROPN
ma-294	228	6	,	,	PUNCT
ma-294	228	7	quasi	quasi	PROPN
ma-294	228	8	-	-	ADJ
ma-294	228	9	newton	newton	PROPN
ma-294	228	10	line	line	NOUN
ma-294	228	11	search	search	NOUN
ma-294	228	12	algorithm	algorithm	NOUN
ma-294	228	13	for	for	ADP
ma-294	228	14	solving	solve	VERB
ma-294	228	15	unconstrained	unconstrained	ADJ
ma-294	228	16	non	non	ADJ
ma-294	228	17	-	-	ADJ
ma-294	228	18	linear	linear	ADJ
ma-294	228	19	least	least	ADJ
ma-294	228	20	squareoptimization	squareoptimization	NOUN
ma-294	228	21	problem	problem	NOUN
ma-294	228	22	,	,	PUNCT
ma-294	228	23	int	int	NOUN
ma-294	228	24	.	.	PUNCT
ma-294	229	1	j.	j.	PROPN
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ma-294	229	3	appl	appl	PROPN
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ma-294	230	2	.	.	PROPN
ma-294	231	1	10	10	NUM
ma-294	231	2	(	(	PUNCT
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ma-294	231	4	)	)	PUNCT
ma-294	232	1	,	,	PUNCT
ma-294	232	2	11	11	NUM
ma-294	232	3	-	-	SYM
ma-294	232	4	21.[21	21.[21	NUM
ma-294	232	5	]	]	PUNCT
ma-294	232	6	i.	i.	PROPN
ma-294	232	7	povalej	povalej	PROPN
ma-294	232	8	,	,	PUNCT
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ma-294	232	10	-	-	PROPN
ma-294	232	11	newton	newton	PROPN
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ma-294	232	13	method	method	NOUN
ma-294	232	14	for	for	ADP
ma-294	232	15	multiobjective	multiobjective	ADJ
ma-294	232	16	optimization	optimization	NOUN
ma-294	232	17	,	,	PUNCT
ma-294	232	18	j.	j.	PROPN
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ma-294	232	20	.	.	PUNCT
ma-294	233	1	appl	appl	PROPN
ma-294	233	2	.	.	PUNCT
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ma-294	233	4	.	.	PUNCT
ma-294	234	1	255	255	NUM
ma-294	234	2	(	(	PUNCT
ma-294	234	3	2014	2014	NUM
ma-294	234	4	)	)	PUNCT
ma-294	235	1	765–777	765–777	NUM
ma-294	235	2	.	.	PUNCT
ma-294	236	1	https://doi.org/10.1016/j.cam.2013.06.045.[22	https://doi.org/10.1016/j.cam.2013.06.045.[22	PROPN
ma-294	236	2	]	]	PUNCT
ma-294	236	3	k.	k.	PROPN
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ma-294	237	2	,	,	PUNCT
ma-294	237	3	r.k	r.k	PROPN
ma-294	237	4	.	.	PROPN
ma-294	237	5	vasudeva	vasudeva	PROPN
ma-294	237	6	,	,	PUNCT
ma-294	237	7	quasi	quasi	PROPN
ma-294	237	8	-	-	ADJ
ma-294	237	9	newton	newton	PROPN
ma-294	237	10	line	line	NOUN
ma-294	237	11	search	search	NOUN
ma-294	237	12	algorithm	algorithm	NOUN
ma-294	237	13	for	for	ADP
ma-294	237	14	solving	solve	VERB
ma-294	237	15	unconstrained	unconstrained	ADJ
ma-294	237	16	non	non	ADJ
ma-294	237	17	-	-	ADJ
ma-294	237	18	linear	linear	ADJ
ma-294	237	19	least	least	ADJ
ma-294	237	20	squareoptimization	squareoptimization	NOUN
ma-294	237	21	problem	problem	NOUN
ma-294	237	22	,	,	PUNCT
ma-294	237	23	int	int	NOUN
ma-294	237	24	.	.	PUNCT
ma-294	238	1	j.	j.	PROPN
ma-294	238	2	basic	basic	ADJ
ma-294	238	3	appl	appl	PROPN
ma-294	238	4	.	.	PUNCT
ma-294	239	1	sci	sci	PROPN
ma-294	239	2	.	.	PROPN
ma-294	239	3	13	13	NUM
ma-294	239	4	(	(	PUNCT
ma-294	239	5	2021	2021	NUM
ma-294	239	6	)	)	PUNCT
ma-294	239	7	9–18.[23	9–18.[23	NUM
ma-294	239	8	]	]	X
ma-294	239	9	g.	g.	PROPN
ma-294	239	10	yuan	yuan	PROPN
ma-294	239	11	,	,	PUNCT
ma-294	239	12	s.	s.	PROPN
ma-294	239	13	lu	lu	PROPN
ma-294	239	14	,	,	PUNCT
ma-294	239	15	z.	z.	PROPN
ma-294	239	16	wei	wei	PROPN
ma-294	239	17	,	,	PUNCT
ma-294	239	18	a	a	DET
ma-294	239	19	line	line	NOUN
ma-294	239	20	search	search	NOUN
ma-294	239	21	algorithm	algorithm	NOUN
ma-294	239	22	for	for	ADP
ma-294	239	23	unconstrained	unconstrained	ADJ
ma-294	239	24	optimization	optimization	NOUN
ma-294	239	25	,	,	PUNCT
ma-294	239	26	j.	j.	PROPN
ma-294	239	27	softw	softw	PROPN
ma-294	239	28	.	.	PUNCT
ma-294	240	1	eng	eng	PROPN
ma-294	240	2	.	.	PROPN
ma-294	240	3	appl	appl	PROPN
ma-294	240	4	.	.	PROPN
ma-294	241	1	3	3	NUM
ma-294	241	2	(	(	PUNCT
ma-294	241	3	2010)503–509	2010)503–509	NUM
ma-294	241	4	.	.	PUNCT
ma-294	242	1	https://doi.org/10.4236/jsea.2010.35057	https://doi.org/10.4236/jsea.2010.35057	PROPN
ma-294	242	2	.	.	PUNCT
ma-294	243	1	https://doi.org/10.28924/ada/ma.5.9	https://doi.org/10.28924/ada/ma.5.9	PROPN
ma-294	243	2	https://doi.org/10.1007/978-3-642-23899-4	https://doi.org/10.1007/978-3-642-23899-4	PROPN
ma-294	243	3	https://doi.org/10.1007/978-1-4614-8453-0	https://doi.org/10.1007/978-1-4614-8453-0	PROPN
ma-294	243	4	https://doi.org/10.1016/j.ejor.2005.06.076	https://doi.org/10.1016/j.ejor.2005.06.076	NUM
ma-294	243	5	https://doi.org/10.1016/j.ejor.2005.06.076	https://doi.org/10.1016/j.ejor.2005.06.076	NOUN
ma-294	243	6	https://doi.org/10.1070/rm1948v003n06abeh003995	https://doi.org/10.1070/rm1948v003n06abeh003995	PROPN
ma-294	243	7	https://doi.org/10.1070/rm1948v003n06abeh003995	https://doi.org/10.1070/rm1948v003n06abeh003995	PROPN
ma-294	243	8	https://doi.org/10.1016/j.cam.2013.06.045	https://doi.org/10.1016/j.cam.2013.06.045	ADV
ma-294	243	9	https://doi.org/10.4236/jsea.2010.35057	https://doi.org/10.4236/jsea.2010.35057	PROPN
ma-294	243	10	1	1	NUM
ma-294	243	11	.	.	PUNCT
ma-294	244	1	introduction	introduction	NOUN
ma-294	244	2	2	2	NUM
ma-294	244	3	.	.	PUNCT
ma-294	244	4	proposed	propose	VERB
ma-294	244	5	method	method	NOUN
ma-294	244	6	2.1	2.1	NUM
ma-294	244	7	.	.	PUNCT
ma-294	245	1	newton	newton	PROPN
ma-294	245	2	's	's	PART
ma-294	245	3	method	method	NOUN
ma-294	245	4	2.2	2.2	NUM
ma-294	245	5	.	.	PUNCT
ma-294	246	1	quasi	quasi	PROPN
ma-294	246	2	-	-	PROPN
ma-294	246	3	newton	newton	PROPN
ma-294	246	4	method	method	NOUN
ma-294	246	5	3	3	NUM
ma-294	246	6	.	.	PUNCT
ma-294	246	7	experimental	experimental	ADJ
ma-294	246	8	results	result	NOUN
ma-294	246	9	and	and	CCONJ
ma-294	246	10	discussions	discussion	NOUN
ma-294	246	11	4	4	NUM
ma-294	246	12	.	.	PUNCT
ma-294	247	1	conclusion	conclusion	NOUN
ma-294	247	2	references	reference	NOUN