id	sid	tid	token	lemma	pos
ap-1795	1	1	acta	acta	PROPN
ap-1795	1	2	polytechnica	polytechnica	PROPN
ap-1795	1	3	acta	acta	PROPN
ap-1795	1	4	polytechnica	polytechnica	PROPN
ap-1795	1	5	53(2):70–74	53(2):70–74	NUM
ap-1795	1	6	,	,	PUNCT
ap-1795	1	7	2013	2013	NUM
ap-1795	1	8	©	©	PROPN
ap-1795	1	9	czech	czech	PROPN
ap-1795	1	10	technical	technical	PROPN
ap-1795	1	11	university	university	PROPN
ap-1795	1	12	in	in	ADP
ap-1795	1	13	prague	prague	PROPN
ap-1795	1	14	,	,	PUNCT
ap-1795	1	15	2013	2013	NUM
ap-1795	1	16	available	available	ADJ
ap-1795	1	17	online	online	ADV
ap-1795	1	18	at	at	ADP
ap-1795	1	19	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1795	1	20	clock	clock	NOUN
ap-1795	1	21	math	math	NOUN
ap-1795	1	22	—	—	PUNCT
ap-1795	1	23	a	a	DET
ap-1795	1	24	system	system	NOUN
ap-1795	1	25	for	for	ADP
ap-1795	1	26	solving	solve	VERB
ap-1795	1	27	sles	sle	NOUN
ap-1795	1	28	exactly	exactly	ADV
ap-1795	1	29	jakub	jakub	PROPN
ap-1795	1	30	hladík	hladík	PROPN
ap-1795	1	31	,	,	PUNCT
ap-1795	1	32	róbert	róbert	PROPN
ap-1795	1	33	lórencz	lórencz	PROPN
ap-1795	1	34	,	,	PUNCT
ap-1795	1	35	ivan	ivan	PROPN
ap-1795	1	36	šimeček∗	šimeček∗	PROPN
ap-1795	1	37	department	department	PROPN
ap-1795	1	38	of	of	ADP
ap-1795	1	39	computer	computer	NOUN
ap-1795	1	40	systems	system	NOUN
ap-1795	1	41	,	,	PUNCT
ap-1795	1	42	faculty	faculty	NOUN
ap-1795	1	43	of	of	ADP
ap-1795	1	44	information	information	NOUN
ap-1795	1	45	technology	technology	NOUN
ap-1795	1	46	,	,	PUNCT
ap-1795	1	47	czech	czech	PROPN
ap-1795	1	48	technical	technical	PROPN
ap-1795	1	49	university	university	PROPN
ap-1795	1	50	in	in	ADP
ap-1795	1	51	prague	prague	PROPN
ap-1795	1	52	,	,	PUNCT
ap-1795	1	53	czech	czech	PROPN
ap-1795	1	54	republic	republic	NOUN
ap-1795	1	55	∗	∗	NOUN
ap-1795	1	56	corresponding	correspond	VERB
ap-1795	1	57	author	author	NOUN
ap-1795	1	58	:	:	PUNCT
ap-1795	1	59	xsimecek@fit.cvut.cz	xsimecek@fit.cvut.cz	PROPN
ap-1795	1	60	abstract	abstract	PROPN
ap-1795	1	61	.	.	PUNCT
ap-1795	2	1	in	in	ADP
ap-1795	2	2	this	this	DET
ap-1795	2	3	paper	paper	NOUN
ap-1795	2	4	,	,	PUNCT
ap-1795	2	5	we	we	PRON
ap-1795	2	6	present	present	VERB
ap-1795	2	7	a	a	DET
ap-1795	2	8	gpu	gpu	NOUN
ap-1795	2	9	-	-	ADJ
ap-1795	2	10	accelerated	accelerate	VERB
ap-1795	2	11	hybrid	hybrid	NOUN
ap-1795	2	12	system	system	NOUN
ap-1795	2	13	that	that	PRON
ap-1795	2	14	solves	solve	VERB
ap-1795	2	15	ill	ill	ADV
ap-1795	2	16	-	-	PUNCT
ap-1795	2	17	conditioned	condition	VERB
ap-1795	2	18	systems	system	NOUN
ap-1795	2	19	of	of	ADP
ap-1795	2	20	linear	linear	PROPN
ap-1795	2	21	equations	equation	NOUN
ap-1795	2	22	exactly	exactly	ADV
ap-1795	2	23	.	.	PUNCT
ap-1795	3	1	exactly	exactly	ADV
ap-1795	3	2	means	mean	VERB
ap-1795	3	3	without	without	ADP
ap-1795	3	4	rounding	round	VERB
ap-1795	3	5	errors	error	NOUN
ap-1795	3	6	due	due	ADJ
ap-1795	3	7	to	to	ADP
ap-1795	3	8	using	use	VERB
ap-1795	3	9	integer	integer	NOUN
ap-1795	3	10	arithmetics	arithmetic	NOUN
ap-1795	3	11	.	.	PUNCT
ap-1795	4	1	first	first	ADV
ap-1795	4	2	,	,	PUNCT
ap-1795	4	3	we	we	PRON
ap-1795	4	4	scale	scale	VERB
ap-1795	4	5	floating	float	VERB
ap-1795	4	6	-	-	PUNCT
ap-1795	4	7	point	point	NOUN
ap-1795	4	8	numbers	number	NOUN
ap-1795	4	9	up	up	ADP
ap-1795	4	10	to	to	ADP
ap-1795	4	11	integers	integer	NOUN
ap-1795	4	12	,	,	PUNCT
ap-1795	4	13	then	then	ADV
ap-1795	4	14	we	we	PRON
ap-1795	4	15	solve	solve	VERB
ap-1795	4	16	dozens	dozen	NOUN
ap-1795	4	17	of	of	ADP
ap-1795	4	18	sles	sle	NOUN
ap-1795	4	19	within	within	ADP
ap-1795	4	20	different	different	ADJ
ap-1795	4	21	modular	modular	ADJ
ap-1795	4	22	arithmetics	arithmetic	NOUN
ap-1795	4	23	and	and	CCONJ
ap-1795	4	24	then	then	ADV
ap-1795	4	25	we	we	PRON
ap-1795	4	26	assemble	assemble	VERB
ap-1795	4	27	sub	sub	NOUN
ap-1795	4	28	-	-	NOUN
ap-1795	4	29	solutions	solution	NOUN
ap-1795	4	30	back	back	ADV
ap-1795	4	31	using	use	VERB
ap-1795	4	32	the	the	DET
ap-1795	4	33	chinese	chinese	ADJ
ap-1795	4	34	remainder	remainder	NOUN
ap-1795	4	35	theorem	theorem	PROPN
ap-1795	4	36	.	.	PUNCT
ap-1795	5	1	this	this	DET
ap-1795	5	2	approach	approach	NOUN
ap-1795	5	3	effectively	effectively	ADV
ap-1795	5	4	bypasses	bypass	VERB
ap-1795	5	5	current	current	ADJ
ap-1795	5	6	cpu	cpu	NOUN
ap-1795	5	7	floating	float	VERB
ap-1795	5	8	-	-	PUNCT
ap-1795	5	9	point	point	NOUN
ap-1795	5	10	limitations	limitation	NOUN
ap-1795	5	11	.	.	PUNCT
ap-1795	6	1	the	the	DET
ap-1795	6	2	system	system	NOUN
ap-1795	6	3	is	be	AUX
ap-1795	6	4	capable	capable	ADJ
ap-1795	6	5	of	of	ADP
ap-1795	6	6	solving	solve	VERB
ap-1795	6	7	hilbert	hilbert	NOUN
ap-1795	6	8	’s	’s	PART
ap-1795	6	9	matrix	matrix	NOUN
ap-1795	6	10	without	without	ADP
ap-1795	6	11	losing	lose	VERB
ap-1795	6	12	a	a	DET
ap-1795	6	13	single	single	ADJ
ap-1795	6	14	bit	bit	NOUN
ap-1795	6	15	of	of	ADP
ap-1795	6	16	precision	precision	NOUN
ap-1795	6	17	,	,	PUNCT
ap-1795	6	18	and	and	CCONJ
ap-1795	6	19	with	with	ADP
ap-1795	6	20	a	a	DET
ap-1795	6	21	significant	significant	ADJ
ap-1795	6	22	speedup	speedup	NOUN
ap-1795	6	23	compared	compare	VERB
ap-1795	6	24	to	to	ADP
ap-1795	6	25	existing	exist	VERB
ap-1795	6	26	cpu	cpu	NOUN
ap-1795	6	27	solvers	solver	NOUN
ap-1795	6	28	.	.	PUNCT
ap-1795	7	1	keywords	keyword	NOUN
ap-1795	7	2	:	:	PUNCT
ap-1795	7	3	integer	integer	PROPN
ap-1795	7	4	arithmetic	arithmetic	ADJ
ap-1795	7	5	,	,	PUNCT
ap-1795	7	6	modular	modular	ADJ
ap-1795	7	7	arithmetic	arithmetic	ADJ
ap-1795	7	8	,	,	PUNCT
ap-1795	7	9	hilbert	hilbert	PROPN
ap-1795	7	10	’s	’s	PART
ap-1795	7	11	matrix	matrix	NOUN
ap-1795	7	12	,	,	PUNCT
ap-1795	7	13	error	error	NOUN
ap-1795	7	14	-	-	PUNCT
ap-1795	7	15	free	free	ADJ
ap-1795	7	16	,	,	PUNCT
ap-1795	7	17	gpgpu	gpgpu	PROPN
ap-1795	7	18	,	,	PUNCT
ap-1795	7	19	solver	solver	ADV
ap-1795	7	20	,	,	PUNCT
ap-1795	7	21	opencl	opencl	NOUN
ap-1795	7	22	,	,	PUNCT
ap-1795	7	23	optimizations	optimization	NOUN
ap-1795	7	24	.	.	PUNCT
ap-1795	8	1	1	1	X
ap-1795	8	2	.	.	X
ap-1795	8	3	introduction	introduction	NOUN
ap-1795	8	4	solving	solve	VERB
ap-1795	8	5	linear	linear	PROPN
ap-1795	8	6	algebraic	algebraic	ADJ
ap-1795	8	7	equations	equation	NOUN
ap-1795	8	8	solution	solution	NOUN
ap-1795	8	9	is	be	AUX
ap-1795	8	10	quite	quite	DET
ap-1795	8	11	a	a	DET
ap-1795	8	12	frequent	frequent	ADJ
ap-1795	8	13	task	task	NOUN
ap-1795	8	14	in	in	ADP
ap-1795	8	15	numerical	numerical	ADJ
ap-1795	8	16	mathematics	mathematic	NOUN
ap-1795	8	17	.	.	PUNCT
ap-1795	9	1	one	one	PRON
ap-1795	9	2	may	may	AUX
ap-1795	9	3	often	often	ADV
ap-1795	9	4	find	find	VERB
ap-1795	9	5	difficulties	difficulty	NOUN
ap-1795	9	6	,	,	PUNCT
ap-1795	9	7	while	while	SCONJ
ap-1795	9	8	solving	solve	VERB
ap-1795	9	9	problems	problem	NOUN
ap-1795	9	10	of	of	ADP
ap-1795	9	11	the	the	DET
ap-1795	9	12	illconditioned	illconditioned	ADJ
ap-1795	9	13	matrix	matrix	NOUN
ap-1795	9	14	.	.	PUNCT
ap-1795	10	1	stability	stability	NOUN
ap-1795	10	2	of	of	ADP
ap-1795	10	3	the	the	DET
ap-1795	10	4	solution	solution	NOUN
ap-1795	10	5	can	can	AUX
ap-1795	10	6	not	not	PART
ap-1795	10	7	be	be	AUX
ap-1795	10	8	ensured	ensure	VERB
ap-1795	10	9	for	for	ADP
ap-1795	10	10	large	large	ADJ
ap-1795	10	11	dense	dense	ADJ
ap-1795	10	12	sets	set	NOUN
ap-1795	10	13	of	of	ADP
ap-1795	10	14	linear	linear	PROPN
ap-1795	10	15	equations	equation	NOUN
ap-1795	10	16	.	.	PUNCT
ap-1795	11	1	rounding	round	VERB
ap-1795	11	2	error	error	NOUN
ap-1795	11	3	during	during	ADP
ap-1795	11	4	the	the	DET
ap-1795	11	5	numerical	numerical	ADJ
ap-1795	11	6	computation	computation	NOUN
ap-1795	11	7	can	can	AUX
ap-1795	11	8	not	not	PART
ap-1795	11	9	be	be	AUX
ap-1795	11	10	tolerated	tolerate	VERB
ap-1795	11	11	.	.	PUNCT
ap-1795	12	1	methods	method	NOUN
ap-1795	12	2	have	have	AUX
ap-1795	12	3	been	be	AUX
ap-1795	12	4	developed	develop	VERB
ap-1795	12	5	that	that	PRON
ap-1795	12	6	minimize	minimize	VERB
ap-1795	12	7	the	the	DET
ap-1795	12	8	influence	influence	NOUN
ap-1795	12	9	of	of	ADP
ap-1795	12	10	rounding	round	VERB
ap-1795	12	11	errors	error	NOUN
ap-1795	12	12	on	on	ADP
ap-1795	12	13	the	the	DET
ap-1795	12	14	solution	solution	NOUN
ap-1795	12	15	.	.	PUNCT
ap-1795	13	1	one	one	NUM
ap-1795	13	2	method	method	NOUN
ap-1795	13	3	that	that	PRON
ap-1795	13	4	we	we	PRON
ap-1795	13	5	use	use	VERB
ap-1795	13	6	relies	relie	NOUN
ap-1795	13	7	on	on	ADP
ap-1795	13	8	modular	modular	ADJ
ap-1795	13	9	arithmetics	arithmetic	NOUN
ap-1795	14	1	[	[	X
ap-1795	14	2	2	2	NUM
ap-1795	14	3	]	]	PUNCT
ap-1795	14	4	in	in	ADP
ap-1795	14	5	order	order	NOUN
ap-1795	14	6	to	to	PART
ap-1795	14	7	solve	solve	VERB
ap-1795	14	8	dense	dense	ADJ
ap-1795	14	9	systems	system	NOUN
ap-1795	14	10	of	of	ADP
ap-1795	14	11	linear	linear	PROPN
ap-1795	14	12	equations	equation	NOUN
ap-1795	14	13	precisely	precisely	ADV
ap-1795	14	14	.	.	PUNCT
ap-1795	15	1	the	the	DET
ap-1795	15	2	underlying	underlying	ADJ
ap-1795	15	3	idea	idea	NOUN
ap-1795	15	4	sounds	sound	VERB
ap-1795	15	5	quite	quite	ADV
ap-1795	15	6	simple	simple	ADJ
ap-1795	15	7	–	–	PUNCT
ap-1795	15	8	bypass	bypass	NOUN
ap-1795	15	9	floating	float	VERB
ap-1795	15	10	point	point	NOUN
ap-1795	15	11	rounding	round	VERB
ap-1795	15	12	limitations	limitation	NOUN
ap-1795	15	13	by	by	ADP
ap-1795	15	14	using	use	VERB
ap-1795	15	15	integer	integer	NOUN
ap-1795	15	16	arithmetics	arithmetic	NOUN
ap-1795	15	17	.	.	PUNCT
ap-1795	16	1	it	it	PRON
ap-1795	16	2	consists	consist	VERB
ap-1795	16	3	of	of	ADP
ap-1795	16	4	three	three	NUM
ap-1795	16	5	parts	part	NOUN
ap-1795	16	6	–	–	PUNCT
ap-1795	16	7	converting	convert	VERB
ap-1795	16	8	floating	float	VERB
ap-1795	16	9	point	point	NOUN
ap-1795	16	10	numbers	number	NOUN
ap-1795	16	11	into	into	ADP
ap-1795	16	12	integers	integer	NOUN
ap-1795	16	13	,	,	PUNCT
ap-1795	16	14	solving	solve	VERB
ap-1795	16	15	multiple	multiple	ADJ
ap-1795	16	16	systems	system	NOUN
ap-1795	16	17	of	of	ADP
ap-1795	16	18	linear	linear	ADJ
ap-1795	16	19	equations	equation	NOUN
ap-1795	16	20	within	within	ADP
ap-1795	16	21	their	their	PRON
ap-1795	16	22	modules	module	NOUN
ap-1795	16	23	,	,	PUNCT
ap-1795	16	24	and	and	CCONJ
ap-1795	16	25	finally	finally	ADV
ap-1795	16	26	converting	convert	VERB
ap-1795	16	27	sub	sub	NOUN
ap-1795	16	28	-	-	NOUN
ap-1795	16	29	solutions	solution	NOUN
ap-1795	16	30	back	back	ADV
ap-1795	16	31	using	use	VERB
ap-1795	16	32	the	the	DET
ap-1795	16	33	chinese	chinese	ADJ
ap-1795	16	34	remainder	remainder	NOUN
ap-1795	16	35	theorem	theorem	PROPN
ap-1795	16	36	.	.	PUNCT
ap-1795	17	1	nowadays	nowadays	ADV
ap-1795	17	2	,	,	PUNCT
ap-1795	17	3	gpgpu	gpgpu	PROPN
ap-1795	17	4	(	(	PUNCT
ap-1795	17	5	general	general	ADJ
ap-1795	17	6	-	-	PUNCT
ap-1795	17	7	purpose	purpose	NOUN
ap-1795	17	8	computing	computing	NOUN
ap-1795	17	9	on	on	ADP
ap-1795	17	10	the	the	DET
ap-1795	17	11	gpu	gpu	NOUN
ap-1795	17	12	)	)	PUNCT
ap-1795	17	13	is	be	AUX
ap-1795	17	14	a	a	DET
ap-1795	17	15	trending	trend	VERB
ap-1795	17	16	topic	topic	NOUN
ap-1795	17	17	in	in	ADP
ap-1795	17	18	high	high	ADJ
ap-1795	17	19	-	-	PUNCT
ap-1795	17	20	performance	performance	NOUN
ap-1795	17	21	computing	computing	NOUN
ap-1795	17	22	.	.	PUNCT
ap-1795	18	1	since	since	SCONJ
ap-1795	18	2	gpgpu	gpgpu	PROPN
ap-1795	18	3	began	begin	VERB
ap-1795	18	4	in	in	ADP
ap-1795	18	5	2006	2006	NUM
ap-1795	18	6	hundreds	hundred	NOUN
ap-1795	18	7	of	of	ADP
ap-1795	18	8	articles	article	NOUN
ap-1795	18	9	have	have	AUX
ap-1795	18	10	been	be	AUX
ap-1795	18	11	published	publish	VERB
ap-1795	18	12	every	every	DET
ap-1795	18	13	year	year	NOUN
ap-1795	18	14	.	.	PUNCT
ap-1795	19	1	gpgpu	gpgpu	PROPN
ap-1795	19	2	is	be	AUX
ap-1795	19	3	usually	usually	ADV
ap-1795	19	4	used	use	VERB
ap-1795	19	5	to	to	PART
ap-1795	19	6	accelerate	accelerate	VERB
ap-1795	19	7	data	data	NOUN
ap-1795	19	8	-	-	PUNCT
ap-1795	19	9	parallel	parallel	ADJ
ap-1795	19	10	algorithms	algorithm	NOUN
ap-1795	19	11	,	,	PUNCT
ap-1795	19	12	and	and	CCONJ
ap-1795	19	13	that	that	PRON
ap-1795	19	14	is	be	AUX
ap-1795	19	15	our	our	PRON
ap-1795	19	16	case	case	NOUN
ap-1795	19	17	.	.	PUNCT
ap-1795	20	1	dozens	dozen	NOUN
ap-1795	20	2	of	of	ADP
ap-1795	20	3	systems	system	NOUN
ap-1795	20	4	of	of	ADP
ap-1795	20	5	linear	linear	PROPN
ap-1795	20	6	equations	equation	NOUN
ap-1795	20	7	emerge	emerge	VERB
ap-1795	20	8	during	during	ADP
ap-1795	20	9	the	the	DET
ap-1795	20	10	second	second	ADJ
ap-1795	20	11	step	step	NOUN
ap-1795	20	12	of	of	ADP
ap-1795	20	13	our	our	PRON
ap-1795	20	14	computation	computation	NOUN
ap-1795	20	15	.	.	PUNCT
ap-1795	21	1	each	each	PRON
ap-1795	21	2	of	of	ADP
ap-1795	21	3	them	they	PRON
ap-1795	21	4	can	can	AUX
ap-1795	21	5	be	be	AUX
ap-1795	21	6	solved	solve	VERB
ap-1795	21	7	in	in	ADP
ap-1795	21	8	parallel	parallel	NOUN
ap-1795	21	9	on	on	ADP
ap-1795	21	10	the	the	DET
ap-1795	21	11	gpu	gpu	NOUN
ap-1795	21	12	,	,	PUNCT
ap-1795	21	13	hence	hence	ADV
ap-1795	21	14	speedup	speedup	NOUN
ap-1795	21	15	is	be	AUX
ap-1795	21	16	achieved	achieve	VERB
ap-1795	21	17	.	.	PUNCT
ap-1795	22	1	in	in	ADP
ap-1795	22	2	this	this	DET
ap-1795	22	3	paper	paper	NOUN
ap-1795	22	4	,	,	PUNCT
ap-1795	22	5	we	we	PRON
ap-1795	22	6	present	present	VERB
ap-1795	22	7	a	a	DET
ap-1795	22	8	gpu	gpu	NOUN
ap-1795	22	9	-	-	ADJ
ap-1795	22	10	accelerated	accelerate	VERB
ap-1795	22	11	solver	solver	NOUN
ap-1795	22	12	of	of	ADP
ap-1795	22	13	ill	ill	ADV
ap-1795	22	14	-	-	PUNCT
ap-1795	22	15	conditioned	condition	VERB
ap-1795	22	16	systems	system	NOUN
ap-1795	22	17	of	of	ADP
ap-1795	22	18	linear	linear	PROPN
ap-1795	22	19	equations	equation	NOUN
ap-1795	22	20	.	.	PUNCT
ap-1795	23	1	section	section	NOUN
ap-1795	23	2	3	3	NUM
ap-1795	23	3	gives	give	VERB
ap-1795	23	4	a	a	DET
ap-1795	23	5	brief	brief	ADJ
ap-1795	23	6	overview	overview	NOUN
ap-1795	23	7	of	of	ADP
ap-1795	23	8	the	the	DET
ap-1795	23	9	mathematics	mathematic	NOUN
ap-1795	23	10	that	that	PRON
ap-1795	23	11	is	be	AUX
ap-1795	23	12	used	use	VERB
ap-1795	23	13	.	.	PUNCT
ap-1795	24	1	section	section	NOUN
ap-1795	24	2	4	4	NUM
ap-1795	24	3	describes	describe	VERB
ap-1795	24	4	the	the	DET
ap-1795	24	5	gpu	gpu	NOUN
ap-1795	24	6	architecture	architecture	NOUN
ap-1795	24	7	in	in	ADP
ap-1795	24	8	general	general	ADJ
ap-1795	24	9	,	,	PUNCT
ap-1795	24	10	and	and	CCONJ
ap-1795	24	11	presents	present	VERB
ap-1795	24	12	issues	issue	NOUN
ap-1795	24	13	that	that	PRON
ap-1795	24	14	we	we	PRON
ap-1795	24	15	faced	face	VERB
ap-1795	24	16	while	while	SCONJ
ap-1795	24	17	optimizing	optimize	VERB
ap-1795	24	18	the	the	DET
ap-1795	24	19	computation	computation	NOUN
ap-1795	24	20	.	.	PUNCT
ap-1795	25	1	finally	finally	ADV
ap-1795	25	2	,	,	PUNCT
ap-1795	25	3	section	section	NOUN
ap-1795	25	4	5	5	NUM
ap-1795	25	5	shows	show	VERB
ap-1795	25	6	our	our	PRON
ap-1795	25	7	measured	measure	VERB
ap-1795	25	8	results	result	NOUN
ap-1795	25	9	–	–	PUNCT
ap-1795	25	10	the	the	DET
ap-1795	25	11	speedup	speedup	NOUN
ap-1795	25	12	and	and	CCONJ
ap-1795	25	13	a	a	DET
ap-1795	25	14	comparison	comparison	NOUN
ap-1795	25	15	with	with	ADP
ap-1795	25	16	existing	exist	VERB
ap-1795	25	17	systems	system	NOUN
ap-1795	25	18	solving	solve	VERB
ap-1795	25	19	similar	similar	ADJ
ap-1795	25	20	problem	problem	NOUN
ap-1795	25	21	.	.	PUNCT
ap-1795	26	1	2	2	X
ap-1795	26	2	.	.	X
ap-1795	26	3	state	state	NOUN
ap-1795	26	4	of	of	ADP
ap-1795	26	5	the	the	DET
ap-1795	26	6	art	art	NOUN
ap-1795	26	7	nearly	nearly	ADV
ap-1795	26	8	one	one	NUM
ap-1795	26	9	half	half	NOUN
ap-1795	26	10	of	of	ADP
ap-1795	26	11	the	the	DET
ap-1795	26	12	problems	problem	NOUN
ap-1795	26	13	solved	solve	VERB
ap-1795	26	14	in	in	ADP
ap-1795	26	15	numerical	numerical	ADJ
ap-1795	26	16	mathematics	mathematics	PROPN
ap-1795	26	17	lead	lead	VERB
ap-1795	26	18	to	to	ADP
ap-1795	26	19	problems	problem	NOUN
ap-1795	26	20	in	in	ADP
ap-1795	26	21	linear	linear	PROPN
ap-1795	26	22	algebra	algebra	NOUN
ap-1795	26	23	.	.	PUNCT
ap-1795	27	1	the	the	DET
ap-1795	27	2	primary	primary	ADJ
ap-1795	27	3	objective	objective	NOUN
ap-1795	27	4	of	of	ADP
ap-1795	27	5	the	the	DET
ap-1795	27	6	numerical	numerical	ADJ
ap-1795	27	7	methods	method	NOUN
ap-1795	27	8	used	use	VERB
ap-1795	27	9	in	in	ADP
ap-1795	27	10	linear	linear	ADJ
ap-1795	27	11	algebra	algebra	NOUN
ap-1795	27	12	is	be	AUX
ap-1795	27	13	to	to	PART
ap-1795	27	14	solve	solve	VERB
ap-1795	27	15	sets	set	NOUN
ap-1795	27	16	of	of	ADP
ap-1795	27	17	linear	linear	ADJ
ap-1795	27	18	equations	equation	NOUN
ap-1795	27	19	.	.	PUNCT
ap-1795	27	20	.	.	PUNCT
ap-1795	28	1	.	.	PUNCT
ap-1795	29	1	they	they	PRON
ap-1795	29	2	are	be	AUX
ap-1795	29	3	solved	solve	VERB
ap-1795	29	4	in	in	ADP
ap-1795	29	5	a	a	DET
ap-1795	29	6	chosen	choose	VERB
ap-1795	29	7	computer	computer	NOUN
ap-1795	29	8	arithmetic	arithmetic	ADJ
ap-1795	29	9	,	,	PUNCT
ap-1795	29	10	most	most	ADV
ap-1795	29	11	often	often	ADV
ap-1795	29	12	floating	float	VERB
ap-1795	29	13	-	-	PUNCT
ap-1795	29	14	point	point	NOUN
ap-1795	29	15	arithmetic	arithmetic	ADJ
ap-1795	29	16	.	.	PUNCT
ap-1795	30	1	floating	float	VERB
ap-1795	30	2	-	-	PUNCT
ap-1795	30	3	point	point	NOUN
ap-1795	30	4	arithmetic	arithmetic	NOUN
ap-1795	30	5	’s	’s	NOUN
ap-1795	30	6	well	well	ADV
ap-1795	30	7	known	know	VERB
ap-1795	30	8	advantages	advantage	NOUN
ap-1795	30	9	have	have	AUX
ap-1795	30	10	led	lead	VERB
ap-1795	30	11	to	to	ADP
ap-1795	30	12	its	its	PRON
ap-1795	30	13	widespread	widespread	ADJ
ap-1795	30	14	usage	usage	NOUN
ap-1795	30	15	,	,	PUNCT
ap-1795	30	16	yet	yet	CCONJ
ap-1795	30	17	it	it	PRON
ap-1795	30	18	also	also	ADV
ap-1795	30	19	has	have	VERB
ap-1795	30	20	its	its	PRON
ap-1795	30	21	important	important	ADJ
ap-1795	30	22	disadvantages	disadvantage	NOUN
ap-1795	30	23	,	,	PUNCT
ap-1795	30	24	sometimes	sometimes	ADV
ap-1795	30	25	resulting	result	VERB
ap-1795	30	26	in	in	ADP
ap-1795	30	27	severe	severe	ADJ
ap-1795	30	28	problems	problem	NOUN
ap-1795	30	29	.	.	PUNCT
ap-1795	31	1	the	the	DET
ap-1795	31	2	disadvantages	disadvantage	NOUN
ap-1795	31	3	of	of	ADP
ap-1795	31	4	floating	float	VERB
ap-1795	31	5	-	-	PUNCT
ap-1795	31	6	point	point	NOUN
ap-1795	31	7	arithmetic	arithmetic	NOUN
ap-1795	31	8	include	include	VERB
ap-1795	31	9	mainly	mainly	ADV
ap-1795	31	10	the	the	DET
ap-1795	31	11	generation	generation	NOUN
ap-1795	31	12	and	and	CCONJ
ap-1795	31	13	accumulation	accumulation	NOUN
ap-1795	31	14	of	of	ADP
ap-1795	31	15	rounding	round	VERB
ap-1795	31	16	errors	error	NOUN
ap-1795	31	17	during	during	ADP
ap-1795	31	18	the	the	DET
ap-1795	31	19	calculation	calculation	NOUN
ap-1795	31	20	,	,	PUNCT
ap-1795	31	21	and	and	CCONJ
ap-1795	31	22	nonuniform	nonuniform	ADJ
ap-1795	31	23	distribution	distribution	NOUN
ap-1795	31	24	of	of	ADP
ap-1795	31	25	values	value	NOUN
ap-1795	31	26	in	in	ADP
ap-1795	31	27	the	the	DET
ap-1795	31	28	real	real	ADJ
ap-1795	31	29	number	number	NOUN
ap-1795	31	30	subset	subset	NOUN
ap-1795	31	31	.	.	PUNCT
ap-1795	32	1	there	there	PRON
ap-1795	32	2	are	be	VERB
ap-1795	32	3	a	a	DET
ap-1795	32	4	variety	variety	NOUN
ap-1795	32	5	of	of	ADP
ap-1795	32	6	alternatives	alternative	NOUN
ap-1795	32	7	to	to	ADP
ap-1795	32	8	floating	float	VERB
ap-1795	32	9	point	point	NOUN
ap-1795	32	10	representation	representation	NOUN
ap-1795	32	11	and	and	CCONJ
ap-1795	32	12	associated	associated	ADJ
ap-1795	32	13	arithmetic	arithmetic	ADJ
ap-1795	32	14	operations	operation	NOUN
ap-1795	32	15	,	,	PUNCT
ap-1795	32	16	including	include	VERB
ap-1795	32	17	modular	modular	ADJ
ap-1795	32	18	,	,	PUNCT
ap-1795	32	19	logarithmic	logarithmic	ADJ
ap-1795	32	20	,	,	PUNCT
ap-1795	32	21	p	p	NOUN
ap-1795	32	22	-	-	PUNCT
ap-1795	32	23	adic	adic	NOUN
ap-1795	32	24	,	,	PUNCT
ap-1795	32	25	and	and	CCONJ
ap-1795	32	26	continued	continued	ADJ
ap-1795	32	27	fraction	fraction	NOUN
ap-1795	32	28	arithmetic	arithmetic	ADJ
ap-1795	32	29	.	.	PUNCT
ap-1795	33	1	many	many	ADJ
ap-1795	33	2	numerical	numerical	ADJ
ap-1795	33	3	problems	problem	NOUN
ap-1795	33	4	lead	lead	VERB
ap-1795	33	5	to	to	ADP
ap-1795	33	6	sles	sle	NOUN
ap-1795	33	7	with	with	ADP
ap-1795	33	8	dense	dense	ADJ
ap-1795	33	9	and	and	CCONJ
ap-1795	33	10	large	large	ADJ
ap-1795	33	11	matrices	matrix	NOUN
ap-1795	33	12	.	.	PUNCT
ap-1795	34	1	the	the	DET
ap-1795	34	2	rounding	round	VERB
ap-1795	34	3	error	error	NOUN
ap-1795	34	4	sensitivity	sensitivity	NOUN
ap-1795	34	5	of	of	ADP
ap-1795	34	6	such	such	ADJ
ap-1795	34	7	systems	system	NOUN
ap-1795	34	8	can	can	AUX
ap-1795	34	9	be	be	AUX
ap-1795	34	10	so	so	ADV
ap-1795	34	11	grave	grave	ADJ
ap-1795	34	12	that	that	SCONJ
ap-1795	34	13	they	they	PRON
ap-1795	34	14	can	can	AUX
ap-1795	34	15	be	be	AUX
ap-1795	34	16	considered	consider	VERB
ap-1795	34	17	to	to	PART
ap-1795	34	18	be	be	AUX
ap-1795	34	19	ill	ill	ADV
ap-1795	34	20	-	-	PUNCT
ap-1795	34	21	conditioned	condition	VERB
ap-1795	34	22	.	.	PUNCT
ap-1795	35	1	to	to	PART
ap-1795	35	2	solve	solve	VERB
ap-1795	35	3	the	the	DET
ap-1795	35	4	problems	problem	NOUN
ap-1795	35	5	,	,	PUNCT
ap-1795	35	6	many	many	ADJ
ap-1795	35	7	numerical	numerical	ADJ
ap-1795	35	8	direct	direct	ADJ
ap-1795	35	9	and	and	CCONJ
ap-1795	35	10	iterative	iterative	NOUN
ap-1795	35	11	methods	method	NOUN
ap-1795	35	12	have	have	AUX
ap-1795	35	13	been	be	AUX
ap-1795	35	14	developed	develop	VERB
ap-1795	35	15	that	that	PRON
ap-1795	35	16	tackle	tackle	VERB
ap-1795	35	17	these	these	DET
ap-1795	35	18	systems	system	NOUN
ap-1795	35	19	with	with	ADP
ap-1795	35	20	higher	high	ADJ
ap-1795	35	21	or	or	CCONJ
ap-1795	35	22	lower	low	ADJ
ap-1795	35	23	success	success	NOUN
ap-1795	35	24	.	.	PUNCT
ap-1795	36	1	apart	apart	ADV
ap-1795	36	2	from	from	ADP
ap-1795	36	3	many	many	ADJ
ap-1795	36	4	numerical	numerical	ADJ
ap-1795	36	5	methods	method	NOUN
ap-1795	36	6	,	,	PUNCT
ap-1795	36	7	various	various	ADJ
ap-1795	36	8	programming	programming	NOUN
ap-1795	36	9	and	and	CCONJ
ap-1795	36	10	computing	computing	NOUN
ap-1795	36	11	tools	tool	NOUN
ap-1795	36	12	have	have	AUX
ap-1795	36	13	been	be	AUX
ap-1795	36	14	developed	develop	VERB
ap-1795	36	15	for	for	ADP
ap-1795	36	16	solving	solve	VERB
ap-1795	36	17	rounding	round	VERB
ap-1795	36	18	error	error	NOUN
ap-1795	36	19	sensitive	sensitive	ADJ
ap-1795	36	20	sles	sle	NOUN
ap-1795	36	21	.	.	PUNCT
ap-1795	37	1	there	there	PRON
ap-1795	37	2	are	be	VERB
ap-1795	37	3	many	many	ADJ
ap-1795	37	4	computer	computer	NOUN
ap-1795	37	5	libraries	library	NOUN
ap-1795	37	6	that	that	PRON
ap-1795	37	7	allow	allow	VERB
ap-1795	37	8	the	the	DET
ap-1795	37	9	user	user	NOUN
ap-1795	37	10	to	to	PART
ap-1795	37	11	choose	choose	VERB
ap-1795	37	12	an	an	DET
ap-1795	37	13	optimal	optimal	ADJ
ap-1795	37	14	virtual	virtual	ADJ
ap-1795	37	15	length	length	NOUN
ap-1795	37	16	of	of	ADP
ap-1795	37	17	a	a	DET
ap-1795	37	18	computer	computer	NOUN
ap-1795	37	19	word	word	NOUN
ap-1795	37	20	that	that	SCONJ
ap-1795	37	21	fully	fully	ADV
ap-1795	37	22	or	or	CCONJ
ap-1795	37	23	partially	partially	ADV
ap-1795	37	24	eliminates	eliminate	VERB
ap-1795	37	25	the	the	DET
ap-1795	37	26	destructive	destructive	ADJ
ap-1795	37	27	influence	influence	NOUN
ap-1795	37	28	of	of	ADP
ap-1795	37	29	rounding	round	VERB
ap-1795	37	30	errors	error	NOUN
ap-1795	37	31	.	.	PUNCT
ap-1795	38	1	there	there	PRON
ap-1795	38	2	are	be	VERB
ap-1795	38	3	also	also	ADV
ap-1795	38	4	arithmetic	arithmetic	ADJ
ap-1795	38	5	units	unit	NOUN
ap-1795	38	6	that	that	PRON
ap-1795	38	7	tackle	tackle	VERB
ap-1795	38	8	this	this	DET
ap-1795	38	9	problem	problem	NOUN
ap-1795	38	10	by	by	ADP
ap-1795	38	11	grouping	group	VERB
ap-1795	38	12	arithmetic	arithmetic	ADJ
ap-1795	38	13	operations	operation	NOUN
ap-1795	38	14	,	,	PUNCT
ap-1795	38	15	and	and	CCONJ
ap-1795	38	16	thus	thus	ADV
ap-1795	38	17	they	they	PRON
ap-1795	38	18	create	create	VERB
ap-1795	38	19	a	a	DET
ap-1795	38	20	longer	long	ADJ
ap-1795	38	21	computer	computer	NOUN
ap-1795	38	22	word	word	NOUN
ap-1795	38	23	for	for	ADP
ap-1795	38	24	operations	operation	NOUN
ap-1795	38	25	sensitive	sensitive	ADJ
ap-1795	38	26	to	to	ADP
ap-1795	38	27	rounding	round	VERB
ap-1795	38	28	.	.	PUNCT
ap-1795	39	1	software	software	NOUN
ap-1795	39	2	tools	tool	NOUN
ap-1795	39	3	that	that	PRON
ap-1795	39	4	eliminate	eliminate	VERB
ap-1795	39	5	rounding	round	VERB
ap-1795	39	6	errors	error	NOUN
ap-1795	39	7	include	include	VERB
ap-1795	39	8	libraries	library	NOUN
ap-1795	39	9	for	for	ADP
ap-1795	39	10	precision	precision	NOUN
ap-1795	39	11	computing	computing	NOUN
ap-1795	39	12	,	,	PUNCT
ap-1795	39	13	such	such	ADJ
ap-1795	39	14	as	as	ADP
ap-1795	39	15	gmp	gmp	PROPN
ap-1795	39	16	(	(	PUNCT
ap-1795	39	17	gnu	gnu	X
ap-1795	39	18	multiple	multiple	NOUN
ap-1795	39	19	70	70	NUM
ap-1795	39	20	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	ADJ
ap-1795	39	21	vol	vol	NOUN
ap-1795	39	22	.	.	PUNCT
ap-1795	40	1	53	53	NUM
ap-1795	40	2	no	no	NOUN
ap-1795	40	3	.	.	PUNCT
ap-1795	41	1	2/2013	2/2013	NUM
ap-1795	41	2	clock	clock	NOUN
ap-1795	41	3	math	math	NOUN
ap-1795	41	4	—	—	PUNCT
ap-1795	41	5	a	a	DET
ap-1795	41	6	system	system	NOUN
ap-1795	41	7	for	for	ADP
ap-1795	41	8	solving	solve	VERB
ap-1795	41	9	sles	sle	NOUN
ap-1795	41	10	exactly	exactly	ADV
ap-1795	41	11	precision	precision	VERB
ap-1795	41	12	arithmetic	arithmetic	ADJ
ap-1795	41	13	library	library	NOUN
ap-1795	41	14	)	)	PUNCT
ap-1795	41	15	.	.	PUNCT
ap-1795	42	1	unfortunately	unfortunately	ADV
ap-1795	42	2	,	,	PUNCT
ap-1795	42	3	these	these	DET
ap-1795	42	4	tools	tool	NOUN
ap-1795	42	5	lead	lead	VERB
ap-1795	42	6	to	to	ADP
ap-1795	42	7	such	such	ADJ
ap-1795	42	8	great	great	ADJ
ap-1795	42	9	time	time	NOUN
ap-1795	42	10	complexity	complexity	NOUN
ap-1795	42	11	when	when	SCONJ
ap-1795	42	12	they	they	PRON
ap-1795	42	13	are	be	AUX
ap-1795	42	14	used	use	VERB
ap-1795	42	15	to	to	PART
ap-1795	42	16	solve	solve	VERB
ap-1795	42	17	rounding	round	VERB
ap-1795	42	18	error	error	NOUN
ap-1795	42	19	sensitive	sensitive	ADJ
ap-1795	42	20	sles	sle	NOUN
ap-1795	42	21	that	that	PRON
ap-1795	42	22	they	they	PRON
ap-1795	42	23	may	may	AUX
ap-1795	42	24	not	not	PART
ap-1795	42	25	be	be	AUX
ap-1795	42	26	applicable	applicable	ADJ
ap-1795	42	27	to	to	ADP
ap-1795	42	28	practical	practical	ADJ
ap-1795	42	29	problems	problem	NOUN
ap-1795	42	30	.	.	PUNCT
ap-1795	43	1	another	another	DET
ap-1795	43	2	limiting	limit	VERB
ap-1795	43	3	factor	factor	NOUN
ap-1795	43	4	when	when	SCONJ
ap-1795	43	5	solving	solve	VERB
ap-1795	43	6	sles	sle	NOUN
ap-1795	43	7	with	with	ADP
ap-1795	43	8	a	a	DET
ap-1795	43	9	square	square	ADJ
ap-1795	43	10	matrix	matrix	NOUN
ap-1795	43	11	is	be	AUX
ap-1795	43	12	the	the	DET
ap-1795	43	13	inherent	inherent	ADJ
ap-1795	43	14	algorithmic	algorithmic	ADJ
ap-1795	43	15	time	time	NOUN
ap-1795	43	16	complexity	complexity	PROPN
ap-1795	43	17	o(n3	o(n3	PROPN
ap-1795	43	18	)	)	PUNCT
ap-1795	43	19	,	,	PUNCT
ap-1795	43	20	where	where	SCONJ
ap-1795	43	21	n	n	PRON
ap-1795	43	22	is	be	AUX
ap-1795	43	23	the	the	DET
ap-1795	43	24	dimension	dimension	NOUN
ap-1795	43	25	of	of	ADP
ap-1795	43	26	the	the	DET
ap-1795	43	27	matrix	matrix	NOUN
ap-1795	43	28	.	.	PUNCT
ap-1795	44	1	to	to	PART
ap-1795	44	2	solve	solve	VERB
ap-1795	44	3	large	large	ADJ
ap-1795	44	4	sles	sle	NOUN
ap-1795	44	5	with	with	ADP
ap-1795	44	6	a	a	DET
ap-1795	44	7	large	large	ADJ
ap-1795	44	8	number	number	NOUN
ap-1795	44	9	of	of	ADP
ap-1795	44	10	equations	equation	NOUN
ap-1795	44	11	,	,	PUNCT
ap-1795	44	12	special	special	ADJ
ap-1795	44	13	computers	computer	NOUN
ap-1795	44	14	and	and	CCONJ
ap-1795	44	15	processors	processor	NOUN
ap-1795	44	16	have	have	AUX
ap-1795	44	17	been	be	AUX
ap-1795	44	18	developed	develop	VERB
ap-1795	44	19	.	.	PUNCT
ap-1795	45	1	these	these	PRON
ap-1795	45	2	are	be	AUX
ap-1795	45	3	vector	vector	NOUN
ap-1795	45	4	computers	computer	NOUN
ap-1795	45	5	.	.	PUNCT
ap-1795	46	1	until	until	ADP
ap-1795	46	2	recently	recently	ADV
ap-1795	46	3	,	,	PUNCT
ap-1795	46	4	the	the	DET
ap-1795	46	5	vector	vector	NOUN
ap-1795	46	6	processors	processor	NOUN
ap-1795	46	7	available	available	ADJ
ap-1795	46	8	on	on	ADP
ap-1795	46	9	the	the	DET
ap-1795	46	10	market	market	NOUN
ap-1795	46	11	were	be	AUX
ap-1795	46	12	cray	cray	NOUN
ap-1795	46	13	sv1ex	sv1ex	NUM
ap-1795	46	14	(	(	PUNCT
ap-1795	46	15	2001	2001	NUM
ap-1795	46	16	)	)	PUNCT
ap-1795	46	17	,	,	PUNCT
ap-1795	46	18	fujitsu	fujitsu	PROPN
ap-1795	46	19	vpp5000	vpp5000	PROPN
ap-1795	46	20	(	(	PUNCT
ap-1795	46	21	1999	1999	NUM
ap-1795	46	22	)	)	PUNCT
ap-1795	46	23	and	and	CCONJ
ap-1795	46	24	vmips	vmip	NOUN
ap-1795	46	25	(	(	PUNCT
ap-1795	46	26	2001	2001	NUM
ap-1795	46	27	)	)	PUNCT
ap-1795	46	28	.	.	PUNCT
ap-1795	47	1	ibm	ibm	PROPN
ap-1795	47	2	virtual	virtual	ADJ
ap-1795	47	3	vector	vector	NOUN
ap-1795	47	4	architecture	architecture	NOUN
ap-1795	47	5	brings	bring	VERB
ap-1795	47	6	vector	vector	NOUN
ap-1795	47	7	processing	processing	NOUN
ap-1795	47	8	features	feature	NOUN
ap-1795	47	9	to	to	ADP
ap-1795	47	10	its	its	PRON
ap-1795	47	11	most	most	ADV
ap-1795	47	12	recent	recent	ADJ
ap-1795	47	13	power6	power6	NOUN
ap-1795	47	14	mainframe	mainframe	NOUN
ap-1795	47	15	processors	processor	NOUN
ap-1795	47	16	(	(	PUNCT
ap-1795	47	17	2007	2007	NUM
ap-1795	47	18	)	)	PUNCT
ap-1795	47	19	.	.	PUNCT
ap-1795	48	1	another	another	DET
ap-1795	48	2	suitable	suitable	ADJ
ap-1795	48	3	architecture	architecture	NOUN
ap-1795	48	4	for	for	ADP
ap-1795	48	5	solving	solve	VERB
ap-1795	48	6	rounding	round	VERB
ap-1795	48	7	error	error	NOUN
ap-1795	48	8	sensitive	sensitive	ADJ
ap-1795	48	9	sles	sle	NOUN
ap-1795	48	10	is	be	AUX
ap-1795	48	11	simd	simd	NOUN
ap-1795	48	12	(	(	PUNCT
ap-1795	48	13	single	single	ADJ
ap-1795	48	14	instruction	instruction	NOUN
ap-1795	48	15	,	,	PUNCT
ap-1795	48	16	multiple	multiple	ADJ
ap-1795	48	17	data	datum	NOUN
ap-1795	48	18	)	)	PUNCT
ap-1795	48	19	.	.	PUNCT
ap-1795	49	1	today	today	NOUN
ap-1795	49	2	the	the	DET
ap-1795	49	3	simd	simd	PROPN
ap-1795	49	4	features	feature	NOUN
ap-1795	49	5	can	can	AUX
ap-1795	49	6	be	be	AUX
ap-1795	49	7	found	find	VERB
ap-1795	49	8	as	as	ADP
ap-1795	49	9	extensions	extension	NOUN
ap-1795	49	10	of	of	ADP
ap-1795	49	11	the	the	DET
ap-1795	49	12	standard	standard	ADJ
ap-1795	49	13	processor	processor	NOUN
ap-1795	49	14	instruction	instruction	NOUN
ap-1795	49	15	set	set	NOUN
ap-1795	49	16	,	,	PUNCT
ap-1795	49	17	for	for	ADP
ap-1795	49	18	example	example	NOUN
ap-1795	49	19	,	,	PUNCT
ap-1795	49	20	intel	intel	NOUN
ap-1795	49	21	-	-	PUNCT
ap-1795	49	22	sse	sse	NOUN
ap-1795	49	23	,	,	PUNCT
ap-1795	49	24	amd-3dnow	amd-3dnow	ADV
ap-1795	49	25	!	!	PUNCT
ap-1795	50	1	or	or	CCONJ
ap-1795	50	2	motorola	motorola	PROPN
ap-1795	50	3	-	-	PUNCT
ap-1795	50	4	altivec	altivec	PROPN
ap-1795	50	5	.	.	PUNCT
ap-1795	51	1	these	these	PRON
ap-1795	51	2	are	be	AUX
ap-1795	51	3	used	use	VERB
ap-1795	51	4	in	in	ADP
ap-1795	51	5	multimedia	multimedia	NOUN
ap-1795	51	6	applications	application	NOUN
ap-1795	51	7	such	such	ADJ
ap-1795	51	8	as	as	ADP
ap-1795	51	9	video	video	NOUN
ap-1795	51	10	,	,	PUNCT
ap-1795	51	11	3d	3d	NUM
ap-1795	51	12	graphics	graphic	NOUN
ap-1795	51	13	,	,	PUNCT
ap-1795	51	14	animation	animation	NOUN
ap-1795	51	15	,	,	PUNCT
ap-1795	51	16	audio	audio	NOUN
ap-1795	51	17	,	,	PUNCT
ap-1795	51	18	etc	etc	X
ap-1795	51	19	.	.	X
ap-1795	52	1	the	the	DET
ap-1795	52	2	recent	recent	ADJ
ap-1795	52	3	trend	trend	NOUN
ap-1795	52	4	is	be	AUX
ap-1795	52	5	gpgpu	gpgpu	NOUN
ap-1795	52	6	.	.	PUNCT
ap-1795	53	1	today	today	NOUN
ap-1795	53	2	,	,	PUNCT
ap-1795	53	3	at	at	ADV
ap-1795	53	4	least	least	ADV
ap-1795	53	5	three	three	NUM
ap-1795	53	6	of	of	ADP
ap-1795	53	7	ten	ten	NUM
ap-1795	53	8	top	top	ADJ
ap-1795	53	9	supercomputers	supercomputer	NOUN
ap-1795	53	10	in	in	ADP
ap-1795	53	11	the	the	DET
ap-1795	53	12	top	top	ADJ
ap-1795	53	13	500	500	NUM
ap-1795	53	14	list	list	NOUN
ap-1795	53	15	use	use	VERB
ap-1795	53	16	gpu	gpu	NOUN
ap-1795	53	17	for	for	ADP
ap-1795	53	18	numerical	numerical	ADJ
ap-1795	53	19	acceleration	acceleration	NOUN
ap-1795	53	20	.	.	PUNCT
ap-1795	54	1	both	both	DET
ap-1795	54	2	major	major	ADJ
ap-1795	54	3	gpu	gpu	NOUN
ap-1795	54	4	manufacturers	manufacturer	NOUN
ap-1795	54	5	,	,	PUNCT
ap-1795	54	6	nvidia	nvidia	PROPN
ap-1795	54	7	and	and	CCONJ
ap-1795	54	8	amd	amd	ADJ
ap-1795	54	9	,	,	PUNCT
ap-1795	54	10	offer	offer	VERB
ap-1795	54	11	the	the	DET
ap-1795	54	12	possibility	possibility	NOUN
ap-1795	54	13	to	to	PART
ap-1795	54	14	run	run	VERB
ap-1795	54	15	general	general	ADJ
ap-1795	54	16	purpose	purpose	NOUN
ap-1795	54	17	computation	computation	NOUN
ap-1795	54	18	on	on	ADP
ap-1795	54	19	their	their	PRON
ap-1795	54	20	gpus	gpu	NOUN
ap-1795	54	21	.	.	PUNCT
ap-1795	55	1	at	at	ADP
ap-1795	55	2	present	present	NOUN
ap-1795	55	3	there	there	PRON
ap-1795	55	4	are	be	VERB
ap-1795	55	5	no	no	DET
ap-1795	55	6	single	single	ADJ
ap-1795	55	7	-	-	PUNCT
ap-1795	55	8	purpose	purpose	NOUN
ap-1795	55	9	numerical	numerical	ADJ
ap-1795	55	10	accelerators	accelerator	NOUN
ap-1795	55	11	for	for	ADP
ap-1795	55	12	solving	solve	VERB
ap-1795	55	13	rounding	round	VERB
ap-1795	55	14	error	error	NOUN
ap-1795	55	15	sensitive	sensitive	ADJ
ap-1795	55	16	sles	sle	NOUN
ap-1795	55	17	.	.	PUNCT
ap-1795	56	1	we	we	PRON
ap-1795	56	2	use	use	VERB
ap-1795	56	3	common	common	ADJ
ap-1795	56	4	nvidia	nvidia	PROPN
ap-1795	56	5	fermi	fermi	NOUN
ap-1795	56	6	graphics	graphic	NOUN
ap-1795	56	7	cards	card	NOUN
ap-1795	56	8	together	together	ADV
ap-1795	56	9	with	with	ADP
ap-1795	56	10	intel	intel	PROPN
ap-1795	56	11	core	core	NOUN
ap-1795	56	12	processors	processor	NOUN
ap-1795	56	13	to	to	PART
ap-1795	56	14	accelerate	accelerate	VERB
ap-1795	56	15	the	the	DET
ap-1795	56	16	solution	solution	NOUN
ap-1795	56	17	.	.	PUNCT
ap-1795	57	1	3	3	X
ap-1795	57	2	.	.	X
ap-1795	57	3	mathematical	mathematical	ADJ
ap-1795	57	4	background	background	NOUN
ap-1795	57	5	let	let	VERB
ap-1795	57	6	us	we	PRON
ap-1795	57	7	take	take	VERB
ap-1795	57	8	a	a	DET
ap-1795	57	9	system	system	NOUN
ap-1795	57	10	of	of	ADP
ap-1795	57	11	linear	linear	ADJ
ap-1795	57	12	equations	equation	NOUN
ap-1795	57	13	(	(	PUNCT
ap-1795	57	14	see	see	VERB
ap-1795	57	15	[	[	X
ap-1795	57	16	1	1	NUM
ap-1795	57	17	]	]	PUNCT
ap-1795	57	18	):	):	PUNCT
ap-1795	57	19	ax	ax	NOUN
ap-1795	57	20	=	=	SYM
ap-1795	57	21	b	b	PROPN
ap-1795	57	22	,	,	PUNCT
ap-1795	57	23	(	(	PUNCT
ap-1795	57	24	1	1	X
ap-1795	57	25	)	)	PUNCT
ap-1795	57	26	where	where	SCONJ
ap-1795	57	27	a	a	DET
ap-1795	57	28	∈	∈	ADJ
ap-1795	57	29	rn×n	rn×n	NOUN
ap-1795	57	30	is	be	AUX
ap-1795	57	31	the	the	DET
ap-1795	57	32	matrix	matrix	NOUN
ap-1795	57	33	of	of	ADP
ap-1795	57	34	a	a	DET
ap-1795	57	35	system	system	NOUN
ap-1795	57	36	of	of	ADP
ap-1795	57	37	n	n	PRON
ap-1795	57	38	equations	equation	NOUN
ap-1795	57	39	of	of	ADP
ap-1795	57	40	n	n	PRON
ap-1795	57	41	unknowns	unknown	NOUN
ap-1795	57	42	,	,	PUNCT
ap-1795	57	43	b	b	PROPN
ap-1795	57	44	∈	∈	PROPN
ap-1795	57	45	rn	rn	PROPN
ap-1795	57	46	is	be	AUX
ap-1795	57	47	the	the	DET
ap-1795	57	48	right	right	ADJ
ap-1795	57	49	-	-	PUNCT
ap-1795	57	50	side	side	NOUN
ap-1795	57	51	vector	vector	NOUN
ap-1795	57	52	and	and	CCONJ
ap-1795	57	53	x	x	SYM
ap-1795	57	54	∈	∈	PROPN
ap-1795	57	55	rn	rn	PROPN
ap-1795	57	56	is	be	AUX
ap-1795	57	57	the	the	DET
ap-1795	57	58	desired	desire	VERB
ap-1795	57	59	vector	vector	NOUN
ap-1795	57	60	,	,	PUNCT
ap-1795	57	61	the	the	DET
ap-1795	57	62	solution	solution	NOUN
ap-1795	57	63	of	of	ADP
ap-1795	57	64	our	our	PRON
ap-1795	57	65	system	system	NOUN
ap-1795	57	66	of	of	ADP
ap-1795	57	67	linear	linear	PROPN
ap-1795	57	68	equations	equation	NOUN
ap-1795	57	69	.	.	PUNCT
ap-1795	58	1	3.1	3.1	NUM
ap-1795	58	2	.	.	PUNCT
ap-1795	58	3	matrix	matrix	NOUN
ap-1795	58	4	scaling	scale	VERB
ap-1795	58	5	matrix	matrix	NOUN
ap-1795	58	6	scaling	scaling	NOUN
ap-1795	58	7	is	be	AUX
ap-1795	58	8	the	the	DET
ap-1795	58	9	first	first	ADJ
ap-1795	58	10	thing	thing	NOUN
ap-1795	58	11	to	to	PART
ap-1795	58	12	do	do	VERB
ap-1795	58	13	.	.	PUNCT
ap-1795	59	1	the	the	DET
ap-1795	59	2	goal	goal	NOUN
ap-1795	59	3	of	of	ADP
ap-1795	59	4	matrix	matrix	NOUN
ap-1795	59	5	scaling	scaling	NOUN
ap-1795	59	6	is	be	AUX
ap-1795	59	7	to	to	PART
ap-1795	59	8	adjust	adjust	VERB
ap-1795	59	9	all	all	DET
ap-1795	59	10	the	the	DET
ap-1795	59	11	floating	float	VERB
ap-1795	59	12	-	-	PUNCT
ap-1795	59	13	point	point	NOUN
ap-1795	59	14	numbers	number	NOUN
ap-1795	59	15	of	of	ADP
ap-1795	59	16	the	the	DET
ap-1795	59	17	matrix	matrix	NOUN
ap-1795	59	18	to	to	ADP
ap-1795	59	19	their	their	PRON
ap-1795	59	20	corresponding	corresponding	ADJ
ap-1795	59	21	integer	integer	NOUN
ap-1795	59	22	versions	version	NOUN
ap-1795	59	23	.	.	PUNCT
ap-1795	60	1	basically	basically	ADV
ap-1795	60	2	,	,	PUNCT
ap-1795	60	3	every	every	DET
ap-1795	60	4	matrix	matrix	NOUN
ap-1795	60	5	row	row	NOUN
ap-1795	60	6	is	be	AUX
ap-1795	60	7	multiplied	multiply	VERB
ap-1795	60	8	by	by	ADP
ap-1795	60	9	its	its	PRON
ap-1795	60	10	scaling	scale	VERB
ap-1795	60	11	constant	constant	ADJ
ap-1795	60	12	(	(	PUNCT
ap-1795	60	13	scalar	scalar	ADJ
ap-1795	60	14	multiplication	multiplication	NOUN
ap-1795	60	15	)	)	PUNCT
ap-1795	60	16	.	.	PUNCT
ap-1795	61	1	this	this	PRON
ap-1795	61	2	has	have	VERB
ap-1795	61	3	to	to	PART
ap-1795	61	4	be	be	AUX
ap-1795	61	5	done	do	VERB
ap-1795	61	6	without	without	ADP
ap-1795	61	7	losing	lose	VERB
ap-1795	61	8	a	a	DET
ap-1795	61	9	single	single	ADJ
ap-1795	61	10	bit	bit	NOUN
ap-1795	61	11	of	of	ADP
ap-1795	61	12	precision	precision	NOUN
ap-1795	61	13	.	.	PUNCT
ap-1795	62	1	this	this	DET
ap-1795	62	2	condition	condition	NOUN
ap-1795	62	3	will	will	AUX
ap-1795	62	4	be	be	AUX
ap-1795	62	5	achieved	achieve	VERB
ap-1795	62	6	only	only	ADV
ap-1795	62	7	when	when	SCONJ
ap-1795	62	8	the	the	DET
ap-1795	62	9	scaling	scaling	ADJ
ap-1795	62	10	constant	constant	ADJ
ap-1795	62	11	is	be	AUX
ap-1795	62	12	2n	2n	NUM
ap-1795	62	13	,	,	PUNCT
ap-1795	62	14	where	where	SCONJ
ap-1795	62	15	n	n	X
ap-1795	62	16	∈	∈	PROPN
ap-1795	62	17	n1	n1	NOUN
ap-1795	62	18	.	.	PUNCT
ap-1795	63	1	the	the	DET
ap-1795	63	2	question	question	NOUN
ap-1795	63	3	now	now	ADV
ap-1795	63	4	is	be	AUX
ap-1795	63	5	how	how	SCONJ
ap-1795	63	6	to	to	PART
ap-1795	63	7	determine	determine	VERB
ap-1795	63	8	the	the	DET
ap-1795	63	9	scaling	scaling	NOUN
ap-1795	63	10	constant	constant	ADJ
ap-1795	63	11	.	.	PUNCT
ap-1795	64	1	first	first	ADV
ap-1795	64	2	,	,	PUNCT
ap-1795	64	3	we	we	PRON
ap-1795	64	4	should	should	AUX
ap-1795	64	5	continue	continue	VERB
ap-1795	64	6	by	by	ADP
ap-1795	64	7	finding	find	VERB
ap-1795	64	8	the	the	DET
ap-1795	64	9	smallest	small	ADJ
ap-1795	64	10	absolute	absolute	ADJ
ap-1795	64	11	value	value	NOUN
ap-1795	64	12	element	element	NOUN
ap-1795	64	13	(	(	PUNCT
ap-1795	64	14	closest	close	ADJ
ap-1795	64	15	to	to	ADP
ap-1795	64	16	zero	zero	NUM
ap-1795	64	17	)	)	PUNCT
ap-1795	64	18	in	in	ADP
ap-1795	64	19	each	each	DET
ap-1795	64	20	row	row	NOUN
ap-1795	64	21	.	.	PUNCT
ap-1795	65	1	then	then	ADV
ap-1795	65	2	,	,	PUNCT
ap-1795	65	3	we	we	PRON
ap-1795	65	4	extract	extract	VERB
ap-1795	65	5	the	the	DET
ap-1795	65	6	absolute	absolute	ADJ
ap-1795	65	7	value	value	NOUN
ap-1795	65	8	of	of	ADP
ap-1795	65	9	its	its	PRON
ap-1795	65	10	exponent	exponent	NOUN
ap-1795	65	11	and	and	CCONJ
ap-1795	65	12	multiply	multiply	VERB
ap-1795	65	13	it	it	PRON
ap-1795	65	14	by	by	ADP
ap-1795	65	15	the	the	DET
ap-1795	65	16	253	253	NUM
ap-1795	65	17	constant	constant	ADJ
ap-1795	65	18	,	,	PUNCT
ap-1795	65	19	because	because	SCONJ
ap-1795	65	20	a	a	DET
ap-1795	65	21	significant	significant	ADJ
ap-1795	65	22	mantissa	mantissa	NOUN
ap-1795	65	23	bit	bit	NOUN
ap-1795	65	24	size	size	NOUN
ap-1795	65	25	in	in	ADP
ap-1795	65	26	the	the	DET
ap-1795	65	27	ieee	ieee	NOUN
ap-1795	65	28	754	754	NUM
ap-1795	65	29	[	[	SYM
ap-1795	65	30	6	6	NUM
ap-1795	65	31	]	]	SYM
ap-1795	65	32	double	double	ADJ
ap-1795	65	33	precision	precision	NOUN
ap-1795	65	34	floating	float	VERB
ap-1795	65	35	point	point	NOUN
ap-1795	65	36	number	number	NOUN
ap-1795	65	37	format	format	NOUN
ap-1795	65	38	is	be	AUX
ap-1795	65	39	53	53	NUM
ap-1795	65	40	bits	bit	NOUN
ap-1795	65	41	long	long	ADV
ap-1795	65	42	.	.	PUNCT
ap-1795	66	1	finally	finally	ADV
ap-1795	66	2	,	,	PUNCT
ap-1795	66	3	the	the	DET
ap-1795	66	4	scaling	scale	VERB
ap-1795	66	5	constant	constant	ADJ
ap-1795	66	6	s	s	VERB
ap-1795	66	7	is	be	AUX
ap-1795	66	8	computed	compute	VERB
ap-1795	66	9	:	:	PUNCT
ap-1795	66	10	s	s	X
ap-1795	66	11	=	=	SYM
ap-1795	66	12	253	253	NUM
ap-1795	66	13	∗	∗	NOUN
ap-1795	66	14	2|exp(minrow)|	2|exp(minrow)|	VERB
ap-1795	66	15	,	,	PUNCT
ap-1795	66	16	(	(	PUNCT
ap-1795	66	17	2	2	X
ap-1795	66	18	)	)	PUNCT
ap-1795	66	19	where	where	SCONJ
ap-1795	66	20	exp	exp	NOUN
ap-1795	66	21	is	be	AUX
ap-1795	66	22	a	a	DET
ap-1795	66	23	function	function	NOUN
ap-1795	66	24	that	that	SCONJ
ap-1795	66	25	extracts	extract	NOUN
ap-1795	66	26	and	and	CCONJ
ap-1795	66	27	returns	return	VERB
ap-1795	66	28	the	the	DET
ap-1795	66	29	exponent	exponent	NOUN
ap-1795	66	30	(	(	PUNCT
ap-1795	66	31	as	as	ADP
ap-1795	66	32	an	an	DET
ap-1795	66	33	integer	integer	NOUN
ap-1795	66	34	–	–	PUNCT
ap-1795	66	35	power	power	NOUN
ap-1795	66	36	of	of	ADP
ap-1795	66	37	2	2	NUM
ap-1795	66	38	)	)	PUNCT
ap-1795	66	39	and	and	CCONJ
ap-1795	66	40	minrow	minrow	NOUN
ap-1795	66	41	is	be	AUX
ap-1795	66	42	the	the	DET
ap-1795	66	43	element	element	NOUN
ap-1795	66	44	in	in	ADP
ap-1795	66	45	the	the	DET
ap-1795	66	46	row	row	NOUN
ap-1795	66	47	closest	close	ADJ
ap-1795	66	48	to	to	ADP
ap-1795	66	49	zero	zero	NUM
ap-1795	66	50	.	.	PUNCT
ap-1795	67	1	the	the	DET
ap-1795	67	2	approach	approach	NOUN
ap-1795	67	3	being	be	AUX
ap-1795	67	4	used	use	VERB
ap-1795	67	5	is	be	AUX
ap-1795	67	6	explained	explain	VERB
ap-1795	67	7	in	in	ADP
ap-1795	67	8	greater	great	ADJ
ap-1795	67	9	detail	detail	NOUN
ap-1795	67	10	(	(	PUNCT
ap-1795	67	11	and	and	CCONJ
ap-1795	67	12	with	with	ADP
ap-1795	67	13	alternatives	alternative	NOUN
ap-1795	67	14	)	)	PUNCT
ap-1795	67	15	in	in	ADP
ap-1795	67	16	[	[	X
ap-1795	67	17	2	2	NUM
ap-1795	67	18	]	]	PUNCT
ap-1795	67	19	.	.	PUNCT
ap-1795	68	1	3.2	3.2	NUM
ap-1795	68	2	.	.	PUNCT
ap-1795	69	1	solving	solve	VERB
ap-1795	69	2	a	a	DET
ap-1795	69	3	system	system	NOUN
ap-1795	69	4	of	of	ADP
ap-1795	69	5	linear	linear	ADJ
ap-1795	69	6	equations	equation	NOUN
ap-1795	69	7	from	from	ADP
ap-1795	69	8	the	the	DET
ap-1795	69	9	previous	previous	ADJ
ap-1795	69	10	step	step	NOUN
ap-1795	69	11	we	we	PRON
ap-1795	69	12	have	have	VERB
ap-1795	69	13	an	an	DET
ap-1795	69	14	properly	properly	ADV
ap-1795	69	15	scaled	scale	VERB
ap-1795	69	16	-	-	PUNCT
ap-1795	69	17	up	up	ADP
ap-1795	69	18	system	system	NOUN
ap-1795	69	19	of	of	ADP
ap-1795	69	20	linear	linear	PROPN
ap-1795	69	21	equations	equation	NOUN
ap-1795	69	22	:	:	PUNCT
ap-1795	69	23	ax	ax	NOUN
ap-1795	69	24	=	=	SYM
ap-1795	69	25	b	b	PROPN
ap-1795	69	26	,	,	PUNCT
ap-1795	69	27	(	(	PUNCT
ap-1795	69	28	3	3	X
ap-1795	69	29	)	)	PUNCT
ap-1795	69	30	where	where	SCONJ
ap-1795	69	31	aij	aij	PROPN
ap-1795	69	32	matrix	matrix	VERB
ap-1795	69	33	a	a	DET
ap-1795	69	34	elements	element	NOUN
ap-1795	69	35	and	and	CCONJ
ap-1795	69	36	xi	xi	NOUN
ap-1795	69	37	and	and	CCONJ
ap-1795	69	38	bi	bi	NOUN
ap-1795	69	39	vector	vector	NOUN
ap-1795	69	40	elements	element	NOUN
ap-1795	69	41	are	be	AUX
ap-1795	69	42	just	just	ADV
ap-1795	69	43	big	big	ADJ
ap-1795	69	44	integers	integer	NOUN
ap-1795	69	45	.	.	PUNCT
ap-1795	70	1	we	we	PRON
ap-1795	70	2	solve	solve	VERB
ap-1795	70	3	it	it	PRON
ap-1795	70	4	using	use	VERB
ap-1795	70	5	a	a	DET
ap-1795	70	6	multi	multi	ADJ
ap-1795	70	7	-	-	ADJ
ap-1795	70	8	modulus	modulus	ADJ
ap-1795	70	9	arithmetics	arithmetic	NOUN
ap-1795	70	10	over	over	ADP
ap-1795	70	11	the	the	DET
ap-1795	70	12	commutative	commutative	ADJ
ap-1795	70	13	ring	ring	NOUN
ap-1795	70	14	(	(	PUNCT
ap-1795	70	15	zβ	zβ	PROPN
ap-1795	70	16	,	,	PUNCT
ap-1795	70	17	⊕	⊕	PROPN
ap-1795	70	18	,	,	PUNCT
ap-1795	70	19	�	�	PROPN
ap-1795	70	20	)	)	PUNCT
ap-1795	70	21	with	with	ADP
ap-1795	70	22	a	a	DET
ap-1795	70	23	base	base	NOUN
ap-1795	70	24	vector	vector	NOUN
ap-1795	70	25	β	β	NOUN
ap-1795	70	26	that	that	PRON
ap-1795	70	27	is	be	AUX
ap-1795	70	28	equivalent	equivalent	ADJ
ap-1795	70	29	to	to	ADP
ap-1795	70	30	the	the	DET
ap-1795	70	31	single	single	ADJ
ap-1795	70	32	-	-	PUNCT
ap-1795	70	33	modulus	modulus	ADJ
ap-1795	70	34	arithmetics	arithmetic	NOUN
ap-1795	70	35	over	over	ADP
ap-1795	70	36	(	(	PUNCT
ap-1795	70	37	zm	zm	PROPN
ap-1795	70	38	,	,	PUNCT
ap-1795	70	39	+	+	PROPN
ap-1795	70	40	,	,	PUNCT
ap-1795	70	41	·	·	PUNCT
ap-1795	70	42	)	)	PUNCT
ap-1795	70	43	and	and	CCONJ
ap-1795	70	44	module	module	NOUN
ap-1795	70	45	m	m	PROPN
ap-1795	70	46	.	.	PUNCT
ap-1795	71	1	m	m	PROPN
ap-1795	71	2	has	have	VERB
ap-1795	71	3	to	to	PART
ap-1795	71	4	be	be	AUX
ap-1795	71	5	a	a	DET
ap-1795	71	6	big	big	ADJ
ap-1795	71	7	enough	enough	ADJ
ap-1795	71	8	positive	positive	ADJ
ap-1795	71	9	integer	integer	NOUN
ap-1795	71	10	to	to	PART
ap-1795	71	11	avoid	avoid	VERB
ap-1795	71	12	rounding	round	VERB
ap-1795	71	13	errors	error	NOUN
ap-1795	71	14	during	during	ADP
ap-1795	71	15	our	our	PRON
ap-1795	71	16	computation	computation	NOUN
ap-1795	71	17	.	.	PUNCT
ap-1795	72	1	hadamard	hadamard	PROPN
ap-1795	72	2	’s	’s	PART
ap-1795	72	3	determinant	determinant	ADJ
ap-1795	72	4	d	d	NOUN
ap-1795	72	5	estimate	estimate	NOUN
ap-1795	72	6	of	of	ADP
ap-1795	72	7	matrix	matrix	NOUN
ap-1795	72	8	a	a	PRON
ap-1795	72	9	can	can	AUX
ap-1795	72	10	be	be	AUX
ap-1795	72	11	used	use	VERB
ap-1795	72	12	to	to	PART
ap-1795	72	13	estimate	estimate	VERB
ap-1795	72	14	the	the	DET
ap-1795	72	15	maximum	maximum	ADJ
ap-1795	72	16	m	m	NOUN
ap-1795	72	17	value	value	NOUN
ap-1795	72	18	:	:	PUNCT
ap-1795	72	19	|d|2	|d|2	PROPN
ap-1795	72	20	≤	≤	PROPN
ap-1795	72	21	n∏	n∏	PROPN
ap-1795	72	22	i=1	i=1	PROPN
ap-1795	73	1	(	(	PUNCT
ap-1795	73	2	|a2	|a2	ADV
ap-1795	73	3	i1|+	i1|+	PROPN
ap-1795	73	4	|a2	|a2	ADV
ap-1795	73	5	i2|+	i2|+	PROPN
ap-1795	73	6	·	·	PUNCT
ap-1795	73	7	·	·	PUNCT
ap-1795	73	8	·	·	PUNCT
ap-1795	73	9	+	+	CCONJ
ap-1795	73	10	|a2	|a2	ADJ
ap-1795	73	11	in|	in|	ADJ
ap-1795	73	12	)	)	PUNCT
ap-1795	73	13	.	.	PUNCT
ap-1795	74	1	(	(	PUNCT
ap-1795	74	2	4	4	X
ap-1795	74	3	)	)	PUNCT
ap-1795	74	4	the	the	DET
ap-1795	74	5	highest	high	ADJ
ap-1795	74	6	value	value	NOUN
ap-1795	74	7	of	of	ADP
ap-1795	74	8	m	m	PRON
ap-1795	74	9	that	that	PRON
ap-1795	74	10	could	could	AUX
ap-1795	74	11	appear	appear	VERB
ap-1795	74	12	during	during	ADP
ap-1795	74	13	the	the	DET
ap-1795	74	14	computation	computation	NOUN
ap-1795	74	15	:	:	PUNCT
ap-1795	75	1	m	m	VERB
ap-1795	75	2	>	>	X
ap-1795	75	3	2	2	NUM
ap-1795	75	4	max	max	NOUN
ap-1795	75	5			PUNCT
ap-1795	75	6	n	n	CCONJ
ap-1795	75	7	n	n	NUM
ap-1795	75	8	2	2	NUM
ap-1795	75	9	max(an	max(an	NUM
ap-1795	75	10	ij	ij	NOUN
ap-1795	75	11	)	)	PUNCT
ap-1795	75	12	,	,	PUNCT
ap-1795	75	13	i	i	PRON
ap-1795	75	14	,	,	PUNCT
ap-1795	75	15	j=1,2,	j=1,2,	NOUN
ap-1795	75	16	...	...	PUNCT
ap-1795	75	17	,n	,n	NOUN
ap-1795	75	18	,	,	PUNCT
ap-1795	75	19	n(n−1	n(n−1	NUM
ap-1795	75	20	)	)	PUNCT
ap-1795	75	21	(	(	PUNCT
ap-1795	75	22	n−1	n−1	PROPN
ap-1795	75	23	)	)	PUNCT
ap-1795	75	24	2	2	NUM
ap-1795	75	25	max(aij)n−1	max(aij)n−1	ADJ
ap-1795	75	26	max(yi	max(yi	NOUN
ap-1795	75	27	)	)	PUNCT
ap-1795	75	28	,	,	PUNCT
ap-1795	75	29	i	i	PRON
ap-1795	75	30	,	,	PUNCT
ap-1795	75	31	j=1,2,	j=1,2,	NOUN
ap-1795	75	32	...	...	PUNCT
ap-1795	75	33	,n	,n	PUNCT
ap-1795	75	34			NOUN
ap-1795	75	35	(	(	PUNCT
ap-1795	75	36	5	5	NUM
ap-1795	75	37	)	)	PUNCT
ap-1795	75	38	and	and	CCONJ
ap-1795	75	39	gcd(m	gcd(m	NOUN
ap-1795	75	40	,	,	PUNCT
ap-1795	75	41	d	d	NOUN
ap-1795	75	42	)	)	PUNCT
ap-1795	75	43	=	=	SYM
ap-1795	75	44	1	1	X
ap-1795	75	45	.	.	PUNCT
ap-1795	75	46	(	(	PUNCT
ap-1795	75	47	6	6	X
ap-1795	75	48	)	)	PUNCT
ap-1795	75	49	we	we	PRON
ap-1795	75	50	also	also	ADV
ap-1795	75	51	need	need	VERB
ap-1795	75	52	the	the	DET
ap-1795	75	53	following	follow	VERB
ap-1795	75	54	conditions	condition	NOUN
ap-1795	75	55	for	for	ADP
ap-1795	75	56	the	the	DET
ap-1795	75	57	vector	vector	NOUN
ap-1795	75	58	β	β	X
ap-1795	75	59	=	=	SYM
ap-1795	75	60	(	(	PUNCT
ap-1795	75	61	m1,m2	m1,m2	PROPN
ap-1795	75	62	,	,	PUNCT
ap-1795	75	63	.	.	PUNCT
ap-1795	75	64	.	.	PUNCT
ap-1795	75	65	.	.	PUNCT
ap-1795	76	1	,	,	PUNCT
ap-1795	76	2	mr	mr	PROPN
ap-1795	76	3	)	)	PUNCT
ap-1795	76	4	and	and	CCONJ
ap-1795	76	5	module	module	NOUN
ap-1795	76	6	m	m	NOUN
ap-1795	76	7	to	to	PART
ap-1795	76	8	be	be	AUX
ap-1795	76	9	satisfied	satisfied	ADJ
ap-1795	76	10	:	:	PUNCT
ap-1795	76	11	•	•	X
ap-1795	77	1	r∏	r∏	NOUN
ap-1795	77	2	i	i	INTJ
ap-1795	77	3	mi	mi	PROPN
ap-1795	78	1	=	=	NOUN
ap-1795	78	2	m	m	PROPN
ap-1795	78	3	;	;	PUNCT
ap-1795	78	4	•	•	NUM
ap-1795	78	5	m1	m1	PROPN
ap-1795	78	6	<	<	X
ap-1795	78	7	m2	m2	PROPN
ap-1795	78	8	<	<	X
ap-1795	78	9	·	·	PUNCT
ap-1795	78	10	·	·	PUNCT
ap-1795	78	11	·	·	PUNCT
ap-1795	79	1	<	<	X
ap-1795	79	2	mr	mr	PROPN
ap-1795	79	3	;	;	PUNCT
ap-1795	79	4	•	•	PUNCT
ap-1795	79	5	m1,m2	m1,m2	PROPN
ap-1795	79	6	,	,	PUNCT
ap-1795	79	7	.	.	PUNCT
ap-1795	79	8	.	.	PUNCT
ap-1795	79	9	.	.	PUNCT
ap-1795	80	1	.mr	.mr	PROPN
ap-1795	80	2	are	be	AUX
ap-1795	80	3	prime	prime	ADJ
ap-1795	80	4	numbers	number	NOUN
ap-1795	80	5	.	.	PUNCT
ap-1795	81	1	the	the	DET
ap-1795	81	2	following	follow	VERB
ap-1795	81	3	condition	condition	NOUN
ap-1795	81	4	for	for	ADP
ap-1795	81	5	the	the	DET
ap-1795	81	6	sle	sle	PROPN
ap-1795	81	7	(	(	PUNCT
ap-1795	81	8	given	give	VERB
ap-1795	81	9	by	by	ADP
ap-1795	81	10	eq	eq	PROPN
ap-1795	81	11	.	.	PUNCT
ap-1795	81	12	(	(	PUNCT
ap-1795	81	13	3	3	NUM
ap-1795	81	14	)	)	PUNCT
ap-1795	81	15	)	)	PUNCT
ap-1795	82	1	determinant	determinant	ADJ
ap-1795	82	2	is	be	AUX
ap-1795	82	3	satisfied	satisfied	ADJ
ap-1795	82	4	when	when	SCONJ
ap-1795	82	5	:	:	PUNCT
ap-1795	82	6	|d|mi	|d|mi	X
ap-1795	82	7	6=	6=	ADP
ap-1795	82	8	0	0	NUM
ap-1795	82	9	,	,	PUNCT
ap-1795	82	10	i	i	PRON
ap-1795	82	11	=	=	NOUN
ap-1795	82	12	1	1	NUM
ap-1795	82	13	,	,	PUNCT
ap-1795	82	14	2	2	NUM
ap-1795	82	15	,	,	PUNCT
ap-1795	82	16	.	.	PUNCT
ap-1795	82	17	.	.	PUNCT
ap-1795	83	1	.	.	PUNCT
ap-1795	84	1	,	,	PUNCT
ap-1795	84	2	r	r	NOUN
ap-1795	84	3	,	,	PUNCT
ap-1795	84	4	(	(	PUNCT
ap-1795	84	5	7	7	X
ap-1795	84	6	)	)	PUNCT
ap-1795	84	7	then	then	ADV
ap-1795	84	8	the	the	DET
ap-1795	84	9	sle	sle	NOUN
ap-1795	84	10	(	(	PUNCT
ap-1795	84	11	from	from	ADP
ap-1795	84	12	eq	eq	ADP
ap-1795	84	13	.	.	PUNCT
ap-1795	85	1	(	(	PUNCT
ap-1795	85	2	3	3	NUM
ap-1795	85	3	)	)	PUNCT
ap-1795	85	4	)	)	PUNCT
ap-1795	85	5	solved	solve	VERB
ap-1795	85	6	within	within	ADP
ap-1795	85	7	(	(	PUNCT
ap-1795	85	8	zβ	zβ	PROPN
ap-1795	85	9	,	,	PUNCT
ap-1795	85	10	⊕	⊕	PROPN
ap-1795	85	11	,	,	PUNCT
ap-1795	85	12	�	�	PROPN
ap-1795	85	13	)	)	PUNCT
ap-1795	85	14	due	due	ADP
ap-1795	85	15	to	to	ADP
ap-1795	85	16	vector	vector	NOUN
ap-1795	85	17	β	β	NOUN
ap-1795	85	18	can	can	AUX
ap-1795	85	19	be	be	AUX
ap-1795	85	20	expressed	express	VERB
ap-1795	85	21	as	as	ADP
ap-1795	85	22	:	:	PUNCT
ap-1795	85	23	|ax|mi	|ax|mi	NOUN
ap-1795	85	24	=	=	SYM
ap-1795	85	25	|b|mi	|b|mi	NOUN
ap-1795	85	26	,	,	PUNCT
ap-1795	85	27	(	(	PUNCT
ap-1795	85	28	8)	8)	NUM
ap-1795	85	29	or	or	CCONJ
ap-1795	85	30	,	,	PUNCT
ap-1795	85	31	for	for	ADP
ap-1795	85	32	individual	individual	ADJ
ap-1795	85	33	modules	module	NOUN
ap-1795	85	34	mi	mi	PROPN
ap-1795	85	35	of	of	ADP
ap-1795	85	36	vector	vector	PROPN
ap-1795	85	37	β	β	NOUN
ap-1795	85	38	:	:	PUNCT
ap-1795	85	39	|ax|mi	|ax|mi	NOUN
ap-1795	85	40	=	=	SYM
ap-1795	85	41	|b|mi	|b|mi	NOUN
ap-1795	85	42	,	,	PUNCT
ap-1795	85	43	i	i	PRON
ap-1795	85	44	=	=	NOUN
ap-1795	85	45	1	1	NUM
ap-1795	85	46	,	,	PUNCT
ap-1795	85	47	2	2	NUM
ap-1795	85	48	,	,	PUNCT
ap-1795	85	49	.	.	PUNCT
ap-1795	85	50	.	.	PUNCT
ap-1795	86	1	.	.	PUNCT
ap-1795	87	1	,	,	PUNCT
ap-1795	87	2	r.	r.	PROPN
ap-1795	87	3	(	(	PUNCT
ap-1795	87	4	9	9	NUM
ap-1795	87	5	)	)	PUNCT
ap-1795	87	6	71	71	NUM
ap-1795	87	7	jakub	jakub	PROPN
ap-1795	87	8	hladík	hladík	PROPN
ap-1795	87	9	,	,	PUNCT
ap-1795	87	10	róbert	róbert	PROPN
ap-1795	87	11	lórencz	lórencz	PROPN
ap-1795	87	12	,	,	PUNCT
ap-1795	87	13	ivan	ivan	PROPN
ap-1795	87	14	šimeček	šimeček	PROPN
ap-1795	87	15	acta	acta	PROPN
ap-1795	87	16	polytechnica	polytechnica	PROPN
ap-1795	87	17	the	the	DET
ap-1795	87	18	following	follow	VERB
ap-1795	87	19	expression	expression	NOUN
ap-1795	87	20	is	be	AUX
ap-1795	87	21	also	also	ADV
ap-1795	87	22	valid	valid	ADJ
ap-1795	87	23	for	for	ADP
ap-1795	87	24	eq	eq	PROPN
ap-1795	87	25	.	.	PUNCT
ap-1795	88	1	(	(	PUNCT
ap-1795	88	2	3	3	NUM
ap-1795	88	3	)	)	PUNCT
ap-1795	88	4	within	within	ADP
ap-1795	88	5	(	(	PUNCT
ap-1795	88	6	zβ	zβ	PROPN
ap-1795	88	7	,	,	PUNCT
ap-1795	88	8	⊕	⊕	PROPN
ap-1795	88	9	,	,	PUNCT
ap-1795	88	10	�	�	PROPN
ap-1795	88	11	):	):	PUNCT
ap-1795	88	12	|aa−1|β	|aa−1|β	PROPN
ap-1795	88	13	=	=	SYM
ap-1795	88	14	|a−1a|β	|a−1a|β	NOUN
ap-1795	88	15	=	=	SYM
ap-1795	88	16	e	e	X
ap-1795	88	17	(	(	PUNCT
ap-1795	88	18	10	10	NUM
ap-1795	88	19	)	)	PUNCT
ap-1795	88	20	and	and	CCONJ
ap-1795	88	21	|x|β	|x|β	NOUN
ap-1795	88	22	=	=	PUNCT
ap-1795	88	23	|a−1b|β	|a−1b|β	INTJ
ap-1795	88	24	,	,	PUNCT
ap-1795	88	25	(	(	PUNCT
ap-1795	88	26	11	11	NUM
ap-1795	88	27	)	)	PUNCT
ap-1795	88	28	where	where	SCONJ
ap-1795	88	29	e	e	NOUN
ap-1795	88	30	is	be	AUX
ap-1795	88	31	the	the	DET
ap-1795	88	32	identity	identity	NOUN
ap-1795	88	33	matrix	matrix	NOUN
ap-1795	88	34	.	.	PUNCT
ap-1795	89	1	to	to	PART
ap-1795	89	2	solve	solve	VERB
ap-1795	89	3	the	the	DET
ap-1795	89	4	sle	sle	NOUN
ap-1795	89	5	from	from	ADP
ap-1795	89	6	eq	eq	PROPN
ap-1795	89	7	.	.	PUNCT
ap-1795	90	1	(	(	PUNCT
ap-1795	90	2	9	9	NUM
ap-1795	90	3	)	)	PUNCT
ap-1795	90	4	within	within	ADP
ap-1795	90	5	the	the	DET
ap-1795	90	6	specific	specific	ADJ
ap-1795	90	7	modular	modular	ADJ
ap-1795	90	8	arithmetics	arithmetic	NOUN
ap-1795	90	9	we	we	PRON
ap-1795	90	10	will	will	AUX
ap-1795	90	11	use	use	VERB
ap-1795	90	12	the	the	DET
ap-1795	90	13	gauss	gauss	PROPN
ap-1795	90	14	-	-	PUNCT
ap-1795	90	15	jordan	jordan	PROPN
ap-1795	90	16	elimination	elimination	NOUN
ap-1795	90	17	algorithm	algorithm	NOUN
ap-1795	90	18	with	with	ADP
ap-1795	90	19	non	non	ADJ
ap-1795	90	20	-	-	ADJ
ap-1795	90	21	zero	zero	NUM
ap-1795	90	22	pivotization	pivotization	NOUN
ap-1795	90	23	.	.	PUNCT
ap-1795	91	1	the	the	DET
ap-1795	91	2	difference	difference	NOUN
ap-1795	91	3	from	from	ADP
ap-1795	91	4	the	the	DET
ap-1795	91	5	original	original	ADJ
ap-1795	91	6	gauss	gauss	PROPN
ap-1795	91	7	-	-	PUNCT
ap-1795	91	8	jordan	jordan	PROPN
ap-1795	91	9	elimination	elimination	NOUN
ap-1795	91	10	is	be	AUX
ap-1795	91	11	the	the	DET
ap-1795	91	12	usage	usage	NOUN
ap-1795	91	13	of	of	ADP
ap-1795	91	14	modular	modular	ADJ
ap-1795	91	15	arithmetics	arithmetic	NOUN
ap-1795	91	16	for	for	ADP
ap-1795	91	17	all	all	DET
ap-1795	91	18	algorithm	algorithm	NOUN
ap-1795	91	19	steps	step	NOUN
ap-1795	91	20	.	.	PUNCT
ap-1795	92	1	there	there	PRON
ap-1795	92	2	is	be	VERB
ap-1795	92	3	also	also	ADV
ap-1795	92	4	pivotization	pivotization	NOUN
ap-1795	92	5	simplification	simplification	NOUN
ap-1795	92	6	–	–	PUNCT
ap-1795	92	7	we	we	PRON
ap-1795	92	8	do	do	AUX
ap-1795	92	9	not	not	PART
ap-1795	92	10	need	need	VERB
ap-1795	92	11	to	to	PART
ap-1795	92	12	find	find	VERB
ap-1795	92	13	the	the	DET
ap-1795	92	14	greatest	great	ADJ
ap-1795	92	15	element	element	NOUN
ap-1795	92	16	in	in	ADP
ap-1795	92	17	the	the	DET
ap-1795	92	18	elimination	elimination	NOUN
ap-1795	92	19	step	step	NOUN
ap-1795	92	20	,	,	PUNCT
ap-1795	92	21	a	a	DET
ap-1795	92	22	nonzero	nonzero	NOUN
ap-1795	92	23	element	element	NOUN
ap-1795	92	24	is	be	AUX
ap-1795	92	25	good	good	ADJ
ap-1795	92	26	enough	enough	ADV
ap-1795	92	27	.	.	PUNCT
ap-1795	93	1	using	use	VERB
ap-1795	93	2	the	the	DET
ap-1795	93	3	gj	gj	NOUN
ap-1795	93	4	elimination	elimination	NOUN
ap-1795	93	5	algorithm	algorithm	NOUN
ap-1795	93	6	,	,	PUNCT
ap-1795	93	7	let	let	VERB
ap-1795	93	8	us	we	PRON
ap-1795	93	9	have	have	VERB
ap-1795	93	10	an	an	DET
ap-1795	93	11	matrix	matrix	NOUN
ap-1795	93	12	w	w	NOUN
ap-1795	93	13	of	of	ADP
ap-1795	93	14	dimensions	dimension	NOUN
ap-1795	93	15	n×	n×	PROPN
ap-1795	93	16	(	(	PUNCT
ap-1795	93	17	n+	n+	NOUN
ap-1795	93	18	1	1	X
ap-1795	93	19	)	)	PUNCT
ap-1795	93	20	consisting	consist	VERB
ap-1795	93	21	of	of	ADP
ap-1795	93	22	matrix	matrix	NOUN
ap-1795	93	23	a	a	PRON
ap-1795	93	24	and	and	CCONJ
ap-1795	93	25	vector	vector	NOUN
ap-1795	93	26	b	b	NOUN
ap-1795	93	27	:	:	PUNCT
ap-1795	93	28	w	w	NOUN
ap-1795	93	29	=	=	PUNCT
ap-1795	93	30			PROPN
ap-1795	93	31	a11	a11	PROPN
ap-1795	93	32	a12	a12	PROPN
ap-1795	93	33	·	·	PUNCT
ap-1795	93	34	·	·	PUNCT
ap-1795	93	35	·	·	PUNCT
ap-1795	94	1	a1n	a1n	NOUN
ap-1795	94	2	b1	b1	VERB
ap-1795	94	3	a21	a21	PROPN
ap-1795	94	4	a22	a22	PROPN
ap-1795	94	5	·	·	PUNCT
ap-1795	94	6	·	·	PUNCT
ap-1795	94	7	·	·	PUNCT
ap-1795	95	1	a2n	a2n	PROPN
ap-1795	95	2	b2	b2	NOUN
ap-1795	95	3	...	...	PUNCT
ap-1795	95	4	...	...	PUNCT
ap-1795	95	5	.	.	PUNCT
ap-1795	95	6	.	.	PUNCT
ap-1795	95	7	.	.	PUNCT
ap-1795	96	1	...	...	PUNCT
ap-1795	96	2	...	...	PUNCT
ap-1795	97	1	an1	an1	PROPN
ap-1795	98	1	an2	an2	PROPN
ap-1795	98	2	·	·	PUNCT
ap-1795	98	3	·	·	PUNCT
ap-1795	98	4	·	·	PUNCT
ap-1795	99	1	ann	ann	PROPN
ap-1795	99	2	bn	bn	PROPN
ap-1795	99	3			PROPN
ap-1795	99	4	.	.	PUNCT
ap-1795	100	1	(	(	PUNCT
ap-1795	100	2	12	12	NUM
ap-1795	100	3	)	)	PUNCT
ap-1795	100	4	the	the	DET
ap-1795	100	5	goal	goal	NOUN
ap-1795	100	6	of	of	ADP
ap-1795	100	7	the	the	DET
ap-1795	100	8	algorithm	algorithm	NOUN
ap-1795	100	9	is	be	AUX
ap-1795	100	10	to	to	PART
ap-1795	100	11	eliminate	eliminate	VERB
ap-1795	100	12	all	all	DET
ap-1795	100	13	w	w	ADJ
ap-1795	100	14	elements	element	NOUN
ap-1795	100	15	one	one	NUM
ap-1795	100	16	by	by	ADP
ap-1795	100	17	one	one	NUM
ap-1795	100	18	to	to	PART
ap-1795	100	19	get	get	VERB
ap-1795	100	20	the	the	DET
ap-1795	100	21	resulting	result	VERB
ap-1795	100	22	x	x	SYM
ap-1795	100	23	vector	vector	NOUN
ap-1795	100	24	to	to	ADP
ap-1795	100	25	eq	eq	PROPN
ap-1795	100	26	.	.	PUNCT
ap-1795	101	1	(	(	PUNCT
ap-1795	101	2	11	11	NUM
ap-1795	101	3	)	)	PUNCT
ap-1795	101	4	after	after	ADP
ap-1795	101	5	≈	≈	PROPN
ap-1795	101	6	n3	n3	ADJ
ap-1795	101	7	elimination	elimination	NOUN
ap-1795	101	8	steps	step	NOUN
ap-1795	101	9	.	.	PUNCT
ap-1795	102	1	3.3	3.3	NUM
ap-1795	102	2	.	.	PUNCT
ap-1795	103	1	inverse	inverse	ADJ
ap-1795	103	2	transformation	transformation	NOUN
ap-1795	103	3	after	after	ADP
ap-1795	103	4	completing	complete	VERB
ap-1795	103	5	the	the	DET
ap-1795	103	6	two	two	NUM
ap-1795	103	7	previous	previous	ADJ
ap-1795	103	8	steps	step	NOUN
ap-1795	103	9	,	,	PUNCT
ap-1795	103	10	we	we	PRON
ap-1795	103	11	have	have	VERB
ap-1795	103	12	a	a	DET
ap-1795	103	13	set	set	NOUN
ap-1795	103	14	of	of	ADP
ap-1795	103	15	vectors	vector	NOUN
ap-1795	103	16	x	x	PUNCT
ap-1795	103	17	within	within	ADP
ap-1795	103	18	each	each	DET
ap-1795	103	19	module	module	NOUN
ap-1795	103	20	from	from	ADP
ap-1795	103	21	β	β	X
ap-1795	103	22	=	=	SYM
ap-1795	103	23	(	(	PUNCT
ap-1795	103	24	m1,m2	m1,m2	PROPN
ap-1795	103	25	,	,	PUNCT
ap-1795	103	26	.	.	PUNCT
ap-1795	103	27	.	.	PUNCT
ap-1795	103	28	.	.	PUNCT
ap-1795	104	1	,	,	PUNCT
ap-1795	104	2	mr	mr	PROPN
ap-1795	104	3	)	)	PUNCT
ap-1795	104	4	.	.	PUNCT
ap-1795	105	1	they	they	PRON
ap-1795	105	2	represent	represent	VERB
ap-1795	105	3	a	a	DET
ap-1795	105	4	sub	sub	NOUN
ap-1795	105	5	-	-	NOUN
ap-1795	105	6	solution	solution	NOUN
ap-1795	105	7	for	for	ADP
ap-1795	105	8	the	the	DET
ap-1795	105	9	specific	specific	ADJ
ap-1795	105	10	(	(	PUNCT
ap-1795	105	11	zmi	zmi	X
ap-1795	105	12	,	,	PUNCT
ap-1795	105	13	+	+	ADJ
ap-1795	105	14	,	,	PUNCT
ap-1795	105	15	·	·	SYM
ap-1795	105	16	)	)	PUNCT
ap-1795	105	17	arithmetic	arithmetic	NOUN
ap-1795	105	18	.	.	PUNCT
ap-1795	106	1	now	now	ADV
ap-1795	106	2	we	we	PRON
ap-1795	106	3	advance	advance	VERB
ap-1795	106	4	to	to	ADP
ap-1795	106	5	the	the	DET
ap-1795	106	6	inverse	inverse	NOUN
ap-1795	106	7	transformation	transformation	NOUN
ap-1795	106	8	back	back	ADV
ap-1795	106	9	to	to	ADP
ap-1795	106	10	(	(	PUNCT
ap-1795	106	11	zβ	zβ	PROPN
ap-1795	106	12	,	,	PUNCT
ap-1795	106	13	⊕	⊕	PROPN
ap-1795	106	14	,	,	PUNCT
ap-1795	106	15	�	�	PROPN
ap-1795	106	16	)	)	PUNCT
ap-1795	106	17	.	.	PUNCT
ap-1795	107	1	the	the	DET
ap-1795	107	2	necessary	necessary	ADJ
ap-1795	107	3	condition	condition	NOUN
ap-1795	107	4	for	for	ADP
ap-1795	107	5	each	each	DET
ap-1795	107	6	β	β	NOUN
ap-1795	107	7	module	module	NOUN
ap-1795	107	8	solution	solution	NOUN
ap-1795	107	9	x	x	PUNCT
ap-1795	107	10	is	be	AUX
ap-1795	107	11	its	its	PRON
ap-1795	107	12	non	non	ADJ
ap-1795	107	13	-	-	ADJ
ap-1795	107	14	zero	zero	NUM
ap-1795	107	15	determinant	determinant	ADJ
ap-1795	107	16	from	from	ADP
ap-1795	107	17	eq	eq	PROPN
ap-1795	107	18	.	.	PUNCT
ap-1795	108	1	(	(	PUNCT
ap-1795	108	2	7	7	NUM
ap-1795	108	3	)	)	PUNCT
ap-1795	108	4	.	.	PUNCT
ap-1795	109	1	the	the	DET
ap-1795	109	2	algorithm	algorithm	NOUN
ap-1795	109	3	used	use	VERB
ap-1795	109	4	for	for	ADP
ap-1795	109	5	this	this	DET
ap-1795	109	6	transformation	transformation	NOUN
ap-1795	109	7	is	be	AUX
ap-1795	109	8	the	the	DET
ap-1795	109	9	chinese	chinese	ADJ
ap-1795	109	10	remainder	remainder	NOUN
ap-1795	109	11	theorem	theorem	VERB
ap-1795	109	12	.	.	PUNCT
ap-1795	110	1	the	the	DET
ap-1795	110	2	product	product	NOUN
ap-1795	110	3	of	of	ADP
ap-1795	110	4	our	our	PRON
ap-1795	110	5	last	last	ADJ
ap-1795	110	6	step	step	NOUN
ap-1795	110	7	consists	consist	VERB
ap-1795	110	8	of	of	ADP
ap-1795	110	9	the	the	DET
ap-1795	110	10	vector	vector	NOUN
ap-1795	110	11	x	x	NOUN
ap-1795	110	12	elements	element	NOUN
ap-1795	110	13	in	in	ADP
ap-1795	110	14	the	the	DET
ap-1795	110	15	form	form	NOUN
ap-1795	110	16	of	of	ADP
ap-1795	110	17	fractions	fraction	NOUN
ap-1795	110	18	that	that	PRON
ap-1795	110	19	contain	contain	VERB
ap-1795	110	20	the	the	DET
ap-1795	110	21	solution	solution	NOUN
ap-1795	110	22	of	of	ADP
ap-1795	110	23	sle	sle	PROPN
ap-1795	110	24	(	(	PUNCT
ap-1795	110	25	3	3	NUM
ap-1795	110	26	)	)	PUNCT
ap-1795	110	27	.	.	PUNCT
ap-1795	111	1	4	4	X
ap-1795	111	2	.	.	X
ap-1795	111	3	gpu	gpu	NOUN
ap-1795	111	4	and	and	CCONJ
ap-1795	111	5	optimizations	optimization	NOUN
ap-1795	111	6	gpgpu	gpgpu	NOUN
ap-1795	111	7	is	be	AUX
ap-1795	111	8	the	the	DET
ap-1795	111	9	area	area	NOUN
ap-1795	111	10	of	of	ADP
ap-1795	111	11	our	our	PRON
ap-1795	111	12	research	research	NOUN
ap-1795	111	13	,	,	PUNCT
ap-1795	111	14	so	so	ADV
ap-1795	111	15	we	we	PRON
ap-1795	111	16	optimize	optimize	VERB
ap-1795	111	17	on	on	ADP
ap-1795	111	18	the	the	DET
ap-1795	111	19	pc	pc	NOUN
ap-1795	111	20	graphical	graphical	ADJ
ap-1795	111	21	hardware	hardware	NOUN
ap-1795	111	22	.	.	PUNCT
ap-1795	112	1	there	there	PRON
ap-1795	112	2	were	be	VERB
ap-1795	112	3	several	several	ADJ
ap-1795	112	4	platforms	platform	NOUN
ap-1795	112	5	to	to	PART
ap-1795	112	6	choose	choose	VERB
ap-1795	112	7	from	from	ADP
ap-1795	112	8	:	:	PUNCT
ap-1795	112	9	•	•	NUM
ap-1795	112	10	nvidia	nvidia	PROPN
ap-1795	112	11	cuda	cuda	NOUN
ap-1795	112	12	,	,	PUNCT
ap-1795	112	13	the	the	DET
ap-1795	112	14	mainstream	mainstream	NOUN
ap-1795	112	15	platform	platform	NOUN
ap-1795	112	16	today	today	NOUN
ap-1795	112	17	,	,	PUNCT
ap-1795	112	18	was	be	AUX
ap-1795	112	19	rejected	reject	VERB
ap-1795	112	20	;	;	PUNCT
ap-1795	112	21	it	it	PRON
ap-1795	112	22	is	be	AUX
ap-1795	112	23	proprietary	proprietary	ADJ
ap-1795	112	24	,	,	PUNCT
ap-1795	112	25	and	and	CCONJ
ap-1795	112	26	its	its	PRON
ap-1795	112	27	usage	usage	NOUN
ap-1795	112	28	is	be	AUX
ap-1795	112	29	limited	limit	VERB
ap-1795	112	30	to	to	ADP
ap-1795	112	31	nvidia	nvidia	PROPN
ap-1795	112	32	hardware	hardware	NOUN
ap-1795	112	33	;	;	PUNCT
ap-1795	112	34	•	•	NUM
ap-1795	112	35	microsoft	microsoft	PROPN
ap-1795	112	36	directx	directx	PROPN
ap-1795	112	37	11	11	NUM
ap-1795	112	38	directcompute	directcompute	NOUN
ap-1795	112	39	was	be	AUX
ap-1795	112	40	rejected	reject	VERB
ap-1795	112	41	;	;	PUNCT
ap-1795	112	42	it	it	PRON
ap-1795	112	43	is	be	AUX
ap-1795	112	44	bound	bind	VERB
ap-1795	112	45	to	to	ADP
ap-1795	112	46	the	the	DET
ap-1795	112	47	microsoft	microsoft	PROPN
ap-1795	112	48	windows	windows	PROPN
ap-1795	112	49	platform	platform	PROPN
ap-1795	112	50	only	only	ADV
ap-1795	112	51	(	(	PUNCT
ap-1795	112	52	not	not	PART
ap-1795	112	53	used	use	VERB
ap-1795	112	54	in	in	ADP
ap-1795	112	55	hpc	hpc	PROPN
ap-1795	112	56	in	in	ADP
ap-1795	112	57	general	general	ADJ
ap-1795	112	58	)	)	PUNCT
ap-1795	112	59	;	;	PUNCT
ap-1795	112	60	•	•	NUM
ap-1795	112	61	opencl	opencl	NOUN
ap-1795	112	62	is	be	AUX
ap-1795	112	63	an	an	DET
ap-1795	112	64	open	open	ADJ
ap-1795	112	65	standard	standard	NOUN
ap-1795	112	66	that	that	PRON
ap-1795	112	67	works	work	VERB
ap-1795	112	68	well	well	ADV
ap-1795	112	69	across	across	ADP
ap-1795	112	70	platforms	platform	NOUN
ap-1795	112	71	(	(	PUNCT
ap-1795	112	72	gnu	gnu	PROPN
ap-1795	112	73	/	/	SYM
ap-1795	112	74	linux	linux	PROPN
ap-1795	112	75	,	,	PUNCT
ap-1795	112	76	microsoft	microsoft	PROPN
ap-1795	112	77	windows	windows	PROPN
ap-1795	112	78	and	and	CCONJ
ap-1795	112	79	apple	apple	PROPN
ap-1795	112	80	mac	mac	PROPN
ap-1795	112	81	)	)	PUNCT
ap-1795	112	82	and	and	CCONJ
ap-1795	112	83	on	on	ADP
ap-1795	112	84	all	all	DET
ap-1795	112	85	latest	late	ADJ
ap-1795	112	86	graphical	graphical	ADJ
ap-1795	112	87	hardware	hardware	NOUN
ap-1795	112	88	(	(	PUNCT
ap-1795	112	89	nvidia	nvidia	PROPN
ap-1795	112	90	,	,	PUNCT
ap-1795	112	91	amd	amd	ADJ
ap-1795	112	92	and	and	CCONJ
ap-1795	112	93	latest	late	ADJ
ap-1795	112	94	intel	intel	PROPN
ap-1795	112	95	gpus	gpus	PROPN
ap-1795	112	96	)	)	PUNCT
ap-1795	112	97	;	;	PUNCT
ap-1795	112	98	we	we	PRON
ap-1795	112	99	use	use	VERB
ap-1795	112	100	opencl	opencl	NOUN
ap-1795	112	101	for	for	ADP
ap-1795	112	102	the	the	DET
ap-1795	112	103	implementation	implementation	NOUN
ap-1795	112	104	.	.	PUNCT
ap-1795	113	1	0	0	NUM
ap-1795	113	2	 	 	SPACE
ap-1795	113	3	%	%	NOUN
ap-1795	113	4	25,00	25,00	NUM
ap-1795	113	5	 	 	SPACE
ap-1795	113	6	%	%	NOUN
ap-1795	113	7	50,00	50,00	NUM
ap-1795	113	8	 	 	SPACE
ap-1795	113	9	%	%	NOUN
ap-1795	113	10	75,00	75,00	NUM
ap-1795	113	11	 	 	SPACE
ap-1795	113	12	%	%	NOUN
ap-1795	113	13	100,00	100,00	NUM
ap-1795	113	14	 	 	SPACE
ap-1795	113	15	%	%	NOUN
ap-1795	113	16	16	16	NUM
ap-1795	113	17	32	32	NUM
ap-1795	113	18	64	64	NUM
ap-1795	113	19	128	128	NUM
ap-1795	113	20	256	256	NUM
ap-1795	113	21	512	512	NUM
ap-1795	113	22	1024	1024	NUM
ap-1795	113	23	co	co	NOUN
ap-1795	113	24	m	m	PROPN
ap-1795	113	25	pu	pu	PROPN
ap-1795	113	26	ta	ta	PROPN
ap-1795	113	27	tio	tio	PROPN
ap-1795	113	28	n	n	INTJ
ap-1795	113	29	sh	sh	PROPN
ap-1795	113	30	ar	ar	PROPN
ap-1795	113	31	e	e	PROPN
ap-1795	114	1	[	[	X
ap-1795	114	2	%	%	X
ap-1795	114	3	]	]	X
ap-1795	114	4	matrix	matrix	NOUN
ap-1795	114	5	size	size	NOUN
ap-1795	114	6	[	[	X
ap-1795	114	7	m	m	X
ap-1795	114	8	]	]	X
ap-1795	114	9	matrix	matrix	NOUN
ap-1795	114	10	scaling	scale	VERB
ap-1795	114	11	beta	beta	ADJ
ap-1795	114	12	vector	vector	NOUN
ap-1795	114	13	computation	computation	NOUN
ap-1795	114	14	sles	sle	NOUN
ap-1795	114	15	solution	solution	NOUN
ap-1795	114	16	inverse	inverse	NOUN
ap-1795	114	17	transformation	transformation	NOUN
ap-1795	114	18	figure	figure	NOUN
ap-1795	114	19	1	1	NUM
ap-1795	114	20	.	.	NUM
ap-1795	114	21	measured	measure	VERB
ap-1795	114	22	computation	computation	NOUN
ap-1795	114	23	shares	share	NOUN
ap-1795	114	24	.	.	PUNCT
ap-1795	115	1	4.1	4.1	NUM
ap-1795	115	2	.	.	PUNCT
ap-1795	116	1	profiling	profile	VERB
ap-1795	116	2	the	the	DET
ap-1795	116	3	whole	whole	ADJ
ap-1795	116	4	sle	sle	NOUN
ap-1795	116	5	solving	solving	NOUN
ap-1795	116	6	process	process	NOUN
ap-1795	116	7	is	be	AUX
ap-1795	116	8	a	a	DET
ap-1795	116	9	rather	rather	ADV
ap-1795	116	10	timeconsuming	timeconsuming	ADJ
ap-1795	116	11	task	task	NOUN
ap-1795	116	12	(	(	PUNCT
ap-1795	116	13	fig	fig	NOUN
ap-1795	116	14	.	.	PUNCT
ap-1795	116	15	1	1	NUM
ap-1795	116	16	)	)	PUNCT
ap-1795	116	17	,	,	PUNCT
ap-1795	116	18	so	so	SCONJ
ap-1795	116	19	optimizations	optimization	NOUN
ap-1795	116	20	had	have	VERB
ap-1795	116	21	to	to	PART
ap-1795	116	22	be	be	AUX
ap-1795	116	23	made	make	VERB
ap-1795	116	24	.	.	PUNCT
ap-1795	117	1	first	first	ADV
ap-1795	117	2	,	,	PUNCT
ap-1795	117	3	all	all	DET
ap-1795	117	4	the	the	DET
ap-1795	117	5	big	big	ADJ
ap-1795	117	6	number	number	NOUN
ap-1795	117	7	alu	alu	NOUN
ap-1795	117	8	operations	operation	NOUN
ap-1795	117	9	–	–	PUNCT
ap-1795	117	10	eq	eq	ADP
ap-1795	117	11	.	.	PUNCT
ap-1795	118	1	(	(	PUNCT
ap-1795	118	2	5	5	NUM
ap-1795	118	3	)	)	PUNCT
ap-1795	118	4	and	and	CCONJ
ap-1795	118	5	section	section	NOUN
ap-1795	118	6	3.3	3.3	NUM
ap-1795	118	7	–	–	PUNCT
ap-1795	118	8	are	be	AUX
ap-1795	118	9	performed	perform	VERB
ap-1795	118	10	using	use	VERB
ap-1795	118	11	the	the	DET
ap-1795	118	12	gmp	gmp	PROPN
ap-1795	118	13	library	library	NOUN
ap-1795	118	14	,	,	PUNCT
ap-1795	118	15	which	which	PRON
ap-1795	118	16	is	be	AUX
ap-1795	118	17	tuned	tune	VERB
ap-1795	118	18	for	for	ADP
ap-1795	118	19	this	this	DET
ap-1795	118	20	platform	platform	NOUN
ap-1795	118	21	.	.	PUNCT
ap-1795	119	1	solving	solve	VERB
ap-1795	119	2	dozens	dozen	NOUN
ap-1795	119	3	of	of	ADP
ap-1795	119	4	systems	system	NOUN
ap-1795	119	5	of	of	ADP
ap-1795	119	6	linear	linear	PROPN
ap-1795	119	7	equations	equation	NOUN
ap-1795	119	8	using	use	VERB
ap-1795	119	9	modular	modular	ADJ
ap-1795	119	10	arithmetics	arithmetic	NOUN
ap-1795	119	11	(	(	PUNCT
ap-1795	119	12	section	section	NOUN
ap-1795	119	13	3.2	3.2	NUM
ap-1795	119	14	)	)	PUNCT
ap-1795	119	15	within	within	ADP
ap-1795	119	16	the	the	DET
ap-1795	119	17	β	β	PROPN
ap-1795	119	18	vector	vector	NOUN
ap-1795	119	19	is	be	AUX
ap-1795	119	20	the	the	DET
ap-1795	119	21	most	most	ADV
ap-1795	119	22	computation	computation	NOUN
ap-1795	119	23	-	-	PUNCT
ap-1795	119	24	intensive	intensive	ADJ
ap-1795	119	25	part	part	NOUN
ap-1795	119	26	of	of	ADP
ap-1795	119	27	our	our	PRON
ap-1795	119	28	task	task	NOUN
ap-1795	119	29	,	,	PUNCT
ap-1795	119	30	see	see	VERB
ap-1795	119	31	fig	fig	NOUN
ap-1795	119	32	.	.	PUNCT
ap-1795	120	1	1	1	NUM
ap-1795	120	2	.	.	PUNCT
ap-1795	120	3	according	accord	VERB
ap-1795	120	4	to	to	ADP
ap-1795	120	5	ahmdal	ahmdal	PROPN
ap-1795	120	6	’s	’s	PART
ap-1795	120	7	law	law	NOUN
ap-1795	120	8	(	(	PUNCT
ap-1795	120	9	expressed	express	VERB
ap-1795	120	10	in	in	ADP
ap-1795	120	11	eq	eq	PROPN
ap-1795	120	12	.	.	PUNCT
ap-1795	121	1	(	(	PUNCT
ap-1795	121	2	13	13	NUM
ap-1795	121	3	)	)	PUNCT
ap-1795	121	4	,	,	PUNCT
ap-1795	121	5	the	the	DET
ap-1795	121	6	benefit	benefit	NOUN
ap-1795	121	7	(	(	PUNCT
ap-1795	121	8	overall	overall	ADJ
ap-1795	121	9	speedup	speedup	NOUN
ap-1795	121	10	)	)	PUNCT
ap-1795	121	11	from	from	ADP
ap-1795	121	12	optimizing	optimize	VERB
ap-1795	121	13	part	part	NOUN
ap-1795	121	14	of	of	ADP
ap-1795	121	15	the	the	DET
ap-1795	121	16	computation	computation	NOUN
ap-1795	121	17	is	be	AUX
ap-1795	121	18	equal	equal	ADJ
ap-1795	121	19	to	to	ADP
ap-1795	121	20	:	:	PUNCT
ap-1795	121	21	speedup	speedup	NOUN
ap-1795	121	22	=	=	SYM
ap-1795	121	23	1	1	NUM
ap-1795	121	24	(	(	PUNCT
ap-1795	121	25	1−	1−	NUM
ap-1795	121	26	p	p	NOUN
ap-1795	121	27	)	)	PUNCT
ap-1795	122	1	+	+	CCONJ
ap-1795	122	2	p	p	X
ap-1795	122	3	s	s	X
ap-1795	122	4	,	,	PUNCT
ap-1795	122	5	(	(	PUNCT
ap-1795	122	6	13	13	NUM
ap-1795	122	7	)	)	PUNCT
ap-1795	122	8	where	where	SCONJ
ap-1795	122	9	p	p	NOUN
ap-1795	122	10	is	be	AUX
ap-1795	122	11	the	the	DET
ap-1795	122	12	proportion	proportion	NOUN
ap-1795	122	13	of	of	ADP
ap-1795	122	14	the	the	DET
ap-1795	122	15	computation	computation	NOUN
ap-1795	122	16	we	we	PRON
ap-1795	122	17	are	be	AUX
ap-1795	122	18	optimizing	optimize	VERB
ap-1795	122	19	and	and	CCONJ
ap-1795	122	20	s	s	NOUN
ap-1795	122	21	is	be	AUX
ap-1795	122	22	its	its	PRON
ap-1795	122	23	speedup	speedup	NOUN
ap-1795	122	24	.	.	PUNCT
ap-1795	123	1	because	because	SCONJ
ap-1795	123	2	modular	modular	ADJ
ap-1795	123	3	arithmetics	arithmetic	NOUN
ap-1795	123	4	sles	sle	NOUN
ap-1795	123	5	take	take	VERB
ap-1795	123	6	a	a	DET
ap-1795	123	7	great	great	ADJ
ap-1795	123	8	amount	amount	NOUN
ap-1795	123	9	of	of	ADP
ap-1795	123	10	time	time	NOUN
ap-1795	123	11	to	to	PART
ap-1795	123	12	solve	solve	VERB
ap-1795	123	13	,	,	PUNCT
ap-1795	123	14	we	we	PRON
ap-1795	123	15	optimize	optimize	VERB
ap-1795	123	16	the	the	DET
ap-1795	123	17	matrix	matrix	NOUN
ap-1795	123	18	elimination	elimination	NOUN
ap-1795	123	19	.	.	PUNCT
ap-1795	124	1	4.2	4.2	NUM
ap-1795	124	2	.	.	PUNCT
ap-1795	124	3	gpu	gpu	NOUN
ap-1795	124	4	architecture	architecture	NOUN
ap-1795	124	5	all	all	DET
ap-1795	124	6	modern	modern	ADJ
ap-1795	124	7	common	common	ADJ
ap-1795	124	8	gpus	gpu	NOUN
ap-1795	124	9	have	have	VERB
ap-1795	124	10	a	a	DET
ap-1795	124	11	similar	similar	ADJ
ap-1795	124	12	architecture	architecture	NOUN
ap-1795	124	13	(	(	PUNCT
ap-1795	124	14	from	from	ADP
ap-1795	124	15	our	our	PRON
ap-1795	124	16	optimization	optimization	NOUN
ap-1795	124	17	type	type	NOUN
ap-1795	124	18	point	point	NOUN
ap-1795	124	19	of	of	ADP
ap-1795	124	20	view	view	NOUN
ap-1795	124	21	)	)	PUNCT
ap-1795	124	22	.	.	PUNCT
ap-1795	125	1	they	they	PRON
ap-1795	125	2	consist	consist	VERB
ap-1795	125	3	of	of	ADP
ap-1795	125	4	a	a	DET
ap-1795	125	5	global	global	ADJ
ap-1795	125	6	memory	memory	NOUN
ap-1795	125	7	(	(	PUNCT
ap-1795	125	8	1–4	1–4	NOUN
ap-1795	125	9	gb	gb	NOUN
ap-1795	125	10	)	)	PUNCT
ap-1795	125	11	and	and	CCONJ
ap-1795	125	12	several	several	ADJ
ap-1795	125	13	(	(	PUNCT
ap-1795	125	14	2–24	2–24	PROPN
ap-1795	125	15	)	)	PUNCT
ap-1795	125	16	smp1	smp1	NOUN
ap-1795	125	17	processors	processor	NOUN
ap-1795	125	18	(	(	PUNCT
ap-1795	125	19	example	example	NOUN
ap-1795	125	20	in	in	ADP
ap-1795	125	21	fig	fig	NOUN
ap-1795	125	22	.	.	PUNCT
ap-1795	126	1	2	2	NUM
ap-1795	126	2	)	)	PUNCT
ap-1795	126	3	.	.	PUNCT
ap-1795	127	1	smp	smp	PROPN
ap-1795	127	2	features	feature	VERB
ap-1795	127	3	a	a	DET
ap-1795	127	4	scheduler	scheduler	NOUN
ap-1795	127	5	of	of	ADP
ap-1795	127	6	lightweight	lightweight	ADJ
ap-1795	127	7	threads	thread	NOUN
ap-1795	127	8	that	that	PRON
ap-1795	127	9	have	have	VERB
ap-1795	127	10	zero	zero	NUM
ap-1795	127	11	overhead	overhead	ADV
ap-1795	127	12	.	.	PUNCT
ap-1795	128	1	each	each	DET
ap-1795	128	2	smp	smp	NOUN
ap-1795	128	3	contains	contain	VERB
ap-1795	128	4	dozens	dozen	NOUN
ap-1795	128	5	(	(	PUNCT
ap-1795	128	6	8–48	8–48	PROPN
ap-1795	128	7	)	)	PUNCT
ap-1795	128	8	of	of	ADP
ap-1795	128	9	processor	processor	NOUN
ap-1795	128	10	cores	core	NOUN
ap-1795	128	11	that	that	PRON
ap-1795	128	12	share	share	VERB
ap-1795	128	13	the	the	DET
ap-1795	128	14	smp	smp	NOUN
ap-1795	128	15	memory	memory	NOUN
ap-1795	128	16	(	(	PUNCT
ap-1795	128	17	shared	share	VERB
ap-1795	128	18	memory	memory	NOUN
ap-1795	128	19	≈	≈	PROPN
ap-1795	128	20	64	64	NUM
ap-1795	128	21	kb	kb	PROPN
ap-1795	128	22	)	)	PUNCT
ap-1795	128	23	and	and	CCONJ
ap-1795	128	24	execute	execute	VERB
ap-1795	128	25	the	the	DET
ap-1795	128	26	same	same	ADJ
ap-1795	128	27	code	code	NOUN
ap-1795	128	28	.	.	PUNCT
ap-1795	129	1	if	if	SCONJ
ap-1795	129	2	it	it	PRON
ap-1795	129	3	happens	happen	VERB
ap-1795	129	4	that	that	SCONJ
ap-1795	129	5	one	one	NUM
ap-1795	129	6	processor	processor	NOUN
ap-1795	129	7	core	core	NOUN
ap-1795	129	8	branches	branch	NOUN
ap-1795	129	9	differently	differently	ADV
ap-1795	129	10	,	,	PUNCT
ap-1795	129	11	the	the	DET
ap-1795	129	12	performance	performance	NOUN
ap-1795	129	13	goes	go	VERB
ap-1795	129	14	down	down	ADP
ap-1795	129	15	dramatically	dramatically	ADV
ap-1795	129	16	.	.	PUNCT
ap-1795	130	1	each	each	DET
ap-1795	130	2	processor	processor	NOUN
ap-1795	130	3	core	core	NOUN
ap-1795	130	4	also	also	ADV
ap-1795	130	5	has	have	VERB
ap-1795	130	6	its	its	PRON
ap-1795	130	7	own	own	ADJ
ap-1795	130	8	integer	integer	NOUN
ap-1795	130	9	and	and	CCONJ
ap-1795	130	10	floating	floating	ADJ
ap-1795	130	11	-	-	PUNCT
ap-1795	130	12	point	point	NOUN
ap-1795	130	13	unit	unit	NOUN
ap-1795	130	14	.	.	PUNCT
ap-1795	131	1	more	more	ADJ
ap-1795	131	2	details	detail	NOUN
ap-1795	131	3	with	with	ADP
ap-1795	131	4	examples	example	NOUN
ap-1795	131	5	and	and	CCONJ
ap-1795	131	6	a	a	DET
ap-1795	131	7	description	description	NOUN
ap-1795	131	8	of	of	ADP
ap-1795	131	9	the	the	DET
ap-1795	131	10	cuda	cuda	NOUN
ap-1795	131	11	platform	platform	NOUN
ap-1795	131	12	are	be	AUX
ap-1795	131	13	given	give	VERB
ap-1795	131	14	in	in	ADP
ap-1795	131	15	[	[	X
ap-1795	131	16	5	5	NUM
ap-1795	131	17	]	]	PUNCT
ap-1795	131	18	.	.	PUNCT
ap-1795	132	1	the	the	DET
ap-1795	132	2	processor	processor	NOUN
ap-1795	132	3	cores	core	NOUN
ap-1795	132	4	have	have	VERB
ap-1795	132	5	access	access	NOUN
ap-1795	132	6	to	to	ADP
ap-1795	132	7	the	the	DET
ap-1795	132	8	gpu	gpu	PROPN
ap-1795	132	9	global	global	ADJ
ap-1795	132	10	ram	ram	NOUN
ap-1795	132	11	,	,	PUNCT
ap-1795	132	12	but	but	CCONJ
ap-1795	132	13	the	the	DET
ap-1795	132	14	memory	memory	NOUN
ap-1795	132	15	access	access	NOUN
ap-1795	132	16	has	have	VERB
ap-1795	132	17	to	to	PART
ap-1795	132	18	be	be	AUX
ap-1795	132	19	aligned	align	VERB
ap-1795	132	20	.	.	PUNCT
ap-1795	133	1	otherwise	otherwise	ADV
ap-1795	133	2	performance	performance	NOUN
ap-1795	133	3	will	will	AUX
ap-1795	133	4	be	be	AUX
ap-1795	133	5	affected	affect	VERB
ap-1795	133	6	.	.	PUNCT
ap-1795	134	1	we	we	PRON
ap-1795	134	2	used	use	VERB
ap-1795	134	3	smp	smp	NOUN
ap-1795	134	4	processor	processor	NOUN
ap-1795	134	5	cores	core	NOUN
ap-1795	134	6	to	to	PART
ap-1795	134	7	load	load	VERB
ap-1795	134	8	part	part	NOUN
ap-1795	134	9	of	of	ADP
ap-1795	134	10	the	the	DET
ap-1795	134	11	matrix	matrix	NOUN
ap-1795	134	12	(	(	PUNCT
ap-1795	134	13	the	the	DET
ap-1795	134	14	row	row	NOUN
ap-1795	134	15	1smp	1smp	NUM
ap-1795	134	16	–	–	PUNCT
ap-1795	134	17	symmetric	symmetric	ADJ
ap-1795	134	18	multiprocessor	multiprocessor	NOUN
ap-1795	134	19	72	72	NUM
ap-1795	134	20	vol	vol	NOUN
ap-1795	134	21	.	.	PUNCT
ap-1795	135	1	53	53	NUM
ap-1795	135	2	no	no	NOUN
ap-1795	135	3	.	.	PUNCT
ap-1795	136	1	2/2013	2/2013	NUM
ap-1795	136	2	clock	clock	NOUN
ap-1795	136	3	math	math	NOUN
ap-1795	136	4	—	—	PUNCT
ap-1795	136	5	a	a	DET
ap-1795	136	6	system	system	NOUN
ap-1795	136	7	for	for	ADP
ap-1795	136	8	solving	solve	VERB
ap-1795	136	9	sles	sle	NOUN
ap-1795	136	10	exactly	exactly	ADV
ap-1795	136	11	matrix	matrix	NOUN
ap-1795	136	12	size	size	NOUN
ap-1795	136	13	[	[	X
ap-1795	136	14	n	n	X
ap-1795	136	15	]	]	PUNCT
ap-1795	136	16	clock	clock	NOUN
ap-1795	136	17	math	math	NOUN
ap-1795	137	1	[	[	X
ap-1795	137	2	s	s	X
ap-1795	137	3	]	]	X
ap-1795	137	4	linsolve-0.7.15	linsolve-0.7.15	PROPN
ap-1795	138	1	[	[	X
ap-1795	138	2	s	s	X
ap-1795	138	3	]	]	X
ap-1795	138	4	speedup	speedup	NOUN
ap-1795	139	1	[	[	X
ap-1795	139	2	%	%	X
ap-1795	139	3	]	]	X
ap-1795	139	4	16	16	NUM
ap-1795	139	5	0.006	0.006	NUM
ap-1795	139	6	0.006425	0.006425	NUM
ap-1795	139	7	16.82	16.82	NUM
ap-1795	139	8	32	32	NUM
ap-1795	139	9	0.006	0.006	NUM
ap-1795	139	10	0.014921	0.014921	NUM
ap-1795	139	11	42.10	42.10	NUM
ap-1795	139	12	64	64	NUM
ap-1795	139	13	0.029	0.029	NUM
ap-1795	139	14	0.046871	0.046871	NUM
ap-1795	139	15	61.97	61.97	NUM
ap-1795	139	16	128	128	NUM
ap-1795	139	17	0.117	0.117	NUM
ap-1795	139	18	0.195461	0.195461	NUM
ap-1795	139	19	67.06	67.06	NUM
ap-1795	139	20	256	256	NUM
ap-1795	139	21	1.043	1.043	NUM
ap-1795	139	22	1.401498	1.401498	NUM
ap-1795	139	23	34.40	34.40	NUM
ap-1795	139	24	512	512	NUM
ap-1795	139	25	11.252	11.252	NUM
ap-1795	139	26	16.215546	16.215546	NUM
ap-1795	139	27	44.11	44.11	NUM
ap-1795	139	28	1024	1024	NUM
ap-1795	139	29	124.375	124.375	NUM
ap-1795	139	30	212.557002	212.557002	NUM
ap-1795	139	31	70.90	70.90	NUM
ap-1795	139	32	table	table	NOUN
ap-1795	139	33	1	1	NUM
ap-1795	139	34	.	.	PUNCT
ap-1795	139	35	measured	measure	VERB
ap-1795	139	36	results	result	NOUN
ap-1795	139	37	:	:	PUNCT
ap-1795	139	38	comparison	comparison	NOUN
ap-1795	139	39	of	of	ADP
ap-1795	139	40	execution	execution	NOUN
ap-1795	139	41	times	time	NOUN
ap-1795	139	42	for	for	ADP
ap-1795	139	43	clock	clock	PROPN
ap-1795	139	44	math	math	NOUN
ap-1795	139	45	solver	solver	NOUN
ap-1795	139	46	,	,	PUNCT
ap-1795	139	47	for	for	ADP
ap-1795	139	48	linsolve-0.7.15	linsolve-0.7.15	NOUN
ap-1795	139	49	and	and	CCONJ
ap-1795	139	50	corresponding	corresponding	ADJ
ap-1795	139	51	speedups	speedup	NOUN
ap-1795	139	52	.	.	PUNCT
ap-1795	140	1	figure	figure	NOUN
ap-1795	140	2	2	2	NUM
ap-1795	140	3	.	.	PUNCT
ap-1795	140	4	nvidia	nvidia	PROPN
ap-1795	140	5	fermi	fermi	PROPN
ap-1795	140	6	smp	smp	NOUN
ap-1795	141	1	[	[	X
ap-1795	141	2	5	5	NUM
ap-1795	141	3	]	]	PUNCT
ap-1795	141	4	.	.	PUNCT
ap-1795	142	1	that	that	PRON
ap-1795	142	2	contains	contain	VERB
ap-1795	142	3	the	the	DET
ap-1795	142	4	current	current	ADJ
ap-1795	142	5	pivot	pivot	NOUN
ap-1795	142	6	)	)	PUNCT
ap-1795	142	7	.	.	PUNCT
ap-1795	143	1	we	we	PRON
ap-1795	143	2	used	use	VERB
ap-1795	143	3	it	it	PRON
ap-1795	143	4	for	for	ADP
ap-1795	143	5	computation	computation	NOUN
ap-1795	143	6	and	and	CCONJ
ap-1795	143	7	then	then	ADV
ap-1795	143	8	stored	store	VERB
ap-1795	143	9	the	the	DET
ap-1795	143	10	elimination	elimination	NOUN
ap-1795	143	11	step	step	NOUN
ap-1795	143	12	results	result	VERB
ap-1795	143	13	back	back	ADV
ap-1795	143	14	to	to	ADP
ap-1795	143	15	global	global	ADJ
ap-1795	143	16	memory	memory	NOUN
ap-1795	143	17	.	.	PUNCT
ap-1795	144	1	4.3	4.3	NUM
ap-1795	144	2	.	.	PUNCT
ap-1795	144	3	gpu	gpu	PROPN
ap-1795	144	4	kernels	kernel	NOUN
ap-1795	144	5	,	,	PUNCT
ap-1795	144	6	optimizations	optimization	VERB
ap-1795	144	7	the	the	DET
ap-1795	144	8	opencl	opencl	NOUN
ap-1795	144	9	framework	framework	NOUN
ap-1795	144	10	defines	define	VERB
ap-1795	144	11	the	the	DET
ap-1795	144	12	term	term	NOUN
ap-1795	144	13	kernel	kernel	NOUN
ap-1795	144	14	.	.	PUNCT
ap-1795	145	1	it	it	PRON
ap-1795	145	2	is	be	AUX
ap-1795	145	3	an	an	DET
ap-1795	145	4	function	function	NOUN
ap-1795	145	5	written	write	VERB
ap-1795	145	6	in	in	ADP
ap-1795	145	7	slightly	slightly	ADV
ap-1795	145	8	modified	modify	VERB
ap-1795	145	9	c99	c99	PROPN
ap-1795	145	10	language	language	NOUN
ap-1795	145	11	which	which	PRON
ap-1795	145	12	is	be	AUX
ap-1795	145	13	to	to	PART
ap-1795	145	14	be	be	AUX
ap-1795	145	15	executed	execute	VERB
ap-1795	145	16	on	on	ADP
ap-1795	145	17	an	an	DET
ap-1795	145	18	opencl	opencl	ADJ
ap-1795	145	19	capable	capable	ADJ
ap-1795	145	20	device	device	NOUN
ap-1795	145	21	.	.	PUNCT
ap-1795	146	1	in	in	ADP
ap-1795	146	2	parallel	parallel	NOUN
ap-1795	146	3	,	,	PUNCT
ap-1795	146	4	opencl	opencl	NOUN
ap-1795	146	5	runtime	runtime	NOUN
ap-1795	146	6	executes	execute	VERB
ap-1795	146	7	the	the	DET
ap-1795	146	8	same	same	ADJ
ap-1795	146	9	kernel	kernel	NOUN
ap-1795	146	10	on	on	ADP
ap-1795	146	11	every	every	DET
ap-1795	146	12	processor	processor	NOUN
ap-1795	146	13	core	core	NOUN
ap-1795	146	14	within	within	ADP
ap-1795	146	15	an	an	DET
ap-1795	146	16	smp	smp	NOUN
ap-1795	146	17	.	.	PUNCT
ap-1795	147	1	in	in	ADP
ap-1795	147	2	the	the	DET
ap-1795	147	3	example	example	NOUN
ap-1795	147	4	of	of	ADP
ap-1795	147	5	the	the	DET
ap-1795	147	6	saxpy	saxpy	ADJ
ap-1795	147	7	function	function	NOUN
ap-1795	147	8	,	,	PUNCT
ap-1795	147	9	we	we	PRON
ap-1795	147	10	are	be	AUX
ap-1795	147	11	able	able	ADJ
ap-1795	147	12	to	to	PART
ap-1795	147	13	process	process	VERB
ap-1795	147	14	(	(	PUNCT
ap-1795	147	15	8–48	8–48	NOUN
ap-1795	147	16	)	)	PUNCT
ap-1795	147	17	vector	vector	NOUN
ap-1795	147	18	elements	element	NOUN
ap-1795	147	19	at	at	ADP
ap-1795	147	20	once	once	ADV
ap-1795	147	21	.	.	PUNCT
ap-1795	148	1	however	however	ADV
ap-1795	148	2	,	,	PUNCT
ap-1795	148	3	our	our	PRON
ap-1795	148	4	case	case	NOUN
ap-1795	148	5	is	be	AUX
ap-1795	148	6	not	not	PART
ap-1795	148	7	so	so	ADV
ap-1795	148	8	simple	simple	ADJ
ap-1795	148	9	.	.	PUNCT
ap-1795	149	1	our	our	PRON
ap-1795	149	2	system	system	NOUN
ap-1795	149	3	is	be	AUX
ap-1795	149	4	currently	currently	ADV
ap-1795	149	5	limited	limit	VERB
ap-1795	149	6	to	to	ADP
ap-1795	149	7	the	the	DET
ap-1795	149	8	matrix	matrix	NOUN
ap-1795	149	9	size	size	NOUN
ap-1795	149	10	of	of	ADP
ap-1795	149	11	4096×4096	4096×4096	PROPN
ap-1795	149	12	.	.	PUNCT
ap-1795	150	1	the	the	DET
ap-1795	150	2	row	row	NOUN
ap-1795	150	3	with	with	ADP
ap-1795	150	4	the	the	DET
ap-1795	150	5	current	current	ADJ
ap-1795	150	6	pivot	pivot	NOUN
ap-1795	150	7	is	be	AUX
ap-1795	150	8	used	use	VERB
ap-1795	150	9	in	in	ADP
ap-1795	150	10	n	n	DET
ap-1795	150	11	multiply	multiply	ADV
ap-1795	150	12	-	-	PUNCT
ap-1795	150	13	add	add	ADJ
ap-1795	150	14	-	-	PUNCT
ap-1795	150	15	modulo	modulo	NOUN
ap-1795	150	16	vector	vector	NOUN
ap-1795	150	17	operations	operation	NOUN
ap-1795	150	18	.	.	PUNCT
ap-1795	151	1	hence	hence	ADV
ap-1795	151	2	,	,	PUNCT
ap-1795	151	3	it	it	PRON
ap-1795	151	4	is	be	AUX
ap-1795	151	5	quite	quite	ADV
ap-1795	151	6	useful	useful	ADJ
ap-1795	151	7	performance	performance	NOUN
ap-1795	151	8	-	-	PUNCT
ap-1795	151	9	wise	wise	ADJ
ap-1795	151	10	to	to	PART
ap-1795	151	11	cache	cache	VERB
ap-1795	151	12	it	it	PRON
ap-1795	151	13	in	in	ADP
ap-1795	151	14	the	the	DET
ap-1795	151	15	smp	smp	NOUN
ap-1795	151	16	shared	share	VERB
ap-1795	151	17	memory	memory	NOUN
ap-1795	151	18	.	.	PUNCT
ap-1795	152	1	current	current	ADJ
ap-1795	152	2	generation	generation	NOUN
ap-1795	152	3	nvidia	nvidia	PROPN
ap-1795	152	4	gpus	gpus	PROPN
ap-1795	152	5	have	have	VERB
ap-1795	152	6	shared	share	VERB
ap-1795	152	7	memory	memory	NOUN
ap-1795	152	8	size	size	NOUN
ap-1795	152	9	of	of	ADP
ap-1795	152	10	48	48	NUM
ap-1795	152	11	kb	kb	PROPN
ap-1795	152	12	.	.	PUNCT
ap-1795	153	1	one	one	NUM
ap-1795	153	2	matrix	matrix	NOUN
ap-1795	153	3	row	row	NOUN
ap-1795	153	4	fits	fit	VERB
ap-1795	153	5	the	the	DET
ap-1795	153	6	local	local	ADJ
ap-1795	153	7	memory	memory	NOUN
ap-1795	153	8	easily	easily	ADV
ap-1795	153	9	(	(	PUNCT
ap-1795	153	10	4096	4096	NUM
ap-1795	153	11	∗	∗	NOUN
ap-1795	153	12	8	8	NUM
ap-1795	153	13	=	=	SYM
ap-1795	153	14	32758b	32758b	NUM
ap-1795	153	15	)	)	PUNCT
ap-1795	153	16	.	.	PUNCT
ap-1795	154	1	the	the	DET
ap-1795	154	2	processor	processor	NOUN
ap-1795	154	3	cores	core	NOUN
ap-1795	154	4	fetch	fetch	VERB
ap-1795	154	5	a	a	DET
ap-1795	154	6	matrix	matrix	NOUN
ap-1795	154	7	row	row	NOUN
ap-1795	154	8	from	from	ADP
ap-1795	154	9	global	global	ADJ
ap-1795	154	10	memory	memory	NOUN
ap-1795	154	11	and	and	CCONJ
ap-1795	154	12	compute	compute	VERB
ap-1795	154	13	the	the	DET
ap-1795	154	14	inverse	inverse	NOUN
ap-1795	154	15	of	of	ADP
ap-1795	154	16	the	the	DET
ap-1795	154	17	pivot	pivot	NOUN
ap-1795	154	18	element	element	NOUN
ap-1795	154	19	.	.	PUNCT
ap-1795	155	1	then	then	ADV
ap-1795	155	2	the	the	DET
ap-1795	155	3	processor	processor	NOUN
ap-1795	155	4	cores	core	NOUN
ap-1795	155	5	multiply	multiply	VERB
ap-1795	155	6	the	the	DET
ap-1795	155	7	cached	cache	VERB
ap-1795	155	8	row	row	NOUN
ap-1795	155	9	and	and	CCONJ
ap-1795	155	10	multiply	multiply	NOUN
ap-1795	155	11	-	-	PUNCT
ap-1795	155	12	add	add	ADJ
ap-1795	155	13	-	-	PUNCT
ap-1795	155	14	modulo	modulo	NOUN
ap-1795	155	15	other	other	ADJ
ap-1795	155	16	rows	row	NOUN
ap-1795	155	17	in	in	ADP
ap-1795	155	18	global	global	ADJ
ap-1795	155	19	memory	memory	NOUN
ap-1795	155	20	.	.	PUNCT
ap-1795	156	1	more	more	ADJ
ap-1795	156	2	details	detail	NOUN
ap-1795	156	3	,	,	PUNCT
ap-1795	156	4	including	include	VERB
ap-1795	156	5	the	the	DET
ap-1795	156	6	processor	processor	NOUN
ap-1795	156	7	core	core	NOUN
ap-1795	156	8	synchronizations	synchronization	NOUN
ap-1795	156	9	and	and	CCONJ
ap-1795	156	10	source	source	NOUN
ap-1795	156	11	code	code	NOUN
ap-1795	156	12	samples	sample	NOUN
ap-1795	156	13	,	,	PUNCT
ap-1795	156	14	are	be	AUX
ap-1795	156	15	available	available	ADJ
ap-1795	156	16	online2	online2	PROPN
ap-1795	156	17	.	.	PUNCT
ap-1795	157	1	5	5	X
ap-1795	157	2	.	.	X
ap-1795	157	3	results	result	NOUN
ap-1795	157	4	after	after	ADP
ap-1795	157	5	embedding	embed	VERB
ap-1795	157	6	architecture	architecture	NOUN
ap-1795	157	7	-	-	PUNCT
ap-1795	157	8	related	relate	VERB
ap-1795	157	9	optimizations	optimization	NOUN
ap-1795	157	10	into	into	ADP
ap-1795	157	11	our	our	PRON
ap-1795	157	12	clock	clock	NOUN
ap-1795	157	13	math	math	NOUN
ap-1795	157	14	solver	solver	NOUN
ap-1795	157	15	and	and	CCONJ
ap-1795	157	16	verifying	verify	VERB
ap-1795	157	17	the	the	DET
ap-1795	157	18	correctness	correctness	NOUN
ap-1795	157	19	of	of	ADP
ap-1795	157	20	our	our	PRON
ap-1795	157	21	results	result	NOUN
ap-1795	157	22	,	,	PUNCT
ap-1795	157	23	we	we	PRON
ap-1795	157	24	were	be	AUX
ap-1795	157	25	finally	finally	ADV
ap-1795	157	26	able	able	ADJ
ap-1795	157	27	to	to	PART
ap-1795	157	28	benchmark	benchmark	VERB
ap-1795	157	29	them	they	PRON
ap-1795	157	30	.	.	PUNCT
ap-1795	158	1	there	there	PRON
ap-1795	158	2	are	be	VERB
ap-1795	158	3	not	not	PART
ap-1795	158	4	many	many	ADJ
ap-1795	158	5	up	up	ADP
ap-1795	158	6	-	-	PUNCT
ap-1795	158	7	to	to	ADP
ap-1795	158	8	-	-	PUNCT
ap-1795	158	9	date	date	NOUN
ap-1795	158	10	solvers	solver	NOUN
ap-1795	158	11	like	like	ADP
ap-1795	158	12	ours	ours	PRON
ap-1795	158	13	currently	currently	ADV
ap-1795	158	14	.	.	PUNCT
ap-1795	159	1	we	we	PRON
ap-1795	159	2	benchmarked	benchmarke	VERB
ap-1795	159	3	primarily	primarily	ADV
ap-1795	159	4	against	against	ADP
ap-1795	159	5	linsolve-0.7.15	linsolve-0.7.15	PROPN
ap-1795	160	1	[	[	X
ap-1795	160	2	7	7	NUM
ap-1795	160	3	]	]	PUNCT
ap-1795	160	4	,	,	PUNCT
ap-1795	160	5	a	a	DET
ap-1795	160	6	highly	highly	ADV
ap-1795	160	7	optimized	optimize	VERB
ap-1795	160	8	solver	solver	NOUN
ap-1795	160	9	with	with	ADP
ap-1795	160	10	performance	performance	NOUN
ap-1795	160	11	critical	critical	ADJ
ap-1795	160	12	parts	part	NOUN
ap-1795	160	13	written	write	VERB
ap-1795	160	14	in	in	ADP
ap-1795	160	15	x86	x86	PROPN
ap-1795	160	16	assembler	assembler	NOUN
ap-1795	160	17	.	.	PUNCT
ap-1795	161	1	the	the	DET
ap-1795	161	2	results	result	NOUN
ap-1795	161	3	(	(	PUNCT
ap-1795	161	4	tab	tab	NOUN
ap-1795	161	5	.	.	NOUN
ap-1795	161	6	1	1	NUM
ap-1795	161	7	)	)	PUNCT
ap-1795	161	8	are	be	AUX
ap-1795	161	9	very	very	ADV
ap-1795	161	10	satisfying	satisfying	ADJ
ap-1795	161	11	.	.	PUNCT
ap-1795	162	1	clock	clock	PROPN
ap-1795	162	2	math	math	PROPN
ap-1795	162	3	solver	solver	PROPN
ap-1795	162	4	outperforms	outperform	NOUN
ap-1795	162	5	linsolve-0.7.15	linsolve-0.7.15	VERB
ap-1795	162	6	almost	almost	ADV
ap-1795	162	7	twice	twice	ADV
ap-1795	162	8	for	for	ADP
ap-1795	162	9	larger	large	ADJ
ap-1795	162	10	matrices	matrix	NOUN
ap-1795	162	11	.	.	PUNCT
ap-1795	163	1	2http://www.github.com/kubbing/clock-math	2http://www.github.com/kubbing/clock-math	NOUN
ap-1795	163	2	73	73	NUM
ap-1795	164	1	jakub	jakub	PROPN
ap-1795	164	2	hladík	hladík	PROPN
ap-1795	164	3	,	,	PUNCT
ap-1795	164	4	róbert	róbert	PROPN
ap-1795	164	5	lórencz	lórencz	PROPN
ap-1795	164	6	,	,	PUNCT
ap-1795	164	7	ivan	ivan	PROPN
ap-1795	164	8	šimeček	šimeček	PROPN
ap-1795	164	9	acta	acta	PROPN
ap-1795	164	10	polytechnica	polytechnica	PROPN
ap-1795	164	11	6	6	NUM
ap-1795	164	12	.	.	PUNCT
ap-1795	165	1	conclusion	conclusion	NOUN
ap-1795	165	2	we	we	PRON
ap-1795	165	3	have	have	AUX
ap-1795	165	4	presented	present	VERB
ap-1795	165	5	the	the	DET
ap-1795	165	6	working	work	VERB
ap-1795	165	7	system	system	NOUN
ap-1795	165	8	for	for	ADP
ap-1795	165	9	solving	solve	VERB
ap-1795	165	10	ill	ill	ADV
ap-1795	165	11	-	-	PUNCT
ap-1795	165	12	conditioned	condition	VERB
ap-1795	165	13	systems	system	NOUN
ap-1795	165	14	of	of	ADP
ap-1795	165	15	linear	linear	PROPN
ap-1795	165	16	equations	equation	NOUN
ap-1795	165	17	exactly	exactly	ADV
ap-1795	165	18	.	.	PUNCT
ap-1795	166	1	we	we	PRON
ap-1795	166	2	have	have	AUX
ap-1795	166	3	managed	manage	VERB
ap-1795	166	4	to	to	PART
ap-1795	166	5	effectively	effectively	ADV
ap-1795	166	6	bypass	bypass	VERB
ap-1795	166	7	floating	float	VERB
ap-1795	166	8	-	-	PUNCT
ap-1795	166	9	point	point	NOUN
ap-1795	166	10	rounding	rounding	NOUN
ap-1795	166	11	error	error	NOUN
ap-1795	166	12	by	by	ADP
ap-1795	166	13	using	use	VERB
ap-1795	166	14	modular	modular	ADJ
ap-1795	166	15	arithmetics	arithmetic	NOUN
ap-1795	166	16	.	.	PUNCT
ap-1795	167	1	most	most	ADJ
ap-1795	167	2	of	of	ADP
ap-1795	167	3	the	the	DET
ap-1795	167	4	entire	entire	ADJ
ap-1795	167	5	computation	computation	NOUN
ap-1795	167	6	has	have	AUX
ap-1795	167	7	taken	take	VERB
ap-1795	167	8	place	place	NOUN
ap-1795	167	9	by	by	ADP
ap-1795	167	10	solving	solve	VERB
ap-1795	167	11	sles	sle	NOUN
ap-1795	167	12	within	within	ADP
ap-1795	167	13	their	their	PRON
ap-1795	167	14	corresponding	correspond	VERB
ap-1795	167	15	modules	module	NOUN
ap-1795	167	16	.	.	PUNCT
ap-1795	168	1	this	this	DET
ap-1795	168	2	part	part	NOUN
ap-1795	168	3	of	of	ADP
ap-1795	168	4	the	the	DET
ap-1795	168	5	computation	computation	NOUN
ap-1795	168	6	can	can	AUX
ap-1795	168	7	be	be	AUX
ap-1795	168	8	(	(	PUNCT
ap-1795	168	9	and	and	CCONJ
ap-1795	168	10	is	be	AUX
ap-1795	168	11	)	)	PUNCT
ap-1795	168	12	solved	solve	VERB
ap-1795	168	13	in	in	ADP
ap-1795	168	14	parallel	parallel	NOUN
ap-1795	168	15	on	on	ADP
ap-1795	168	16	the	the	DET
ap-1795	168	17	common	common	ADJ
ap-1795	168	18	-	-	PUNCT
ap-1795	168	19	grade	grade	NOUN
ap-1795	168	20	gpu	gpu	PROPN
ap-1795	168	21	.	.	PROPN
ap-1795	169	1	gpu	gpu	PROPN
ap-1795	169	2	is	be	AUX
ap-1795	169	3	capable	capable	ADJ
ap-1795	169	4	of	of	ADP
ap-1795	169	5	solving	solve	VERB
ap-1795	169	6	several	several	ADJ
ap-1795	169	7	sles	sle	NOUN
ap-1795	169	8	at	at	ADP
ap-1795	169	9	once	once	ADV
ap-1795	169	10	(	(	PUNCT
ap-1795	169	11	8–16	8–16	PROPN
ap-1795	169	12	,	,	PUNCT
ap-1795	169	13	depending	depend	VERB
ap-1795	169	14	on	on	ADP
ap-1795	169	15	its	its	PRON
ap-1795	169	16	memory	memory	NOUN
ap-1795	169	17	size	size	NOUN
ap-1795	169	18	)	)	PUNCT
ap-1795	169	19	and	and	CCONJ
ap-1795	169	20	also	also	ADV
ap-1795	169	21	each	each	DET
ap-1795	169	22	system	system	NOUN
ap-1795	169	23	in	in	ADP
ap-1795	169	24	parallel	parallel	NOUN
ap-1795	169	25	on	on	ADP
ap-1795	169	26	its	its	PRON
ap-1795	169	27	spe	spe	NOUN
ap-1795	169	28	(	(	PUNCT
ap-1795	169	29	8–40	8–40	NOUN
ap-1795	169	30	cores	core	NOUN
ap-1795	169	31	)	)	PUNCT
ap-1795	169	32	.	.	PUNCT
ap-1795	170	1	double	double	ADJ
ap-1795	170	2	parallelism	parallelism	NOUN
ap-1795	170	3	has	have	AUX
ap-1795	170	4	been	be	AUX
ap-1795	170	5	utilized	utilize	VERB
ap-1795	170	6	,	,	PUNCT
ap-1795	170	7	so	so	ADV
ap-1795	170	8	significant	significant	ADJ
ap-1795	170	9	speedup	speedup	NOUN
ap-1795	170	10	is	be	AUX
ap-1795	170	11	achieved	achieve	VERB
ap-1795	170	12	compared	compare	VERB
ap-1795	170	13	to	to	ADP
ap-1795	170	14	other	other	ADJ
ap-1795	170	15	implementations	implementation	NOUN
ap-1795	170	16	.	.	PUNCT
ap-1795	171	1	we	we	PRON
ap-1795	171	2	are	be	AUX
ap-1795	171	3	currently	currently	ADV
ap-1795	171	4	working	work	VERB
ap-1795	171	5	on	on	ADP
ap-1795	171	6	advanced	advanced	ADJ
ap-1795	171	7	kernel	kernel	NOUN
ap-1795	171	8	optimizations	optimization	NOUN
ap-1795	171	9	with	with	ADP
ap-1795	171	10	larger	large	ADJ
ap-1795	171	11	matrix	matrix	NOUN
ap-1795	171	12	support	support	NOUN
ap-1795	171	13	.	.	PUNCT
ap-1795	172	1	7	7	X
ap-1795	172	2	.	.	X
ap-1795	172	3	future	future	ADJ
ap-1795	172	4	work	work	NOUN
ap-1795	172	5	as	as	SCONJ
ap-1795	172	6	we	we	PRON
ap-1795	172	7	now	now	ADV
ap-1795	172	8	have	have	VERB
ap-1795	172	9	a	a	DET
ap-1795	172	10	working	work	VERB
ap-1795	172	11	system	system	NOUN
ap-1795	172	12	,	,	PUNCT
ap-1795	172	13	we	we	PRON
ap-1795	172	14	would	would	AUX
ap-1795	172	15	like	like	VERB
ap-1795	172	16	to	to	PART
ap-1795	172	17	proceed	proceed	VERB
ap-1795	172	18	to	to	PART
ap-1795	172	19	:	:	PUNCT
ap-1795	172	20	•	•	ADP
ap-1795	172	21	add	add	VERB
ap-1795	172	22	support	support	NOUN
ap-1795	172	23	for	for	ADP
ap-1795	172	24	both	both	CCONJ
ap-1795	172	25	single	single	ADJ
ap-1795	172	26	and	and	CCONJ
ap-1795	172	27	double	double	ADJ
ap-1795	172	28	precision	precision	NOUN
ap-1795	172	29	for	for	ADP
ap-1795	172	30	matrix	matrix	NOUN
ap-1795	172	31	elimination	elimination	NOUN
ap-1795	172	32	,	,	PUNCT
ap-1795	172	33	as	as	SCONJ
ap-1795	172	34	the	the	DET
ap-1795	172	35	β	β	PROPN
ap-1795	172	36	vector	vector	NOUN
ap-1795	172	37	module	module	NOUN
ap-1795	172	38	count	count	NOUN
ap-1795	172	39	and	and	CCONJ
ap-1795	172	40	gpu	gpu	NOUN
ap-1795	172	41	performance	performance	NOUN
ap-1795	172	42	may	may	AUX
ap-1795	172	43	differ	differ	VERB
ap-1795	172	44	;	;	PUNCT
ap-1795	172	45	•	•	ADV
ap-1795	172	46	add	add	VERB
ap-1795	172	47	support	support	NOUN
ap-1795	172	48	for	for	ADP
ap-1795	172	49	larger	large	ADJ
ap-1795	172	50	matrices	matrix	NOUN
ap-1795	172	51	than	than	ADP
ap-1795	172	52	4096×	4096×	NUM
ap-1795	172	53	4096	4096	NUM
ap-1795	172	54	–	–	PUNCT
ap-1795	172	55	optimize	optimize	NOUN
ap-1795	172	56	smp	smp	NOUN
ap-1795	172	57	shared	share	VERB
ap-1795	172	58	memory	memory	NOUN
ap-1795	172	59	usage	usage	NOUN
ap-1795	172	60	;	;	PUNCT
ap-1795	172	61	•	•	ADP
ap-1795	172	62	add	add	VERB
ap-1795	172	63	support	support	NOUN
ap-1795	172	64	for	for	ADP
ap-1795	172	65	automatic	automatic	ADJ
ap-1795	172	66	kernel	kernel	NOUN
ap-1795	172	67	group	group	NOUN
ap-1795	172	68	size	size	NOUN
ap-1795	172	69	tuning	tune	VERB
ap-1795	172	70	for	for	ADP
ap-1795	172	71	larger	large	ADJ
ap-1795	172	72	matrices	matrix	NOUN
ap-1795	172	73	,	,	PUNCT
ap-1795	172	74	as	as	SCONJ
ap-1795	172	75	the	the	DET
ap-1795	172	76	group	group	NOUN
ap-1795	172	77	size	size	NOUN
ap-1795	172	78	lowers	lower	VERB
ap-1795	172	79	the	the	DET
ap-1795	172	80	memory	memory	NOUN
ap-1795	172	81	access	access	NOUN
ap-1795	172	82	time	time	NOUN
ap-1795	172	83	on	on	ADP
ap-1795	172	84	different	different	ADJ
ap-1795	172	85	gpus	gpu	NOUN
ap-1795	172	86	/	/	SYM
ap-1795	172	87	architectures	architecture	NOUN
ap-1795	172	88	;	;	PUNCT
ap-1795	172	89	•	•	NUM
ap-1795	172	90	examine	examine	VERB
ap-1795	172	91	the	the	DET
ap-1795	172	92	modulus	modulus	ADJ
ap-1795	172	93	operation	operation	NOUN
ap-1795	172	94	performance	performance	NOUN
ap-1795	172	95	across	across	ADP
ap-1795	172	96	different	different	ADJ
ap-1795	172	97	gpu	gpu	NOUN
ap-1795	172	98	architectures	architecture	NOUN
ap-1795	172	99	and	and	CCONJ
ap-1795	172	100	further	far	ADV
ap-1795	172	101	optimize	optimize	VERB
ap-1795	172	102	the	the	DET
ap-1795	172	103	saxpy	saxpy	NOUN
ap-1795	172	104	,	,	PUNCT
ap-1795	172	105	respectively	respectively	ADV
ap-1795	172	106	daxpy	daxpy	VERB
ap-1795	172	107	functions	function	NOUN
ap-1795	172	108	(	(	PUNCT
ap-1795	172	109	modm	modm	NOUN
ap-1795	172	110	)	)	PUNCT
ap-1795	172	111	;	;	PUNCT
ap-1795	172	112	•	•	X
ap-1795	172	113	utilize	utilize	VERB
ap-1795	172	114	openmpi	openmpi	ADJ
ap-1795	172	115	library	library	NOUN
ap-1795	172	116	to	to	PART
ap-1795	172	117	add	add	VERB
ap-1795	172	118	cluster	cluster	NOUN
ap-1795	172	119	support	support	NOUN
ap-1795	172	120	;	;	PUNCT
ap-1795	172	121	•	•	ADP
ap-1795	172	122	adjust	adjust	VERB
ap-1795	172	123	and	and	CCONJ
ap-1795	172	124	run	run	VERB
ap-1795	172	125	the	the	DET
ap-1795	172	126	solver	solver	NOUN
ap-1795	172	127	on	on	ADP
ap-1795	172	128	our	our	PRON
ap-1795	172	129	university	university	NOUN
ap-1795	172	130	star	star	NOUN
ap-1795	172	131	cluster	cluster	NOUN
ap-1795	172	132	to	to	PART
ap-1795	172	133	test	test	VERB
ap-1795	172	134	amd	amd	PROPN
ap-1795	172	135	’s	’s	PART
ap-1795	172	136	opencl	opencl	PROPN
ap-1795	172	137	cpu	cpu	PROPN
ap-1795	172	138	implementation	implementation	NOUN
ap-1795	172	139	.	.	PUNCT
ap-1795	173	1	acknowledgements	acknowledgement	NOUN
ap-1795	173	2	this	this	DET
ap-1795	173	3	research	research	NOUN
ap-1795	173	4	has	have	AUX
ap-1795	173	5	been	be	AUX
ap-1795	173	6	supported	support	VERB
ap-1795	173	7	by	by	ADP
ap-1795	173	8	cesnet	cesnet	PROPN
ap-1795	173	9	development	development	NOUN
ap-1795	173	10	fund	fund	PROPN
ap-1795	173	11	project	project	NOUN
ap-1795	173	12	390/2010	390/2010	NUM
ap-1795	173	13	and	and	CCONJ
ap-1795	173	14	by	by	ADP
ap-1795	173	15	the	the	DET
ap-1795	173	16	grant	grant	PROPN
ap-1795	173	17	sgs12/097	sgs12/097	PROPN
ap-1795	173	18	/	/	SYM
ap-1795	173	19	ohk3/1t/18	ohk3/1t/18	PROPN
ap-1795	173	20	.	.	PUNCT
ap-1795	174	1	references	reference	NOUN
ap-1795	174	2	[	[	X
ap-1795	174	3	1	1	NUM
ap-1795	174	4	]	]	X
ap-1795	174	5	lórencz	lórencz	PROPN
ap-1795	174	6	,	,	PUNCT
ap-1795	174	7	r.	r.	PROPN
ap-1795	174	8	:	:	PUNCT
ap-1795	174	9	aplikovaná	aplikovaná	PROPN
ap-1795	174	10	numerická	numerická	PROPN
ap-1795	174	11	matematika	matematika	X
ap-1795	174	12	a	a	DET
ap-1795	174	13	kryptografie	kryptografie	PROPN
ap-1795	174	14	.	.	PUNCT
ap-1795	175	1	vydavatelství	vydavatelství	PROPN
ap-1795	175	2	čvut	čvut	PROPN
ap-1795	175	3	,	,	PUNCT
ap-1795	175	4	2004	2004	NUM
ap-1795	175	5	[	[	X
ap-1795	175	6	2	2	NUM
ap-1795	175	7	]	]	PUNCT
ap-1795	175	8	gregory	gregory	PROPN
ap-1795	175	9	,	,	PUNCT
ap-1795	175	10	r.t	r.t	PROPN
ap-1795	175	11	.	.	PROPN
ap-1795	175	12	:	:	PUNCT
ap-1795	175	13	error	error	NOUN
ap-1795	175	14	-	-	PUNCT
ap-1795	175	15	free	free	ADJ
ap-1795	175	16	computation	computation	NOUN
ap-1795	175	17	:	:	PUNCT
ap-1795	175	18	why	why	SCONJ
ap-1795	175	19	it	it	PRON
ap-1795	175	20	is	be	AUX
ap-1795	175	21	needed	need	VERB
ap-1795	175	22	and	and	CCONJ
ap-1795	175	23	methods	method	NOUN
ap-1795	175	24	for	for	ADP
ap-1795	175	25	doing	do	VERB
ap-1795	175	26	it	it	PRON
ap-1795	175	27	.	.	PUNCT
ap-1795	176	1	r.	r.	PROPN
ap-1795	176	2	e.	e.	PROPN
ap-1795	176	3	krieger	krieger	PROPN
ap-1795	176	4	pub	pub	PROPN
ap-1795	176	5	co	co	NOUN
ap-1795	176	6	,	,	PUNCT
ap-1795	176	7	1980	1980	NUM
ap-1795	176	8	[	[	X
ap-1795	176	9	3	3	NUM
ap-1795	176	10	]	]	X
ap-1795	176	11	lórencz	lórencz	PROPN
ap-1795	176	12	,	,	PUNCT
ap-1795	176	13	r.	r.	PROPN
ap-1795	176	14	,	,	PUNCT
ap-1795	176	15	morháč	morháč	PROPN
ap-1795	176	16	,	,	PUNCT
ap-1795	176	17	m.	m.	NOUN
ap-1795	176	18	:	:	PUNCT
ap-1795	176	19	a	a	DET
ap-1795	176	20	modular	modular	ADJ
ap-1795	176	21	system	system	NOUN
ap-1795	176	22	for	for	ADP
ap-1795	176	23	solving	solve	VERB
ap-1795	176	24	linear	linear	ADJ
ap-1795	176	25	equations	equation	NOUN
ap-1795	176	26	exactly	exactly	ADV
ap-1795	176	27	.	.	PUNCT
ap-1795	177	1	computers	computer	NOUN
ap-1795	177	2	and	and	CCONJ
ap-1795	177	3	artificial	artificial	ADJ
ap-1795	177	4	intelligence	intelligence	NOUN
ap-1795	177	5	,	,	PUNCT
ap-1795	177	6	vol	vol	NOUN
ap-1795	177	7	.	.	PROPN
ap-1795	177	8	12	12	NUM
ap-1795	177	9	,	,	PUNCT
ap-1795	177	10	1992	1992	NUM
ap-1795	177	11	[	[	X
ap-1795	177	12	4	4	NUM
ap-1795	177	13	]	]	PUNCT
ap-1795	177	14	zahradnický	zahradnický	NOUN
ap-1795	177	15	,	,	PUNCT
ap-1795	177	16	t.	t.	PROPN
ap-1795	177	17	:	:	PUNCT
ap-1795	177	18	mosfet	mosfet	PROPN
ap-1795	177	19	parameter	parameter	NOUN
ap-1795	177	20	extraction	extraction	NOUN
ap-1795	177	21	optimization	optimization	NOUN
ap-1795	177	22	.	.	PUNCT
ap-1795	178	1	ph.d	ph.d	PROPN
ap-1795	178	2	.	.	PUNCT
ap-1795	179	1	thesis	thesis	NOUN
ap-1795	179	2	,	,	PUNCT
ap-1795	179	3	department	department	NOUN
ap-1795	179	4	of	of	ADP
ap-1795	179	5	computer	computer	NOUN
ap-1795	179	6	systems	system	NOUN
ap-1795	179	7	,	,	PUNCT
ap-1795	179	8	faculty	faculty	NOUN
ap-1795	179	9	of	of	ADP
ap-1795	179	10	information	information	NOUN
ap-1795	179	11	technology	technology	NOUN
ap-1795	179	12	,	,	PUNCT
ap-1795	179	13	czech	czech	PROPN
ap-1795	179	14	technical	technical	PROPN
ap-1795	179	15	university	university	PROPN
ap-1795	179	16	in	in	ADP
ap-1795	179	17	prague	prague	PROPN
ap-1795	179	18	,	,	PUNCT
ap-1795	179	19	2010	2010	NUM
ap-1795	180	1	[	[	X
ap-1795	180	2	5	5	NUM
ap-1795	180	3	]	]	SYM
ap-1795	180	4	kirk	kirk	PROPN
ap-1795	180	5	,	,	PUNCT
ap-1795	180	6	d.b	d.b	PROPN
ap-1795	180	7	.	.	PROPN
ap-1795	180	8	,	,	PUNCT
ap-1795	180	9	hwu	hwu	PROPN
ap-1795	180	10	,	,	PUNCT
ap-1795	180	11	w.w	w.w	PROPN
ap-1795	180	12	.	.	PROPN
ap-1795	180	13	:	:	PUNCT
ap-1795	180	14	programming	program	VERB
ap-1795	180	15	massively	massively	ADV
ap-1795	180	16	parallel	parallel	ADJ
ap-1795	180	17	processors	processor	NOUN
ap-1795	180	18	,	,	PUNCT
ap-1795	180	19	a	a	DET
ap-1795	180	20	hands	hand	NOUN
ap-1795	180	21	-	-	PUNCT
ap-1795	180	22	on	on	ADP
ap-1795	180	23	approach	approach	NOUN
ap-1795	180	24	.	.	PUNCT
ap-1795	181	1	morgan	morgan	PROPN
ap-1795	181	2	kaufmann	kaufmann	PROPN
ap-1795	181	3	publishers	publishers	PROPN
ap-1795	181	4	,	,	PUNCT
ap-1795	181	5	2010	2010	NUM
ap-1795	181	6	[	[	X
ap-1795	181	7	6	6	NUM
ap-1795	181	8	]	]	PUNCT
ap-1795	181	9	ieee	ieee	NOUN
ap-1795	181	10	standard	standard	NOUN
ap-1795	181	11	for	for	ADP
ap-1795	181	12	floating	float	VERB
ap-1795	181	13	-	-	PUNCT
ap-1795	181	14	point	point	NOUN
ap-1795	181	15	arithmetic	arithmetic	ADJ
ap-1795	181	16	.	.	PUNCT
ap-1795	182	1	ieee	ieee	NOUN
ap-1795	182	2	std	std	NOUN
ap-1795	182	3	754	754	NUM
ap-1795	182	4	-	-	SYM
ap-1795	182	5	2008	2008	NUM
ap-1795	182	6	,	,	PUNCT
ap-1795	182	7	pages	page	NOUN
ap-1795	182	8	1	1	NUM
ap-1795	182	9	-	-	SYM
ap-1795	182	10	58	58	NUM
ap-1795	182	11	,	,	PUNCT
ap-1795	182	12	2008	2008	NUM
ap-1795	183	1	[	[	X
ap-1795	183	2	7	7	NUM
ap-1795	183	3	]	]	X
ap-1795	183	4	vondra	vondra	PROPN
ap-1795	183	5	,	,	PUNCT
ap-1795	183	6	l.	l.	PROPN
ap-1795	183	7	,	,	PUNCT
ap-1795	183	8	lórencz	lórencz	PROPN
ap-1795	183	9	,	,	PUNCT
ap-1795	183	10	r.	r.	PROPN
ap-1795	183	11	:	:	PUNCT
ap-1795	183	12	system	system	NOUN
ap-1795	183	13	for	for	ADP
ap-1795	183	14	solving	solve	VERB
ap-1795	183	15	linear	linear	ADJ
ap-1795	183	16	equation	equation	NOUN
ap-1795	183	17	systems	system	NOUN
ap-1795	183	18	.	.	PUNCT
ap-1795	184	1	seminar	seminar	NOUN
ap-1795	184	2	on	on	ADP
ap-1795	184	3	numerical	numerical	ADJ
ap-1795	184	4	analysis	analysis	NOUN
ap-1795	184	5	,	,	PUNCT
ap-1795	184	6	pages	page	NOUN
ap-1795	184	7	171	171	NUM
ap-1795	184	8	-	-	SYM
ap-1795	184	9	174	174	NUM
ap-1795	184	10	,	,	PUNCT
ap-1795	184	11	technical	technical	ADJ
ap-1795	184	12	university	university	NOUN
ap-1795	184	13	liberec	liberec	NOUN
ap-1795	184	14	,	,	PUNCT
ap-1795	184	15	2012	2012	NUM
ap-1795	184	16	74	74	NUM
ap-1795	184	17	acta	acta	PROPN
ap-1795	184	18	polytechnica	polytechnica	PROPN
ap-1795	184	19	53(2):70	53(2):70	PROPN
ap-1795	184	20	-	-	PUNCT
ap-1795	184	21	-74	-74	NUM
ap-1795	184	22	,	,	PUNCT
ap-1795	184	23	2013	2013	NUM
ap-1795	184	24	1	1	NUM
ap-1795	184	25	introduction	introduction	NOUN
ap-1795	184	26	2	2	NUM
ap-1795	184	27	state	state	NOUN
ap-1795	184	28	of	of	ADP
ap-1795	184	29	the	the	DET
ap-1795	184	30	art	art	NOUN
ap-1795	184	31	3	3	NUM
ap-1795	184	32	mathematical	mathematical	ADJ
ap-1795	184	33	background	background	NOUN
ap-1795	184	34	3.1	3.1	NUM
ap-1795	184	35	matrix	matrix	NOUN
ap-1795	184	36	scaling	scale	VERB
ap-1795	184	37	3.2	3.2	NUM
ap-1795	184	38	solving	solve	VERB
ap-1795	184	39	a	a	DET
ap-1795	184	40	system	system	NOUN
ap-1795	184	41	of	of	ADP
ap-1795	184	42	linear	linear	ADJ
ap-1795	184	43	equations	equation	NOUN
ap-1795	184	44	3.3	3.3	NUM
ap-1795	184	45	inverse	inverse	NOUN
ap-1795	184	46	transformation	transformation	NOUN
ap-1795	184	47	4	4	NUM
ap-1795	184	48	gpu	gpu	NOUN
ap-1795	184	49	and	and	CCONJ
ap-1795	184	50	optimizations	optimization	VERB
ap-1795	184	51	4.1	4.1	NUM
ap-1795	184	52	profiling	profiling	NOUN
ap-1795	184	53	4.2	4.2	NUM
ap-1795	184	54	gpu	gpu	NOUN
ap-1795	184	55	architecture	architecture	NOUN
ap-1795	184	56	4.3	4.3	NUM
ap-1795	184	57	gpu	gpu	NOUN
ap-1795	184	58	kernels	kernel	NOUN
ap-1795	184	59	,	,	PUNCT
ap-1795	184	60	optimizations	optimization	NOUN
ap-1795	184	61	5	5	NUM
ap-1795	184	62	results	result	VERB
ap-1795	184	63	6	6	NUM
ap-1795	184	64	conclusion	conclusion	NOUN
ap-1795	184	65	7	7	NUM
ap-1795	184	66	future	future	ADJ
ap-1795	184	67	work	work	NOUN
ap-1795	184	68	acknowledgements	acknowledgement	NOUN
ap-1795	184	69	references	reference	NOUN