id	sid	tid	token	lemma	pos
iajs-554	1	1	mathematics	mathematics	PROPN
iajs-554	1	2	367	367	NUM
iajs-554	1	3	مجلة	مجلة	NOUN
iajs-554	1	4	إبن	إبن	VERB
iajs-554	1	5	الهيثم	الهيثم	ADJ
iajs-554	1	6	للعلوم	للعلوم	NOUN
iajs-554	1	7	الصرفة	الصرفة	NOUN
iajs-554	2	1	و	و	PRON
iajs-554	2	2	التطبيقية	التطبيقية	ADJ
iajs-554	2	3	2012	2012	NUM
iajs-554	2	4	السنة	السنة	NOUN
iajs-554	2	5	25	25	NUM
iajs-554	2	6	المجلد	المجلد	NOUN
iajs-554	2	7	3	3	NUM
iajs-554	2	8	العدد	العدد	PROPN
iajs-554	2	9	ibn	ibn	PROPN
iajs-554	2	10	al	al	PROPN
iajs-554	2	11	-	-	PUNCT
iajs-554	2	12	haitham	haitham	PROPN
iajs-554	2	13	journal	journal	PROPN
iajs-554	2	14	for	for	ADP
iajs-554	2	15	pure	pure	ADJ
iajs-554	2	16	and	and	CCONJ
iajs-554	2	17	applied	apply	VERB
iajs-554	2	18	science	science	NOUN
iajs-554	2	19	no	no	NOUN
iajs-554	2	20	.	.	NOUN
iajs-554	2	21	3	3	NUM
iajs-554	2	22	vol	vol	NOUN
iajs-554	2	23	.	.	PUNCT
iajs-554	3	1	25	25	NUM
iajs-554	3	2	year	year	NOUN
iajs-554	3	3	2012	2012	NUM
iajs-554	3	4	discuss	discuss	NOUN
iajs-554	3	5	of	of	ADP
iajs-554	3	6	error	error	NOUN
iajs-554	3	7	analysis	analysis	NOUN
iajs-554	3	8	of	of	ADP
iajs-554	3	9	gauss	gauss	ADJ
iajs-554	3	10	-	-	PUNCT
iajs-554	3	11	jordan	jordan	PROPN
iajs-554	3	12	elimination	elimination	NOUN
iajs-554	3	13	for	for	ADP
iajs-554	3	14	linear	linear	ADJ
iajs-554	3	15	algebraic	algebraic	PROPN
iajs-554	3	16	systems	systems	PROPN
iajs-554	3	17	s.ab	s.ab	PROPN
iajs-554	3	18	.	.	PROPN
iajs-554	3	19	m.	m.	PROPN
iajs-554	3	20	abbas	abbas	PROPN
iajs-554	3	21	department	department	PROPN
iajs-554	3	22	of	of	ADP
iajs-554	3	23	mathematics	mathematics	PROPN
iajs-554	3	24	college	college	PROPN
iajs-554	3	25	of	of	ADP
iajs-554	3	26	science	science	PROPN
iajs-554	3	27	university	university	PROPN
iajs-554	3	28	of	of	ADP
iajs-554	3	29	baghdad	baghdad	PROPN
iajs-554	3	30	received	receive	VERB
iajs-554	3	31	in:22	in:22	PROPN
iajs-554	3	32	january	january	PROPN
iajs-554	3	33	2012	2012	NUM
iajs-554	3	34	accepted	accept	VERB
iajs-554	3	35	in:21	in:21	PROPN
iajs-554	3	36	may	may	AUX
iajs-554	3	37	2012	2012	NUM
iajs-554	3	38	abstract	abstract	ADV
iajs-554	3	39	the	the	DET
iajs-554	3	40	paper	paper	NOUN
iajs-554	3	41	establishes	establish	VERB
iajs-554	3	42	explicit	explicit	ADJ
iajs-554	3	43	representations	representation	NOUN
iajs-554	3	44	of	of	ADP
iajs-554	3	45	the	the	DET
iajs-554	3	46	errors	error	NOUN
iajs-554	3	47	and	and	CCONJ
iajs-554	3	48	residuals	residual	NOUN
iajs-554	3	49	of	of	ADP
iajs-554	3	50	approximate	approximate	ADJ
iajs-554	3	51	solutions	solution	NOUN
iajs-554	3	52	of	of	ADP
iajs-554	3	53	triangular	triangular	ADJ
iajs-554	3	54	linear	linear	NOUN
iajs-554	3	55	systems	system	NOUN
iajs-554	3	56	by	by	ADP
iajs-554	3	57	jordan	jordan	PROPN
iajs-554	3	58	elimination	elimination	PROPN
iajs-554	3	59	and	and	CCONJ
iajs-554	3	60	of	of	ADP
iajs-554	3	61	general	general	ADJ
iajs-554	3	62	linear	linear	PROPN
iajs-554	3	63	algebraic	algebraic	PROPN
iajs-554	3	64	systems	system	NOUN
iajs-554	3	65	by	by	ADP
iajs-554	3	66	gauss	gauss	PROPN
iajs-554	3	67	-	-	PUNCT
iajs-554	3	68	jordan	jordan	PROPN
iajs-554	3	69	elimination	elimination	NOUN
iajs-554	3	70	as	as	ADP
iajs-554	3	71	functions	function	NOUN
iajs-554	3	72	of	of	ADP
iajs-554	3	73	the	the	DET
iajs-554	3	74	data	data	NOUN
iajs-554	3	75	perturbations	perturbation	NOUN
iajs-554	3	76	and	and	CCONJ
iajs-554	3	77	the	the	DET
iajs-554	3	78	rounding	round	VERB
iajs-554	3	79	errors	error	NOUN
iajs-554	3	80	in	in	ADP
iajs-554	3	81	arithmetic	arithmetic	ADJ
iajs-554	3	82	floating	float	VERB
iajs-554	3	83	-	-	PUNCT
iajs-554	3	84	point	point	NOUN
iajs-554	3	85	operations	operation	NOUN
iajs-554	3	86	.	.	PUNCT
iajs-554	4	1	from	from	ADP
iajs-554	4	2	these	these	DET
iajs-554	4	3	representations	representation	NOUN
iajs-554	4	4	strict	strict	ADJ
iajs-554	4	5	optimal	optimal	ADJ
iajs-554	4	6	componentwise	componentwise	NOUN
iajs-554	4	7	error	error	NOUN
iajs-554	4	8	and	and	CCONJ
iajs-554	4	9	residual	residual	ADJ
iajs-554	4	10	bounds	bound	NOUN
iajs-554	4	11	are	be	AUX
iajs-554	4	12	derived	derive	VERB
iajs-554	4	13	.	.	PUNCT
iajs-554	5	1	further	far	ADV
iajs-554	5	2	,	,	PUNCT
iajs-554	5	3	stability	stability	NOUN
iajs-554	5	4	estimates	estimate	NOUN
iajs-554	5	5	for	for	ADP
iajs-554	5	6	the	the	DET
iajs-554	5	7	solutions	solution	NOUN
iajs-554	5	8	are	be	AUX
iajs-554	5	9	discussed	discuss	VERB
iajs-554	5	10	.	.	PUNCT
iajs-554	6	1	the	the	DET
iajs-554	6	2	error	error	NOUN
iajs-554	6	3	bounds	bound	VERB
iajs-554	6	4	for	for	ADP
iajs-554	6	5	the	the	DET
iajs-554	6	6	solutions	solution	NOUN
iajs-554	6	7	of	of	ADP
iajs-554	6	8	triangular	triangular	ADJ
iajs-554	6	9	linear	linear	NOUN
iajs-554	6	10	systems	system	NOUN
iajs-554	6	11	are	be	AUX
iajs-554	6	12	compared	compare	VERB
iajs-554	6	13	to	to	ADP
iajs-554	6	14	the	the	DET
iajs-554	6	15	optimal	optimal	ADJ
iajs-554	6	16	error	error	NOUN
iajs-554	6	17	bounds	bound	NOUN
iajs-554	6	18	for	for	ADP
iajs-554	6	19	the	the	DET
iajs-554	6	20	solutions	solution	NOUN
iajs-554	6	21	by	by	ADP
iajs-554	6	22	back	back	ADJ
iajs-554	6	23	substitution	substitution	NOUN
iajs-554	6	24	and	and	CCONJ
iajs-554	6	25	by	by	ADP
iajs-554	6	26	gaussian	gaussian	ADJ
iajs-554	6	27	elimination	elimination	NOUN
iajs-554	6	28	with	with	ADP
iajs-554	6	29	back	back	ADJ
iajs-554	6	30	substitution	substitution	NOUN
iajs-554	6	31	,	,	PUNCT
iajs-554	6	32	respectively	respectively	ADV
iajs-554	6	33	.	.	PUNCT
iajs-554	7	1	the	the	DET
iajs-554	7	2	results	result	NOUN
iajs-554	7	3	confirm	confirm	VERB
iajs-554	7	4	in	in	ADP
iajs-554	7	5	a	a	DET
iajs-554	7	6	very	very	ADV
iajs-554	7	7	detailed	detailed	ADJ
iajs-554	7	8	form	form	NOUN
iajs-554	7	9	that	that	SCONJ
iajs-554	7	10	the	the	DET
iajs-554	7	11	errors	error	NOUN
iajs-554	7	12	of	of	ADP
iajs-554	7	13	the	the	DET
iajs-554	7	14	solutions	solution	NOUN
iajs-554	7	15	by	by	ADP
iajs-554	7	16	jordan	jordan	PROPN
iajs-554	7	17	elimination	elimination	PROPN
iajs-554	7	18	and	and	CCONJ
iajs-554	7	19	by	by	ADP
iajs-554	7	20	gauss	gauss	ADJ
iajs-554	7	21	-	-	PUNCT
iajs-554	7	22	jordan	jordan	PROPN
iajs-554	7	23	elimination	elimination	NOUN
iajs-554	7	24	can	can	AUX
iajs-554	7	25	not	not	PART
iajs-554	7	26	be	be	AUX
iajs-554	7	27	essentially	essentially	ADV
iajs-554	7	28	greater	great	ADJ
iajs-554	7	29	than	than	ADP
iajs-554	7	30	the	the	DET
iajs-554	7	31	possible	possible	ADJ
iajs-554	7	32	maximal	maximal	ADJ
iajs-554	7	33	errors	error	NOUN
iajs-554	7	34	of	of	ADP
iajs-554	7	35	the	the	DET
iajs-554	7	36	solutions	solution	NOUN
iajs-554	7	37	by	by	ADP
iajs-554	7	38	back	back	ADJ
iajs-554	7	39	substitution	substitution	NOUN
iajs-554	7	40	and	and	CCONJ
iajs-554	7	41	by	by	ADP
iajs-554	7	42	gaussian	gaussian	ADJ
iajs-554	7	43	elimination	elimination	NOUN
iajs-554	7	44	,	,	PUNCT
iajs-554	7	45	respectively	respectively	ADV
iajs-554	7	46	.	.	PUNCT
iajs-554	8	1	finally	finally	ADV
iajs-554	8	2	,	,	PUNCT
iajs-554	8	3	the	the	DET
iajs-554	8	4	theoretical	theoretical	ADJ
iajs-554	8	5	results	result	NOUN
iajs-554	8	6	are	be	AUX
iajs-554	8	7	illustrated	illustrate	VERB
iajs-554	8	8	by	by	ADP
iajs-554	8	9	two	two	NUM
iajs-554	8	10	numerical	numerical	ADJ
iajs-554	8	11	examples	example	NOUN
iajs-554	8	12	.	.	PUNCT
iajs-554	9	1	key	key	ADJ
iajs-554	9	2	words	word	NOUN
iajs-554	9	3	:	:	PUNCT
iajs-554	9	4	jordan	jordan	PROPN
iajs-554	9	5	elimination	elimination	PROPN
iajs-554	9	6	,	,	PUNCT
iajs-554	9	7	data	datum	NOUN
iajs-554	9	8	perturbations	perturbation	NOUN
iajs-554	9	9	,	,	PUNCT
iajs-554	9	10	error	error	NOUN
iajs-554	9	11	bounds	bound	NOUN
iajs-554	9	12	,	,	PUNCT
iajs-554	9	13	gaussian	gaussian	ADJ
iajs-554	9	14	elimination	elimination	NOUN
iajs-554	9	15	.	.	PUNCT
iajs-554	10	1	introduction	introduction	NOUN
iajs-554	10	2	the	the	DET
iajs-554	10	3	gauss	gauss	PROPN
iajs-554	10	4	-	-	PUNCT
iajs-554	10	5	jordan	jordan	PROPN
iajs-554	10	6	algorithm	algorithm	PROPN
iajs-554	10	7	is	be	AUX
iajs-554	10	8	ideally	ideally	ADV
iajs-554	10	9	suited	suit	VERB
iajs-554	10	10	for	for	ADP
iajs-554	10	11	vector	vector	NOUN
iajs-554	10	12	computers	computer	NOUN
iajs-554	10	13	[	[	X
iajs-554	10	14	1	1	NUM
iajs-554	10	15	]	]	PUNCT
iajs-554	10	16	.	.	PUNCT
iajs-554	11	1	this	this	PRON
iajs-554	11	2	justifies	justify	VERB
iajs-554	11	3	the	the	DET
iajs-554	11	4	study	study	NOUN
iajs-554	11	5	of	of	ADP
iajs-554	11	6	the	the	DET
iajs-554	11	7	numerical	numerical	ADJ
iajs-554	11	8	stability	stability	NOUN
iajs-554	11	9	of	of	ADP
iajs-554	11	10	the	the	DET
iajs-554	11	11	algorithm	algorithm	NOUN
iajs-554	11	12	under	under	ADP
iajs-554	11	13	data	data	NOUN
iajs-554	11	14	perturbations	perturbation	NOUN
iajs-554	11	15	and	and	CCONJ
iajs-554	11	16	rounding	round	VERB
iajs-554	11	17	errors	error	NOUN
iajs-554	11	18	of	of	ADP
iajs-554	11	19	floating	float	VERB
iajs-554	11	20	-	-	PUNCT
iajs-554	11	21	point	point	NOUN
iajs-554	11	22	arithmetic	arithmetic	NOUN
iajs-554	11	23	.	.	PUNCT
iajs-554	12	1	it	it	PRON
iajs-554	12	2	uses	use	VERB
iajs-554	12	3	the	the	DET
iajs-554	12	4	same	same	ADJ
iajs-554	12	5	direct	direct	ADJ
iajs-554	12	6	method	method	NOUN
iajs-554	12	7	of	of	ADP
iajs-554	12	8	forward	forward	ADJ
iajs-554	12	9	analysis	analysis	NOUN
iajs-554	12	10	as	as	ADP
iajs-554	12	11	our	our	PRON
iajs-554	12	12	rounding	round	VERB
iajs-554	12	13	error	error	NOUN
iajs-554	12	14	analysis	analysis	NOUN
iajs-554	12	15	of	of	ADP
iajs-554	12	16	gaussian	gaussian	ADJ
iajs-554	12	17	elimination	elimination	NOUN
iajs-554	12	18	in	in	ADP
iajs-554	12	19	[	[	X
iajs-554	12	20	2	2	NUM
iajs-554	12	21	]	]	PUNCT
iajs-554	12	22	.	.	PUNCT
iajs-554	13	1	both	both	CCONJ
iajs-554	13	2	the	the	DET
iajs-554	13	3	solution	solution	NOUN
iajs-554	13	4	of	of	ADP
iajs-554	13	5	general	general	ADJ
iajs-554	13	6	linear	linear	PROPN
iajs-554	13	7	systems	system	NOUN
iajs-554	13	8	by	by	ADP
iajs-554	13	9	the	the	DET
iajs-554	13	10	gauss	gauss	PROPN
iajs-554	13	11	-	-	PUNCT
iajs-554	13	12	jordan	jordan	PROPN
iajs-554	13	13	algorithm	algorithm	PROPN
iajs-554	13	14	and	and	CCONJ
iajs-554	13	15	of	of	ADP
iajs-554	13	16	upper	upper	ADJ
iajs-554	13	17	triangular	triangular	NOUN
iajs-554	13	18	linear	linear	NOUN
iajs-554	13	19	system	system	NOUN
iajs-554	13	20	by	by	ADP
iajs-554	13	21	jordan	jordan	PROPN
iajs-554	13	22	elimination	elimination	PROPN
iajs-554	13	23	are	be	AUX
iajs-554	13	24	analyzed[3	analyzed[3	ADJ
iajs-554	13	25	]	]	X
iajs-554	13	26	.	.	PUNCT
iajs-554	14	1	the	the	DET
iajs-554	14	2	main	main	ADJ
iajs-554	14	3	results	result	NOUN
iajs-554	14	4	of	of	ADP
iajs-554	14	5	the	the	DET
iajs-554	14	6	paper	paper	NOUN
iajs-554	14	7	are	be	AUX
iajs-554	14	8	optimal	optimal	ADJ
iajs-554	14	9	componentwise	componentwise	NOUN
iajs-554	14	10	error	error	NOUN
iajs-554	14	11	and	and	CCONJ
iajs-554	14	12	residual	residual	ADJ
iajs-554	14	13	estimates	estimate	NOUN
iajs-554	14	14	,	,	PUNCT
iajs-554	14	15	bounds	bound	VERB
iajs-554	14	16	for	for	ADP
iajs-554	14	17	the	the	DET
iajs-554	14	18	stability	stability	NOUN
iajs-554	14	19	of	of	ADP
iajs-554	14	20	solutions	solution	NOUN
iajs-554	14	21	and	and	CCONJ
iajs-554	14	22	residuals	residual	NOUN
iajs-554	14	23	,	,	PUNCT
iajs-554	14	24	and	and	CCONJ
iajs-554	14	25	upper	upper	ADJ
iajs-554	14	26	bound	bind	VERB
iajs-554	14	27	for	for	ADP
iajs-554	14	28	the	the	DET
iajs-554	14	29	errors	error	NOUN
iajs-554	14	30	of	of	ADP
iajs-554	14	31	the	the	DET
iajs-554	14	32	solutions	solution	NOUN
iajs-554	14	33	of	of	ADP
iajs-554	14	34	jordan	jordan	PROPN
iajs-554	14	35	elimination	elimination	PROPN
iajs-554	14	36	and	and	CCONJ
iajs-554	14	37	gauss	gauss	PROPN
iajs-554	14	38	-	-	PUNCT
iajs-554	14	39	jordan	jordan	PROPN
iajs-554	14	40	elimination	elimination	NOUN
iajs-554	14	41	in	in	ADP
iajs-554	14	42	terms	term	NOUN
iajs-554	14	43	of	of	ADP
iajs-554	14	44	the	the	DET
iajs-554	14	45	optimal	optimal	ADJ
iajs-554	14	46	error	error	NOUN
iajs-554	14	47	bounds	bound	NOUN
iajs-554	14	48	for	for	ADP
iajs-554	14	49	back	back	NOUN
iajs-554	14	50	substitution	substitution	NOUN
iajs-554	14	51	and	and	CCONJ
iajs-554	14	52	gaussian	gaussian	ADJ
iajs-554	14	53	elimination	elimination	NOUN
iajs-554	14	54	respectively	respectively	ADV
iajs-554	14	55	.	.	PUNCT
iajs-554	15	1	the	the	DET
iajs-554	15	2	results	result	NOUN
iajs-554	15	3	will	will	AUX
iajs-554	15	4	prove	prove	VERB
iajs-554	15	5	that	that	SCONJ
iajs-554	15	6	the	the	DET
iajs-554	15	7	error	error	NOUN
iajs-554	15	8	of	of	ADP
iajs-554	15	9	the	the	DET
iajs-554	15	10	gauss	gauss	PROPN
iajs-554	15	11	-	-	PUNCT
iajs-554	15	12	jordan	jordan	PROPN
iajs-554	15	13	solution	solution	NOUN
iajs-554	15	14	can	can	AUX
iajs-554	15	15	not	not	PART
iajs-554	15	16	be	be	AUX
iajs-554	15	17	much	much	ADV
iajs-554	15	18	greater	great	ADJ
iajs-554	15	19	than	than	ADP
iajs-554	15	20	the	the	DET
iajs-554	15	21	possible	possible	ADJ
iajs-554	15	22	maximal	maximal	ADJ
iajs-554	15	23	error	error	NOUN
iajs-554	15	24	of	of	ADP
iajs-554	15	25	the	the	DET
iajs-554	15	26	solution	solution	NOUN
iajs-554	15	27	by	by	ADP
iajs-554	15	28	gaussian	gaussian	ADJ
iajs-554	15	29	elimination	elimination	NOUN
iajs-554	15	30	with	with	ADP
iajs-554	15	31	back	back	ADJ
iajs-554	15	32	substitution	substitution	NOUN
iajs-554	15	33	.	.	PUNCT
iajs-554	16	1	however	however	ADV
iajs-554	16	2	,	,	PUNCT
iajs-554	16	3	the	the	DET
iajs-554	16	4	residual	residual	ADJ
iajs-554	16	5	bounds	bound	NOUN
iajs-554	16	6	of	of	ADP
iajs-554	16	7	the	the	DET
iajs-554	16	8	gauss	gauss	PROPN
iajs-554	16	9	-	-	PUNCT
iajs-554	16	10	jordan	jordan	PROPN
iajs-554	16	11	solution	solution	NOUN
iajs-554	16	12	can	can	AUX
iajs-554	16	13	be	be	AUX
iajs-554	16	14	big	big	ADJ
iajs-554	16	15	if	if	SCONJ
iajs-554	16	16	the	the	DET
iajs-554	16	17	solution	solution	NOUN
iajs-554	16	18	vector	vector	NOUN
iajs-554	16	19	has	have	VERB
iajs-554	16	20	components	component	NOUN
iajs-554	16	21	with	with	ADP
iajs-554	16	22	big	big	ADJ
iajs-554	16	23	relative	relative	ADJ
iajs-554	16	24	errors	error	NOUN
iajs-554	16	25	.	.	PUNCT
iajs-554	17	1	the	the	DET
iajs-554	17	2	first	first	ADJ
iajs-554	17	3	step	step	NOUN
iajs-554	17	4	of	of	ADP
iajs-554	17	5	the	the	DET
iajs-554	17	6	error	error	NOUN
iajs-554	17	7	analysis	analysis	NOUN
iajs-554	17	8	consists	consist	VERB
iajs-554	17	9	in	in	ADP
iajs-554	17	10	the	the	DET
iajs-554	17	11	derivation	derivation	NOUN
iajs-554	17	12	of	of	ADP
iajs-554	17	13	explicit	explicit	ADJ
iajs-554	17	14	analytical	analytical	ADJ
iajs-554	17	15	representations	representation	NOUN
iajs-554	17	16	of	of	ADP
iajs-554	17	17	the	the	DET
iajs-554	17	18	errors	error	NOUN
iajs-554	17	19	and	and	CCONJ
iajs-554	17	20	residuals	residual	NOUN
iajs-554	17	21	of	of	ADP
iajs-554	17	22	approximate	approximate	ADJ
iajs-554	17	23	solutions	solution	NOUN
iajs-554	17	24	of	of	ADP
iajs-554	17	25	linear	linear	PROPN
iajs-554	17	26	algebraic	algebraic	ADJ
iajs-554	17	27	systems	system	NOUN
iajs-554	17	28	as	as	ADP
iajs-554	17	29	functions	function	NOUN
iajs-554	17	30	of	of	ADP
iajs-554	17	31	the	the	DET
iajs-554	17	32	data	datum	NOUN
iajs-554	17	33	errors	error	NOUN
iajs-554	17	34	and	and	CCONJ
iajs-554	17	35	the	the	DET
iajs-554	17	36	rounding	round	VERB
iajs-554	17	37	errors	error	NOUN
iajs-554	17	38	of	of	ADP
iajs-554	17	39	the	the	DET
iajs-554	17	40	arithmetic	arithmetic	ADJ
iajs-554	17	41	floatingoperations	floatingoperation	NOUN
iajs-554	17	42	.	.	PUNCT
iajs-554	18	1	under	under	ADP
iajs-554	18	2	standard	standard	ADJ
iajs-554	18	3	assumptions	assumption	NOUN
iajs-554	18	4	on	on	ADP
iajs-554	18	5	the	the	DET
iajs-554	18	6	data	data	NOUN
iajs-554	18	7	errors	error	NOUN
iajs-554	18	8	of	of	ADP
iajs-554	18	9	the	the	DET
iajs-554	18	10	problem	problem	NOUN
iajs-554	18	11	and	and	CCONJ
iajs-554	18	12	the	the	DET
iajs-554	18	13	rounding	round	VERB
iajs-554	18	14	errors	error	NOUN
iajs-554	18	15	of	of	ADP
iajs-554	18	16	the	the	DET
iajs-554	18	17	floating	float	VERB
iajs-554	18	18	-	-	PUNCT
iajs-554	18	19	point	point	NOUN
iajs-554	18	20	arithmetic	arithmetic	ADJ
iajs-554	18	21	these	these	DET
iajs-554	18	22	error	error	NOUN
iajs-554	18	23	and	and	CCONJ
iajs-554	18	24	residual	residual	ADJ
iajs-554	18	25	representations	representation	NOUN
iajs-554	18	26	readily	readily	ADV
iajs-554	18	27	yield	yield	VERB
iajs-554	18	28	strict	strict	ADJ
iajs-554	18	29	componentwise	componentwise	NOUN
iajs-554	18	30	and	and	CCONJ
iajs-554	18	31	,	,	PUNCT
iajs-554	18	32	save	save	VERB
iajs-554	18	33	for	for	ADP
iajs-554	18	34	terms	term	NOUN
iajs-554	18	35	of	of	ADP
iajs-554	18	36	higher	high	ADJ
iajs-554	18	37	order	order	NOUN
iajs-554	18	38	in	in	ADP
iajs-554	18	39	the	the	DET
iajs-554	18	40	accuracy	accuracy	NOUN
iajs-554	18	41	constant	constant	PROPN
iajs-554	18	42	η	η	PROPN
iajs-554	18	43	.	.	PROPN
iajs-554	18	44	optimal	optimal	ADJ
iajs-554	18	45	error	error	NOUN
iajs-554	18	46	and	and	CCONJ
iajs-554	18	47	residual	residual	ADJ
iajs-554	18	48	estimates	estimate	NOUN
iajs-554	18	49	for	for	ADP
iajs-554	18	50	the	the	DET
iajs-554	18	51	solutions	solution	NOUN
iajs-554	18	52	of	of	ADP
iajs-554	18	53	upper	upper	ADJ
iajs-554	18	54	triangular	triangular	NOUN
iajs-554	18	55	linear	linear	NOUN
iajs-554	18	56	systems	system	NOUN
iajs-554	18	57	in	in	ADP
iajs-554	18	58	the	the	DET
iajs-554	18	59	following	following	NOUN
iajs-554	18	60	theorem	theorem	NOUN
iajs-554	18	61	{	{	PUNCT
iajs-554	18	62	the	the	DET
iajs-554	18	63	residual	residual	NOUN
iajs-554	18	64	of	of	ADP
iajs-554	18	65	the	the	DET
iajs-554	18	66	computed	compute	VERB
iajs-554	18	67	approximate	approximate	ADJ
iajs-554	18	68	solution	solution	NOUN
iajs-554	18	69	vector	vector	NOUN
iajs-554	18	70	x	x	PROPN
iajs-554	18	71	of	of	ADP
iajs-554	18	72	the	the	DET
iajs-554	18	73	mathematics	mathematic	NOUN
iajs-554	18	74	368	368	NUM
iajs-554	18	75	مجلة	مجلة	NOUN
iajs-554	18	76	إبن	إبن	VERB
iajs-554	18	77	الهيثم	الهيثم	ADJ
iajs-554	18	78	للعلوم	للعلوم	NOUN
iajs-554	18	79	الصرفة	الصرفة	NOUN
iajs-554	19	1	و	و	PRON
iajs-554	19	2	التطبيقية	التطبيقية	ADJ
iajs-554	19	3	2012	2012	NUM
iajs-554	19	4	السنة	السنة	NOUN
iajs-554	19	5	25	25	NUM
iajs-554	19	6	المجلد	المجلد	NOUN
iajs-554	19	7	3	3	NUM
iajs-554	19	8	العدد	العدد	PROPN
iajs-554	19	9	ibn	ibn	PROPN
iajs-554	19	10	al	al	PROPN
iajs-554	19	11	-	-	PUNCT
iajs-554	19	12	haitham	haitham	PROPN
iajs-554	19	13	journal	journal	PROPN
iajs-554	19	14	for	for	ADP
iajs-554	19	15	pure	pure	ADJ
iajs-554	19	16	and	and	CCONJ
iajs-554	19	17	applied	apply	VERB
iajs-554	19	18	science	science	NOUN
iajs-554	19	19	no	no	NOUN
iajs-554	19	20	.	.	NOUN
iajs-554	19	21	3	3	NUM
iajs-554	19	22	vol	vol	NOUN
iajs-554	19	23	.	.	PUNCT
iajs-554	20	1	25	25	NUM
iajs-554	20	2	year	year	NOUN
iajs-554	20	3	2012	2012	NUM
iajs-554	20	4	triangular	triangular	NOUN
iajs-554	20	5	linear	linear	NOUN
iajs-554	20	6	system	system	NOUN
iajs-554	20	7	is	be	AUX
iajs-554	20	8	bounded	bounded	ADJ
iajs-554	20	9	componentwise	componentwise	NOUN
iajs-554	20	10	,	,	PUNCT
iajs-554	20	11	optimally	optimally	ADV
iajs-554	20	12	with	with	ADP
iajs-554	20	13	respect	respect	NOUN
iajs-554	20	14	to	to	ADP
iajs-554	20	15	the	the	DET
iajs-554	20	16	error	error	NOUN
iajs-554	20	17	distributions	distribution	NOUN
iajs-554	20	18	by	by	ADV
iajs-554	20	19	,	,	PUNCT
iajs-554	20	20	r	r	NOUN
iajs-554	20	21	r	r	NOUN
iajs-554	20	22	d	d	NOUN
iajs-554	20	23	d	d	X
iajs-554	20	24	tttzxu	tttzxu	NOUN
iajs-554	20	25	ηηη	ηηη	ADJ
iajs-554	21	1	+	+	NOUN
iajs-554	21	2	=	=	NOUN
iajs-554	21	3	≤−	≤−	ADJ
iajs-554	21	4	[	[	X
iajs-554	21	5	2	2	NUM
iajs-554	21	6	]	]	PUNCT
iajs-554	21	7	where	where	SCONJ
iajs-554	21	8	u	u	PROPN
iajs-554	21	9	upper	upper	ADJ
iajs-554	21	10	triangular	triangular	NOUN
iajs-554	21	11	linear	linear	NOUN
iajs-554	21	12	system	system	NOUN
iajs-554	21	13	,	,	PUNCT
iajs-554	21	14	η	η	PROPN
iajs-554	21	15	accuracy	accuracy	NOUN
iajs-554	21	16	constant	constant	ADJ
iajs-554	21	17	,	,	PUNCT
iajs-554	21	18	0	0	NUM
iajs-554	21	19	<	<	X
iajs-554	21	20	ηr	ηr	X
iajs-554	21	21	<	<	X
iajs-554	21	22	4/(3n	4/(3n	NUM
iajs-554	21	23	)	)	PUNCT
iajs-554	21	24	,	,	PUNCT
iajs-554	21	25	ηd	ηd	PROPN
iajs-554	21	26	data	datum	NOUN
iajs-554	21	27	accuracy	accuracy	NOUN
iajs-554	21	28	,	,	PUNCT
iajs-554	21	29	ηr	ηr	AUX
iajs-554	21	30	rounding	round	VERB
iajs-554	21	31	accuracy	accuracy	NOUN
iajs-554	21	32	in	in	ADP
iajs-554	21	33	application	application	NOUN
iajs-554	21	34	ηr<<ηd	ηr<<ηd	NOUN
iajs-554	21	35	,	,	PUNCT
iajs-554	21	36	matrix	matrix	NOUN
iajs-554	21	37	z	z	NOUN
iajs-554	21	38	defined	define	VERB
iajs-554	21	39	in	in	ADP
iajs-554	21	40	the	the	DET
iajs-554	21	41	jordan	jordan	PROPN
iajs-554	21	42	algorithm	algorithm	PROPN
iajs-554	21	43	see	see	VERB
iajs-554	21	44	[	[	X
iajs-554	21	45	1	1	X
iajs-554	21	46	]	]	PUNCT
iajs-554	21	47	for	for	ADP
iajs-554	21	48	the	the	DET
iajs-554	21	49	solution	solution	NOUN
iajs-554	21	50	of	of	ADP
iajs-554	21	51	regular	regular	ADJ
iajs-554	21	52	triangular	triangular	NOUN
iajs-554	21	53	linear	linear	NOUN
iajs-554	21	54	systems	system	NOUN
iajs-554	21	55	;	;	PUNCT
iajs-554	22	1	u11x1	u11x1	PROPN
iajs-554	22	2	+	+	SYM
iajs-554	22	3	u12x2+	u12x2+	PROPN
iajs-554	22	4	…	…	PUNCT
iajs-554	22	5	+	+	NOUN
iajs-554	22	6	u1nxn	u1nxn	NOUN
iajs-554	22	7	=	=	SYM
iajs-554	22	8	z1	z1	VERB
iajs-554	22	9	ux	ux	NOUN
iajs-554	22	10	=	=	SYM
iajs-554	22	11	z	z	PROPN
iajs-554	22	12	:	:	PUNCT
iajs-554	22	13	u22x2+	u22x2+	NOUN
iajs-554	22	14	…	…	PUNCT
iajs-554	22	15	+	+	ADJ
iajs-554	22	16	u2nxn	u2nxn	ADJ
iajs-554	22	17	=	=	SYM
iajs-554	22	18	z2	z2	ADJ
iajs-554	22	19	unnxn	unnxn	NOUN
iajs-554	22	20	=	=	PUNCT
iajs-554	22	21	zn	zn	PROPN
iajs-554	22	22	a	a	DET
iajs-554	22	23	general	general	ADJ
iajs-554	22	24	linear	linear	PROPN
iajs-554	22	25	systems	system	NOUN
iajs-554	22	26	in	in	ADP
iajs-554	22	27	the	the	DET
iajs-554	22	28	following	following	NOUN
iajs-554	22	29	theorem	theorem	NOUN
iajs-554	22	30	{	{	PUNCT
iajs-554	22	31	the	the	DET
iajs-554	22	32	residuals	residual	NOUN
iajs-554	22	33	of	of	ADP
iajs-554	22	34	the	the	DET
iajs-554	22	35	approximate	approximate	ADJ
iajs-554	22	36	solutions	solution	NOUN
iajs-554	22	37	x	x	X
iajs-554	22	38	of	of	ADP
iajs-554	22	39	general	general	ADJ
iajs-554	22	40	linear	linear	PROPN
iajs-554	22	41	systems	system	NOUN
iajs-554	22	42	by	by	ADP
iajs-554	22	43	gauss	gauss	PROPN
iajs-554	22	44	-	-	PUNCT
iajs-554	22	45	jordan	jordan	PROPN
iajs-554	22	46	elimination	elimination	NOUN
iajs-554	22	47	satisfy	satisfy	VERB
iajs-554	22	48	the	the	DET
iajs-554	22	49	componentwise	componentwise	NOUN
iajs-554	22	50	optimal	optimal	ADJ
iajs-554	22	51	estimates	estimate	NOUN
iajs-554	22	52	,	,	PUNCT
iajs-554	22	53	myx	myx	PROPN
iajs-554	22	54	≤−α	≤−α	PUNCT
iajs-554	23	1	[	[	X
iajs-554	23	2	4	4	NUM
iajs-554	23	3	]	]	PUNCT
iajs-554	23	4	.	.	PUNCT
iajs-554	24	1	where	where	SCONJ
iajs-554	24	2	y	y	PROPN
iajs-554	24	3	is	be	AUX
iajs-554	24	4	column	column	NOUN
iajs-554	24	5	vector	vector	NOUN
iajs-554	24	6	,	,	PUNCT
iajs-554	24	7	η	η	PROPN
iajs-554	24	8	accuracy	accuracy	NOUN
iajs-554	24	9	constant	constant	ADJ
iajs-554	24	10	a	a	DET
iajs-554	24	11	basic	basic	ADJ
iajs-554	24	12	tool	tool	NOUN
iajs-554	24	13	for	for	ADP
iajs-554	24	14	the	the	DET
iajs-554	24	15	formulation	formulation	NOUN
iajs-554	24	16	of	of	ADP
iajs-554	24	17	the	the	DET
iajs-554	24	18	error	error	NOUN
iajs-554	24	19	and	and	CCONJ
iajs-554	24	20	residual	residual	ADJ
iajs-554	24	21	bounds	bound	NOUN
iajs-554	24	22	are	be	AUX
iajs-554	24	23	the	the	DET
iajs-554	24	24	associated	associated	ADJ
iajs-554	24	25	data	datum	NOUN
iajs-554	24	26	,	,	PUNCT
iajs-554	24	27	rounding	round	VERB
iajs-554	24	28	,	,	PUNCT
iajs-554	24	29	and	and	CCONJ
iajs-554	24	30	total	total	ADJ
iajs-554	24	31	condition	condition	NOUN
iajs-554	24	32	numbers	number	NOUN
iajs-554	25	1	i	i	PRON
iajs-554	25	2	r	r	VERB
iajs-554	26	1	i	i	PRON
iajs-554	27	1	d	d	NOUN
iajs-554	27	2	i	i	PRON
iajs-554	27	3	σσσ	σσσ	VERB
iajs-554	27	4	,	,	PUNCT
iajs-554	27	5	,	,	PUNCT
iajs-554	27	6	of	of	ADP
iajs-554	27	7	the	the	DET
iajs-554	27	8	components	component	NOUN
iajs-554	27	9	of	of	ADP
iajs-554	27	10	the	the	DET
iajs-554	27	11	computed	compute	VERB
iajs-554	27	12	solutions	solution	NOUN
iajs-554	27	13	ix	ix	ADV
iajs-554	28	1	and	and	CCONJ
iajs-554	28	2	j	j	PROPN
iajs-554	29	1	r	r	NOUN
iajs-554	29	2	j	j	PROPN
iajs-554	30	1	d	d	X
iajs-554	30	2	j	j	PROPN
iajs-554	30	3	ttt	ttt	PROPN
iajs-554	30	4	,	,	PUNCT
iajs-554	30	5	,	,	PUNCT
iajs-554	30	6	of	of	ADP
iajs-554	30	7	the	the	DET
iajs-554	30	8	components	component	NOUN
iajs-554	30	9	of	of	ADP
iajs-554	30	10	the	the	DET
iajs-554	30	11	associated	associated	ADJ
iajs-554	30	12	residuals	residual	NOUN
iajs-554	30	13	jyxa	jyxa	PROPN
iajs-554	30	14	)	)	PUNCT
iajs-554	30	15	(	(	PUNCT
iajs-554	30	16	−	−	PROPN
iajs-554	30	17	.	.	PUNCT
iajs-554	31	1	in	in	ADP
iajs-554	31	2	addition	addition	NOUN
iajs-554	31	3	,	,	PUNCT
iajs-554	31	4	using	use	VERB
iajs-554	31	5	these	these	DET
iajs-554	31	6	condition	condition	NOUN
iajs-554	31	7	numbers	number	NOUN
iajs-554	31	8	,	,	PUNCT
iajs-554	31	9	the	the	DET
iajs-554	31	10	stability	stability	NOUN
iajs-554	31	11	constants	constant	VERB
iajs-554	32	1	d	d	INTJ
iajs-554	32	2	i	i	PRON
iajs-554	32	3	r	r	NOUN
iajs-554	32	4	iiw	iiw	PROPN
iajs-554	32	5	σσ	σσ	ADP
iajs-554	32	6	/=	/=	PROPN
iajs-554	32	7	of	of	ADP
iajs-554	32	8	the	the	DET
iajs-554	32	9	solutions	solution	NOUN
iajs-554	32	10	and	and	CCONJ
iajs-554	32	11	d	d	X
iajs-554	32	12	j	j	PROPN
iajs-554	32	13	r	r	NOUN
iajs-554	32	14	jj	jj	PROPN
iajs-554	32	15	tt	tt	PROPN
iajs-554	32	16	/=ψ	/=ψ	ADV
iajs-554	32	17	of	of	ADP
iajs-554	32	18	the	the	DET
iajs-554	32	19	residuals	residual	NOUN
iajs-554	32	20	are	be	AUX
iajs-554	32	21	formed	form	VERB
iajs-554	32	22	which	which	PRON
iajs-554	32	23	measure	measure	NOUN
iajs-554	32	24	the	the	DET
iajs-554	32	25	ratio	ratio	NOUN
iajs-554	32	26	of	of	ADP
iajs-554	32	27	the	the	DET
iajs-554	32	28	contribution	contribution	NOUN
iajs-554	32	29	to	to	ADP
iajs-554	32	30	the	the	DET
iajs-554	32	31	total	total	ADJ
iajs-554	32	32	error	error	NOUN
iajs-554	32	33	bound	bind	VERB
iajs-554	32	34	due	due	ADP
iajs-554	32	35	to	to	ADP
iajs-554	32	36	the	the	DET
iajs-554	32	37	rounding	round	VERB
iajs-554	32	38	errors	error	NOUN
iajs-554	32	39	in	in	ADP
iajs-554	32	40	floating	float	VERB
iajs-554	32	41	-	-	PUNCT
iajs-554	32	42	point	point	NOUN
iajs-554	32	43	operations	operation	NOUN
iajs-554	32	44	on	on	ADP
iajs-554	32	45	the	the	DET
iajs-554	32	46	one	one	NUM
iajs-554	32	47	hand	hand	NOUN
iajs-554	32	48	and	and	CCONJ
iajs-554	32	49	the	the	DET
iajs-554	32	50	data	data	NOUN
iajs-554	32	51	perturbations	perturbation	NOUN
iajs-554	32	52	on	on	ADP
iajs-554	32	53	the	the	DET
iajs-554	32	54	other	other	ADJ
iajs-554	32	55	hand	hand	NOUN
iajs-554	32	56	.	.	PUNCT
iajs-554	33	1	the	the	DET
iajs-554	33	2	size	size	NOUN
iajs-554	33	3	of	of	ADP
iajs-554	33	4	the	the	DET
iajs-554	33	5	possible	possible	ADJ
iajs-554	33	6	residuals	residual	NOUN
iajs-554	33	7	can	can	AUX
iajs-554	33	8	be	be	AUX
iajs-554	33	9	assessed	assess	VERB
iajs-554	33	10	by	by	ADP
iajs-554	33	11	means	mean	NOUN
iajs-554	33	12	of	of	ADP
iajs-554	33	13	the	the	DET
iajs-554	33	14	residual	residual	ADJ
iajs-554	33	15	stability	stability	NOUN
iajs-554	33	16	constants	constant	VERB
iajs-554	33	17	ψj	ψj	ADV
iajs-554	33	18	,	,	PUNCT
iajs-554	33	19	for	for	ADP
iajs-554	33	20	jordan	jordan	PROPN
iajs-554	33	21	solutions	solutions	PROPN
iajs-554	33	22	n	n	CCONJ
iajs-554	33	23	,	,	PUNCT
iajs-554	33	24	,	,	PUNCT
iajs-554	33	25	…	…	PUNCT
iajs-554	33	26	2	2	NUM
iajs-554	33	27	,	,	PUNCT
iajs-554	33	28	1	1	NUM
iajs-554	33	29	,	,	PUNCT
iajs-554	33	30	=	=	PRON
iajs-554	33	31	i,0≠ix	i,0≠ix	ADJ
iajs-554	33	32	of	of	ADP
iajs-554	33	33	upper	upper	ADJ
iajs-554	33	34	triangular	triangular	NOUN
iajs-554	33	35	linear	linear	NOUN
iajs-554	33	36	systems	system	NOUN
iajs-554	33	37	the	the	DET
iajs-554	33	38	upper	upper	ADJ
iajs-554	33	39	bound	bind	VERB
iajs-554	33	40	r	r	NOUN
iajs-554	33	41	r	r	NOUN
iajs-554	33	42	m	m	NOUN
iajs-554	33	43	r	r	NOUN
iajs-554	33	44	m	m	NOUN
iajs-554	33	45	d	d	NOUN
iajs-554	33	46	j	j	PROPN
iajs-554	33	47	r	r	NOUN
iajs-554	33	48	j	j	PROPN
iajs-554	33	49	j	j	PROPN
iajs-554	33	50	t	t	PROPN
iajs-554	33	51	t	t	PROPN
iajs-554	33	52	ηρ	ηρ	VERB
iajs-554	33	53	ρψ	ρψ	PROPN
iajs-554	33	54	−	−	PROPN
iajs-554	33	55	≤=	≤=	PROPN
iajs-554	33	56	1	1	NUM
iajs-554	33	57	,	,	PUNCT
iajs-554	33	58	j=	j=	ADV
iajs-554	33	59	1	1	NUM
iajs-554	33	60	,	,	PUNCT
iajs-554	33	61	2	2	NUM
iajs-554	33	62	,	,	PUNCT
iajs-554	33	63	…	…	PUNCT
iajs-554	33	64	,	,	PUNCT
iajs-554	33	65	n	n	CCONJ
iajs-554	33	66	,	,	PUNCT
iajs-554	33	67	whewe	whewe	VERB
iajs-554	33	68	ρm	ρm	PRON
iajs-554	34	1	r	r	NOUN
iajs-554	34	2	is	be	AUX
iajs-554	34	3	the	the	DET
iajs-554	34	4	maximal	maximal	ADJ
iajs-554	34	5	relative	relative	ADJ
iajs-554	34	6	rounding	round	VERB
iajs-554	34	7	condition	condition	NOUN
iajs-554	34	8	number	number	NOUN
iajs-554	34	9	of	of	ADP
iajs-554	34	10	the	the	DET
iajs-554	34	11	solution	solution	NOUN
iajs-554	34	12	vector	vector	NOUN
iajs-554	34	13	,	,	PUNCT
iajs-554	34	14	ηr	ηr	AUX
iajs-554	34	15	rounding	round	VERB
iajs-554	34	16	aceurauy	aceurauy	NOUN
iajs-554	34	17	[	[	X
iajs-554	34	18	4	4	NUM
iajs-554	34	19	]	]	PUNCT
iajs-554	34	20	.	.	PUNCT
iajs-554	35	1	if	if	SCONJ
iajs-554	35	2	1r	1r	NUM
iajs-554	35	3	r	r	NOUN
iajs-554	35	4	m	m	VERB
iajs-554	35	5	<	<	X
iajs-554	35	6	ηρ	ηρ	X
iajs-554	35	7	.	.	PUNCT
iajs-554	36	1	an	an	DET
iajs-554	36	2	analagus	analagus	ADJ
iajs-554	36	3	estimate	estimate	NOUN
iajs-554	36	4	holds	hold	VERB
iajs-554	36	5	for	for	ADP
iajs-554	36	6	general	general	ADJ
iajs-554	36	7	linear	linear	ADJ
iajs-554	36	8	system	system	NOUN
iajs-554	36	9	.	.	PUNCT
iajs-554	37	1	the	the	DET
iajs-554	37	2	magnitudes	magnitude	NOUN
iajs-554	37	3	of	of	ADP
iajs-554	37	4	the	the	DET
iajs-554	37	5	possible	possible	ADJ
iajs-554	37	6	maximal	maximal	ADJ
iajs-554	37	7	errors	error	NOUN
iajs-554	37	8	are	be	AUX
iajs-554	37	9	measured	measure	VERB
iajs-554	37	10	componentwise	componentwise	NOUN
iajs-554	37	11	,	,	PUNCT
iajs-554	37	12	using	use	VERB
iajs-554	37	13	the	the	DET
iajs-554	37	14	total	total	ADJ
iajs-554	37	15	condition	condition	NOUN
iajs-554	37	16	numbers	number	NOUN
iajs-554	37	17	j	j	PROPN
iajs-554	37	18	,	,	PUNCT
iajs-554	37	19	iσ	iσ	VERB
iajs-554	37	20	and	and	CCONJ
iajs-554	37	21	g	g	NOUN
iajs-554	37	22	,	,	PUNCT
iajs-554	37	23	iσ	iσ	INTJ
iajs-554	37	24	,	,	PUNCT
iajs-554	37	25	i=	i=	PROPN
iajs-554	37	26	1	1	NUM
iajs-554	37	27	,	,	PUNCT
iajs-554	37	28	2	2	NUM
iajs-554	37	29	,	,	PUNCT
iajs-554	37	30	…	…	PUNCT
iajs-554	37	31	,	,	PUNCT
iajs-554	37	32	n	n	CCONJ
iajs-554	37	33	,	,	PUNCT
iajs-554	37	34	by	by	ADP
iajs-554	37	35	10	10	NUM
iajs-554	37	36	,	,	PUNCT
iajs-554	38	1	ii	ii	PROPN
iajs-554	38	2	r	r	NOUN
iajs-554	38	3	ir	ir	NOUN
iajs-554	38	4	r	r	NOUN
iajs-554	38	5	i	i	PROPN
iajs-554	38	6	d	d	PROPN
iajs-554	38	7	d	d	PROPN
iajs-554	38	8	ii	ii	PROPN
iajs-554	38	9	σσσησησησ	σσσησησησ	NOUN
iajs-554	39	1	+	+	X
iajs-554	40	1	=	=	ADJ
iajs-554	40	2	+	+	NOUN
iajs-554	40	3	=	=	NOUN
iajs-554	40	4	the	the	DET
iajs-554	40	5	term	term	NOUN
iajs-554	40	6	d	d	NOUN
iajs-554	40	7	d	d	NOUN
iajs-554	40	8	i	i	PRON
iajs-554	40	9	ησ	ησ	PROPN
iajs-554	40	10	is	be	AUX
iajs-554	40	11	the	the	DET
iajs-554	40	12	bound	bind	VERB
iajs-554	40	13	for	for	ADP
iajs-554	40	14	the	the	DET
iajs-554	40	15	contribution	contribution	NOUN
iajs-554	40	16	of	of	ADP
iajs-554	40	17	the	the	DET
iajs-554	40	18	data	data	NOUN
iajs-554	40	19	perturbations	perturbation	NOUN
iajs-554	40	20	to	to	ADP
iajs-554	40	21	the	the	DET
iajs-554	40	22	total	total	ADJ
iajs-554	40	23	error	error	NOUN
iajs-554	40	24	of	of	ADP
iajs-554	40	25	the	the	DET
iajs-554	40	26	solution	solution	NOUN
iajs-554	40	27	,	,	PUNCT
iajs-554	40	28	the	the	DET
iajs-554	40	29	term	term	NOUN
iajs-554	40	30	r	r	NOUN
iajs-554	40	31	1	1	NUM
iajs-554	40	32	ir	ir	NOUN
iajs-554	40	33	0	0	NUM
iajs-554	41	1	i	i	PRON
iajs-554	41	2	,	,	PUNCT
iajs-554	41	3	ησησ	ησησ	PROPN
iajs-554	41	4	bound	bind	VERB
iajs-554	41	5	the	the	DET
iajs-554	41	6	contributions	contribution	NOUN
iajs-554	41	7	by	by	ADP
iajs-554	41	8	eliminations	elimination	NOUN
iajs-554	41	9	in	in	ADP
iajs-554	41	10	the	the	DET
iajs-554	41	11	lower	low	ADJ
iajs-554	41	12	and	and	CCONJ
iajs-554	41	13	in	in	ADP
iajs-554	41	14	the	the	DET
iajs-554	41	15	upper	upper	ADJ
iajs-554	41	16	triangle	triangle	NOUN
iajs-554	41	17	of	of	ADP
iajs-554	41	18	the	the	DET
iajs-554	41	19	coefficient	coefficient	NOUN
iajs-554	41	20	matrix	matrix	NOUN
iajs-554	41	21	,	,	PUNCT
iajs-554	41	22	respectively	respectively	ADV
iajs-554	41	23	establishes	establish	VERB
iajs-554	41	24	the	the	DET
iajs-554	41	25	estimate	estimate	NOUN
iajs-554	41	26	.	.	PUNCT
iajs-554	42	1	(	(	PUNCT
iajs-554	42	2	)	)	PUNCT
iajs-554	42	3	]	]	PUNCT
iajs-554	42	4	3	3	NUM
iajs-554	42	5	[	[	NOUN
iajs-554	42	6	,	,	PUNCT
iajs-554	42	7	,	,	PUNCT
iajs-554	42	8	1	1	NUM
iajs-554	42	9	,	,	PUNCT
iajs-554	42	10	2	2	NUM
iajs-554	42	11	0	0	NUM
iajs-554	42	12	,	,	PUNCT
iajs-554	42	13	,	,	PUNCT
iajs-554	42	14	0	0	NUM
iajs-554	42	15	,	,	PUNCT
iajs-554	42	16	,	,	PUNCT
iajs-554	42	17	rjim	rjim	VERB
iajs-554	42	18	rgjd	rgjd	NOUN
iajs-554	43	1	d	d	ADP
iajs-554	43	2	girjid	girjid	PROPN
iajs-554	44	1	d	d	X
iajs-554	44	2	ji	ji	PROPN
iajs-554	44	3	gpq	gpq	PROPN
iajs-554	44	4	q	q	PROPN
iajs-554	44	5	ηησ	ηησ	PROPN
iajs-554	44	6	ησησησησ	ησησησησ	VERB
iajs-554	44	7	+	+	X
iajs-554	45	1	+	+	ADJ
iajs-554	45	2	≤+	≤+	NOUN
iajs-554	45	3	for	for	ADP
iajs-554	45	4	solutions	solution	NOUN
iajs-554	45	5	0,0	0,0	NOUN
iajs-554	45	6	,	,	PUNCT
iajs-554	45	7	,	,	PUNCT
iajs-554	45	8	≠≠	≠≠	ADJ
iajs-554	45	9	giji	giji	NOUN
iajs-554	45	10	xx	xx	NUM
iajs-554	46	1	i	i	NOUN
iajs-554	46	2	=	=	NOUN
iajs-554	46	3	1	1	NUM
iajs-554	46	4	,	,	PUNCT
iajs-554	46	5	2	2	NUM
iajs-554	46	6	,	,	PUNCT
iajs-554	46	7	…	…	PUNCT
iajs-554	46	8	,	,	PUNCT
iajs-554	46	9	n	n	CCONJ
iajs-554	46	10	,	,	PUNCT
iajs-554	46	11	for	for	ADP
iajs-554	46	12	sufficient	sufficient	ADJ
iajs-554	46	13	small	small	ADJ
iajs-554	46	14	accuracy	accuracy	NOUN
iajs-554	46	15	constant	constant	ADJ
iajs-554	46	16	)	)	PUNCT
iajs-554	46	17	,	,	PUNCT
iajs-554	46	18	max	max	PROPN
iajs-554	46	19	(	(	PUNCT
iajs-554	46	20	rd	rd	NOUN
iajs-554	46	21	ηηη	ηηη	VERB
iajs-554	46	22	=	=	PUNCT
iajs-554	46	23	the	the	DET
iajs-554	46	24	constant	constant	ADJ
iajs-554	46	25	q	q	NOUN
iajs-554	46	26	is	be	AUX
iajs-554	46	27	close	close	ADJ
iajs-554	46	28	to	to	ADP
iajs-554	46	29	1	1	NUM
iajs-554	46	30	.	.	NOUN
iajs-554	47	1	1	1	NUM
iajs-554	47	2	.	.	PUNCT
iajs-554	48	1	the	the	DET
iajs-554	48	2	gauss	gauss	PROPN
iajs-554	48	3	-	-	PUNCT
iajs-554	48	4	jordan	jordan	PROPN
iajs-554	48	5	method	method	NOUN
iajs-554	48	6	the	the	DET
iajs-554	48	7	following	follow	VERB
iajs-554	48	8	error	error	NOUN
iajs-554	48	9	analysis	analysis	NOUN
iajs-554	48	10	deals	deal	NOUN
iajs-554	48	11	with	with	ADP
iajs-554	48	12	the	the	DET
iajs-554	48	13	gaussjordan	gaussjordan	PROPN
iajs-554	48	14	algorithm	algorithm	NOUN
iajs-554	48	15	for	for	ADP
iajs-554	48	16	solving	solve	VERB
iajs-554	48	17	linear	linear	NOUN
iajs-554	48	18	systems	system	NOUN
iajs-554	48	19	mathematics	mathematic	NOUN
iajs-554	48	20	369	369	NUM
iajs-554	48	21	مجلة	مجلة	NOUN
iajs-554	48	22	إبن	إبن	VERB
iajs-554	48	23	الهيثم	الهيثم	ADJ
iajs-554	48	24	للعلوم	للعلوم	NOUN
iajs-554	48	25	الصرفة	الصرفة	NOUN
iajs-554	49	1	و	و	PRON
iajs-554	49	2	التطبيقية	التطبيقية	ADJ
iajs-554	49	3	2012	2012	NUM
iajs-554	49	4	السنة	السنة	NOUN
iajs-554	49	5	25	25	NUM
iajs-554	49	6	المجلد	المجلد	NOUN
iajs-554	49	7	3	3	NUM
iajs-554	49	8	العدد	العدد	PROPN
iajs-554	49	9	ibn	ibn	PROPN
iajs-554	49	10	al	al	PROPN
iajs-554	49	11	-	-	PUNCT
iajs-554	49	12	haitham	haitham	PROPN
iajs-554	49	13	journal	journal	PROPN
iajs-554	49	14	for	for	ADP
iajs-554	49	15	pure	pure	ADJ
iajs-554	49	16	and	and	CCONJ
iajs-554	49	17	applied	apply	VERB
iajs-554	49	18	science	science	NOUN
iajs-554	49	19	no	no	NOUN
iajs-554	49	20	.	.	NOUN
iajs-554	49	21	3	3	NUM
iajs-554	49	22	vol	vol	NOUN
iajs-554	49	23	.	.	PUNCT
iajs-554	50	1	25	25	NUM
iajs-554	50	2	year	year	NOUN
iajs-554	50	3	2012	2012	NUM
iajs-554	50	4	niyxayx	niyxayx	NOUN
iajs-554	50	5	kik	kik	PROPN
iajs-554	50	6	n	n	CCONJ
iajs-554	50	7	k	k	PROPN
iajs-554	50	8	,	,	PUNCT
iajs-554	50	9	...	...	PUNCT
iajs-554	50	10	2,1	2,1	NUM
iajs-554	50	11	,	,	PUNCT
iajs-554	50	12	:	:	PUNCT
iajs-554	50	13	1	1	NUM
iajs-554	50	14	=	=	X
iajs-554	50	15	=	=	SYM
iajs-554	50	16	=	=	NOUN
iajs-554	50	17	α	α	PRON
iajs-554	50	18	∑	∑	NOUN
iajs-554	50	19	=	=	SYM
iajs-554	50	20	…	…	PUNCT
iajs-554	50	21	(	(	PUNCT
iajs-554	50	22	1	1	X
iajs-554	50	23	)	)	PUNCT
iajs-554	50	24	we	we	PRON
iajs-554	50	25	shall	shall	AUX
iajs-554	50	26	assume	assume	VERB
iajs-554	50	27	that	that	SCONJ
iajs-554	50	28	a=	a=	PROPN
iajs-554	50	29	(	(	PUNCT
iajs-554	50	30	ika	ika	NOUN
iajs-554	50	31	)	)	PUNCT
iajs-554	50	32	is	be	AUX
iajs-554	50	33	nonsingular	nonsingular	ADJ
iajs-554	50	34	and	and	CCONJ
iajs-554	50	35	that	that	SCONJ
iajs-554	50	36	rows	row	NOUN
iajs-554	50	37	and	and	CCONJ
iajs-554	50	38	columns	column	NOUN
iajs-554	50	39	of	of	ADP
iajs-554	50	40	a	a	PRON
iajs-554	50	41	have	have	AUX
iajs-554	50	42	been	be	AUX
iajs-554	50	43	ordered	order	VERB
iajs-554	50	44	such	such	ADJ
iajs-554	50	45	that	that	SCONJ
iajs-554	50	46	a	a	DET
iajs-554	50	47	possesses	possesse	NOUN
iajs-554	50	48	a	a	DET
iajs-554	50	49	triangular	triangular	NOUN
iajs-554	50	50	factorization	factorization	NOUN
iajs-554	50	51	.	.	PUNCT
iajs-554	51	1	in	in	ADP
iajs-554	51	2	[	[	X
iajs-554	51	3	5	5	X
iajs-554	51	4	]	]	PUNCT
iajs-554	51	5	we	we	PRON
iajs-554	51	6	have	have	AUX
iajs-554	51	7	shown	show	VERB
iajs-554	51	8	how	how	SCONJ
iajs-554	51	9	error	error	NOUN
iajs-554	51	10	and	and	CCONJ
iajs-554	51	11	residual	residual	ADJ
iajs-554	51	12	estimates	estimate	NOUN
iajs-554	51	13	are	be	AUX
iajs-554	51	14	used	use	VERB
iajs-554	51	15	when	when	SCONJ
iajs-554	51	16	pivoting	pivot	VERB
iajs-554	51	17	is	be	AUX
iajs-554	51	18	taken	take	VERB
iajs-554	51	19	into	into	ADP
iajs-554	51	20	account	account	NOUN
iajs-554	51	21	.	.	PUNCT
iajs-554	52	1	let	let	VERB
iajs-554	52	2	a1	a1	NOUN
iajs-554	52	3	=	=	PUNCT
iajs-554	52	4	(	(	PUNCT
iajs-554	52	5	a	a	PRON
iajs-554	52	6	,	,	PUNCT
iajs-554	52	7	y	y	PROPN
iajs-554	52	8	)	)	PUNCT
iajs-554	52	9	=(	=(	NOUN
iajs-554	52	10	1	1	NUM
iajs-554	52	11	ika	ika	NOUN
iajs-554	52	12	)	)	PUNCT
iajs-554	52	13	be	be	AUX
iajs-554	52	14	the	the	DET
iajs-554	52	15	n×n+1	n×n+1	NUM
iajs-554	52	16	coefficient	coefficient	NOUN
iajs-554	52	17	matrix	matrix	NOUN
iajs-554	52	18	of	of	ADP
iajs-554	52	19	the	the	DET
iajs-554	52	20	linear	linear	ADJ
iajs-554	52	21	system	system	NOUN
iajs-554	52	22	(	(	PUNCT
iajs-554	52	23	1	1	NUM
iajs-554	52	24	)	)	PUNCT
iajs-554	52	25	.	.	PUNCT
iajs-554	53	1	the	the	DET
iajs-554	53	2	gauss	gauss	PROPN
iajs-554	53	3	-	-	PUNCT
iajs-554	53	4	jordan	jordan	PROPN
iajs-554	53	5	algorithm	algorithm	PROPN
iajs-554	53	6	successively	successively	ADV
iajs-554	53	7	eliminates	eliminate	VERB
iajs-554	53	8	by	by	ADP
iajs-554	53	9	means	mean	NOUN
iajs-554	53	10	of	of	ADP
iajs-554	53	11	the	the	DET
iajs-554	53	12	pivotal	pivotal	ADJ
iajs-554	53	13	equation	equation	NOUN
iajs-554	53	14	t	t	X
iajs-554	53	15	the	the	DET
iajs-554	53	16	unknown	unknown	NOUN
iajs-554	53	17	xt	xt	ADP
iajs-554	53	18	where	where	SCONJ
iajs-554	53	19	the	the	DET
iajs-554	53	20	vector	vector	NOUN
iajs-554	53	21	x=	x=	PUNCT
iajs-554	53	22	(	(	PUNCT
iajs-554	53	23	xℓ	xℓ	PROPN
iajs-554	53	24	,	,	PUNCT
iajs-554	53	25	xℓ+1	xℓ+1	NUM
iajs-554	53	26	,	,	PUNCT
iajs-554	53	27	…	…	PUNCT
iajs-554	53	28	,	,	PUNCT
iajs-554	53	29	xn	xn	NUM
iajs-554	53	30	)	)	PUNCT
iajs-554	53	31	of	of	ADP
iajs-554	53	32	(	(	PUNCT
iajs-554	53	33	1	1	X
iajs-554	53	34	)	)	PUNCT
iajs-554	53	35	is	be	AUX
iajs-554	53	36	obtained	obtain	VERB
iajs-554	53	37	simply	simply	ADV
iajs-554	53	38	by	by	ADP
iajs-554	53	39	niuwx	niuwx	NOUN
iajs-554	53	40	iiii	iiii	NOUN
iajs-554	53	41	,	,	PUNCT
iajs-554	53	42	...	...	PUNCT
iajs-554	53	43	,	,	PUNCT
iajs-554	53	44	1	1	NUM
iajs-554	53	45	,	,	PUNCT
iajs-554	53	46	/	/	PUNCT
iajs-554	54	1	=	=	SYM
iajs-554	54	2	=	=	PUNCT
iajs-554	54	3	from	from	ADP
iajs-554	54	4	all	all	DET
iajs-554	54	5	other	other	ADJ
iajs-554	54	6	equations	equation	NOUN
iajs-554	54	7	i=	i=	PROPN
iajs-554	54	8	1	1	NUM
iajs-554	54	9	,	,	PUNCT
iajs-554	54	10	2	2	NUM
iajs-554	54	11	,	,	PUNCT
iajs-554	54	12	…	…	PUNCT
iajs-554	54	13	.	.	NUM
iajs-554	54	14	,	,	PUNCT
iajs-554	54	15	n	n	CCONJ
iajs-554	54	16	,	,	PUNCT
iajs-554	54	17	i≠t	i≠t	PRON
iajs-554	54	18	,	,	PUNCT
iajs-554	54	19	for	for	ADP
iajs-554	54	20	t=1	t=1	ADP
iajs-554	54	21	,	,	PUNCT
iajs-554	54	22	…	…	PUNCT
iajs-554	54	23	,	,	PUNCT
iajs-554	54	24	n.	n.	VERB
iajs-554	54	25	the	the	DET
iajs-554	54	26	coefficients	coefficient	NOUN
iajs-554	54	27	t	t	PROPN
iajs-554	54	28	ikt	ikt	PROPN
iajs-554	54	29	aa	aa	PROPN
iajs-554	54	30	)	)	PUNCT
iajs-554	54	31	(=	(=	NOUN
iajs-554	54	32	of	of	ADP
iajs-554	54	33	the	the	DET
iajs-554	54	34	reduced	reduce	VERB
iajs-554	54	35	linear	linear	PROPN
iajs-554	54	36	systems	system	NOUN
iajs-554	54	37	thus	thus	ADV
iajs-554	54	38	obtained	obtain	VERB
iajs-554	54	39	are	be	AUX
iajs-554	54	40	specified	specify	VERB
iajs-554	54	41	by	by	ADP
iajs-554	54	42	the	the	DET
iajs-554	54	43	equations	equation	NOUN
iajs-554	54	44	1,	1,	NUM
iajs-554	54	45	...	...	PUNCT
iajs-554	54	46	,1	,1	ADJ
iajs-554	54	47	,	,	PUNCT
iajs-554	54	48	,	,	PUNCT
iajs-554	54	49	...	...	PUNCT
iajs-554	54	50	,	,	PUNCT
iajs-554	55	1	1,1	1,1	NUM
iajs-554	55	2	+	+	NOUN
iajs-554	55	3	=	=	SYM
iajs-554	55	4	=	=	ADJ
iajs-554	55	5	−=+	−=+	PROPN
iajs-554	55	6	n	n	PRON
iajs-554	55	7	kniumaa	kniumaa	NOUN
iajs-554	55	8	tkit	tkit	NOUN
iajs-554	55	9	t	t	PROPN
iajs-554	55	10	ik	ik	PROPN
iajs-554	55	11	t	t	PROPN
iajs-554	55	12	ik	ik	PROPN
iajs-554	55	13	…	…	PUNCT
iajs-554	55	14	(	(	PUNCT
iajs-554	55	15	2	2	X
iajs-554	55	16	)	)	PUNCT
iajs-554	55	17	using	use	VERB
iajs-554	55	18	the	the	DET
iajs-554	55	19	coefficients	coefficient	NOUN
iajs-554	55	20	utk	utk	PROPN
iajs-554	55	21	of	of	ADP
iajs-554	55	22	the	the	DET
iajs-554	55	23	pivot	pivot	NOUN
iajs-554	55	24	equation	equation	NOUN
iajs-554	55	25	t	t	PROPN
iajs-554	55	26	and	and	CCONJ
iajs-554	55	27	the	the	DET
iajs-554	55	28	row	row	NOUN
iajs-554	55	29	multipliers	multiplier	NOUN
iajs-554	55	30	mit	mit	PROPN
iajs-554	55	31	,	,	PUNCT
iajs-554	55	32	defined	define	VERB
iajs-554	55	33	by	by	ADP
iajs-554	55	34	;	;	PUNCT
iajs-554	55	35	1;0;1,	1;0;1,	NUM
iajs-554	55	36	...	...	PUNCT
iajs-554	55	37	1	1	NUM
iajs-554	55	38	;	;	PUNCT
iajs-554	55	39	,	,	PUNCT
iajs-554	55	40	...	...	PUNCT
iajs-554	55	41	,	,	PUNCT
iajs-554	55	42	,	,	PUNCT
iajs-554	55	43	2,1	2,1	NUM
iajs-554	55	44	,	,	PUNCT
iajs-554	55	45	,	,	PUNCT
iajs-554	55	46	=	=	PRON
iajs-554	55	47	≠+=	≠+=	VERB
iajs-554	55	48	≠=	≠=	PRON
iajs-554	56	1	=	=	PRON
iajs-554	56	2	=	=	NOUN
iajs-554	56	3	tttt	tttt	X
iajs-554	56	4	tt	tt	PROPN
iajs-554	56	5	t	t	NOUN
iajs-554	56	6	it	it	PRON
iajs-554	57	1	it	it	PRON
iajs-554	57	2	t	t	INTJ
iajs-554	57	3	tktk	tktk	PROPN
iajs-554	57	4	munk	munk	NOUN
iajs-554	57	5	tiniua	tiniua	NOUN
iajs-554	57	6	mau	mau	PROPN
iajs-554	57	7	.	.	PUNCT
iajs-554	57	8	…	…	PUNCT
iajs-554	57	9	.(3	.(3	X
iajs-554	57	10	)	)	PUNCT
iajs-554	57	11	for	for	ADP
iajs-554	57	12	t=1	t=1	PROPN
iajs-554	57	13	,	,	PUNCT
iajs-554	57	14	…	…	PUNCT
iajs-554	57	15	,	,	PUNCT
iajs-554	57	16	n.	n.	NOUN
iajs-554	57	17	in	in	ADP
iajs-554	57	18	this	this	DET
iajs-554	57	19	way	way	NOUN
iajs-554	57	20	,	,	PUNCT
iajs-554	57	21	ntt	ntt	PROPN
iajs-554	57	22	knikiat	knikiat	PROPN
iajs-554	57	23	ik	ik	PROPN
iajs-554	57	24	,	,	PUNCT
iajs-554	57	25	...	...	PUNCT
iajs-554	57	26	,	,	PUNCT
iajs-554	57	27	1,,	1,,	NOUN
iajs-554	57	28	...	...	PUNCT
iajs-554	57	29	,1	,1	NOUN
iajs-554	57	30	,	,	PUNCT
iajs-554	57	31	,	,	PUNCT
iajs-554	57	32	...	...	PUNCT
iajs-554	57	33	,	,	PUNCT
iajs-554	57	34	1,,01	1,,01	NUM
iajs-554	57	35	=	=	SYM
iajs-554	57	36	=	=	SYM
iajs-554	57	37	=	=	PROPN
iajs-554	57	38	≠=+	≠=+	PROPN
iajs-554	57	39	…	…	PUNCT
iajs-554	57	40	..	..	PUNCT
iajs-554	57	41	(	(	PUNCT
iajs-554	57	42	4	4	NUM
iajs-554	57	43	)	)	PUNCT
iajs-554	57	44	that	that	PRON
iajs-554	57	45	is	be	AUX
iajs-554	57	46	,	,	PUNCT
iajs-554	57	47	in	in	ADP
iajs-554	57	48	the	the	DET
iajs-554	57	49	first	first	ADJ
iajs-554	57	50	t	t	NOUN
iajs-554	57	51	columns	column	NOUN
iajs-554	57	52	of	of	ADP
iajs-554	57	53	the	the	DET
iajs-554	57	54	matrix	matrix	NOUN
iajs-554	57	55	at+1	at+1	ADP
iajs-554	57	56	all	all	DET
iajs-554	57	57	offdiagonal	offdiagonal	ADJ
iajs-554	57	58	entries	entry	NOUN
iajs-554	57	59	are	be	AUX
iajs-554	57	60	zero	zero	NUM
iajs-554	57	61	.	.	PUNCT
iajs-554	58	1	hence	hence	ADV
iajs-554	58	2	the	the	DET
iajs-554	58	3	coefficient	coefficient	NOUN
iajs-554	58	4	matrix	matrix	NOUN
iajs-554	58	5	an+1	an+1	NOUN
iajs-554	58	6	has	have	VERB
iajs-554	58	7	the	the	DET
iajs-554	58	8	form	form	NOUN
iajs-554	58	9	an+1=	an+1=	NOUN
iajs-554	58	10	(	(	PUNCT
iajs-554	58	11	d	d	X
iajs-554	58	12	,	,	PUNCT
iajs-554	58	13	w	w	PROPN
iajs-554	58	14	)	)	PUNCT
iajs-554	58	15	with	with	ADP
iajs-554	58	16	an	an	DET
iajs-554	58	17	n	n	CCONJ
iajs-554	58	18	-	-	PUNCT
iajs-554	58	19	by	by	ADP
iajs-554	58	20	-	-	PUNCT
iajs-554	58	21	n	n	CCONJ
iajs-554	58	22	diagonal	diagonal	ADJ
iajs-554	58	23	matrix	matrix	NOUN
iajs-554	58	24	d	d	NOUN
iajs-554	58	25	and	and	CCONJ
iajs-554	58	26	the	the	DET
iajs-554	58	27	vector	vector	NOUN
iajs-554	58	28	w	w	ADP
iajs-554	58	29	where	where	SCONJ
iajs-554	58	30	niaw	niaw	NOUN
iajs-554	58	31	wwuudiagd	wwuudiagd	VERB
iajs-554	58	32	n	n	PRON
iajs-554	58	33	nii	nii	PROPN
iajs-554	58	34	inn	inn	PROPN
iajs-554	58	35	,	,	PUNCT
iajs-554	58	36	...	...	PUNCT
iajs-554	58	37	,	,	PUNCT
iajs-554	58	38	1	1	NUM
iajs-554	58	39	,	,	PUNCT
iajs-554	58	40	)	)	PUNCT
iajs-554	58	41	,	,	PUNCT
iajs-554	58	42	(	(	PUNCT
iajs-554	58	43	)	)	PUNCT
iajs-554	58	44	;	;	PUNCT
iajs-554	58	45	,	,	PUNCT
iajs-554	58	46	...	...	PUNCT
iajs-554	58	47	,	,	PUNCT
iajs-554	58	48	(	(	PUNCT
iajs-554	58	49	1	1	NUM
iajs-554	58	50	1	1	NUM
iajs-554	58	51	,	,	PUNCT
iajs-554	58	52	11	11	NUM
iajs-554	58	53	=	=	SYM
iajs-554	58	54	=	=	SYM
iajs-554	58	55	=	=	PUNCT
iajs-554	58	56	=	=	X
iajs-554	58	57	+	+	X
iajs-554	58	58	+	+	CCONJ
iajs-554	58	59	…	…	PUNCT
iajs-554	58	60	..	..	PUNCT
iajs-554	58	61	(	(	PUNCT
iajs-554	58	62	5	5	NUM
iajs-554	58	63	)	)	PUNCT
iajs-554	58	64	from	from	ADP
iajs-554	58	65	the	the	DET
iajs-554	58	66	associated	associated	ADJ
iajs-554	58	67	reduced	reduce	VERB
iajs-554	58	68	linear	linear	NOUN
iajs-554	58	69	system	system	NOUN
iajs-554	58	70	,	,	PUNCT
iajs-554	58	71	,	,	PUNCT
iajs-554	58	72	...	...	PUNCT
iajs-554	58	73	,	,	PUNCT
iajs-554	58	74	1	1	NUM
iajs-554	58	75	,	,	PUNCT
iajs-554	58	76	:	:	PUNCT
iajs-554	58	77	niw	niw	PROPN
iajs-554	58	78	xuwdx	xuwdx	PROPN
iajs-554	59	1	i	i	PRON
iajs-554	59	2	iii	iii	X
iajs-554	59	3	=	=	PUNCT
iajs-554	59	4	=	=	NOUN
iajs-554	59	5	=	=	SYM
iajs-554	59	6	…	…	PUNCT
iajs-554	59	7	..	..	PUNCT
iajs-554	59	8	(	(	PUNCT
iajs-554	59	9	6	6	X
iajs-554	59	10	)	)	PUNCT
iajs-554	59	11	the	the	DET
iajs-554	59	12	solution	solution	NOUN
iajs-554	59	13	vector	vector	NOUN
iajs-554	59	14	x=(x1	x=(x1	PROPN
iajs-554	59	15	,	,	PUNCT
iajs-554	59	16	…	…	PUNCT
iajs-554	59	17	,	,	PUNCT
iajs-554	59	18	xn	xn	NUM
iajs-554	59	19	)	)	PUNCT
iajs-554	59	20	of	of	ADP
iajs-554	59	21	(	(	PUNCT
iajs-554	59	22	1	1	X
iajs-554	59	23	)	)	PUNCT
iajs-554	59	24	is	be	AUX
iajs-554	59	25	obtained	obtain	VERB
iajs-554	59	26	simply	simply	ADV
iajs-554	59	27	by	by	ADP
iajs-554	59	28	ix	ix	ADV
iajs-554	59	29	=	=	PUNCT
iajs-554	59	30	iw	iw	PROPN
iajs-554	59	31	/uii	/uii	NOUN
iajs-554	59	32	,	,	PUNCT
iajs-554	59	33	i=1,	i=1,	PROPN
iajs-554	59	34	…	…	PUNCT
iajs-554	59	35	,n	,n	NOUN
iajs-554	59	36	,	,	PUNCT
iajs-554	59	37	[	[	X
iajs-554	59	38	6	6	NUM
iajs-554	59	39	]	]	PUNCT
iajs-554	59	40	the	the	DET
iajs-554	59	41	residual	residual	NOUN
iajs-554	59	42	of	of	ADP
iajs-554	59	43	the	the	DET
iajs-554	59	44	computed	compute	VERB
iajs-554	59	45	approximate	approximate	ADJ
iajs-554	59	46	solution	solution	NOUN
iajs-554	59	47	vector	vector	NOUN
iajs-554	59	48	x	x	X
iajs-554	59	49	of	of	ADP
iajs-554	59	50	the	the	DET
iajs-554	59	51	triangular	triangular	ADJ
iajs-554	59	52	linear	linear	NOUN
iajs-554	59	53	system	system	NOUN
iajs-554	59	54	is	be	AUX
iajs-554	59	55	bounded	bounded	ADJ
iajs-554	59	56	componentwise	componentwise	NOUN
iajs-554	59	57	,	,	PUNCT
iajs-554	59	58	optimally	optimally	ADV
iajs-554	59	59	with	with	ADP
iajs-554	59	60	respect	respect	NOUN
iajs-554	59	61	to	to	ADP
iajs-554	59	62	the	the	DET
iajs-554	59	63	error	error	NOUN
iajs-554	59	64	distribution	distribution	NOUN
iajs-554	59	65	by	by	ADP
iajs-554	59	66	r	r	NOUN
iajs-554	59	67	r	r	NOUN
iajs-554	59	68	d	d	PROPN
iajs-554	59	69	d	d	X
iajs-554	59	70	t	t	X
iajs-554	59	71	ttzxu	ttzxu	NOUN
iajs-554	59	72	ηηη	ηηη	INTJ
iajs-554	59	73	+	+	ADJ
iajs-554	59	74	=	=	ADJ
iajs-554	59	75	≤−	≤−	ADJ
iajs-554	59	76	mathematics	mathematic	NOUN
iajs-554	59	77	370	370	NUM
iajs-554	59	78	مجلة	مجلة	NOUN
iajs-554	59	79	إبن	إبن	VERB
iajs-554	59	80	الهيثم	الهيثم	ADJ
iajs-554	59	81	للعلوم	للعلوم	NOUN
iajs-554	59	82	الصرفة	الصرفة	NOUN
iajs-554	60	1	و	و	PRON
iajs-554	60	2	التطبيقية	التطبيقية	ADJ
iajs-554	60	3	2012	2012	NUM
iajs-554	60	4	السنة	السنة	NOUN
iajs-554	60	5	25	25	NUM
iajs-554	60	6	المجلد	المجلد	NOUN
iajs-554	60	7	3	3	NUM
iajs-554	60	8	العدد	العدد	PROPN
iajs-554	60	9	ibn	ibn	PROPN
iajs-554	60	10	al	al	PROPN
iajs-554	60	11	-	-	PUNCT
iajs-554	60	12	haitham	haitham	PROPN
iajs-554	60	13	journal	journal	PROPN
iajs-554	60	14	for	for	ADP
iajs-554	60	15	pure	pure	ADJ
iajs-554	60	16	and	and	CCONJ
iajs-554	60	17	applied	apply	VERB
iajs-554	60	18	science	science	NOUN
iajs-554	60	19	no	no	NOUN
iajs-554	60	20	.	.	NOUN
iajs-554	60	21	3	3	NUM
iajs-554	60	22	vol	vol	NOUN
iajs-554	60	23	.	.	PUNCT
iajs-554	61	1	25	25	NUM
iajs-554	61	2	year	year	NOUN
iajs-554	61	3	2012	2012	NUM
iajs-554	61	4	if	if	SCONJ
iajs-554	61	5	0x	0x	ADJ
iajs-554	61	6	≠	≠	PROPN
iajs-554	61	7	for	for	ADP
iajs-554	61	8	i	i	PRON
iajs-554	61	9	=	=	NOUN
iajs-554	61	10	1	1	NUM
iajs-554	61	11	,	,	PUNCT
iajs-554	61	12	.	.	PUNCT
iajs-554	61	13	.	.	PUNCT
iajs-554	61	14	.	.	PUNCT
iajs-554	62	1	,	,	PUNCT
iajs-554	63	1	n	n	PROPN
iajs-554	63	2	and	and	CCONJ
iajs-554	63	3	1	1	NUM
iajs-554	63	4	m	m	NOUN
iajs-554	63	5	<	<	X
iajs-554	63	6	ηρ	ηρ	X
iajs-554	63	7	,	,	PUNCT
iajs-554	63	8	the	the	DET
iajs-554	63	9	absolute	absolute	ADJ
iajs-554	63	10	and	and	CCONJ
iajs-554	63	11	relative	relative	ADJ
iajs-554	63	12	error	error	NOUN
iajs-554	63	13	of	of	ADP
iajs-554	63	14	the	the	DET
iajs-554	63	15	approximate	approximate	ADJ
iajs-554	63	16	solution	solution	NOUN
iajs-554	63	17	x	x	PART
iajs-554	63	18	satisfy	satisfy	VERB
iajs-554	63	19	componentwise	componentwise	NOUN
iajs-554	63	20	,	,	PUNCT
iajs-554	63	21	in	in	ADP
iajs-554	63	22	first	first	ADJ
iajs-554	63	23	order	order	NOUN
iajs-554	63	24	optimal	optimal	ADJ
iajs-554	63	25	error	error	NOUN
iajs-554	63	26	estimates	estimate	NOUN
iajs-554	63	27	holds	hold	VERB
iajs-554	63	28	.	.	PUNCT
iajs-554	64	1	,	,	PUNCT
iajs-554	64	2	1	1	NUM
iajs-554	64	3	ηρ	ηρ	NOUN
iajs-554	64	4	ησ	ησ	PROPN
iajs-554	64	5	m	m	VERB
iajs-554	64	6	i	i	NOUN
iajs-554	64	7	ii	ii	NOUN
iajs-554	65	1	xx	xx	NUM
iajs-554	65	2	−	−	PROPN
iajs-554	65	3	≤−	≤−	PROPN
iajs-554	65	4	n	n	CCONJ
iajs-554	65	5	,	,	PUNCT
iajs-554	65	6	.	.	PUNCT
iajs-554	65	7	,	,	PUNCT
iajs-554	65	8	.	.	PUNCT
iajs-554	66	1	1	1	NUM
iajs-554	66	2	,	,	PUNCT
iajs-554	66	3	.	.	PUNCT
iajs-554	67	1	i	i	PRON
iajs-554	67	2	,	,	PUNCT
iajs-554	67	3	1	1	X
iajs-554	67	4	=	=	SYM
iajs-554	67	5	−	−	PROPN
iajs-554	67	6	≤	≤	ADV
iajs-554	67	7	−	−	NOUN
iajs-554	67	8	ηρ	ηρ	X
iajs-554	67	9	ηρ	ηρ	VERB
iajs-554	67	10	m	m	VERB
iajs-554	67	11	i	i	PRON
iajs-554	67	12	i	i	PRON
iajs-554	67	13	ii	ii	VERB
iajs-554	67	14	x	x	SYM
iajs-554	67	15	xx	xx	NUM
iajs-554	68	1	[	[	X
iajs-554	68	2	5	5	NUM
iajs-554	68	3	]	]	PUNCT
iajs-554	68	4	…	…	PUNCT
iajs-554	68	5	..	..	PUNCT
iajs-554	68	6	(	(	PUNCT
iajs-554	68	7	7	7	X
iajs-554	68	8	)	)	PUNCT
iajs-554	68	9	lemma	lemma	PROPN
iajs-554	68	10	:	:	PUNCT
iajs-554	68	11	the	the	DET
iajs-554	68	12	vector	vector	NOUN
iajs-554	68	13	of	of	ADP
iajs-554	68	14	data	datum	NOUN
iajs-554	68	15	condition	condition	NOUN
iajs-554	68	16	numbers	number	NOUN
iajs-554	68	17	is	be	AUX
iajs-554	68	18	bounded	bound	VERB
iajs-554	68	19	from	from	ADP
iajs-554	68	20	below	below	ADP
iajs-554	68	21	by	by	ADP
iajs-554	68	22	:	:	PUNCT
iajs-554	68	23	r	r	NOUN
iajs-554	68	24	rd	rd	NOUN
iajs-554	68	25	x	x	SYM
iajs-554	68	26	ησσ	ησσ	X
iajs-554	68	27	−≥	−≥	X
iajs-554	68	28	2	2	NUM
iajs-554	68	29	;	;	PUNCT
iajs-554	68	30	[	[	X
iajs-554	68	31	2	2	X
iajs-554	68	32	]	]	X
iajs-554	68	33	the	the	DET
iajs-554	68	34	rounding	round	VERB
iajs-554	68	35	condition	condition	NOUN
iajs-554	68	36	numbers	number	NOUN
iajs-554	68	37	can	can	AUX
iajs-554	68	38	be	be	AUX
iajs-554	68	39	written	write	VERB
iajs-554	68	40	in	in	ADP
iajs-554	68	41	the	the	DET
iajs-554	68	42	form	form	NOUN
iajs-554	68	43	n	n	ADP
iajs-554	68	44	r	r	NOUN
iajs-554	68	45	n	n	NOUN
iajs-554	68	46	x≥σ	x≥σ	ADV
iajs-554	68	47	.	.	PUNCT
iajs-554	69	1	jordan	jordan	PROPN
iajs-554	69	2	elimination	elimination	PROPN
iajs-554	69	3	in	in	ADP
iajs-554	69	4	comparison	comparison	NOUN
iajs-554	69	5	with	with	ADP
iajs-554	69	6	back	back	ADJ
iajs-554	69	7	substitution	substitution	NOUN
iajs-554	69	8	1	1	NUM
iajs-554	69	9	.	.	PUNCT
iajs-554	70	1	the	the	DET
iajs-554	70	2	behaviour	behaviour	NOUN
iajs-554	70	3	of	of	ADP
iajs-554	70	4	the	the	DET
iajs-554	70	5	errors	error	NOUN
iajs-554	70	6	of	of	ADP
iajs-554	70	7	approximated	approximate	VERB
iajs-554	70	8	solutions	solution	NOUN
iajs-554	70	9	of	of	ADP
iajs-554	70	10	triangular	triangular	ADJ
iajs-554	70	11	linear	linear	NOUN
iajs-554	70	12	systems	system	NOUN
iajs-554	70	13	by	by	ADP
iajs-554	70	14	jordan	jordan	PROPN
iajs-554	70	15	elimination	elimination	PROPN
iajs-554	70	16	(	(	PUNCT
iajs-554	70	17	j	j	NOUN
iajs-554	70	18	)	)	PUNCT
iajs-554	70	19	will	will	AUX
iajs-554	70	20	now	now	ADV
iajs-554	70	21	be	be	AUX
iajs-554	70	22	compared	compare	VERB
iajs-554	70	23	with	with	ADP
iajs-554	70	24	that	that	PRON
iajs-554	70	25	of	of	ADP
iajs-554	70	26	solutions	solution	NOUN
iajs-554	70	27	by	by	ADP
iajs-554	70	28	gaussian	gaussian	NOUN
iajs-554	70	29	with	with	ADP
iajs-554	70	30	back	back	NOUN
iajs-554	70	31	substitution	substitution	NOUN
iajs-554	70	32	(	(	PUNCT
iajs-554	70	33	g	g	NOUN
iajs-554	70	34	)	)	PUNCT
iajs-554	70	35	in	in	ADP
iajs-554	70	36	linear	linear	PROPN
iajs-554	70	37	algebra	algebra	PROPN
iajs-554	70	38	,	,	PUNCT
iajs-554	70	39	jordan	jordan	PROPN
iajs-554	70	40	elimination	elimination	NOUN
iajs-554	70	41	brings	bring	VERB
iajs-554	70	42	a	a	DET
iajs-554	70	43	matrix	matrix	NOUN
iajs-554	70	44	to	to	ADP
iajs-554	70	45	reduced	reduce	VERB
iajs-554	70	46	row	row	NOUN
iajs-554	70	47	echelon	echelon	NOUN
iajs-554	70	48	form	form	NOUN
iajs-554	70	49	,	,	PUNCT
iajs-554	70	50	whereas	whereas	SCONJ
iajs-554	70	51	gaussian	gaussian	ADJ
iajs-554	70	52	elimination	elimination	NOUN
iajs-554	70	53	takes	take	VERB
iajs-554	70	54	it	it	PRON
iajs-554	70	55	only	only	ADV
iajs-554	70	56	as	as	ADP
iajs-554	70	57	for	for	ADP
iajs-554	70	58	as	as	ADP
iajs-554	70	59	row	row	NOUN
iajs-554	70	60	echelon	echelon	NOUN
iajs-554	70	61	form	form	NOUN
iajs-554	70	62	.	.	PUNCT
iajs-554	71	1	every	every	DET
iajs-554	71	2	matrix	matrix	NOUN
iajs-554	71	3	has	have	VERB
iajs-554	71	4	a	a	DET
iajs-554	71	5	reduced	reduce	VERB
iajs-554	71	6	row	row	NOUN
iajs-554	71	7	echelon	echelon	NOUN
iajs-554	71	8	form	form	NOUN
iajs-554	71	9	,	,	PUNCT
iajs-554	71	10	and	and	CCONJ
iajs-554	71	11	this	this	DET
iajs-554	71	12	algorithm	algorithm	NOUN
iajs-554	71	13	is	be	AUX
iajs-554	71	14	guaranteed	guarantee	VERB
iajs-554	71	15	to	to	PART
iajs-554	71	16	produced	produce	VERB
iajs-554	71	17	it	it	PRON
iajs-554	71	18	see	see	VERB
iajs-554	71	19	[	[	X
iajs-554	71	20	6	6	NUM
iajs-554	71	21	]	]	PUNCT
iajs-554	71	22	.	.	PUNCT
iajs-554	72	1	it	it	PRON
iajs-554	72	2	will	will	AUX
iajs-554	72	3	be	be	AUX
iajs-554	72	4	shown	show	VERB
iajs-554	72	5	that	that	SCONJ
iajs-554	72	6	the	the	DET
iajs-554	72	7	vectors	vector	NOUN
iajs-554	72	8	of	of	ADP
iajs-554	72	9	data	datum	NOUN
iajs-554	72	10	and	and	CCONJ
iajs-554	72	11	rounding	round	VERB
iajs-554	72	12	condition	condition	NOUN
iajs-554	72	13	number	number	NOUN
iajs-554	72	14	r	r	NOUN
iajs-554	72	15	j	j	PROPN
iajs-554	73	1	d	d	X
iajs-554	73	2	j	j	PROPN
iajs-554	73	3	σσ	σσ	ADV
iajs-554	73	4	,	,	PUNCT
iajs-554	73	5	of	of	ADP
iajs-554	73	6	the	the	DET
iajs-554	73	7	jordan	jordan	PROPN
iajs-554	73	8	solutions	solution	NOUN
iajs-554	73	9	can	can	AUX
iajs-554	73	10	be	be	AUX
iajs-554	73	11	bounded	bound	VERB
iajs-554	73	12	from	from	ADP
iajs-554	73	13	above	above	ADV
iajs-554	73	14	by	by	ADP
iajs-554	73	15	the	the	DET
iajs-554	73	16	corresponding	correspond	VERB
iajs-554	73	17	condition	condition	NOUN
iajs-554	73	18	numbers	number	NOUN
iajs-554	73	19	r	r	NOUN
iajs-554	73	20	g	g	NOUN
iajs-554	73	21	d	d	X
iajs-554	73	22	g	g	NOUN
iajs-554	73	23	σσ	σσ	ADV
iajs-554	73	24	,	,	PUNCT
iajs-554	73	25	of	of	ADP
iajs-554	73	26	the	the	DET
iajs-554	73	27	solutions	solution	NOUN
iajs-554	73	28	by	by	ADP
iajs-554	73	29	back	back	ADJ
iajs-554	73	30	substitution	substitution	NOUN
iajs-554	73	31	.	.	PUNCT
iajs-554	74	1	this	this	DET
iajs-554	74	2	result	result	NOUN
iajs-554	74	3	means	mean	VERB
iajs-554	74	4	that	that	SCONJ
iajs-554	74	5	the	the	DET
iajs-554	74	6	errors	error	NOUN
iajs-554	74	7	of	of	ADP
iajs-554	74	8	the	the	DET
iajs-554	74	9	computed	compute	VERB
iajs-554	74	10	jordan	jordan	PROPN
iajs-554	74	11	solutions	solutions	PROPN
iajs-554	74	12	jx	jx	PROPN
iajs-554	74	13	can	can	AUX
iajs-554	74	14	not	not	PART
iajs-554	74	15	be	be	AUX
iajs-554	74	16	essentially	essentially	ADV
iajs-554	74	17	bigger	big	ADJ
iajs-554	74	18	than	than	ADP
iajs-554	74	19	the	the	DET
iajs-554	74	20	possible	possible	ADJ
iajs-554	74	21	maximal	maximal	ADJ
iajs-554	74	22	errors	error	NOUN
iajs-554	74	23	of	of	ADP
iajs-554	74	24	the	the	DET
iajs-554	74	25	corresponding	corresponding	ADJ
iajs-554	74	26	computed	compute	VERB
iajs-554	74	27	solutions	solution	NOUN
iajs-554	74	28	gx	gx	PROPN
iajs-554	74	29	by	by	ADP
iajs-554	74	30	back	back	ADJ
iajs-554	74	31	substitution	substitution	NOUN
iajs-554	74	32	.	.	PUNCT
iajs-554	75	1	2	2	X
iajs-554	75	2	.	.	X
iajs-554	75	3	when	when	SCONJ
iajs-554	75	4	triangular	triangular	NOUN
iajs-554	75	5	linear	linear	NOUN
iajs-554	75	6	systems	system	NOUN
iajs-554	75	7	are	be	AUX
iajs-554	75	8	solved	solve	VERB
iajs-554	75	9	by	by	ADP
iajs-554	75	10	back	back	ADJ
iajs-554	75	11	substitution	substitution	NOUN
iajs-554	75	12	the	the	DET
iajs-554	75	13	associated	associated	ADJ
iajs-554	75	14	solution	solution	NOUN
iajs-554	75	15	and	and	CCONJ
iajs-554	75	16	residual	residual	ADJ
iajs-554	75	17	stability	stability	NOUN
iajs-554	75	18	constants	constant	VERB
iajs-554	75	19	giw	giw	PROPN
iajs-554	75	20	,	,	PUNCT
iajs-554	75	21	,	,	PUNCT
iajs-554	75	22	gj	gj	INTJ
iajs-554	75	23	,	,	PUNCT
iajs-554	75	24	ψ	ψ	PROPN
iajs-554	75	25	of	of	ADP
iajs-554	75	26	the	the	DET
iajs-554	75	27	solutions	solution	NOUN
iajs-554	75	28	gix	gix	NOUN
iajs-554	75	29	,	,	PUNCT
iajs-554	75	30	are	be	AUX
iajs-554	75	31	bounded	bound	VERB
iajs-554	75	32	below	below	ADP
iajs-554	75	33	and	and	CCONJ
iajs-554	75	34	above	above	ADV
iajs-554	75	35	by	by	ADP
iajs-554	75	36			ADJ
iajs-554	75	37			PROPN
iajs-554	75	38			PROPN
iajs-554	75	39			PROPN
iajs-554	75	40			PROPN
iajs-554	75	41			PROPN
iajs-554	75	42	≠	≠	PROPN
iajs-554	75	43	−−	−−	NOUN
iajs-554	75	44	−+	−+	PROPN
iajs-554	75	45	≤≤	≤≤	X
iajs-554	76	1	+	+	CCONJ
iajs-554	76	2	≠	≠	PROPN
iajs-554	76	3	−−	−−	NOUN
iajs-554	76	4	−+	−+	PROPN
iajs-554	76	5	≤≤	≤≤	PROPN
iajs-554	77	1	+	+	CCONJ
iajs-554	77	2	nj	nj	PROPN
iajs-554	77	3	jn	jn	PROPN
iajs-554	77	4	jn	jn	PROPN
iajs-554	77	5	ni	ni	PROPN
iajs-554	77	6	in	in	ADP
iajs-554	77	7	inw	inw	PROPN
iajs-554	77	8	r	r	NOUN
iajs-554	77	9	gj	gj	NOUN
iajs-554	77	10	r	r	NOUN
iajs-554	77	11	r	r	NOUN
iajs-554	77	12	gi	gi	NOUN
iajs-554	77	13	r	r	NOUN
iajs-554	77	14	for	for	ADP
iajs-554	77	15	,	,	PUNCT
iajs-554	77	16	)	)	PUNCT
iajs-554	77	17	(	(	PUNCT
iajs-554	77	18	2	2	NUM
iajs-554	77	19	2	2	NUM
iajs-554	77	20	2	2	NUM
iajs-554	77	21	1	1	NUM
iajs-554	77	22	for	for	ADP
iajs-554	77	23	,	,	PUNCT
iajs-554	77	24	)	)	PUNCT
iajs-554	77	25	(	(	PUNCT
iajs-554	77	26	2	2	NUM
iajs-554	77	27	2	2	NUM
iajs-554	77	28	2	2	NUM
iajs-554	77	29	1	1	NUM
iajs-554	77	30	,	,	PUNCT
iajs-554	77	31	,	,	PUNCT
iajs-554	77	32	η	η	PROPN
iajs-554	77	33	ω	ω	PROPN
iajs-554	77	34	µ	µ	PRON
iajs-554	77	35	ηµ	ηµ	VERB
iajs-554	77	36	for	for	ADP
iajs-554	77	37	i	i	PROPN
iajs-554	77	38	,	,	PUNCT
iajs-554	77	39	j=1,	j=1,	NOUN
iajs-554	77	40	…	…	SYM
iajs-554	77	41	,n	,n	X
iajs-554	77	42	…	…	PUNCT
iajs-554	77	43	..	..	PUNCT
iajs-554	77	44	(	(	PUNCT
iajs-554	77	45	8)	8)	NUM
iajs-554	77	46	these	these	DET
iajs-554	77	47	estimates	estimate	NOUN
iajs-554	77	48	are	be	AUX
iajs-554	77	49	obtained	obtain	VERB
iajs-554	77	50	from	from	ADP
iajs-554	77	51	the	the	DET
iajs-554	77	52	error	error	NOUN
iajs-554	77	53	and	and	CCONJ
iajs-554	77	54	residual	residual	ADJ
iajs-554	77	55	bounds	bound	NOUN
iajs-554	77	56	in	in	ADP
iajs-554	77	57	[	[	X
iajs-554	77	58	2	2	NUM
iajs-554	77	59	]	]	SYM
iajs-554	77	60	3	3	NUM
iajs-554	77	61	.	.	X
iajs-554	78	1	solving	solve	VERB
iajs-554	78	2	a	a	DET
iajs-554	78	3	triangular	triangular	ADJ
iajs-554	78	4	linear	linear	NOUN
iajs-554	78	5	system	system	NOUN
iajs-554	78	6	both	both	PRON
iajs-554	78	7	by	by	ADP
iajs-554	78	8	jordan	jordan	PROPN
iajs-554	78	9	elimination	elimination	PROPN
iajs-554	78	10	and	and	CCONJ
iajs-554	78	11	by	by	ADP
iajs-554	78	12	back	back	ADJ
iajs-554	78	13	substitution	substitution	NOUN
iajs-554	78	14	gives	give	VERB
iajs-554	78	15	two	two	NUM
iajs-554	78	16	approximations	approximation	NOUN
iajs-554	78	17	jx	jx	PROPN
iajs-554	78	18	,	,	PUNCT
iajs-554	78	19	gx	gx	PROPN
iajs-554	78	20	for	for	ADP
iajs-554	78	21	the	the	DET
iajs-554	78	22	searched	search	VERB
iajs-554	78	23	solution	solution	NOUN
iajs-554	78	24	vector	vector	NOUN
iajs-554	78	25	x	x	AUX
iajs-554	78	26	see	see	VERB
iajs-554	78	27	[	[	X
iajs-554	78	28	7	7	NUM
iajs-554	78	29	]	]	PUNCT
iajs-554	78	30	.	.	PUNCT
iajs-554	79	1	these	these	DET
iajs-554	79	2	two	two	NUM
iajs-554	79	3	approximations	approximation	NOUN
iajs-554	79	4	satisfy	satisfy	VERB
iajs-554	79	5	the	the	DET
iajs-554	79	6	error	error	NOUN
iajs-554	79	7	estimates	estimate	NOUN
iajs-554	79	8	of	of	ADP
iajs-554	79	9	residual	residual	NOUN
iajs-554	79	10	of	of	ADP
iajs-554	79	11	the	the	DET
iajs-554	79	12	computed	compute	VERB
iajs-554	79	13	approximate	approximate	ADJ
iajs-554	79	14	solution	solution	NOUN
iajs-554	79	15	vector	vector	NOUN
iajs-554	79	16	x	x	X
iajs-554	79	17	of	of	ADP
iajs-554	79	18	the	the	DET
iajs-554	79	19	triangular	triangular	ADJ
iajs-554	79	20	linear	linear	NOUN
iajs-554	79	21	system	system	NOUN
iajs-554	79	22	is	be	AUX
iajs-554	79	23	bounded	bounded	ADJ
iajs-554	79	24	componentwise	componentwise	NOUN
iajs-554	79	25	,	,	PUNCT
iajs-554	79	26	optimally	optimally	ADV
iajs-554	79	27	with	with	ADP
iajs-554	79	28	respect	respect	NOUN
iajs-554	79	29	to	to	ADP
iajs-554	79	30	the	the	DET
iajs-554	79	31	error	error	NOUN
iajs-554	79	32	distributions	distribution	NOUN
iajs-554	79	33	by	by	ADP
iajs-554	79	34	rrd	rrd	PROPN
iajs-554	79	35	d	d	PROPN
iajs-554	79	36	t	t	PROPN
iajs-554	79	37	ttzxu	ttzxu	NOUN
iajs-554	79	38	ηηη	ηηη	INTJ
iajs-554	80	1	+	+	NOUN
iajs-554	80	2	=	=	NOUN
iajs-554	80	3	≤−	≤−	NOUN
iajs-554	80	4	in	in	ADP
iajs-554	80	5	first	first	ADJ
iajs-554	80	6	order	order	NOUN
iajs-554	80	7	optimal	optimal	ADJ
iajs-554	80	8	estimates	estimate	NOUN
iajs-554	80	9	,	,	PUNCT
iajs-554	80	10	that	that	ADV
iajs-554	80	11	is	is	ADV
iajs-554	80	12	,	,	PUNCT
iajs-554	80	13	,	,	PUNCT
iajs-554	80	14	,	,	PUNCT
iajs-554	80	15	1	1	NUM
iajs-554	80	16	,	,	PUNCT
iajs-554	80	17	,	,	PUNCT
iajs-554	80	18	,	,	PUNCT
iajs-554	80	19	ηρ	ηρ	PROPN
iajs-554	81	1	ηρ	ηρ	PROPN
iajs-554	81	2	j	j	PROPN
iajs-554	81	3	j	j	PROPN
iajs-554	81	4	x	x	PROPN
iajs-554	82	1	xx	xx	NUM
iajs-554	82	2	m	m	VERB
iajs-554	83	1	i	i	PRON
iajs-554	83	2	ji	ji	PROPN
iajs-554	83	3	iji	iji	VERB
iajs-554	83	4	−	−	PROPN
iajs-554	83	5	≤	≤	NUM
iajs-554	83	6	−	−	ADP
iajs-554	83	7	,	,	PUNCT
iajs-554	83	8	,	,	PUNCT
iajs-554	83	9	1	1	NUM
iajs-554	83	10	,	,	PUNCT
iajs-554	83	11	,	,	PUNCT
iajs-554	83	12	,	,	PUNCT
iajs-554	83	13	ηρ	ηρ	X
iajs-554	83	14	ηρ	ηρ	X
iajs-554	83	15	g	g	PROPN
iajs-554	83	16	g	g	PROPN
iajs-554	83	17	x	x	PROPN
iajs-554	84	1	xx	xx	NUM
iajs-554	84	2	m	m	VERB
iajs-554	85	1	i	i	PRON
iajs-554	85	2	gi	gi	VERB
iajs-554	85	3	igi	igi	NOUN
iajs-554	85	4	−	−	PROPN
iajs-554	85	5	≤	≤	NUM
iajs-554	86	1	−	−	PROPN
iajs-554	86	2	…	…	SYM
iajs-554	86	3	.(9	.(9	NUM
iajs-554	86	4	)	)	PUNCT
iajs-554	86	5	mathematics	mathematic	NOUN
iajs-554	86	6	371	371	NUM
iajs-554	86	7	مجلة	مجلة	VERB
iajs-554	86	8	إبن	إبن	NOUN
iajs-554	86	9	الهيثم	الهيثم	ADJ
iajs-554	86	10	للعلوم	للعلوم	NOUN
iajs-554	86	11	الصرفة	الصرفة	NOUN
iajs-554	86	12	و	و	PRON
iajs-554	86	13	التطبيقية	التطبيقية	ADJ
iajs-554	86	14	2012	2012	NUM
iajs-554	86	15	السنة	السنة	NOUN
iajs-554	86	16	25	25	NUM
iajs-554	86	17	المجلد	المجلد	NOUN
iajs-554	86	18	3	3	NUM
iajs-554	86	19	العدد	العدد	PROPN
iajs-554	86	20	ibn	ibn	PROPN
iajs-554	86	21	al	al	PROPN
iajs-554	86	22	-	-	PUNCT
iajs-554	86	23	haitham	haitham	PROPN
iajs-554	86	24	journal	journal	PROPN
iajs-554	86	25	for	for	ADP
iajs-554	86	26	pure	pure	ADJ
iajs-554	86	27	and	and	CCONJ
iajs-554	86	28	applied	apply	VERB
iajs-554	86	29	science	science	NOUN
iajs-554	86	30	no	no	NOUN
iajs-554	86	31	.	.	NOUN
iajs-554	86	32	3	3	NUM
iajs-554	86	33	vol	vol	NOUN
iajs-554	86	34	.	.	PUNCT
iajs-554	87	1	25	25	NUM
iajs-554	87	2	year	year	NOUN
iajs-554	87	3	2012	2012	NUM
iajs-554	87	4	for	for	ADP
iajs-554	87	5	i	i	PROPN
iajs-554	87	6	=	=	NOUN
iajs-554	87	7	1	1	NUM
iajs-554	87	8	,	,	PUNCT
iajs-554	87	9	…	…	PUNCT
iajs-554	87	10	,	,	PUNCT
iajs-554	87	11	n	n	CCONJ
iajs-554	87	12	,	,	PUNCT
iajs-554	87	13	where	where	SCONJ
iajs-554	87	14	1	1	X
iajs-554	87	15	.	.	PUNCT
iajs-554	87	16	1≠ηρ	1≠ηρ	NUM
iajs-554	87	17	gm	gm	PROPN
iajs-554	87	18	2	2	NUM
iajs-554	87	19	.	.	PUNCT
iajs-554	87	20	1≠ηρ	1≠ηρ	NUM
iajs-554	87	21	jm	jm	PROPN
iajs-554	87	22	3	3	PROPN
iajs-554	87	23	.	.	PUNCT
iajs-554	87	24	ρi	ρi	NOUN
iajs-554	87	25	,	,	PUNCT
iajs-554	87	26	is	be	AUX
iajs-554	87	27	defined	define	VERB
iajs-554	87	28	i	i	PRON
iajs-554	88	1	i	i	PRON
iajs-554	89	1	i	i	VERB
iajs-554	89	2	x	x	PROPN
iajs-554	89	3	σ	σ	NOUN
iajs-554	89	4	ρ	ρ	PROPN
iajs-554	90	1	=	=	PUNCT
iajs-554	90	2	,	,	PUNCT
iajs-554	90	3	i	i	NOUN
iajs-554	90	4	=	=	NOUN
iajs-554	90	5	1	1	NUM
iajs-554	90	6	,	,	PUNCT
iajs-554	90	7	.	.	PUNCT
iajs-554	90	8	.	.	PUNCT
iajs-554	91	1	.	.	PUNCT
iajs-554	92	1	,	,	PUNCT
iajs-554	92	2	n.	n.	NOUN
iajs-554	92	3	4	4	NUM
iajs-554	92	4	.	.	NOUN
iajs-554	92	5	0	0	NUM
iajs-554	92	6	,	,	PUNCT
iajs-554	92	7	≠jix	≠jix	PROPN
iajs-554	92	8	5	5	NUM
iajs-554	92	9	.	.	NOUN
iajs-554	92	10	0	0	NUM
iajs-554	92	11	,	,	PUNCT
iajs-554	92	12	≠gix	≠gix	NOUN
iajs-554	92	13	for	for	ADP
iajs-554	92	14	comparing	compare	VERB
iajs-554	92	15	the	the	DET
iajs-554	92	16	error	error	NOUN
iajs-554	92	17	behavior	behavior	NOUN
iajs-554	92	18	of	of	ADP
iajs-554	92	19	the	the	DET
iajs-554	92	20	two	two	NUM
iajs-554	92	21	algorithms	algorithm	NOUN
iajs-554	92	22	.we	.we	NUM
iajs-554	92	23	need	need	VERB
iajs-554	92	24	the	the	DET
iajs-554	92	25	following	follow	VERB
iajs-554	92	26	result	result	NOUN
iajs-554	92	27	lemma[8	lemma[8	PROPN
iajs-554	92	28	]	]	PUNCT
iajs-554	92	29	:	:	PUNCT
iajs-554	92	30	let	let	VERB
iajs-554	92	31	the	the	DET
iajs-554	92	32	two	two	NUM
iajs-554	92	33	approximate	approximate	ADJ
iajs-554	92	34	solutions	solution	NOUN
iajs-554	92	35	jx	jx	PROPN
iajs-554	92	36	,	,	PUNCT
iajs-554	92	37	gx	gx	PROPN
iajs-554	92	38	have	have	VERB
iajs-554	92	39	non	non	ADJ
iajs-554	92	40	-	-	ADJ
iajs-554	92	41	vanishing	vanishing	ADJ
iajs-554	92	42	components	component	NOUN
iajs-554	92	43	and	and	CCONJ
iajs-554	92	44	let	let	VERB
iajs-554	92	45	the	the	DET
iajs-554	92	46	maximal	maximal	ADJ
iajs-554	92	47	relative	relative	ADJ
iajs-554	92	48	total	total	ADJ
iajs-554	92	49	condition	condition	NOUN
iajs-554	92	50	numbers	number	NOUN
iajs-554	92	51	of	of	ADP
iajs-554	92	52	these	these	DET
iajs-554	92	53	solution	solution	NOUN
iajs-554	92	54	be	be	AUX
iajs-554	92	55	bounded	bound	VERB
iajs-554	92	56	by	by	ADP
iajs-554	92	57	(	(	PUNCT
iajs-554	92	58	ρm	ρm	PROPN
iajs-554	92	59	,	,	PUNCT
iajs-554	92	60	j+	j+	NUM
iajs-554	92	61	ρm	ρm	PROPN
iajs-554	92	62	,	,	PUNCT
iajs-554	92	63	g)η	g)η	NOUN
iajs-554	92	64	<	<	X
iajs-554	92	65	2	2	NUM
iajs-554	92	66	1	1	NUM
iajs-554	92	67	then	then	ADV
iajs-554	92	68	the	the	DET
iajs-554	92	69	componentwise	componentwise	NOUN
iajs-554	92	70	estimates	estimate	VERB
iajs-554	92	71	jggj	jggj	PROPN
iajs-554	92	72	xqxxqx	xqxxqx	PROPN
iajs-554	92	73	≤≤	≤≤	PROPN
iajs-554	92	74	,	,	PUNCT
iajs-554	92	75	are	be	AUX
iajs-554	92	76	valid	valid	ADJ
iajs-554	92	77	using	use	VERB
iajs-554	92	78	the	the	DET
iajs-554	92	79	constant	constant	ADJ
iajs-554	92	80	01,01	01,01	NOUN
iajs-554	92	81	and	and	CCONJ
iajs-554	92	82	,	,	PUNCT
iajs-554	92	83	1	1	NUM
iajs-554	92	84	11	11	NUM
iajs-554	92	85	1/1	1/1	NUM
iajs-554	92	86	≠−≠−	≠−≠−	NOUN
iajs-554	92	87	>	>	PUNCT
iajs-554	92	88			PROPN
iajs-554	92	89			PUNCT
iajs-554	93	1			PROPN
iajs-554	94	1			INTJ
iajs-554	94	2			NOUN
iajs-554	94	3			VERB
iajs-554	94	4	−	−	ADP
iajs-554	94	5	−	−	PROPN
iajs-554	94	6	−	−	PROPN
iajs-554	94	7	−=	−=	NOUN
iajs-554	94	8	ηρηρ	ηρηρ	X
iajs-554	94	9	ηρ	ηρ	X
iajs-554	94	10	ηρ	ηρ	X
iajs-554	94	11	ηρ	ηρ	X
iajs-554	94	12	ηρ	ηρ	PROPN
iajs-554	94	13	gj	gj	NOUN
iajs-554	94	14	g	g	PROPN
iajs-554	94	15	g	g	PROPN
iajs-554	94	16	j	j	PROPN
iajs-554	94	17	jq	jq	PROPN
iajs-554	95	1	mm	mm	INTJ
iajs-554	95	2	m	m	VERB
iajs-554	95	3	m	m	VERB
iajs-554	95	4	m	m	VERB
iajs-554	95	5	m	m	VERB
iajs-554	95	6	lemma	lemma	ADJ
iajs-554	95	7	:	:	PUNCT
iajs-554	95	8	let	let	VERB
iajs-554	95	9	the	the	DET
iajs-554	95	10	two	two	NUM
iajs-554	95	11	approximate	approximate	ADJ
iajs-554	95	12	solutions	solution	NOUN
iajs-554	95	13	gj	gj	NOUN
iajs-554	95	14	xx	xx	NUM
iajs-554	95	15	,	,	PUNCT
iajs-554	95	16	have	have	AUX
iajs-554	95	17	nonvanishing	nonvanishe	VERB
iajs-554	95	18	components	component	NOUN
iajs-554	95	19	and	and	CCONJ
iajs-554	95	20	let	let	VERB
iajs-554	95	21	the	the	DET
iajs-554	95	22	maximal	maximal	ADJ
iajs-554	95	23	relative	relative	ADJ
iajs-554	95	24	total	total	ADJ
iajs-554	95	25	condition	condition	NOUN
iajs-554	95	26	numbers	number	NOUN
iajs-554	95	27	of	of	ADP
iajs-554	95	28	these	these	DET
iajs-554	95	29	solutions	solution	NOUN
iajs-554	95	30	be	be	AUX
iajs-554	95	31	bounded	bound	VERB
iajs-554	95	32	by	by	ADP
iajs-554	95	33	(	(	PUNCT
iajs-554	95	34	ρm	ρm	PROPN
iajs-554	95	35	,	,	PUNCT
iajs-554	95	36	j	j	PROPN
iajs-554	95	37	+	+	CCONJ
iajs-554	95	38	ρmg	ρmg	PROPN
iajs-554	95	39	)	)	PUNCT
iajs-554	95	40	η	η	PROPN
iajs-554	95	41	<	<	X
iajs-554	95	42	2	2	NUM
iajs-554	95	43	1	1	NUM
iajs-554	95	44	then	then	ADV
iajs-554	95	45	the	the	DET
iajs-554	95	46	component	component	NOUN
iajs-554	95	47	wise	wise	ADJ
iajs-554	95	48	estimates	estimate	VERB
iajs-554	95	49	jggj	jggj	PROPN
iajs-554	95	50	xqxxqx	xqxxqx	PROPN
iajs-554	95	51	≤≤	≤≤	PROPN
iajs-554	95	52	,	,	PUNCT
iajs-554	95	53	are	be	AUX
iajs-554	95	54	valid	valid	ADJ
iajs-554	95	55	theorem	theorem	ADJ
iajs-554	95	56	:	:	PUNCT
iajs-554	95	57	(	(	PUNCT
iajs-554	95	58	under	under	ADP
iajs-554	95	59	the	the	DET
iajs-554	95	60	assumption	assumption	NOUN
iajs-554	95	61	of	of	ADP
iajs-554	95	62	above	above	ADV
iajs-554	95	63	lemma	lemma	PROPN
iajs-554	95	64	the	the	DET
iajs-554	95	65	estimates	estimate	NOUN
iajs-554	95	66	0rdenominado	0rdenominado	NUM
iajs-554	95	67	provided	provide	VERB
iajs-554	95	68	,	,	PUNCT
iajs-554	95	69	1	1	NUM
iajs-554	95	70	1	1	NUM
iajs-554	95	71	,	,	PUNCT
iajs-554	95	72	,	,	PUNCT
iajs-554	95	73	2	2	NUM
iajs-554	95	74	,	,	PUNCT
iajs-554	95	75	≠	≠	PROPN
iajs-554	95	76	−	−	PROPN
iajs-554	95	77	≤	≤	PUNCT
iajs-554	95	78	gq	gq	VERB
iajs-554	95	79	q	q	PROPN
iajs-554	96	1	d	d	INTJ
iajs-554	96	2	i	i	NOUN
iajs-554	96	3	r	r	NOUN
iajs-554	96	4	d	d	NOUN
iajs-554	96	5	gmji	gmji	NOUN
iajs-554	96	6	d	d	PROPN
iajs-554	96	7	ji	ji	PROPN
iajs-554	96	8	σ	σ	X
iajs-554	96	9	ηρω	ηρω	PROPN
iajs-554	96	10	σ	σ	X
iajs-554	96	11	.	.	PUNCT
iajs-554	97	1	2	2	NUM
iajs-554	97	2	3	3	NUM
iajs-554	97	3	,	,	PUNCT
iajs-554	97	4	≤r	≤r	VERB
iajs-554	97	5	jiσ	jiσ	X
iajs-554	97	6	(	(	PUNCT
iajs-554	97	7	)	)	PUNCT
iajs-554	97	8	n	n	CCONJ
iajs-554	97	9	,	,	PUNCT
iajs-554	97	10	1	1	NUM
iajs-554	97	11	,	,	PUNCT
iajs-554	97	12	ifor	ifor	NOUN
iajs-554	97	13	hold	hold	NOUN
iajs-554	97	14	.	.	PUNCT
iajs-554	98	1	1	1	NUM
iajs-554	98	2	2	2	NUM
iajs-554	98	3	3	3	NUM
iajs-554	98	4	3	3	NUM
iajs-554	98	5	5	5	NUM
iajs-554	98	6	4	4	NUM
iajs-554	98	7	31	31	NUM
iajs-554	98	8	1	1	NUM
iajs-554	98	9	,	,	PUNCT
iajs-554	98	10	,	,	PUNCT
iajs-554	98	11	2	2	NUM
iajs-554	98	12	…	…	SYM
iajs-554	98	13	=	=	SYM
iajs-554	98	14			NOUN
iajs-554	98	15			PROPN
iajs-554	98	16			PROPN
iajs-554	98	17			NOUN
iajs-554	98	18			PRON
iajs-554	98	19			PROPN
iajs-554	98	20	−++	−++	PROPN
iajs-554	98	21			PUNCT
iajs-554	99	1			PROPN
iajs-554	99	2			PROPN
iajs-554	99	3			NOUN
iajs-554	99	4			VERB
iajs-554	99	5	−+−	−+−	PROPN
iajs-554	99	6	−+	−+	NOUN
iajs-554	99	7	r	r	NOUN
iajs-554	99	8	gi	gi	NOUN
iajs-554	99	9	r	r	NOUN
iajs-554	99	10	r	r	NOUN
iajs-554	99	11	gm	gm	PROPN
iajs-554	100	1	q	q	X
iajs-554	101	1	qinin	qinin	PROPN
iajs-554	101	2	in	in	ADP
iajs-554	101	3	σ	σ	NOUN
iajs-554	101	4	ηρ	ηρ	NOUN
iajs-554	101	5	when	when	SCONJ
iajs-554	101	6	.	.	PUNCT
iajs-554	102	1	rη	rη	NOUN
iajs-554	102	2	is	be	AUX
iajs-554	102	3	so	so	ADV
iajs-554	102	4	small	small	ADJ
iajs-554	102	5	that	that	SCONJ
iajs-554	102	6	the	the	DET
iajs-554	102	7	denominators	denominator	NOUN
iajs-554	102	8	are	be	AUX
iajs-554	102	9	positive,[8	positive,[8	NUM
iajs-554	102	10	]	]	PUNCT
iajs-554	102	11	solution	solution	NOUN
iajs-554	102	12	of	of	ADP
iajs-554	102	13	general	general	ADJ
iajs-554	102	14	linear	linear	NOUN
iajs-554	102	15	system	system	NOUN
iajs-554	102	16	by	by	ADP
iajs-554	102	17	gaussjordan	gaussjordan	PROPN
iajs-554	102	18	elimination	elimination	NOUN
iajs-554	102	19	the	the	DET
iajs-554	102	20	solution	solution	NOUN
iajs-554	102	21	of	of	ADP
iajs-554	102	22	general	general	ADJ
iajs-554	102	23	linear	linear	PROPN
iajs-554	102	24	systems	system	NOUN
iajs-554	102	25	yx	yx	X
iajs-554	103	1	=	=	NOUN
iajs-554	103	2	α	α	NOUN
iajs-554	103	3	by	by	ADP
iajs-554	103	4	gaussjordan	gaussjordan	PROPN
iajs-554	103	5	elimination	elimination	NOUN
iajs-554	103	6	will	will	AUX
iajs-554	103	7	be	be	AUX
iajs-554	103	8	analyzed	analyze	VERB
iajs-554	103	9	.	.	PUNCT
iajs-554	104	1	in	in	ADP
iajs-554	104	2	the	the	DET
iajs-554	104	3	context	context	NOUN
iajs-554	104	4	of	of	ADP
iajs-554	104	5	rounding	round	VERB
iajs-554	104	6	error	error	NOUN
iajs-554	104	7	analysis	analysis	NOUN
iajs-554	104	8	the	the	DET
iajs-554	104	9	algorithm	algorithm	NOUN
iajs-554	104	10	is	be	AUX
iajs-554	104	11	considered	consider	VERB
iajs-554	104	12	as	as	ADP
iajs-554	104	13	being	be	AUX
iajs-554	104	14	mathematics	mathematics	NOUN
iajs-554	104	15	372	372	NUM
iajs-554	104	16	مجلة	مجلة	NOUN
iajs-554	104	17	إبن	إبن	VERB
iajs-554	104	18	الهيثم	الهيثم	ADJ
iajs-554	104	19	للعلوم	للعلوم	NOUN
iajs-554	104	20	الصرفة	الصرفة	NOUN
iajs-554	105	1	و	و	PRON
iajs-554	105	2	التطبيقية	التطبيقية	ADJ
iajs-554	105	3	2012	2012	NUM
iajs-554	105	4	السنة	السنة	NOUN
iajs-554	105	5	25	25	NUM
iajs-554	105	6	المجلد	المجلد	NOUN
iajs-554	105	7	3	3	NUM
iajs-554	105	8	العدد	العدد	PROPN
iajs-554	105	9	ibn	ibn	PROPN
iajs-554	105	10	al	al	PROPN
iajs-554	105	11	-	-	PUNCT
iajs-554	105	12	haitham	haitham	PROPN
iajs-554	105	13	journal	journal	PROPN
iajs-554	105	14	for	for	ADP
iajs-554	105	15	pure	pure	ADJ
iajs-554	105	16	and	and	CCONJ
iajs-554	105	17	applied	apply	VERB
iajs-554	105	18	science	science	NOUN
iajs-554	105	19	no	no	NOUN
iajs-554	105	20	.	.	NOUN
iajs-554	105	21	3	3	NUM
iajs-554	105	22	vol	vol	NOUN
iajs-554	105	23	.	.	PUNCT
iajs-554	106	1	25	25	NUM
iajs-554	106	2	year	year	NOUN
iajs-554	106	3	2012	2012	NUM
iajs-554	106	4	composed	compose	VERB
iajs-554	106	5	of	of	ADP
iajs-554	106	6	gaussian	gaussian	ADJ
iajs-554	106	7	forward	forward	ADJ
iajs-554	106	8	elimination	elimination	NOUN
iajs-554	106	9	and	and	CCONJ
iajs-554	106	10	a	a	DET
iajs-554	106	11	subsequent	subsequent	ADJ
iajs-554	106	12	solution	solution	NOUN
iajs-554	106	13	of	of	ADP
iajs-554	106	14	the	the	DET
iajs-554	106	15	upper	upper	ADJ
iajs-554	106	16	triangular	triangular	NOUN
iajs-554	106	17	linear	linear	NOUN
iajs-554	106	18	system	system	NOUN
iajs-554	106	19	zux	zux	X
iajs-554	106	20	=	=	PUNCT
iajs-554	106	21	by	by	ADP
iajs-554	106	22	jordan	jordan	PROPN
iajs-554	106	23	elimination	elimination	PROPN
iajs-554	106	24	see	see	VERB
iajs-554	106	25	[	[	X
iajs-554	106	26	3	3	NUM
iajs-554	106	27	]	]	PUNCT
iajs-554	106	28	.	.	PUNCT
iajs-554	107	1	the	the	DET
iajs-554	107	2	computed	compute	VERB
iajs-554	107	3	trapezoidal	trapezoidal	ADJ
iajs-554	107	4	factors	factor	NOUN
iajs-554	107	5	1,ul	1,ul	NUM
iajs-554	107	6	of	of	ADP
iajs-554	107	7	a1=	a1=	PROPN
iajs-554	107	8	(	(	PUNCT
iajs-554	107	9	a	a	PRON
iajs-554	107	10	,	,	PUNCT
iajs-554	107	11	y	y	NOUN
iajs-554	107	12	)	)	PUNCT
iajs-554	107	13	or	or	CCONJ
iajs-554	107	14	,	,	PUNCT
iajs-554	107	15	under	under	ADP
iajs-554	107	16	data	data	NOUN
iajs-554	107	17	perturbations	perturbation	NOUN
iajs-554	107	18	,	,	PUNCT
iajs-554	107	19	)	)	PUNCT
iajs-554	107	20	y	y	PROPN
iajs-554	107	21	,	,	PUNCT
iajs-554	107	22	a	a	DET
iajs-554	107	23	(	(	PUNCT
iajs-554	107	24	a1	a1	NOUN
iajs-554	107	25	=	=	PUNCT
iajs-554	107	26	satisfy	satisfy	NOUN
iajs-554	107	27	,	,	PUNCT
iajs-554	107	28	according	accord	VERB
iajs-554	107	29	to	to	ADP
iajs-554	107	30	[	[	X
iajs-554	107	31	2	2	NUM
iajs-554	107	32	,	,	PUNCT
iajs-554	107	33	1	1	NUM
iajs-554	107	34	.	.	PUNCT
iajs-554	107	35	(	(	PUNCT
iajs-554	107	36	13	13	NUM
iajs-554	107	37	)	)	PUNCT
iajs-554	107	38	]	]	PUNCT
iajs-554	107	39	,	,	PUNCT
iajs-554	107	40	the	the	DET
iajs-554	107	41	relation	relation	NOUN
iajs-554	107	42	gfaul	gfaul	NOUN
iajs-554	107	43	+	+	NOUN
iajs-554	107	44	=	=	SYM
iajs-554	107	45	11	11	NUM
iajs-554	107	46	…	…	PUNCT
iajs-554	107	47	..	..	PUNCT
iajs-554	107	48	(	(	PUNCT
iajs-554	107	49	10	10	NUM
iajs-554	107	50	)	)	PUNCT
iajs-554	107	51	with	with	ADP
iajs-554	107	52	an	an	DET
iajs-554	107	53	error	error	NOUN
iajs-554	107	54	matrix	matrix	NOUN
iajs-554	107	55	fg	fg	X
iajs-554	107	56	.	.	PUNCT
iajs-554	107	57	using	use	VERB
iajs-554	107	58	trapezoidal	trapezoidal	ADJ
iajs-554	107	59	factorization	factorization	NOUN
iajs-554	107	60	a1	a1	NOUN
iajs-554	107	61	=	=	NOUN
iajs-554	107	62	lu1	lu1	NOUN
iajs-554	107	63	of	of	ADP
iajs-554	107	64	the	the	DET
iajs-554	107	65	n	n	CCONJ
iajs-554	107	66	-	-	PUNCT
iajs-554	107	67	by-(n+1	by-(n+1	ADJ
iajs-554	107	68	)	)	PUNCT
iajs-554	107	69	coefficient	coefficient	NOUN
iajs-554	107	70	matrix	matrix	NOUN
iajs-554	107	71	,	,	PUNCT
iajs-554	107	72	one	one	NUM
iajs-554	107	73	readily	readily	ADV
iajs-554	107	74	derives	derive	VERB
iajs-554	107	75	from	from	ADP
iajs-554	107	76	(	(	PUNCT
iajs-554	107	77	10	10	NUM
iajs-554	107	78	)	)	PUNCT
iajs-554	107	79	the	the	DET
iajs-554	107	80	equation	equation	NOUN
iajs-554	107	81	gfaullu	gfaullu	NOUN
iajs-554	107	82	+	+	PROPN
iajs-554	107	83	∆=∆+∆	∆=∆+∆	PROPN
iajs-554	107	84	111	111	NUM
iajs-554	107	85	…	…	SYM
iajs-554	107	86	.(11	.(11	NUM
iajs-554	107	87	)	)	PUNCT
iajs-554	107	88	since	since	SCONJ
iajs-554	107	89	01	01	NUM
iajs-554	107	90	=	=	NUM
iajs-554	107	91	−=	−=	NOUN
iajs-554	107	92	∧	∧	PROPN
iajs-554	107	93	zuxxu	zuxxu	NOUN
iajs-554	107	94	…	…	PUNCT
iajs-554	107	95	(	(	PUNCT
iajs-554	107	96	12	12	NUM
iajs-554	107	97	)	)	PUNCT
iajs-554	107	98	gfaullu	gfaullu	NOUN
iajs-554	108	1	+	+	PROPN
iajs-554	108	2	∆=∆+∆	∆=∆+∆	PROPN
iajs-554	108	3	111	111	NUM
iajs-554	108	4	implies	imply	VERB
iajs-554	108	5	the	the	DET
iajs-554	108	6	representation	representation	NOUN
iajs-554	108	7	ˆ)(ˆ	ˆ)(ˆ	NOUN
iajs-554	108	8	1	1	NUM
iajs-554	108	9	1	1	NUM
iajs-554	108	10	1	1	NUM
iajs-554	108	11	xfalxu	xfalxu	NOUN
iajs-554	108	12	g+∆=∆	g+∆=∆	NOUN
iajs-554	108	13	−	−	PROPN
iajs-554	108	14	…	…	PUNCT
iajs-554	108	15	(	(	PUNCT
iajs-554	108	16	13	13	NUM
iajs-554	108	17	)	)	PUNCT
iajs-554	108	18	this	this	DET
iajs-554	108	19	result	result	NOUN
iajs-554	108	20	establishes	establish	VERB
iajs-554	108	21	the	the	DET
iajs-554	108	22	dependence	dependence	NOUN
iajs-554	108	23	of	of	ADP
iajs-554	108	24	the	the	DET
iajs-554	108	25	errors	error	NOUN
iajs-554	108	26	1u∆	1u∆	NUM
iajs-554	108	27	of	of	ADP
iajs-554	108	28	the	the	DET
iajs-554	108	29	n	n	CCONJ
iajs-554	108	30	-	-	PUNCT
iajs-554	108	31	by-(n+1	by-(n+1	ADJ
iajs-554	108	32	)	)	PUNCT
iajs-554	108	33	coefficient	coefficient	NOUN
iajs-554	108	34	matrix	matrix	NOUN
iajs-554	108	35	1u	1u	NUM
iajs-554	108	36	of	of	ADP
iajs-554	108	37	the	the	DET
iajs-554	108	38	upper	upper	ADJ
iajs-554	108	39	triangular	triangular	NOUN
iajs-554	108	40	linear	linear	NOUN
iajs-554	108	41	system	system	NOUN
iajs-554	108	42	,	,	PUNCT
iajs-554	108	43	which	which	PRON
iajs-554	108	44	has	have	VERB
iajs-554	108	45	to	to	PART
iajs-554	108	46	be	be	AUX
iajs-554	108	47	solved	solve	VERB
iajs-554	108	48	by	by	ADP
iajs-554	108	49	jordan	jordan	PROPN
iajs-554	108	50	elimination	elimination	PROPN
iajs-554	108	51	,	,	PUNCT
iajs-554	108	52	upon	upon	SCONJ
iajs-554	108	53	the	the	DET
iajs-554	108	54	data	data	NOUN
iajs-554	108	55	errors	error	NOUN
iajs-554	108	56	and	and	CCONJ
iajs-554	108	57	the	the	DET
iajs-554	108	58	rounding	round	VERB
iajs-554	108	59	errors	error	NOUN
iajs-554	108	60	in	in	ADP
iajs-554	108	61	forward	forward	ADJ
iajs-554	108	62	elimination	elimination	NOUN
iajs-554	108	63	,	,	PUNCT
iajs-554	108	64	where	where	SCONJ
iajs-554	108	65	fg	fg	PROPN
iajs-554	108	66	denotes	denote	VERB
iajs-554	108	67	the	the	DET
iajs-554	108	68	errors	error	NOUN
iajs-554	108	69	matrix	matrix	NOUN
iajs-554	108	70	of	of	ADP
iajs-554	108	71	forward	forward	ADJ
iajs-554	108	72	elimination	elimination	NOUN
iajs-554	108	73	in	in	ADP
iajs-554	108	74	and	and	CCONJ
iajs-554	108	75	fj	fj	PRON
iajs-554	108	76	the	the	DET
iajs-554	108	77	errors	error	NOUN
iajs-554	108	78	matrix	matrix	NOUN
iajs-554	108	79	of	of	ADP
iajs-554	108	80	the	the	DET
iajs-554	108	81	solution	solution	NOUN
iajs-554	108	82	by	by	ADP
iajs-554	108	83	jordan	jordan	PROPN
iajs-554	108	84	elimination	elimination	PROPN
iajs-554	108	85	.	.	PUNCT
iajs-554	109	1	comparsion	comparsion	NOUN
iajs-554	109	2	of	of	ADP
iajs-554	109	3	gauss	gauss	PROPN
iajs-554	109	4	-	-	PUNCT
iajs-554	109	5	jordan	jordan	PROPN
iajs-554	109	6	elimination	elimination	NOUN
iajs-554	109	7	with	with	ADP
iajs-554	109	8	gaussian	gaussian	ADJ
iajs-554	109	9	elimination	elimination	NOUN
iajs-554	109	10	the	the	DET
iajs-554	109	11	behavior	behavior	NOUN
iajs-554	109	12	of	of	ADP
iajs-554	109	13	the	the	DET
iajs-554	109	14	error	error	NOUN
iajs-554	109	15	of	of	ADP
iajs-554	109	16	the	the	DET
iajs-554	109	17	solution	solution	NOUN
iajs-554	109	18	of	of	ADP
iajs-554	109	19	general	general	ADJ
iajs-554	109	20	linear	linear	NOUN
iajs-554	109	21	system	system	NOUN
iajs-554	109	22	by	by	ADP
iajs-554	109	23	gaussian	gaussian	ADJ
iajs-554	109	24	elimination	elimination	NOUN
iajs-554	109	25	on	on	ADP
iajs-554	109	26	the	the	DET
iajs-554	109	27	one	one	NUM
iajs-554	109	28	hand	hand	NOUN
iajs-554	109	29	and	and	CCONJ
iajs-554	109	30	gauss	gauss	ADJ
iajs-554	109	31	-	-	PUNCT
iajs-554	109	32	jordan	jordan	PROPN
iajs-554	109	33	elimination	elimination	NOUN
iajs-554	109	34	on	on	ADP
iajs-554	109	35	the	the	DET
iajs-554	109	36	other	other	ADJ
iajs-554	109	37	hand	hand	NOUN
iajs-554	109	38	will	will	AUX
iajs-554	109	39	be	be	AUX
iajs-554	109	40	compared	compare	VERB
iajs-554	109	41	with	with	ADP
iajs-554	109	42	each	each	DET
iajs-554	109	43	other	other	ADJ
iajs-554	109	44	.	.	PUNCT
iajs-554	110	1	in	in	ADP
iajs-554	110	2	both	both	DET
iajs-554	110	3	cases	case	NOUN
iajs-554	110	4	we	we	PRON
iajs-554	110	5	assume	assume	VERB
iajs-554	110	6	the	the	DET
iajs-554	110	7	same	same	ADJ
iajs-554	110	8	perturbed	perturb	VERB
iajs-554	110	9	data	datum	NOUN
iajs-554	110	10	.	.	PUNCT
iajs-554	111	1	,	,	PUNCT
iajs-554	111	2	ya	ya	PRON
iajs-554	111	3	then	then	ADV
iajs-554	111	4	for	for	ADP
iajs-554	111	5	both	both	DET
iajs-554	111	6	methods	method	NOUN
iajs-554	111	7	also	also	ADV
iajs-554	111	8	computed	compute	VERB
iajs-554	111	9	triangular	triangular	NOUN
iajs-554	111	10	factors	factor	NOUN
iajs-554	111	11	ul	ul	INTJ
iajs-554	111	12	,	,	PUNCT
iajs-554	111	13	of	of	ADP
iajs-554	111	14	a	a	DET
iajs-554	111	15	and	and	CCONJ
iajs-554	111	16	computed	computed	ADJ
iajs-554	111	17	coefficients	coefficient	NOUN
iajs-554	111	18	zu	zu	NOUN
iajs-554	111	19	,	,	PUNCT
iajs-554	111	20	of	of	ADP
iajs-554	111	21	the	the	DET
iajs-554	111	22	upper	upper	ADJ
iajs-554	111	23	triangular	triangular	NOUN
iajs-554	111	24	factor	factor	NOUN
iajs-554	111	25	system	system	NOUN
iajs-554	111	26	are	be	AUX
iajs-554	111	27	the	the	DET
iajs-554	111	28	same	same	ADJ
iajs-554	111	29	.	.	PUNCT
iajs-554	112	1	the	the	DET
iajs-554	112	2	vector	vector	NOUN
iajs-554	112	3	of	of	ADP
iajs-554	112	4	data	datum	NOUN
iajs-554	112	5	and	and	CCONJ
iajs-554	112	6	rounding	round	VERB
iajs-554	112	7	condition	condition	NOUN
iajs-554	112	8	numbers	number	NOUN
iajs-554	112	9	of	of	ADP
iajs-554	112	10	gaussian	gaussian	ADJ
iajs-554	112	11	elimination	elimination	NOUN
iajs-554	112	12	are	be	AUX
iajs-554	112	13	specified	specify	VERB
iajs-554	112	14	by	by	ADP
iajs-554	112	15	(	(	PUNCT
iajs-554	112	16	see	see	VERB
iajs-554	112	17	[	[	X
iajs-554	112	18	8	8	NUM
iajs-554	112	19	,	,	PUNCT
iajs-554	112	20	64	64	NUM
iajs-554	112	21	]	]	PUNCT
iajs-554	112	22	)	)	PUNCT
iajs-554	112	23	.	.	PUNCT
iajs-554	113	1	the	the	DET
iajs-554	113	2	solution	solution	NOUN
iajs-554	113	3	vector	vector	NOUN
iajs-554	113	4	gj	gj	NOUN
iajs-554	113	5	xx	xx	NOUN
iajs-554	113	6	,	,	PUNCT
iajs-554	113	7	of	of	ADP
iajs-554	113	8	the	the	DET
iajs-554	113	9	two	two	NUM
iajs-554	113	10	method	method	NOUN
iajs-554	113	11	satisfy	satisfy	NOUN
iajs-554	113	12	error	error	NOUN
iajs-554	113	13	estimates	estimate	NOUN
iajs-554	113	14	of	of	ADP
iajs-554	113	15	the	the	DET
iajs-554	113	16	form	form	NOUN
iajs-554	113	17	.,,1	.,,1	NOUN
iajs-554	113	18	,	,	PUNCT
iajs-554	113	19	1	1	NUM
iajs-554	113	20	,	,	PUNCT
iajs-554	113	21	1	1	NUM
iajs-554	113	22	ni	ni	PROPN
iajs-554	113	23	mx	mx	PROPN
iajs-554	114	1	xx	xx	NUM
iajs-554	114	2	m	m	VERB
iajs-554	114	3	xx	xx	NUM
iajs-554	115	1	i	i	PRON
iajs-554	115	2	i	i	PROPN
iajs-554	115	3	iii	iii	VERB
iajs-554	115	4	ii	ii	PROPN
iajs-554	115	5	=	=	NOUN
iajs-554	115	6	−	−	NOUN
iajs-554	115	7	≤	≤	NUM
iajs-554	115	8	−	−	ADP
iajs-554	115	9	−	−	NOUN
iajs-554	115	10	≤−	≤−	PROPN
iajs-554	115	11	ηη	ηη	PROPN
iajs-554	115	12	ρ	ρ	PROPN
iajs-554	115	13	ηρ	ηρ	PROPN
iajs-554	115	14	ρ	ρ	PROPN
iajs-554	115	15	ησ	ησ	PROPN
iajs-554	115	16	the	the	DET
iajs-554	115	17	following	follow	VERB
iajs-554	115	18	equation	equation	NOUN
iajs-554	115	19	shows	show	VERB
iajs-554	115	20	that	that	SCONJ
iajs-554	115	21	the	the	DET
iajs-554	115	22	total	total	ADJ
iajs-554	115	23	condition	condition	NOUN
iajs-554	115	24	numbers	number	NOUN
iajs-554	115	25	(	(	PUNCT
iajs-554	115	26	)	)	PUNCT
iajs-554	115	27	,	,	PUNCT
iajs-554	115	28	,	,	PUNCT
iajs-554	115	29	max,,,1	max,,,1	NOUN
iajs-554	115	30	,	,	PUNCT
iajs-554	115	31	,	,	PUNCT
iajs-554	115	32	,	,	PUNCT
iajs-554	115	33	,	,	PUNCT
iajs-554	115	34	rd	rd	PROPN
iajs-554	115	35	r	r	PROPN
iajs-554	115	36	ji	ji	PROPN
iajs-554	115	37	rd	rd	PROPN
iajs-554	115	38	ji	ji	PROPN
iajs-554	116	1	d	d	PROPN
iajs-554	116	2	ji	ji	PROPN
iajs-554	116	3	ni	ni	PROPN
iajs-554	116	4	ηηησ	ηηησ	PROPN
iajs-554	116	5	η	η	PROPN
iajs-554	116	6	ησ	ησ	PROPN
iajs-554	116	7	η	η	PROPN
iajs-554	116	8	ησ	ησ	PROPN
iajs-554	116	9	=	=	PROPN
iajs-554	116	10	=	=	PROPN
iajs-554	116	11	+	+	NOUN
iajs-554	116	12	=	=	ADJ
iajs-554	116	13			NUM
iajs-554	116	14	of	of	ADP
iajs-554	116	15	the	the	DET
iajs-554	116	16	gauss	gauss	PROPN
iajs-554	116	17	–	–	PUNCT
iajs-554	116	18	jordan	jordan	PROPN
iajs-554	116	19	algorithm	algorithm	PROPN
iajs-554	116	20	can	can	AUX
iajs-554	116	21	be	be	AUX
iajs-554	116	22	bounded	bound	VERB
iajs-554	116	23	from	from	ADP
iajs-554	116	24	above	above	ADV
iajs-554	116	25	by	by	ADP
iajs-554	116	26	for	for	ADP
iajs-554	116	27	corresponding	correspond	VERB
iajs-554	116	28	total	total	ADJ
iajs-554	116	29	condition	condition	NOUN
iajs-554	116	30	number	number	NOUN
iajs-554	116	31	σi	σi	PROPN
iajs-554	116	32	,	,	PUNCT
iajs-554	116	33	g	g	PROPN
iajs-554	116	34	of	of	ADP
iajs-554	116	35	gaussian	gaussian	ADJ
iajs-554	116	36	elimination	elimination	NOUN
iajs-554	116	37	for	for	ADP
iajs-554	116	38	sufficiently	sufficiently	ADV
iajs-554	116	39	small	small	ADJ
iajs-554	116	40	accuracy	accuracy	NOUN
iajs-554	116	41	constant	constant	PROPN
iajs-554	116	42	η	η	PROPN
iajs-554	116	43	,	,	PUNCT
iajs-554	116	44	the	the	DET
iajs-554	116	45	condition	condition	NOUN
iajs-554	116	46	number	number	NOUN
iajs-554	116	47	σi	σi	PROPN
iajs-554	116	48	,	,	PUNCT
iajs-554	116	49	j	j	PROPN
iajs-554	116	50	is	be	AUX
iajs-554	116	51	,	,	PUNCT
iajs-554	116	52	in	in	ADP
iajs-554	116	53	essence	essence	NOUN
iajs-554	116	54	,	,	PUNCT
iajs-554	116	55	less	less	ADJ
iajs-554	116	56	than	than	ADP
iajs-554	116	57	or	or	CCONJ
iajs-554	116	58	equal	equal	ADJ
iajs-554	116	59	to	to	ADP
iajs-554	116	60	(	(	PUNCT
iajs-554	116	61	)	)	PUNCT
iajs-554	116	62	in	in	ADP
iajs-554	116	63	−+1	−+1	NOUN
iajs-554	116	64	2	2	NUM
iajs-554	116	65	3	3	NUM
iajs-554	116	66	−	−	PROPN
iajs-554	116	67	times	time	NOUN
iajs-554	116	68	σi	σi	PROPN
iajs-554	116	69	,	,	PUNCT
iajs-554	116	70	j	j	PROPN
iajs-554	116	71	because	because	SCONJ
iajs-554	116	72	the	the	DET
iajs-554	116	73	constant	constant	ADJ
iajs-554	116	74	q	q	NOUN
iajs-554	116	75	and	and	CCONJ
iajs-554	116	76	the	the	DET
iajs-554	116	77	denominator	denominator	NOUN
iajs-554	116	78	are	be	AUX
iajs-554	116	79	close	close	ADJ
iajs-554	116	80	to	to	ADP
iajs-554	116	81	1.the	1.the	DET
iajs-554	116	82	condition	condition	NOUN
iajs-554	116	83	number	number	NOUN
iajs-554	116	84	σi	σi	PRON
iajs-554	116	85	constitute	constitute	VERB
iajs-554	116	86	,	,	PUNCT
iajs-554	116	87	save	save	VERB
iajs-554	116	88	for	for	ADP
iajs-554	116	89	terms	term	NOUN
iajs-554	116	90	of	of	ADP
iajs-554	116	91	higher	high	ADJ
iajs-554	116	92	order	order	NOUN
iajs-554	116	93	in	in	ADP
iajs-554	116	94	η	η	PROPN
iajs-554	116	95	,	,	PUNCT
iajs-554	116	96	optimal	optimal	ADJ
iajs-554	116	97	bounds	bound	NOUN
iajs-554	116	98	for	for	ADP
iajs-554	116	99	the	the	DET
iajs-554	116	100	absolute	absolute	ADJ
iajs-554	116	101	errors	error	NOUN
iajs-554	116	102	.iii	.iii	PUNCT
iajs-554	116	103	xxx	xxx	VERB
iajs-554	117	1	−=∆	−=∆	DET
iajs-554	117	2	hence	hence	ADV
iajs-554	117	3	,	,	PUNCT
iajs-554	117	4	the	the	DET
iajs-554	117	5	result	result	NOUN
iajs-554	117	6	say	say	VERB
iajs-554	117	7	that	that	SCONJ
iajs-554	117	8	for	for	ADP
iajs-554	117	9	sufficiently	sufficiently	ADV
iajs-554	117	10	small	small	ADJ
iajs-554	117	11	η	η	PROPN
iajs-554	117	12	the	the	DET
iajs-554	117	13	absolute	absolute	ADJ
iajs-554	117	14	errors	error	NOUN
iajs-554	117	15	∆xi	∆xi	NUM
iajs-554	117	16	,	,	PUNCT
iajs-554	117	17	j	j	PROPN
iajs-554	117	18	of	of	ADP
iajs-554	117	19	the	the	DET
iajs-554	117	20	solutions	solution	NOUN
iajs-554	117	21	by	by	ADP
iajs-554	117	22	gauss	gauss	ADJ
iajs-554	117	23	mathematics	mathematics	PROPN
iajs-554	117	24	373	373	NUM
iajs-554	117	25	مجلة	مجلة	NOUN
iajs-554	117	26	إبن	إبن	VERB
iajs-554	117	27	الهيثم	الهيثم	ADJ
iajs-554	117	28	للعلوم	للعلوم	NOUN
iajs-554	117	29	الصرفة	الصرفة	NOUN
iajs-554	117	30	و	و	PRON
iajs-554	117	31	التطبيقية	التطبيقية	ADJ
iajs-554	117	32	2012	2012	NUM
iajs-554	117	33	السنة	السنة	NOUN
iajs-554	117	34	25	25	NUM
iajs-554	117	35	المجلد	المجلد	NOUN
iajs-554	117	36	3	3	NUM
iajs-554	117	37	العدد	العدد	PROPN
iajs-554	117	38	ibn	ibn	PROPN
iajs-554	117	39	al	al	PROPN
iajs-554	117	40	-	-	PUNCT
iajs-554	117	41	haitham	haitham	PROPN
iajs-554	117	42	journal	journal	PROPN
iajs-554	117	43	for	for	ADP
iajs-554	117	44	pure	pure	ADJ
iajs-554	117	45	and	and	CCONJ
iajs-554	117	46	applied	apply	VERB
iajs-554	117	47	science	science	NOUN
iajs-554	117	48	no	no	NOUN
iajs-554	117	49	.	.	NOUN
iajs-554	117	50	3	3	NUM
iajs-554	117	51	vol	vol	NOUN
iajs-554	117	52	.	.	PUNCT
iajs-554	118	1	25	25	NUM
iajs-554	118	2	year	year	NOUN
iajs-554	118	3	2012	2012	NUM
iajs-554	118	4	jordan	jordan	PROPN
iajs-554	118	5	elimination	elimination	NOUN
iajs-554	118	6	can	can	AUX
iajs-554	118	7	not	not	PART
iajs-554	118	8	be	be	AUX
iajs-554	118	9	,	,	PUNCT
iajs-554	118	10	in	in	ADP
iajs-554	118	11	absolute	absolute	ADJ
iajs-554	118	12	value	value	NOUN
iajs-554	118	13	,	,	PUNCT
iajs-554	118	14	essentially	essentially	ADV
iajs-554	118	15	grater	grater	NOUN
iajs-554	118	16	than	than	ADP
iajs-554	118	17	(	(	PUNCT
iajs-554	118	18	)	)	PUNCT
iajs-554	118	19	timesin	timesin	NOUN
iajs-554	118	20	−−+1	−−+1	PUNCT
iajs-554	118	21	2	2	NUM
iajs-554	118	22	3	3	NUM
iajs-554	118	23	the	the	DET
iajs-554	118	24	possible	possible	ADJ
iajs-554	118	25	maximal	maximal	ADJ
iajs-554	118	26	errors	error	NOUN
iajs-554	118	27	nxxx	nxxx	ADJ
iajs-554	118	28	igigi	igigi	NOUN
iajs-554	118	29	,	,	PUNCT
iajs-554	118	30	,	,	PUNCT
iajs-554	118	31	,	,	PUNCT
iajs-554	118	32	1	1	NUM
iajs-554	118	33	,	,	PUNCT
iajs-554	118	34	,	,	PUNCT
iajs-554	118	35	,	,	PUNCT
iajs-554	118	36	−=∆	−=∆	PROPN
iajs-554	118	37	of	of	ADP
iajs-554	118	38	the	the	DET
iajs-554	118	39	solution	solution	NOUN
iajs-554	118	40	by	by	ADP
iajs-554	118	41	gaussian	gaussian	ADJ
iajs-554	118	42	elimination	elimination	NOUN
iajs-554	118	43	.	.	PUNCT
iajs-554	119	1	numerical	numerical	ADJ
iajs-554	119	2	example	example	NOUN
iajs-554	119	3	the	the	DET
iajs-554	119	4	results	result	NOUN
iajs-554	119	5	of	of	ADP
iajs-554	119	6	the	the	DET
iajs-554	119	7	paper	paper	NOUN
iajs-554	119	8	are	be	AUX
iajs-554	119	9	now	now	ADV
iajs-554	119	10	illustrated	illustrate	VERB
iajs-554	119	11	by	by	ADP
iajs-554	119	12	simple	simple	ADJ
iajs-554	119	13	numerical	numerical	ADJ
iajs-554	119	14	example	example	NOUN
iajs-554	119	15	.	.	PUNCT
iajs-554	120	1	the	the	DET
iajs-554	120	2	first	first	ADJ
iajs-554	120	3	example	example	NOUN
iajs-554	120	4	is	be	AUX
iajs-554	120	5	the	the	DET
iajs-554	120	6	upper	upper	ADJ
iajs-554	120	7	triangular	triangular	NOUN
iajs-554	120	8	linear	linear	NOUN
iajs-554	120	9	system	system	NOUN
iajs-554	120	10	0.826354	0.826354	NUM
iajs-554	120	11	x1	x1	PROPN
iajs-554	121	1	+	+	PROPN
iajs-554	121	2	0.432175	0.432175	NUM
iajs-554	121	3	x2	x2	PROPN
iajs-554	121	4	+	+	PROPN
iajs-554	121	5	0.613256	0.613256	NUM
iajs-554	121	6	x3	x3	ADJ
iajs-554	121	7	+	+	NOUN
iajs-554	121	8	0.614227	0.614227	NUM
iajs-554	121	9	x4	x4	NOUN
iajs-554	121	10	=	=	NOUN
iajs-554	122	1	0.722872	0.722872	NUM
iajs-554	122	2	0.000547x2	0.000547x2	NUM
iajs-554	122	3	+	+	NUM
iajs-554	122	4	0.814712	0.814712	NUM
iajs-554	122	5	x3	x3	ADJ
iajs-554	122	6	+	+	NOUN
iajs-554	122	7	0.816328	0.816328	NUM
iajs-554	122	8	x4	x4	NOUN
iajs-554	122	9	=	=	NOUN
iajs-554	122	10	0.15424	0.15424	NUM
iajs-554	122	11	0.915316	0.915316	NUM
iajs-554	122	12	x3	x3	ADJ
iajs-554	122	13	+	+	PROPN
iajs-554	122	14	0.814275	0.814275	NUM
iajs-554	122	15	x4	x4	PROPN
iajs-554	122	16	=	=	VERB
iajs-554	122	17	0.109844	0.109844	NUM
iajs-554	122	18	…	…	PUNCT
iajs-554	122	19	.(14	.(14	X
iajs-554	122	20	)	)	PUNCT
iajs-554	122	21	0.982176	0.982176	NUM
iajs-554	122	22	x4	x4	NOUN
iajs-554	123	1	=	=	NOUN
iajs-554	123	2	0.602286	0.602286	NUM
iajs-554	123	3	of	of	ADP
iajs-554	123	4	peters	peters	PROPN
iajs-554	123	5	-	-	PUNCT
iajs-554	123	6	wilkinson	wilkinson	PROPN
iajs-554	123	7	[	[	X
iajs-554	123	8	2].table	2].table	ADJ
iajs-554	123	9	1	1	NUM
iajs-554	123	10	contains	contain	VERB
iajs-554	123	11	the	the	DET
iajs-554	123	12	condition	condition	NOUN
iajs-554	123	13	numbers	number	NOUN
iajs-554	123	14	,	,	PUNCT
iajs-554	123	15	stability	stability	NOUN
iajs-554	123	16	constants	constant	NOUN
iajs-554	123	17	and	and	CCONJ
iajs-554	123	18	the	the	DET
iajs-554	123	19	solution	solution	NOUN
iajs-554	123	20	by	by	ADP
iajs-554	123	21	jordan	jordan	PROPN
iajs-554	123	22	elimination	elimination	PROPN
iajs-554	123	23	which	which	PRON
iajs-554	123	24	were	be	AUX
iajs-554	123	25	computed	compute	VERB
iajs-554	123	26	in	in	ADP
iajs-554	123	27	high	high	ADJ
iajs-554	123	28	accuracy	accuracy	NOUN
iajs-554	123	29	and	and	CCONJ
iajs-554	123	30	then	then	ADV
iajs-554	123	31	rounded	rounded	ADJ
iajs-554	123	32	to	to	ADP
iajs-554	123	33	6	6	NUM
iajs-554	123	34	decimal	decimal	ADJ
iajs-554	123	35	digits	digit	NOUN
iajs-554	123	36	.	.	PUNCT
iajs-554	124	1	table	table	NOUN
iajs-554	124	2	2	2	NUM
iajs-554	124	3	shows	show	VERB
iajs-554	124	4	the	the	DET
iajs-554	124	5	corresponding	corresponding	ADJ
iajs-554	124	6	results	result	NOUN
iajs-554	124	7	of	of	ADP
iajs-554	124	8	the	the	DET
iajs-554	124	9	solution	solution	NOUN
iajs-554	124	10	by	by	ADP
iajs-554	124	11	back	back	ADJ
iajs-554	124	12	substitution	substitution	NOUN
iajs-554	124	13	.	.	PUNCT
iajs-554	125	1	since	since	SCONJ
iajs-554	125	2	the	the	DET
iajs-554	125	3	data	data	NOUN
iajs-554	125	4	condition	condition	NOUN
iajs-554	125	5	numbers	number	NOUN
iajs-554	126	1	d	d	X
iajs-554	126	2	i	i	PRON
iajs-554	127	1	d	d	VERB
iajs-554	127	2	i	i	PRON
iajs-554	127	3	τρ	τρ	ADV
iajs-554	127	4	,	,	PUNCT
iajs-554	127	5	in	in	ADP
iajs-554	127	6	essence	essence	NOUN
iajs-554	127	7	,	,	PUNCT
iajs-554	127	8	depend	depend	VERB
iajs-554	127	9	on	on	ADP
iajs-554	127	10	the	the	DET
iajs-554	127	11	problem	problem	NOUN
iajs-554	127	12	only	only	ADV
iajs-554	127	13	but	but	CCONJ
iajs-554	127	14	not	not	PART
iajs-554	127	15	on	on	ADP
iajs-554	127	16	the	the	DET
iajs-554	127	17	algorithm	algorithm	NOUN
iajs-554	127	18	these	these	DET
iajs-554	127	19	condition	condition	NOUN
iajs-554	127	20	numbers	number	NOUN
iajs-554	127	21	coincide	coincide	VERB
iajs-554	127	22	in	in	ADP
iajs-554	127	23	both	both	DET
iajs-554	127	24	algorithms	algorithm	NOUN
iajs-554	127	25	in	in	ADP
iajs-554	127	26	the	the	DET
iajs-554	127	27	first	first	ADJ
iajs-554	127	28	6	6	NUM
iajs-554	127	29	digits	digit	NOUN
iajs-554	127	30	.	.	PUNCT
iajs-554	128	1	the	the	DET
iajs-554	128	2	residual	residual	ADJ
iajs-554	128	3	condition	condition	NOUN
iajs-554	128	4	number	number	NOUN
iajs-554	128	5	3343	3343	NUM
iajs-554	128	6	,	,	PUNCT
iajs-554	128	7	=	=	NOUN
iajs-554	128	8	r	r	NOUN
iajs-554	128	9	jiτ	jiτ	NOUN
iajs-554	128	10	of	of	ADP
iajs-554	128	11	the	the	DET
iajs-554	128	12	jordan	jordan	PROPN
iajs-554	128	13	solution	solution	NOUN
iajs-554	128	14	and	and	CCONJ
iajs-554	128	15	the	the	DET
iajs-554	128	16	corresponding	corresponding	ADJ
iajs-554	128	17	residual	residual	ADJ
iajs-554	128	18	stability	stability	NOUN
iajs-554	128	19	constant	constant	VERB
iajs-554	128	20	1699,1	1699,1	NOUN
iajs-554	129	1	=	=	PRON
iajs-554	129	2	jψ	jψ	NOUN
iajs-554	129	3	(	(	PUNCT
iajs-554	129	4	see	see	VERB
iajs-554	129	5	table	table	NOUN
iajs-554	129	6	1	1	NUM
iajs-554	129	7	)	)	PUNCT
iajs-554	129	8	are	be	AUX
iajs-554	129	9	much	much	ADV
iajs-554	129	10	bigger	big	ADJ
iajs-554	129	11	in	in	ADP
iajs-554	129	12	this	this	DET
iajs-554	129	13	example	example	NOUN
iajs-554	129	14	than	than	ADP
iajs-554	129	15	those	those	PRON
iajs-554	129	16	of	of	ADP
iajs-554	129	17	the	the	DET
iajs-554	129	18	solution	solution	NOUN
iajs-554	129	19	by	by	ADP
iajs-554	129	20	back	back	ADJ
iajs-554	129	21	substitution	substitution	NOUN
iajs-554	129	22	where	where	SCONJ
iajs-554	129	23	3.1	3.1	NUM
iajs-554	129	24	,	,	PUNCT
iajs-554	129	25	≤	≤	NUM
iajs-554	129	26	gj	gj	NOUN
iajs-554	129	27	ψ	ψ	NOUN
iajs-554	129	28	for	for	ADP
iajs-554	129	29	j=1	j=1	PROPN
iajs-554	129	30	,	,	PUNCT
iajs-554	129	31	…	…	PUNCT
iajs-554	129	32	,	,	PUNCT
iajs-554	129	33	4	4	X
iajs-554	129	34	.	.	PUNCT
iajs-554	130	1	(	(	PUNCT
iajs-554	130	2	see	see	VERB
iajs-554	130	3	table	table	NOUN
iajs-554	130	4	2	2	NUM
iajs-554	130	5	)	)	PUNCT
iajs-554	130	6	in	in	ADP
iajs-554	130	7	contrast	contrast	NOUN
iajs-554	130	8	,	,	PUNCT
iajs-554	130	9	the	the	DET
iajs-554	130	10	relative	relative	ADJ
iajs-554	130	11	rounding	round	VERB
iajs-554	130	12	condition	condition	NOUN
iajs-554	130	13	numbers	number	NOUN
iajs-554	130	14	of	of	ADP
iajs-554	130	15	the	the	DET
iajs-554	130	16	solutions	solution	NOUN
iajs-554	130	17	and	and	CCONJ
iajs-554	130	18	thus	thus	ADV
iajs-554	130	19	the	the	DET
iajs-554	130	20	solution	solution	NOUN
iajs-554	130	21	stability	stability	NOUN
iajs-554	130	22	constants	constant	VERB
iajs-554	130	23	iw	iw	INTJ
iajs-554	130	24	do	do	AUX
iajs-554	130	25	not	not	PART
iajs-554	130	26	differ	differ	VERB
iajs-554	130	27	much	much	ADJ
iajs-554	130	28	for	for	ADP
iajs-554	130	29	the	the	DET
iajs-554	130	30	two	two	NUM
iajs-554	130	31	algorithms	algorithm	NOUN
iajs-554	130	32	.	.	PUNCT
iajs-554	131	1	2	2	X
iajs-554	131	2	.	.	X
iajs-554	131	3	the	the	DET
iajs-554	131	4	second	second	ADJ
iajs-554	131	5	example	example	NOUN
iajs-554	131	6	is	be	AUX
iajs-554	131	7	a	a	DET
iajs-554	131	8	linear	linear	ADJ
iajs-554	131	9	system	system	NOUN
iajs-554	131	10	with	with	ADP
iajs-554	131	11	the	the	DET
iajs-554	131	12	5×5	5×5	NUM
iajs-554	131	13	hilbert	hilbert	NOUN
iajs-554	131	14	matrix	matrix	NOUN
iajs-554	131	15	a	a	PRON
iajs-554	131	16	of	of	ADP
iajs-554	131	17	wilkinson	wilkinson	PROPN
iajs-554	131	18	[	[	X
iajs-554	131	19	10	10	NUM
iajs-554	131	20	,	,	PUNCT
iajs-554	131	21	iii	iii	NOUN
iajs-554	131	22	,	,	PUNCT
iajs-554	131	23	34	34	NUM
iajs-554	131	24	]	]	PUNCT
iajs-554	131	25	and	and	CCONJ
iajs-554	131	26	the	the	DET
iajs-554	131	27	right	right	ADJ
iajs-554	131	28	-	-	PUNCT
iajs-554	131	29	hand	hand	NOUN
iajs-554	131	30	side	side	NOUN
iajs-554	131	31	1	1	NUM
iajs-554	131	32	.	.	PUNCT
iajs-554	131	33	)	)	PUNCT
iajs-554	132	1	1,1,1,1,1(,;1	1,1,1,1,1(,;1	NUM
iajs-554	132	2	10	10	NUM
iajs-554	132	3	!	!	PUNCT
iajs-554	133	1	10	10	NUM
iajs-554	133	2	*	*	SYM
iajs-554	133	3	50	50	NUM
iajs-554	133	4	5,	5,	NUM
iajs-554	133	5	...	...	PUNCT
iajs-554	133	6	,1	,1	NOUN
iajs-554	133	7	,	,	PUNCT
iajs-554	133	8	8	8	NUM
iajs-554	133	9	=	=	NOUN
iajs-554	133	10			NOUN
iajs-554	133	11			PUNCT
iajs-554	134	1			PROPN
iajs-554	134	2			NOUN
iajs-554	134	3			NOUN
iajs-554	134	4			VERB
iajs-554	134	5	+	+	CCONJ
iajs-554	135	1	=	=	NOUN
iajs-554	135	2	α	α	NOUN
iajs-554	135	3	=	=	PUNCT
iajs-554	135	4	t	t	X
iajs-554	135	5	ki	ki	PROPN
iajs-554	136	1	y	y	PROPN
iajs-554	136	2	ki	ki	PROPN
iajs-554	136	3	…	…	PUNCT
iajs-554	136	4	.(15	.(15	X
iajs-554	136	5	)	)	PUNCT
iajs-554	137	1	the	the	DET
iajs-554	137	2	first	first	ADJ
iajs-554	137	3	6	6	NUM
iajs-554	137	4	digit	digit	NOUN
iajs-554	137	5	of	of	ADP
iajs-554	137	6	the	the	DET
iajs-554	137	7	solution	solution	NOUN
iajs-554	137	8	,	,	PUNCT
iajs-554	137	9	the	the	DET
iajs-554	137	10	condition	condition	NOUN
iajs-554	137	11	numbers	number	NOUN
iajs-554	137	12	and	and	CCONJ
iajs-554	137	13	stability	stability	NOUN
iajs-554	137	14	constants	constant	NOUN
iajs-554	137	15	for	for	ADP
iajs-554	137	16	gaussjordan	gaussjordan	PROPN
iajs-554	137	17	elimination	elimination	NOUN
iajs-554	137	18	and	and	CCONJ
iajs-554	137	19	gaussian	gaussian	ADJ
iajs-554	137	20	elimination	elimination	NOUN
iajs-554	137	21	,	,	PUNCT
iajs-554	137	22	all	all	PRON
iajs-554	137	23	computed	compute	VERB
iajs-554	137	24	in	in	ADP
iajs-554	137	25	high	high	ADJ
iajs-554	137	26	accuracy	accuracy	NOUN
iajs-554	137	27	,	,	PUNCT
iajs-554	137	28	are	be	AUX
iajs-554	137	29	found	find	VERB
iajs-554	137	30	in	in	ADP
iajs-554	137	31	table	table	NOUN
iajs-554	137	32	3	3	NUM
iajs-554	137	33	and	and	CCONJ
iajs-554	137	34	table	table	NOUN
iajs-554	137	35	4	4	NUM
iajs-554	137	36	.	.	PUNCT
iajs-554	138	1	the	the	DET
iajs-554	138	2	matrix	matrix	NOUN
iajs-554	138	3	a	a	PRON
iajs-554	138	4	is	be	AUX
iajs-554	138	5	ill	ill	ADV
iajs-554	138	6	-	-	PUNCT
iajs-554	138	7	conditioned	condition	VERB
iajs-554	138	8	so	so	SCONJ
iajs-554	138	9	that	that	SCONJ
iajs-554	138	10	the	the	DET
iajs-554	138	11	relative	relative	ADJ
iajs-554	138	12	data	datum	NOUN
iajs-554	138	13	and	and	CCONJ
iajs-554	138	14	rounding	round	VERB
iajs-554	138	15	condition	condition	NOUN
iajs-554	138	16	numbers	number	NOUN
iajs-554	139	1	r	r	NOUN
iajs-554	139	2	i	i	NOUN
iajs-554	140	1	d	d	NOUN
iajs-554	140	2	i	i	PRON
iajs-554	140	3	ρρ	ρρ	PROPN
iajs-554	140	4	,	,	PUNCT
iajs-554	140	5	are	be	AUX
iajs-554	140	6	big	big	ADJ
iajs-554	140	7	in	in	ADP
iajs-554	140	8	value	value	NOUN
iajs-554	140	9	.	.	PUNCT
iajs-554	141	1	the	the	DET
iajs-554	141	2	relative	relative	ADJ
iajs-554	141	3	error	error	NOUN
iajs-554	141	4	of	of	ADP
iajs-554	141	5	the	the	DET
iajs-554	141	6	computed	compute	VERB
iajs-554	141	7	solution	solution	NOUN
iajs-554	141	8	may	may	AUX
iajs-554	141	9	effect	effect	VERB
iajs-554	141	10	up	up	ADP
iajs-554	141	11	to	to	PART
iajs-554	141	12	6	6	NUM
iajs-554	141	13	decimal	decimal	ADJ
iajs-554	141	14	digits	digit	NOUN
iajs-554	141	15	.	.	PUNCT
iajs-554	142	1	nevertheless	nevertheless	ADV
iajs-554	142	2	,	,	PUNCT
iajs-554	142	3	the	the	DET
iajs-554	142	4	maximal	maximal	ADJ
iajs-554	142	5	residual	residual	ADJ
iajs-554	142	6	stability	stability	NOUN
iajs-554	142	7	constant	constant	ADJ
iajs-554	142	8	5.15	5.15	NUM
iajs-554	142	9	,	,	PUNCT
iajs-554	142	10	=	=	NOUN
iajs-554	142	11	jiψ	jiψ	NOUN
iajs-554	142	12	of	of	ADP
iajs-554	142	13	gauss	gauss	PROPN
iajs-554	142	14	-	-	PUNCT
iajs-554	142	15	jordan	jordan	PROPN
iajs-554	142	16	elimination	elimination	NOUN
iajs-554	142	17	is	be	AUX
iajs-554	142	18	only	only	ADV
iajs-554	142	19	about	about	ADV
iajs-554	142	20	5.3times	5.3times	NUM
iajs-554	142	21	bigger	big	ADJ
iajs-554	142	22	than	than	ADP
iajs-554	142	23	the	the	DET
iajs-554	142	24	maximal	maximal	ADJ
iajs-554	142	25	residual	residual	ADJ
iajs-554	142	26	stability	stability	NOUN
iajs-554	142	27	constant	constant	ADJ
iajs-554	142	28	9.2,4	9.2,4	NOUN
iajs-554	142	29	=	=	VERB
iajs-554	142	30	gψ	gψ	NOUN
iajs-554	142	31	of	of	ADP
iajs-554	142	32	gaussian	gaussian	ADJ
iajs-554	142	33	elimination	elimination	NOUN
iajs-554	142	34	.	.	PUNCT
iajs-554	143	1	mathematics	mathematic	NOUN
iajs-554	143	2	374	374	NUM
iajs-554	143	3	مجلة	مجلة	NOUN
iajs-554	143	4	إبن	إبن	NOUN
iajs-554	143	5	الهيثم	الهيثم	ADJ
iajs-554	143	6	للعلوم	للعلوم	NOUN
iajs-554	143	7	الصرفة	الصرفة	NOUN
iajs-554	143	8	و	و	PRON
iajs-554	143	9	التطبيقية	التطبيقية	ADJ
iajs-554	143	10	2012	2012	NUM
iajs-554	143	11	السنة	السنة	NOUN
iajs-554	143	12	25	25	NUM
iajs-554	143	13	المجلد	المجلد	NOUN
iajs-554	143	14	3	3	NUM
iajs-554	143	15	العدد	العدد	PROPN
iajs-554	143	16	ibn	ibn	PROPN
iajs-554	143	17	al	al	PROPN
iajs-554	143	18	-	-	PUNCT
iajs-554	143	19	haitham	haitham	PROPN
iajs-554	143	20	journal	journal	PROPN
iajs-554	143	21	for	for	ADP
iajs-554	143	22	pure	pure	ADJ
iajs-554	143	23	and	and	CCONJ
iajs-554	143	24	applied	apply	VERB
iajs-554	143	25	science	science	NOUN
iajs-554	143	26	no	no	NOUN
iajs-554	143	27	.	.	NOUN
iajs-554	143	28	3	3	NUM
iajs-554	143	29	vol	vol	NOUN
iajs-554	143	30	.	.	PUNCT
iajs-554	143	31	25	25	NUM
iajs-554	143	32	year	year	NOUN
iajs-554	143	33	2012	2012	NUM
iajs-554	143	34	the	the	DET
iajs-554	143	35	relative	relative	ADJ
iajs-554	143	36	rounding	round	VERB
iajs-554	143	37	condition	condition	NOUN
iajs-554	143	38	numbers	number	NOUN
iajs-554	143	39	r	r	NOUN
iajs-554	143	40	iρ	iρ	NOUN
iajs-554	143	41	of	of	ADP
iajs-554	143	42	the	the	DET
iajs-554	143	43	two	two	NUM
iajs-554	143	44	algorithms	algorithm	NOUN
iajs-554	143	45	are	be	AUX
iajs-554	143	46	practically	practically	ADV
iajs-554	143	47	equal	equal	ADJ
iajs-554	143	48	.	.	PUNCT
iajs-554	144	1	therefore	therefore	ADV
iajs-554	144	2	also	also	ADV
iajs-554	144	3	the	the	DET
iajs-554	144	4	stability	stability	NOUN
iajs-554	144	5	constants	constant	VERB
iajs-554	144	6	wi	wi	PROPN
iajs-554	144	7	of	of	ADP
iajs-554	144	8	the	the	DET
iajs-554	144	9	two	two	NUM
iajs-554	144	10	algorithms	algorithm	NOUN
iajs-554	144	11	coincide	coincide	NOUN
iajs-554	144	12	in	in	ADP
iajs-554	144	13	the	the	DET
iajs-554	144	14	leading	lead	VERB
iajs-554	144	15	decimal	decimal	ADJ
iajs-554	144	16	digits	digit	NOUN
iajs-554	144	17	.	.	PUNCT
iajs-554	145	1	conclusion	conclusion	NOUN
iajs-554	145	2	error	error	NOUN
iajs-554	145	3	and	and	CCONJ
iajs-554	145	4	residual	residual	ADJ
iajs-554	145	5	bounds	bound	NOUN
iajs-554	145	6	can	can	AUX
iajs-554	145	7	be	be	AUX
iajs-554	145	8	computed	compute	VERB
iajs-554	145	9	numerically	numerically	ADV
iajs-554	145	10	together	together	ADV
iajs-554	145	11	with	with	ADP
iajs-554	145	12	the	the	DET
iajs-554	145	13	solutions	solution	NOUN
iajs-554	145	14	of	of	ADP
iajs-554	145	15	the	the	DET
iajs-554	145	16	linear	linear	PROPN
iajs-554	145	17	systems	system	NOUN
iajs-554	145	18	.	.	PUNCT
iajs-554	146	1	the	the	DET
iajs-554	146	2	calculated	calculate	VERB
iajs-554	146	3	condition	condition	NOUN
iajs-554	146	4	numbers	number	NOUN
iajs-554	146	5	and	and	CCONJ
iajs-554	146	6	stability	stability	NOUN
iajs-554	146	7	constants	constant	NOUN
iajs-554	146	8	of	of	ADP
iajs-554	146	9	the	the	DET
iajs-554	146	10	solutions	solution	NOUN
iajs-554	146	11	by	by	ADP
iajs-554	146	12	gauss	gauss	PROPN
iajs-554	146	13	-	-	PUNCT
iajs-554	146	14	jordan	jordan	PROPN
iajs-554	146	15	elimination	elimination	NOUN
iajs-554	146	16	as	as	ADV
iajs-554	146	17	well	well	ADV
iajs-554	146	18	as	as	ADP
iajs-554	146	19	by	by	ADP
iajs-554	146	20	gaussian	gaussian	ADJ
iajs-554	146	21	elimination	elimination	NOUN
iajs-554	146	22	are	be	AUX
iajs-554	146	23	determined	determine	VERB
iajs-554	146	24	.	.	PUNCT
iajs-554	147	1	the	the	DET
iajs-554	147	2	examples	example	NOUN
iajs-554	147	3	show	show	VERB
iajs-554	147	4	in	in	ADP
iajs-554	147	5	accordance	accordance	NOUN
iajs-554	147	6	with	with	ADP
iajs-554	147	7	the	the	DET
iajs-554	147	8	theoretical	theoretical	ADJ
iajs-554	147	9	results	result	NOUN
iajs-554	147	10	that	that	PRON
iajs-554	147	11	the	the	DET
iajs-554	147	12	numerical	numerical	ADJ
iajs-554	147	13	solutions	solution	NOUN
iajs-554	147	14	by	by	ADP
iajs-554	147	15	the	the	DET
iajs-554	147	16	two	two	NUM
iajs-554	147	17	methods	method	NOUN
iajs-554	147	18	are	be	AUX
iajs-554	147	19	of	of	ADP
iajs-554	147	20	comparable	comparable	ADJ
iajs-554	147	21	accuracy	accuracy	NOUN
iajs-554	147	22	in	in	ADP
iajs-554	147	23	spite	spite	NOUN
iajs-554	147	24	of	of	ADP
iajs-554	147	25	the	the	DET
iajs-554	147	26	ill	ill	ADV
iajs-554	147	27	-	-	PUNCT
iajs-554	147	28	conditioning	conditioning	NOUN
iajs-554	147	29	of	of	ADP
iajs-554	147	30	the	the	DET
iajs-554	147	31	two	two	NUM
iajs-554	147	32	problems	problem	NOUN
iajs-554	147	33	.	.	PUNCT
iajs-554	148	1	references	reference	NOUN
iajs-554	148	2	1	1	NUM
iajs-554	148	3	.	.	PUNCT
iajs-554	148	4	schonauer	schonauer	PROPN
iajs-554	148	5	,	,	PUNCT
iajs-554	148	6	w.	w.	PROPN
iajs-554	148	7	(	(	PUNCT
iajs-554	148	8	1987	1987	NUM
iajs-554	148	9	)	)	PUNCT
iajs-554	148	10	"	"	PUNCT
iajs-554	148	11	scientific	scientific	ADJ
iajs-554	148	12	computing	computing	NOUN
iajs-554	148	13	on	on	ADP
iajs-554	148	14	vector	vector	NOUN
iajs-554	148	15	computers	computer	NOUN
iajs-554	148	16	"	"	PUNCT
iajs-554	148	17	elsevier	elsevier	PROPN
iajs-554	148	18	science	science	PROPN
iajs-554	148	19	publish	publish	PROPN
iajs-554	148	20	b.	b.	PROPN
iajs-554	149	1	v.	v.	CCONJ
iajs-554	149	2	north	north	PROPN
iajs-554	149	3	-	-	PUNCT
iajs-554	149	4	holland	holland	NOUN
iajs-554	149	5	,	,	PUNCT
iajs-554	149	6	amstrdam	amstrdam	NOUN
iajs-554	149	7	,	,	PUNCT
iajs-554	149	8	.	.	PUNCT
iajs-554	150	1	2	2	X
iajs-554	150	2	.	.	X
iajs-554	150	3	stummel	stummel	VERB
iajs-554	150	4	,	,	PUNCT
iajs-554	150	5	f.(1986	f.(1986	PROPN
iajs-554	150	6	)	)	PUNCT
iajs-554	150	7	"	"	PUNCT
iajs-554	150	8	strict	strict	ADJ
iajs-554	150	9	optimal	optimal	ADJ
iajs-554	150	10	a	a	DET
iajs-554	150	11	posterior	posterior	NOUN
iajs-554	150	12	:	:	PUNCT
iajs-554	150	13	error	error	NOUN
iajs-554	150	14	and	and	CCONJ
iajs-554	150	15	residual	residual	ADJ
iajs-554	150	16	bounds	bound	NOUN
iajs-554	150	17	for	for	ADP
iajs-554	150	18	gaussian	gaussian	ADJ
iajs-554	150	19	elimination	elimination	NOUN
iajs-554	150	20	in	in	ADP
iajs-554	150	21	floating	float	VERB
iajs-554	150	22	-	-	PUNCT
iajs-554	150	23	point	point	NOUN
iajs-554	150	24	arithmetic	arithmetic	NOUN
iajs-554	150	25	"	"	PUNCT
iajs-554	150	26	.	.	PUNCT
iajs-554	151	1	computing	computing	NOUN
iajs-554	151	2	,	,	PUNCT
iajs-554	151	3	37	37	NUM
iajs-554	151	4	:	:	SYM
iajs-554	151	5	103	103	NUM
iajs-554	151	6	-	-	SYM
iajs-554	151	7	124	124	NUM
iajs-554	151	8	.	.	PUNCT
iajs-554	152	1	3	3	X
iajs-554	152	2	.	.	X
iajs-554	152	3	peters	peters	PROPN
iajs-554	152	4	,	,	PUNCT
iajs-554	152	5	g.	g.	PROPN
iajs-554	152	6	,	,	PUNCT
iajs-554	152	7	and	and	CCONJ
iajs-554	152	8	wilkinson	wilkinson	PROPN
iajs-554	152	9	,	,	PUNCT
iajs-554	152	10	j.	j.	PROPN
iajs-554	152	11	h.	h.	PROPN
iajs-554	152	12	(	(	PUNCT
iajs-554	152	13	1975	1975	NUM
iajs-554	152	14	)	)	PUNCT
iajs-554	152	15	"	"	PUNCT
iajs-554	152	16	on	on	ADP
iajs-554	152	17	the	the	DET
iajs-554	152	18	stability	stability	NOUN
iajs-554	152	19	of	of	ADP
iajs-554	152	20	gaussjordan	gaussjordan	PROPN
iajs-554	152	21	elimination	elimination	NOUN
iajs-554	152	22	with	with	ADP
iajs-554	152	23	pivoting	pivot	VERB
iajs-554	152	24	"	"	PUNCT
iajs-554	152	25	,	,	PUNCT
iajs-554	152	26	commun	commun	PROPN
iajs-554	152	27	,	,	PUNCT
iajs-554	152	28	acm	acm	PROPN
iajs-554	152	29	.	.	PUNCT
iajs-554	153	1	18	18	NUM
iajs-554	153	2	:	:	SYM
iajs-554	153	3	20	20	NUM
iajs-554	153	4	-	-	SYM
iajs-554	153	5	24	24	NUM
iajs-554	153	6	.	.	PUNCT
iajs-554	154	1	4	4	NUM
iajs-554	154	2	.	.	X
iajs-554	154	3	stummel	stummel	VERB
iajs-554	154	4	,	,	PUNCT
iajs-554	154	5	f.	f.	PROPN
iajs-554	154	6	,(1985	,(1985	PROPN
iajs-554	154	7	)	)	PUNCT
iajs-554	155	1	,	,	PUNCT
iajs-554	155	2	"	"	PUNCT
iajs-554	155	3	forward	forward	ADV
iajs-554	155	4	errors	error	VERB
iajs-554	155	5	analysis	analysis	NOUN
iajs-554	155	6	of	of	ADP
iajs-554	155	7	gaussian	gaussian	ADJ
iajs-554	155	8	elimination	elimination	NOUN
iajs-554	155	9	"	"	PUNCT
iajs-554	155	10	,	,	PUNCT
iajs-554	155	11	numer	numer	PROPN
iajs-554	155	12	,	,	PUNCT
iajs-554	155	13	math	math	NOUN
iajs-554	155	14	.	.	PUNCT
iajs-554	156	1	46	46	NUM
iajs-554	156	2	:	:	PUNCT
iajs-554	156	3	365	365	NUM
iajs-554	156	4	-	-	SYM
iajs-554	156	5	415	415	NUM
iajs-554	156	6	.	.	PUNCT
iajs-554	157	1	5	5	X
iajs-554	157	2	.	.	X
iajs-554	157	3	stummel	stummel	VERB
iajs-554	157	4	,	,	PUNCT
iajs-554	157	5	f.(1985),"fortran	f.(1985),"fortran	NOUN
iajs-554	157	6	-	-	PUNCT
iajs-554	157	7	programs	program	NOUN
iajs-554	157	8	for	for	ADP
iajs-554	157	9	the	the	DET
iajs-554	157	10	rounding	round	VERB
iajs-554	157	11	error	error	NOUN
iajs-554	157	12	analysis	analysis	NOUN
iajs-554	157	13	of	of	ADP
iajs-554	157	14	gaussian	gaussian	ADJ
iajs-554	157	15	elimination	elimination	NOUN
iajs-554	157	16	"	"	PUNCT
iajs-554	157	17	.	.	PUNCT
iajs-554	158	1	center	center	VERB
iajs-554	158	2	for	for	ADP
iajs-554	158	3	mathematical	mathematical	ADJ
iajs-554	158	4	analysis	analysis	NOUN
iajs-554	158	5	,	,	PUNCT
iajs-554	158	6	the	the	DET
iajs-554	158	7	australian	australian	ADJ
iajs-554	158	8	national	national	PROPN
iajs-554	158	9	university	university	PROPN
iajs-554	158	10	,	,	PUNCT
iajs-554	158	11	canberra	canberra	PROPN
iajs-554	158	12	,	,	PUNCT
iajs-554	158	13	cma	cma	NOUN
iajs-554	158	14	,	,	PUNCT
iajs-554	158	15	.	.	PUNCT
iajs-554	159	1	p.	p.	NOUN
iajs-554	159	2	72	72	NUM
iajs-554	159	3	-	-	SYM
iajs-554	159	4	85	85	NUM
iajs-554	159	5	.	.	NOUN
iajs-554	159	6	6	6	NUM
iajs-554	159	7	.	.	X
iajs-554	159	8	neumaier	neumai	ADJ
iajs-554	159	9	,	,	PUNCT
iajs-554	159	10	a.	a.	NOUN
iajs-554	159	11	,	,	PUNCT
iajs-554	159	12	(	(	PUNCT
iajs-554	159	13	1990	1990	NUM
iajs-554	159	14	)	)	PUNCT
iajs-554	159	15	,	,	PUNCT
iajs-554	159	16	"	"	PUNCT
iajs-554	159	17	interval	interval	NOUN
iajs-554	159	18	methods	method	NOUN
iajs-554	159	19	for	for	ADP
iajs-554	159	20	systems	system	NOUN
iajs-554	159	21	of	of	ADP
iajs-554	159	22	equations	equation	NOUN
iajs-554	159	23	"	"	PUNCT
iajs-554	159	24	,	,	PUNCT
iajs-554	159	25	cambridge	cambridge	PROPN
iajs-554	159	26	university	university	PROPN
iajs-554	159	27	press	press	PROPN
iajs-554	159	28	,	,	PUNCT
iajs-554	159	29	cambridge	cambridge	PROPN
iajs-554	159	30	.	.	PROPN
iajs-554	160	1	7	7	X
iajs-554	160	2	.	.	X
iajs-554	160	3	lipschutz	lipschutz	ADJ
iajs-554	160	4	,	,	PUNCT
iajs-554	160	5	seymour	seymour	ADJ
iajs-554	160	6	,	,	PUNCT
iajs-554	160	7	and	and	CCONJ
iajs-554	160	8	lipson	lipson	NOUN
iajs-554	160	9	,	,	PUNCT
iajs-554	160	10	(	(	PUNCT
iajs-554	160	11	2001	2001	NUM
iajs-554	160	12	)	)	PUNCT
iajs-554	160	13	"	"	PUNCT
iajs-554	160	14	schaum	schaum	PROPN
iajs-554	160	15	's	's	PART
iajs-554	160	16	out	out	ADJ
iajs-554	160	17	-	-	PUNCT
iajs-554	160	18	lines	line	NOUN
iajs-554	160	19	:	:	PUNCT
iajs-554	160	20	linear	linear	PROPN
iajs-554	160	21	algebra	algebra	PROPN
iajs-554	160	22	tata	tata	PROPN
iajs-554	160	23	mcgraw	mcgraw	PROPN
iajs-554	160	24	-	-	PUNCT
iajs-554	160	25	hill	hill	NOUN
iajs-554	160	26	edition	edition	NOUN
iajs-554	160	27	"	"	PUNCT
iajs-554	160	28	,	,	PUNCT
iajs-554	160	29	delhi	delhi	ADJ
iajs-554	160	30	,	,	PUNCT
iajs-554	160	31	9	9	NUM
iajs-554	160	32	:	:	SYM
iajs-554	160	33	568	568	NUM
iajs-554	160	34	.	.	NOUN
iajs-554	160	35	8	8	NUM
iajs-554	160	36	.	.	X
iajs-554	161	1	stummel	stummel	VERB
iajs-554	161	2	,	,	PUNCT
iajs-554	161	3	f.	f.	PROPN
iajs-554	161	4	(	(	PUNCT
iajs-554	161	5	1986	1986	NUM
iajs-554	161	6	)	)	PUNCT
iajs-554	161	7	"	"	PUNCT
iajs-554	161	8	strict	strict	ADJ
iajs-554	161	9	optimal	optimal	ADJ
iajs-554	161	10	error	error	NOUN
iajs-554	161	11	and	and	CCONJ
iajs-554	161	12	residual	residual	ADJ
iajs-554	161	13	estimates	estimate	NOUN
iajs-554	161	14	for	for	ADP
iajs-554	161	15	the	the	DET
iajs-554	161	16	solution	solution	NOUN
iajs-554	161	17	of	of	ADP
iajs-554	161	18	linear	linear	PROPN
iajs-554	161	19	algebraic	algebraic	ADJ
iajs-554	161	20	systems	system	NOUN
iajs-554	161	21	by	by	ADP
iajs-554	161	22	elimination	elimination	NOUN
iajs-554	161	23	method	method	NOUN
iajs-554	161	24	in	in	ADP
iajs-554	161	25	high	high	ADJ
iajs-554	161	26	-	-	PUNCT
iajs-554	161	27	accuracy	accuracy	NOUN
iajs-554	161	28	arithmetic	arithmetic	NOUN
iajs-554	161	29	"	"	PUNCT
iajs-554	161	30	,	,	PUNCT
iajs-554	161	31	proc	proc	PROPN
iajs-554	161	32	.	.	PROPN
iajs-554	161	33	,	,	PUNCT
iajs-554	161	34	symp	symp	PROPN
iajs-554	161	35	.	.	PUNCT
iajs-554	162	1	accurate	accurate	ADJ
iajs-554	162	2	scientific	scientific	ADJ
iajs-554	162	3	computation	computation	NOUN
iajs-554	162	4	,	,	PUNCT
iajs-554	162	5	bad	bad	ADJ
iajs-554	162	6	neuenahr	neuenahr	ADJ
iajs-554	162	7	1985	1985	NUM
iajs-554	162	8	,	,	PUNCT
iajs-554	162	9	eds	eds	PROPN
iajs-554	162	10	.	.	PUNCT
iajs-554	163	1	w.	w.	PROPN
iajs-554	163	2	l.	l.	PROPN
iajs-554	163	3	miranker	miranker	PROPN
iajs-554	163	4	,	,	PUNCT
iajs-554	163	5	r.	r.	PROPN
iajs-554	163	6	a.	a.	NOUN
iajs-554	163	7	toupin	toupin	PROPN
iajs-554	163	8	.	.	PUNCT
iajs-554	164	1	lecture	lecture	NOUN
iajs-554	164	2	notes	note	NOUN
iajs-554	164	3	in	in	ADP
iajs-554	164	4	computer	computer	NOUN
iajs-554	164	5	scince	scince	NOUN
iajs-554	164	6	,	,	PUNCT
iajs-554	164	7	235:119	235:119	NUM
iajs-554	164	8	-	-	SYM
iajs-554	164	9	141	141	NUM
iajs-554	164	10	.	.	PUNCT
iajs-554	165	1	9	9	NUM
iajs-554	165	2	.	.	X
iajs-554	166	1	gilbert	gilbert	PROPN
iajs-554	166	2	,	,	PUNCT
iajs-554	166	3	s.	s.	PROPN
iajs-554	166	4	(	(	PUNCT
iajs-554	166	5	2003),"siam	2003),"siam	PROPN
iajs-554	166	6	introduction	introduction	NOUN
iajs-554	166	7	to	to	ADP
iajs-554	166	8	linear	linear	PROPN
iajs-554	166	9	algebra	algebra	PROPN
iajs-554	166	10	"	"	PUNCT
iajs-554	166	11	,	,	PUNCT
iajs-554	166	12	3rd	3rd	ADJ
iajs-554	166	13	edition	edition	NOUN
iajs-554	166	14	,	,	PUNCT
iajs-554	166	15	wellesley	wellesley	PROPN
iajs-554	166	16	,	,	PUNCT
iajs-554	166	17	massachusetts	massachusetts	PROPN
iajs-554	166	18	:	:	PUNCT
iajs-554	166	19	wallesely	wallesely	ADJ
iajs-554	166	20	-	-	PUNCT
iajs-554	166	21	cambridge	cambridge	PROPN
iajs-554	166	22	press	press	NOUN
iajs-554	166	23	,	,	PUNCT
iajs-554	166	24	siam	siam	NOUN
iajs-554	166	25	,	,	PUNCT
iajs-554	166	26	book	book	NOUN
iajs-554	166	27	google	google	NOUN
iajs-554	166	28	,	,	PUNCT
iajs-554	166	29	p.	p.	NOUN
iajs-554	166	30	74	74	NUM
iajs-554	166	31	76	76	NUM
iajs-554	166	32	.	.	PUNCT
iajs-554	167	1	10	10	NUM
iajs-554	167	2	.	.	PUNCT
iajs-554	168	1	fox	fox	PROPN
iajs-554	168	2	,	,	PUNCT
iajs-554	168	3	l.	l.	PROPN
iajs-554	168	4	(	(	PUNCT
iajs-554	168	5	1964	1964	NUM
iajs-554	168	6	)	)	PUNCT
iajs-554	168	7	,	,	PUNCT
iajs-554	168	8	"	"	PUNCT
iajs-554	168	9	an	an	DET
iajs-554	168	10	introduction	introduction	NOUN
iajs-554	168	11	to	to	ADP
iajs-554	168	12	numerical	numerical	PROPN
iajs-554	168	13	linear	linear	PROPN
iajs-554	168	14	algebra	algebra	PROPN
iajs-554	168	15	"	"	PUNCT
iajs-554	168	16	,	,	PUNCT
iajs-554	168	17	clarendon	clarendon	PROPN
iajs-554	168	18	press	press	NOUN
iajs-554	168	19	,	,	PUNCT
iajs-554	168	20	oxford	oxford	PROPN
iajs-554	168	21	.	.	PUNCT
iajs-554	168	22	,	,	PUNCT
iajs-554	168	23	11	11	NUM
iajs-554	168	24	.	.	PUNCT
iajs-554	169	1	wilkinson	wilkinson	PROPN
iajs-554	169	2	,	,	PUNCT
iajs-554	169	3	j.	j.	PROPN
iajs-554	169	4	h.	h.	PROPN
iajs-554	169	5	(	(	PUNCT
iajs-554	169	6	1963),"rounding	1963),"rounding	NOUN
iajs-554	169	7	errors	error	NOUN
iajs-554	169	8	in	in	ADP
iajs-554	169	9	algebraic	algebraic	ADJ
iajs-554	169	10	processes	process	NOUN
iajs-554	169	11	"	"	PUNCT
iajs-554	169	12	,	,	PUNCT
iajs-554	169	13	prenticel	prenticel	PROPN
iajs-554	169	14	hall	hall	PROPN
iajs-554	169	15	,	,	PUNCT
iajs-554	169	16	englewood	englewood	PROPN
iajs-554	169	17	cliffs	cliff	NOUN
iajs-554	169	18	.	.	PUNCT
iajs-554	170	1	12	12	NUM
iajs-554	170	2	.	.	PUNCT
iajs-554	171	1	stummel	stummel	PROPN
iajs-554	171	2	,	,	PUNCT
iajs-554	171	3	f.	f.	PROPN
iajs-554	171	4	(	(	PUNCT
iajs-554	171	5	1986),"strict	1986),"strict	PROPN
iajs-554	171	6	optimal	optimal	ADJ
iajs-554	171	7	a	a	DET
iajs-554	171	8	posteriori	posteriori	NOUN
iajs-554	171	9	error	error	NOUN
iajs-554	171	10	and	and	CCONJ
iajs-554	171	11	residual	residual	ADJ
iajs-554	171	12	bounds	bound	NOUN
iajs-554	171	13	for	for	ADP
iajs-554	171	14	gaussian	gaussian	ADJ
iajs-554	171	15	elimination	elimination	NOUN
iajs-554	171	16	in	in	ADP
iajs-554	171	17	floating	float	VERB
iajs-554	171	18	point	point	NOUN
iajs-554	171	19	arithmetic	arithmetic	ADJ
iajs-554	171	20	computing	computing	NOUN
iajs-554	171	21	"	"	PUNCT
iajs-554	171	22	,	,	PUNCT
iajs-554	171	23	37	37	NUM
iajs-554	171	24	:	:	SYM
iajs-554	171	25	103	103	NUM
iajs-554	171	26	–	–	SYM
iajs-554	171	27	124	124	NUM
iajs-554	171	28	.	.	NOUN
iajs-554	172	1	13	13	NUM
iajs-554	172	2	.	.	X
iajs-554	173	1	moore	moore	PROPN
iajs-554	173	2	,	,	PUNCT
iajs-554	173	3	r.	r.	PROPN
iajs-554	173	4	e.	e.	PROPN
iajs-554	173	5	(	(	PUNCT
iajs-554	173	6	1995),"the	1995),"the	DET
iajs-554	173	7	automatic	automatic	ADJ
iajs-554	173	8	analysis	analysis	NOUN
iajs-554	173	9	and	and	CCONJ
iajs-554	173	10	control	control	NOUN
iajs-554	173	11	of	of	ADP
iajs-554	173	12	error	error	NOUN
iajs-554	173	13	in	in	ADP
iajs-554	173	14	digital	digital	ADJ
iajs-554	173	15	computing	computing	NOUN
iajs-554	173	16	based	base	VERB
iajs-554	173	17	on	on	ADP
iajs-554	173	18	the	the	DET
iajs-554	173	19	use	use	NOUN
iajs-554	173	20	of	of	ADP
iajs-554	173	21	interval	interval	NOUN
iajs-554	173	22	numbers	number	NOUN
iajs-554	173	23	,	,	PUNCT
iajs-554	173	24	in	in	ADP
iajs-554	173	25	error	error	NOUN
iajs-554	173	26	in	in	ADP
iajs-554	173	27	digital	digital	ADJ
iajs-554	173	28	computation	computation	NOUN
iajs-554	173	29	"	"	PUNCT
iajs-554	173	30	new	new	PROPN
iajs-554	173	31	york	york	PROPN
iajs-554	173	32	,	,	PUNCT
iajs-554	173	33	1	1	NUM
iajs-554	173	34	:	:	SYM
iajs-554	173	35	30	30	NUM
iajs-554	173	36	-	-	SYM
iajs-554	173	37	61	61	NUM
iajs-554	173	38	.	.	PUNCT
iajs-554	174	1	mathematics	mathematic	NOUN
iajs-554	174	2	375	375	NUM
iajs-554	174	3	مجلة	مجلة	NOUN
iajs-554	174	4	إبن	إبن	VERB
iajs-554	174	5	الهيثم	الهيثم	ADJ
iajs-554	174	6	للعلوم	للعلوم	NOUN
iajs-554	174	7	الصرفة	الصرفة	NOUN
iajs-554	175	1	و	و	PRON
iajs-554	175	2	التطبيقية	التطبيقية	ADJ
iajs-554	175	3	2012	2012	NUM
iajs-554	175	4	السنة	السنة	NOUN
iajs-554	175	5	25	25	NUM
iajs-554	175	6	المجلد	المجلد	NOUN
iajs-554	175	7	3	3	NUM
iajs-554	175	8	العدد	العدد	PROPN
iajs-554	175	9	ibn	ibn	PROPN
iajs-554	175	10	al	al	PROPN
iajs-554	175	11	-	-	PUNCT
iajs-554	175	12	haitham	haitham	PROPN
iajs-554	175	13	journal	journal	PROPN
iajs-554	175	14	for	for	ADP
iajs-554	175	15	pure	pure	ADJ
iajs-554	175	16	and	and	CCONJ
iajs-554	175	17	applied	apply	VERB
iajs-554	175	18	science	science	NOUN
iajs-554	175	19	no	no	NOUN
iajs-554	175	20	.	.	NOUN
iajs-554	175	21	3	3	NUM
iajs-554	175	22	vol	vol	NOUN
iajs-554	175	23	.	.	PUNCT
iajs-554	176	1	25	25	NUM
iajs-554	176	2	year	year	NOUN
iajs-554	176	3	2012	2012	NUM
iajs-554	176	4	table(1	table(1	PROPN
iajs-554	176	5	):	):	PUNCT
iajs-554	176	6	condition	condition	NOUN
iajs-554	176	7	numbers	number	NOUN
iajs-554	176	8	,	,	PUNCT
iajs-554	176	9	stability	stability	NOUN
iajs-554	176	10	constants	constant	NOUN
iajs-554	176	11	and	and	CCONJ
iajs-554	176	12	solution	solution	NOUN
iajs-554	176	13	of	of	ADP
iajs-554	176	14	the	the	DET
iajs-554	176	15	jordan	jordan	PROPN
iajs-554	176	16	algorithm	algorithm	PROPN
iajs-554	176	17	for	for	ADP
iajs-554	176	18	triangular	triangular	NOUN
iajs-554	176	19	linear	linear	NOUN
iajs-554	176	20	system	system	NOUN
iajs-554	176	21	(	(	PUNCT
iajs-554	176	22	15	15	NUM
iajs-554	176	23	)	)	PUNCT
iajs-554	176	24	.	.	PUNCT
iajs-554	177	1	i	i	PRON
iajs-554	177	2	iχ	iχ	VERB
iajs-554	177	3	d	d	X
iajs-554	177	4	iρ	iρ	NOUN
iajs-554	177	5	r	r	NOUN
iajs-554	177	6	iρ	iρ	NOUN
iajs-554	177	7	iw	iw	NOUN
iajs-554	177	8	d	d	NOUN
iajs-554	177	9	iτ	iτ	NOUN
iajs-554	177	10	r	r	NOUN
iajs-554	177	11	iτ	iτ	NOUN
iajs-554	177	12	iψ	iψ	VERB
iajs-554	177	13	1	1	NUM
iajs-554	177	14	0.413155	0.413155	NUM
iajs-554	177	15	4639	4639	NUM
iajs-554	177	16	7207	7207	NUM
iajs-554	177	17	1.55	1.55	NUM
iajs-554	177	18	1.97	1.97	NUM
iajs-554	177	19	3343	3343	NUM
iajs-554	177	20	1699	1699	NUM
iajs-554	177	21	2	2	NUM
iajs-554	177	22	0.614928	0.614928	NUM
iajs-554	177	23	5955	5955	NUM
iajs-554	177	24	3313	3313	NUM
iajs-554	177	25	0.56	0.56	NUM
iajs-554	177	26	1.00	1.00	NUM
iajs-554	177	27	3.20	3.20	NUM
iajs-554	177	28	3.19	3.19	NUM
iajs-554	177	29	3	3	NUM
iajs-554	177	30	-0.425517	-0.425517	NOUN
iajs-554	177	31	5.13	5.13	NUM
iajs-554	177	32	4.56	4.56	NUM
iajs-554	177	33	0.89	0.89	NUM
iajs-554	177	34	0.99	0.99	NUM
iajs-554	177	35	2.28	2.28	NUM
iajs-554	177	36	2.28	2.28	NUM
iajs-554	177	37	4	4	NUM
iajs-554	177	38	0.613216	0.613216	NUM
iajs-554	177	39	2.00	2.00	NUM
iajs-554	177	40	1.00	1.00	NUM
iajs-554	177	41	0.50	0.50	NUM
iajs-554	177	42	1.21	1.21	NUM
iajs-554	177	43	0.60	0.60	NUM
iajs-554	177	44	0.50	0.50	NUM
iajs-554	178	1	table(2	table(2	NOUN
iajs-554	178	2	):	):	PUNCT
iajs-554	178	3	condition	condition	NOUN
iajs-554	178	4	numbers	number	NOUN
iajs-554	178	5	,	,	PUNCT
iajs-554	178	6	stability	stability	NOUN
iajs-554	178	7	constants	constant	NOUN
iajs-554	178	8	and	and	CCONJ
iajs-554	178	9	solution	solution	NOUN
iajs-554	178	10	by	by	ADP
iajs-554	178	11	back	back	ADJ
iajs-554	178	12	substitution	substitution	NOUN
iajs-554	178	13	of	of	ADP
iajs-554	178	14	the	the	DET
iajs-554	178	15	triangular	triangular	ADJ
iajs-554	178	16	linear	linear	NOUN
iajs-554	178	17	system	system	NOUN
iajs-554	178	18	(	(	PUNCT
iajs-554	178	19	15	15	NUM
iajs-554	178	20	)	)	PUNCT
iajs-554	178	21	.	.	PUNCT
iajs-554	179	1	i	i	PRON
iajs-554	179	2	iχ	iχ	VERB
iajs-554	179	3	d	d	X
iajs-554	179	4	iρ	iρ	NOUN
iajs-554	179	5	r	r	NOUN
iajs-554	179	6	iρ	iρ	NOUN
iajs-554	179	7	iw	iw	NOUN
iajs-554	179	8	d	d	NOUN
iajs-554	179	9	iτ	iτ	NOUN
iajs-554	179	10	r	r	NOUN
iajs-554	179	11	iτ	iτ	NOUN
iajs-554	179	12	iψ	iψ	VERB
iajs-554	179	13	1	1	NUM
iajs-554	179	14	0.413155	0.413155	NUM
iajs-554	179	15	4639	4639	NUM
iajs-554	179	16	5531	5531	NUM
iajs-554	179	17	1.19	1.19	NUM
iajs-554	179	18	1.97	1.97	NUM
iajs-554	179	19	2.54	2.54	NUM
iajs-554	179	20	1.29	1.29	NUM
iajs-554	179	21	2	2	NUM
iajs-554	179	22	0.614928	0.614928	NUM
iajs-554	179	23	5955	5955	NUM
iajs-554	179	24	7100	7100	NUM
iajs-554	179	25	1.19	1.19	NUM
iajs-554	179	26	1.00	1.00	NUM
iajs-554	179	27	1.19	1.19	NUM
iajs-554	179	28	1.19	1.19	NUM
iajs-554	179	29	3	3	NUM
iajs-554	179	30	-0.425517	-0.425517	NOUN
iajs-554	179	31	5.13	5.13	NUM
iajs-554	179	32	4.56	4.56	NUM
iajs-554	179	33	0.89	0.89	NUM
iajs-554	179	34	0.99	0.99	NUM
iajs-554	179	35	1.28	1.28	NUM
iajs-554	179	36	1.28	1.28	NUM
iajs-554	179	37	4	4	NUM
iajs-554	179	38	0.613216	0.613216	NUM
iajs-554	179	39	2.00	2.00	NUM
iajs-554	179	40	1.00	1.00	NUM
iajs-554	179	41	0.50	0.50	NUM
iajs-554	179	42	1.21	1.21	NUM
iajs-554	179	43	0.60	0.60	NUM
iajs-554	179	44	0.50	0.50	NUM
iajs-554	179	45	table(3	table(3	PROPN
iajs-554	179	46	):	):	PUNCT
iajs-554	179	47	condition	condition	NOUN
iajs-554	179	48	numbers	number	NOUN
iajs-554	179	49	,	,	PUNCT
iajs-554	179	50	stability	stability	NOUN
iajs-554	179	51	constants	constant	NOUN
iajs-554	179	52	and	and	CCONJ
iajs-554	179	53	solution	solution	NOUN
iajs-554	179	54	of	of	ADP
iajs-554	179	55	the	the	DET
iajs-554	179	56	“	"	PUNCT
iajs-554	179	57	gauss	gauss	ADJ
iajs-554	179	58	–	–	PUNCT
iajs-554	179	59	jordan	jordan	PROPN
iajs-554	179	60	”	"	PUNCT
iajs-554	179	61	algorithm	algorithm	NOUN
iajs-554	179	62	for	for	ADP
iajs-554	179	63	the	the	DET
iajs-554	179	64	linear	linear	ADJ
iajs-554	179	65	system	system	NOUN
iajs-554	179	66	ax	ax	NOUN
iajs-554	179	67	=	=	NOUN
iajs-554	179	68	y.	y.	NOUN
iajs-554	179	69	i	i	PRON
iajs-554	179	70	iχ	iχ	VERB
iajs-554	179	71	d	d	NOUN
iajs-554	179	72	iρ	iρ	NOUN
iajs-554	179	73	r	r	NOUN
iajs-554	179	74	iρ	iρ	NOUN
iajs-554	179	75	iw	iw	NOUN
iajs-554	179	76	d	d	NOUN
iajs-554	179	77	iτ	iτ	NOUN
iajs-554	179	78	r	r	NOUN
iajs-554	179	79	iτ	iτ	NOUN
iajs-554	179	80	iψ	iψ	VERB
iajs-554	179	81	1	1	NUM
iajs-554	179	82	1.65344	1.65344	NUM
iajs-554	179	83	1.07	1.07	NUM
iajs-554	179	84	1.36	1.36	NUM
iajs-554	179	85	1.27	1.27	NUM
iajs-554	179	86	1.29	1.29	NUM
iajs-554	179	87	2.00	2.00	NUM
iajs-554	179	88	15.5	15.5	NUM
iajs-554	179	89	2	2	NUM
iajs-554	179	90	-2.31481	-2.31481	NOUN
iajs-554	179	91	8.69	8.69	NUM
iajs-554	179	92	1.11	1.11	NUM
iajs-554	179	93	1.28	1.28	NUM
iajs-554	179	94	5.05	5.05	NUM
iajs-554	179	95	1.61	1.61	NUM
iajs-554	179	96	15.3	15.3	NUM
iajs-554	179	97	3	3	NUM
iajs-554	179	98	9.25926	9.25926	NUM
iajs-554	179	99	7.33	7.33	NUM
iajs-554	179	100	9.38	9.38	NUM
iajs-554	179	101	1.28	1.28	NUM
iajs-554	179	102	8.90	8.90	NUM
iajs-554	179	103	1.32	1.32	NUM
iajs-554	179	104	14.8	14.8	NUM
iajs-554	179	105	4	4	NUM
iajs-554	179	106	-1.38889	-1.38889	NOUN
iajs-554	179	107	6.34	6.34	NUM
iajs-554	179	108	8.13	8.13	NUM
iajs-554	179	109	1.28	1.28	NUM
iajs-554	179	110	7.72	7.72	NUM
iajs-554	179	111	1.12	1.12	NUM
iajs-554	179	112	14.5	14.5	NUM
iajs-554	179	113	5	5	NUM
iajs-554	179	114	6.94444	6.94444	NUM
iajs-554	179	115	5.59	5.59	NUM
iajs-554	179	116	7.18	7.18	NUM
iajs-554	179	117	1.28	1.28	NUM
iajs-554	179	118	6.82	6.82	NUM
iajs-554	179	119	9.69	9.69	NUM
iajs-554	179	120	14.2	14.2	NUM
iajs-554	179	121	table(4	table(4	NUM
iajs-554	179	122	):	):	PUNCT
iajs-554	179	123	condition	condition	NOUN
iajs-554	179	124	numbers	number	NOUN
iajs-554	179	125	,	,	PUNCT
iajs-554	179	126	stability	stability	NOUN
iajs-554	179	127	constants	constant	NOUN
iajs-554	179	128	and	and	CCONJ
iajs-554	179	129	solution	solution	NOUN
iajs-554	179	130	of	of	ADP
iajs-554	179	131	“	"	PUNCT
iajs-554	179	132	gaussian	gaussian	ADJ
iajs-554	179	133	elimination	elimination	NOUN
iajs-554	179	134	”	"	PUNCT
iajs-554	179	135	of	of	ADP
iajs-554	179	136	the	the	DET
iajs-554	179	137	linear	linear	ADJ
iajs-554	179	138	system	system	NOUN
iajs-554	179	139	ax	ax	NOUN
iajs-554	179	140	=	=	NOUN
iajs-554	179	141	y.	y.	NOUN
iajs-554	179	142	i	i	PRON
iajs-554	179	143	iχ	iχ	VERB
iajs-554	179	144	d	d	NOUN
iajs-554	179	145	iρ	iρ	NOUN
iajs-554	179	146	r	r	NOUN
iajs-554	179	147	iρ	iρ	NOUN
iajs-554	179	148	iw	iw	NOUN
iajs-554	179	149	d	d	NOUN
iajs-554	179	150	iτ	iτ	NOUN
iajs-554	179	151	r	r	NOUN
iajs-554	179	152	iτ	iτ	NOUN
iajs-554	179	153	iψ	iψ	VERB
iajs-554	179	154	1	1	NUM
iajs-554	179	155	1.65344	1.65344	NUM
iajs-554	179	156	1.07	1.07	NUM
iajs-554	179	157	1.36	1.36	NUM
iajs-554	179	158	1.27	1.27	NUM
iajs-554	179	159	1.29	1.29	NUM
iajs-554	179	160	1.93	1.93	NUM
iajs-554	179	161	1.50	1.50	NUM
iajs-554	179	162	2	2	NUM
iajs-554	179	163	-2.31481	-2.31481	NOUN
iajs-554	179	164	8.69	8.69	NUM
iajs-554	179	165	1.11	1.11	NUM
iajs-554	179	166	1.28	1.28	NUM
iajs-554	179	167	1.05	1.05	NUM
iajs-554	179	168	2.63	2.63	NUM
iajs-554	179	169	2.50	2.50	NUM
iajs-554	179	170	3	3	NUM
iajs-554	179	171	9.25926	9.25926	NUM
iajs-554	179	172	7.33	7.33	NUM
iajs-554	179	173	9.38	9.38	NUM
iajs-554	179	174	1.28	1.28	NUM
iajs-554	179	175	8.90	8.90	NUM
iajs-554	179	176	2.47	2.47	NUM
iajs-554	179	177	2.77	2.77	NUM
iajs-554	179	178	4	4	NUM
iajs-554	179	179	-1.38889	-1.38889	NOUN
iajs-554	179	180	6.34	6.34	NUM
iajs-554	179	181	8.13	8.13	NUM
iajs-554	179	182	1.28	1.28	NUM
iajs-554	179	183	7.72	7.72	NUM
iajs-554	179	184	2.21	2.21	NUM
iajs-554	179	185	2.86	2.86	NUM
iajs-554	179	186	5	5	NUM
iajs-554	179	187	6.94444	6.94444	NUM
iajs-554	179	188	5.59	5.59	NUM
iajs-554	179	189	7.18	7.18	NUM
iajs-554	179	190	1.29	1.29	NUM
iajs-554	179	191	6.82	6.82	NUM
iajs-554	179	192	1.99	1.99	NUM
iajs-554	179	193	2.92	2.92	NUM
iajs-554	179	194	mathematics	mathematic	NOUN
iajs-554	179	195	376	376	NUM
iajs-554	179	196	مجلة	مجلة	NOUN
iajs-554	179	197	إبن	إبن	VERB
iajs-554	179	198	الهيثم	الهيثم	ADJ
iajs-554	179	199	للعلوم	للعلوم	NOUN
iajs-554	179	200	الصرفة	الصرفة	NOUN
iajs-554	180	1	و	و	PRON
iajs-554	180	2	التطبيقية	التطبيقية	ADJ
iajs-554	180	3	2012	2012	NUM
iajs-554	180	4	السنة	السنة	NOUN
iajs-554	180	5	25	25	NUM
iajs-554	180	6	المجلد	المجلد	NOUN
iajs-554	180	7	3	3	NUM
iajs-554	180	8	العدد	العدد	PROPN
iajs-554	180	9	ibn	ibn	PROPN
iajs-554	180	10	al	al	PROPN
iajs-554	180	11	-	-	PUNCT
iajs-554	180	12	haitham	haitham	PROPN
iajs-554	180	13	journal	journal	PROPN
iajs-554	180	14	for	for	ADP
iajs-554	180	15	pure	pure	ADJ
iajs-554	180	16	and	and	CCONJ
iajs-554	180	17	applied	apply	VERB
iajs-554	180	18	science	science	NOUN
iajs-554	180	19	no	no	NOUN
iajs-554	180	20	.	.	NOUN
iajs-554	180	21	3	3	NUM
iajs-554	180	22	vol	vol	NOUN
iajs-554	180	23	.	.	PUNCT
iajs-554	181	1	25	25	NUM
iajs-554	181	2	year	year	NOUN
iajs-554	181	3	2012	2012	NUM
iajs-554	181	4	مناقشة	مناقشة	PROPN
iajs-554	181	5	تحليل	تحليل	PROPN
iajs-554	181	6	األخطاء	األخطاء	PROPN
iajs-554	181	7	لكاوس	لكاوس	PROPN
iajs-554	181	8	جوردن	جوردن	ADJ
iajs-554	181	9	للحذف	للحذف	PROPN
iajs-554	181	10	لمنظومة	لمنظومة	PROPN
iajs-554	181	11	المعادالت	المعادالت	PROPN
iajs-554	181	12	الخطية	الخطية	PROPN
iajs-554	181	13	شوقي	شوقي	NOUN
iajs-554	181	14	عبد	عبد	ADJ
iajs-554	181	15	المطلب	المطلب	NOUN
iajs-554	181	16	عباس	عباس	VERB
iajs-554	181	17	جامعة	جامعة	PROPN
iajs-554	181	18	بغداد	بغداد	PROPN
iajs-554	181	19	،	،	PROPN
iajs-554	181	20	كلية	كلية	PROPN
iajs-554	181	21	العلوم	العلوم	NOUN
iajs-554	181	22	،	،	PROPN
iajs-554	182	1	قسم	قسم	PROPN
iajs-554	182	2	الرياضيات	الرياضيات	PROPN
iajs-554	183	1	2012ايار	2012ايار	PROPN
iajs-554	183	2	21	21	NUM
iajs-554	183	3	قبل	قبل	NOUN
iajs-554	183	4	البحث	البحث	NOUN
iajs-554	183	5	في	في	ADP
iajs-554	183	6	:	:	PUNCT
iajs-554	184	1	2012كانون	2012كانون	PROPN
iajs-554	184	2	الثاني	الثاني	NOUN
iajs-554	184	3	22استلم	22استلم	NUM
iajs-554	184	4	البحث	البحث	VERB
iajs-554	184	5	في	في	PROPN
iajs-554	184	6	:	:	PUNCT
iajs-554	184	7	الخالصة	الخالصة	NOUN
iajs-554	184	8	جوردن	جوردن	PROPN
iajs-554	184	9	ةوالبواقي	ةوالبواقي	PROPN
iajs-554	184	10	للحلول	للحلول	PROPN
iajs-554	184	11	التقريبية	التقريبية	PROPN
iajs-554	184	12	لألنظمة	لألنظمة	PROPN
iajs-554	185	1	الخطية	الخطية	PROPN
iajs-554	185	2	المثلثية	المثلثية	PROPN
iajs-554	185	3	بطريقيتعلق	بطريقيتعلق	VERB
iajs-554	185	4	هذا	هذا	NOUN
iajs-554	185	5	البحث	البحث	PROPN
iajs-554	185	6	بالتمثيالت	بالتمثيالت	PROPN
iajs-554	185	7	الصريحة	الصريحة	VERB
iajs-554	185	8	لألخطاء	لألخطاء	PROPN
iajs-554	185	9	للبيانات	للبيانات	PROPN
iajs-554	185	10	ةجوردن	ةجوردن	PROPN
iajs-554	185	11	للحذف	للحذف	PROPN
iajs-554	185	12	توصف	توصف	PROPN
iajs-554	185	13	على	على	PROPN
iajs-554	185	14	أنها	أنها	NOUN
iajs-554	185	15	دال	دال	NOUN
iajs-554	185	16	–	–	PUNCT
iajs-554	185	17	.	.	PUNCT
iajs-554	186	1	أن	أن	ADP
iajs-554	186	2	حل	حل	PROPN
iajs-554	186	3	المعادالت	المعادالت	NOUN
iajs-554	186	4	الجبرية	الجبرية	VERB
iajs-554	186	5	الخطية	الخطية	NOUN
iajs-554	186	6	بطريقه	بطريقه	ADJ
iajs-554	186	7	كاوس	كاوس	ADJ
iajs-554	186	8	ةلعاماللحذف	ةلعاماللحذف	ADJ
iajs-554	186	9	والطريقة	والطريقة	NOUN
iajs-554	186	10	األساسي	األساسي	PROPN
iajs-554	186	11	المتصل	المتصل	PROPN
iajs-554	186	12	باألخطاء	باألخطاء	PROPN
iajs-554	186	13	ومن	ومن	PROPN
iajs-554	186	14	هذه	هذه	PROPN
iajs-554	186	15	التمثيالت	التمثيالت	VERB
iajs-554	186	16	تم	تم	X
iajs-554	186	17	اشتقاق	اشتقاق	PROPN
iajs-554	186	18	الجزء	الجزء	PROPN
iajs-554	186	19	ةوعمليات	ةوعمليات	PROPN
iajs-554	186	20	أخطاء	أخطاء	PROPN
iajs-554	186	21	التدوير	التدوير	PROPN
iajs-554	186	22	لحساب	لحساب	PROPN
iajs-554	186	23	الفارزة	الفارزة	PROPN
iajs-554	186	24	السائب	السائب	PROPN
iajs-554	186	25	ةالقلق	ةالقلق	VERB
iajs-554	186	26	وتحديد	وتحديد	ADP
iajs-554	186	27	البواقي	البواقي	PROPN
iajs-554	186	28	.	.	PUNCT
iajs-554	187	1	ن	ن	PRON
iajs-554	187	2	تخمين	تخمين	NOUN
iajs-554	187	3	االستقرار	االستقرار	NOUN
iajs-554	187	4	للحلول	للحلول	PROPN
iajs-554	188	1	قد	قد	INTJ
iajs-554	188	2	تم	تم	PROPN
iajs-554	188	3	شرحه	شرحه	VERB
iajs-554	188	4	في	في	ADP
iajs-554	188	5	هذا	هذا	NOUN
iajs-554	188	6	البحث	البحث	NOUN
iajs-554	188	7	.	.	PUNCT
iajs-554	189	1	كما	كما	PROPN
iajs-554	189	2	حددت	حددت	PROPN
iajs-554	189	3	قيود	قيود	PROPN
iajs-554	189	4	األخطاء	األخطاء	PROPN
iajs-554	189	5	للحلول	للحلول	PROPN
iajs-554	189	6	ومقارنتها	ومقارنتها	PROPN
iajs-554	189	7	مع	مع	PROPN
iajs-554	189	8	أفضل	أفضل	PROPN
iajs-554	189	9	الحدود	الحدود	VERB
iajs-554	189	10	إ	إ	PROPN
iajs-554	189	11	النتائج	النتائج	PROPN
iajs-554	189	12	وبشكل	وبشكل	PROPN
iajs-554	189	13	مفصل	مفصل	PROPN
iajs-554	189	14	ان	ان	ADP
iajs-554	189	15	الحلول	الحلول	PROPN
iajs-554	189	16	الحذف	الحذف	PROPN
iajs-554	189	17	لكاوس	لكاوس	PROPN
iajs-554	189	18	على	على	NOUN
iajs-554	189	19	التوالي	التوالي	NOUN
iajs-554	189	20	.	.	PUNCT
iajs-554	190	1	وتؤكد	وتؤكد	PROPN
iajs-554	190	2	ةلألخطاء	ةلألخطاء	PROPN
iajs-554	190	3	التي	التي	PROPN
iajs-554	190	4	احتسبت	احتسبت	PROPN
iajs-554	190	5	بالتعويض	بالتعويض	PROPN
iajs-554	191	1	المتراجع	المتراجع	X
iajs-554	191	2	وطريق	وطريق	ADV
iajs-554	191	3	جوردن	جوردن	ADJ
iajs-554	191	4	للحذف	للحذف	X
iajs-554	191	5	هي	هي	PROPN
iajs-554	191	6	ليست	ليست	PROPN
iajs-554	191	7	أساسًا	أساسًا	VERB
iajs-554	191	8	أعظم	أعظم	NOUN
iajs-554	191	9	من	من	PROPN
iajs-554	191	10	األخطاء	األخطاء	NOUN
iajs-554	191	11	الكبيرة	الكبيرة	NOUN
iajs-554	191	12	المحتملة	المحتملة	X
iajs-554	191	13	بطريقه	بطريقه	ADJ
iajs-554	191	14	–	–	PUNCT
iajs-554	191	15	كاوس	كاوس	ADJ
iajs-554	191	16	ةبطريقتي	ةبطريقتي	NOUN
iajs-554	191	17	جوردن	جوردن	ADJ
iajs-554	191	18	للحذف	للحذف	PROPN
iajs-554	191	19	وطريق	وطريق	PROPN
iajs-554	191	20	النتائج	النتائج	PROPN
iajs-554	191	21	النظرية	النظرية	PROPN
iajs-554	191	22	بمثالين	بمثالين	NOUN
iajs-554	191	23	عددين	عددين	VERB
iajs-554	191	24	.	.	PUNCT
iajs-554	192	1	تالتعويض	تالتعويض	NOUN
iajs-554	192	2	المتراجع	المتراجع	PROPN
iajs-554	192	3	والحذف	والحذف	PROPN
iajs-554	192	4	لكاوس	لكاوس	PROPN
iajs-554	192	5	على	على	NOUN
iajs-554	192	6	التوالي	التوالي	NOUN
iajs-554	192	7	.	.	PUNCT
iajs-554	193	1	ولقد	ولقد	PROPN
iajs-554	193	2	وضح	وضح	PROPN
iajs-554	193	3	جوردن	جوردن	X
iajs-554	193	4	للحذف	للحذف	PROPN
iajs-554	193	5	.	.	PUNCT
iajs-554	194	1	–	–	PUNCT
iajs-554	194	2	كاوس	كاوس	ADJ
iajs-554	194	3	ةيانات	ةيانات	ADJ
iajs-554	194	4	المضطربة	المضطربة	PROPN
iajs-554	194	5	،	،	PROPN
iajs-554	194	6	حدود	حدود	PROPN
iajs-554	194	7	األخطاء	األخطاء	PROPN
iajs-554	194	8	،	،	PROPN
iajs-554	194	9	طريقجوردن	طريقجوردن	PROPN
iajs-554	194	10	للحذف	للحذف	PROPN
iajs-554	194	11	،	،	PROPN
iajs-554	194	12	الب	الب	PROPN
iajs-554	194	13	ةطريق	ةطريق	PROPN
iajs-554	194	14	:	:	PUNCT
iajs-554	194	15	ةالكلمات	ةالكلمات	VERB
iajs-554	194	16	المفتاحي	المفتاحي	ADJ