id	sid	tid	token	lemma	pos
ap-662	1	1	ap05_1.vp	ap05_1.vp	NOUN
ap-662	1	2	1	1	NUM
ap-662	1	3	introduction	introduction	NOUN
ap-662	1	4	project	project	NOUN
ap-662	1	5	gama	gama	NOUN
ap-662	1	6	for	for	ADP
ap-662	1	7	adjustment	adjustment	NOUN
ap-662	1	8	of	of	ADP
ap-662	1	9	geodetic	geodetic	ADJ
ap-662	1	10	networks	network	NOUN
ap-662	1	11	was	be	AUX
ap-662	1	12	started	start	VERB
ap-662	1	13	at	at	ADP
ap-662	1	14	the	the	DET
ap-662	1	15	department	department	NOUN
ap-662	1	16	of	of	ADP
ap-662	1	17	mapping	mapping	NOUN
ap-662	1	18	and	and	CCONJ
ap-662	1	19	cartography	cartography	NOUN
ap-662	1	20	,	,	PUNCT
ap-662	1	21	faculty	faculty	NOUN
ap-662	1	22	of	of	ADP
ap-662	1	23	civil	civil	ADJ
ap-662	1	24	engineering	engineering	NOUN
ap-662	1	25	,	,	PUNCT
ap-662	1	26	czech	czech	PROPN
ap-662	1	27	tu	tu	PROPN
ap-662	1	28	prague	prague	PROPN
ap-662	1	29	,	,	PUNCT
ap-662	1	30	in	in	ADP
ap-662	1	31	1998	1998	NUM
ap-662	1	32	.	.	PUNCT
ap-662	2	1	at	at	ADP
ap-662	2	2	first	first	ADV
ap-662	2	3	it	it	PRON
ap-662	2	4	was	be	AUX
ap-662	2	5	planned	plan	VERB
ap-662	2	6	to	to	PART
ap-662	2	7	be	be	AUX
ap-662	2	8	only	only	ADV
ap-662	2	9	a	a	DET
ap-662	2	10	local	local	ADJ
ap-662	2	11	project	project	NOUN
ap-662	2	12	with	with	ADP
ap-662	2	13	the	the	DET
ap-662	2	14	main	main	ADJ
ap-662	2	15	goal	goal	NOUN
ap-662	2	16	of	of	ADP
ap-662	2	17	demonstrating	demonstrate	VERB
ap-662	2	18	to	to	ADP
ap-662	2	19	students	student	NOUN
ap-662	2	20	the	the	DET
ap-662	2	21	power	power	NOUN
ap-662	2	22	of	of	ADP
ap-662	2	23	object	object	NOUN
ap-662	2	24	programming	programming	NOUN
ap-662	2	25	and	and	CCONJ
ap-662	2	26	at	at	ADP
ap-662	2	27	the	the	DET
ap-662	2	28	same	same	ADJ
ap-662	2	29	time	time	NOUN
ap-662	2	30	being	be	AUX
ap-662	2	31	a	a	DET
ap-662	2	32	free	free	ADJ
ap-662	2	33	independent	independent	ADJ
ap-662	2	34	tool	tool	NOUN
ap-662	2	35	for	for	ADP
ap-662	2	36	comparing	compare	VERB
ap-662	2	37	of	of	ADP
ap-662	2	38	adjustment	adjustment	NOUN
ap-662	2	39	results	result	NOUN
ap-662	2	40	from	from	ADP
ap-662	2	41	various	various	ADJ
ap-662	2	42	sources	source	NOUN
ap-662	2	43	.	.	PUNCT
ap-662	3	1	the	the	DET
ap-662	3	2	gama	gama	NOUN
ap-662	3	3	project	project	NOUN
ap-662	3	4	received	receive	VERB
ap-662	3	5	the	the	DET
ap-662	3	6	official	official	ADJ
ap-662	3	7	status	status	NOUN
ap-662	3	8	of	of	ADP
ap-662	3	9	gnu	gnu	PROPN
ap-662	3	10	software	software	NOUN
ap-662	3	11	in	in	ADP
ap-662	3	12	2001	2001	NUM
ap-662	3	13	,	,	PUNCT
ap-662	3	14	and	and	CCONJ
ap-662	3	15	now	now	ADV
ap-662	3	16	consists	consist	VERB
ap-662	3	17	of	of	ADP
ap-662	3	18	a	a	DET
ap-662	3	19	c	c	PROPN
ap-662	3	20	�	�	NOUN
ap-662	3	21	�	�	PROPN
ap-662	3	22	library	library	NOUN
ap-662	3	23	(	(	PUNCT
ap-662	3	24	including	include	VERB
ap-662	3	25	small	small	ADJ
ap-662	3	26	c	c	PROPN
ap-662	3	27	�	�	NOUN
ap-662	3	28	�	�	NOUN
ap-662	3	29	matrix	matrix	NOUN
ap-662	3	30	/	/	SYM
ap-662	3	31	vector	vector	NOUN
ap-662	3	32	template	template	NOUN
ap-662	3	33	library	library	NOUN
ap-662	3	34	gmatvec	gmatvec	NOUN
ap-662	3	35	)	)	PUNCT
ap-662	3	36	and	and	CCONJ
ap-662	3	37	two	two	NUM
ap-662	3	38	programs	program	NOUN
ap-662	3	39	gama	gama	NOUN
ap-662	3	40	-	-	PUNCT
ap-662	3	41	local	local	ADJ
ap-662	3	42	and	and	CCONJ
ap-662	3	43	gama	gama	NOUN
ap-662	3	44	-	-	PUNCT
ap-662	3	45	g3	g3	NOUN
ap-662	3	46	,	,	PUNCT
ap-662	3	47	which	which	PRON
ap-662	3	48	correspond	correspond	VERB
ap-662	3	49	to	to	ADP
ap-662	3	50	two	two	NUM
ap-662	3	51	development	development	NOUN
ap-662	3	52	branches	branch	NOUN
ap-662	3	53	of	of	ADP
ap-662	3	54	the	the	DET
ap-662	3	55	project	project	NOUN
ap-662	3	56	.	.	PUNCT
ap-662	4	1	the	the	DET
ap-662	4	2	stable	stable	ADJ
ap-662	4	3	branch	branch	NOUN
ap-662	4	4	of	of	ADP
ap-662	4	5	the	the	DET
ap-662	4	6	gama	gama	NOUN
ap-662	4	7	project	project	NOUN
ap-662	4	8	consists	consist	VERB
ap-662	4	9	of	of	ADP
ap-662	4	10	the	the	DET
ap-662	4	11	command	command	NOUN
ap-662	4	12	line	line	NOUN
ap-662	4	13	program	program	NOUN
ap-662	4	14	gama	gama	NOUN
ap-662	4	15	-	-	PUNCT
ap-662	4	16	local	local	ADJ
ap-662	4	17	for	for	ADP
ap-662	4	18	adjustment	adjustment	NOUN
ap-662	4	19	of	of	ADP
ap-662	4	20	three	three	NUM
ap-662	4	21	-	-	PUNCT
ap-662	4	22	dimensional	dimensional	ADJ
ap-662	4	23	geodetic	geodetic	ADJ
ap-662	4	24	networks	network	NOUN
ap-662	4	25	in	in	ADP
ap-662	4	26	a	a	DET
ap-662	4	27	local	local	ADJ
ap-662	4	28	coordinates	coordinate	NOUN
ap-662	4	29	system	system	NOUN
ap-662	4	30	(	(	PUNCT
ap-662	4	31	platform	platform	NOUN
ap-662	4	32	independent	independent	ADJ
ap-662	4	33	qt	qt	PROPN
ap-662	4	34	based	base	VERB
ap-662	4	35	gui	gui	PROPN
ap-662	4	36	roci	roci	PROPN
ap-662	4	37	-	-	PUNCT
ap-662	4	38	local	local	PROPN
ap-662	4	39	is	be	AUX
ap-662	4	40	also	also	ADV
ap-662	4	41	available	available	ADJ
ap-662	4	42	)	)	PUNCT
ap-662	4	43	.	.	PUNCT
ap-662	5	1	the	the	DET
ap-662	5	2	new	new	ADJ
ap-662	5	3	development	development	NOUN
ap-662	5	4	branch	branch	NOUN
ap-662	5	5	of	of	ADP
ap-662	5	6	the	the	DET
ap-662	5	7	project	project	NOUN
ap-662	5	8	(	(	PUNCT
ap-662	5	9	gama	gama	NOUN
ap-662	5	10	-	-	PUNCT
ap-662	5	11	g3	g3	NOUN
ap-662	5	12	)	)	PUNCT
ap-662	5	13	aims	aim	VERB
ap-662	5	14	to	to	PART
ap-662	5	15	adjust	adjust	VERB
ap-662	5	16	the	the	DET
ap-662	5	17	geodetic	geodetic	ADJ
ap-662	5	18	networks	network	NOUN
ap-662	5	19	in	in	ADP
ap-662	5	20	a	a	DET
ap-662	5	21	global	global	ADJ
ap-662	5	22	geocentric	geocentric	ADJ
ap-662	5	23	system	system	NOUN
ap-662	5	24	.	.	PUNCT
ap-662	6	1	the	the	DET
ap-662	6	2	stable	stable	ADJ
ap-662	6	3	branch	branch	NOUN
ap-662	6	4	(	(	PUNCT
ap-662	6	5	gama	gama	NOUN
ap-662	6	6	-	-	PUNCT
ap-662	6	7	local	local	ADJ
ap-662	6	8	)	)	PUNCT
ap-662	6	9	enables	enable	VERB
ap-662	6	10	common	common	ADJ
ap-662	6	11	adjustment	adjustment	NOUN
ap-662	6	12	of	of	ADP
ap-662	6	13	possibly	possibly	ADV
ap-662	6	14	correlated	correlate	VERB
ap-662	6	15	horizontal	horizontal	ADJ
ap-662	6	16	directions	direction	NOUN
ap-662	6	17	and	and	CCONJ
ap-662	6	18	distances	distance	NOUN
ap-662	6	19	,	,	PUNCT
ap-662	6	20	horizontal	horizontal	ADJ
ap-662	6	21	angles	angle	NOUN
ap-662	6	22	,	,	PUNCT
ap-662	6	23	slope	slope	NOUN
ap-662	6	24	distances	distance	NOUN
ap-662	6	25	and	and	CCONJ
ap-662	6	26	zenith	zenith	NOUN
ap-662	6	27	angles	angle	NOUN
ap-662	6	28	,	,	PUNCT
ap-662	6	29	height	height	NOUN
ap-662	6	30	differences	difference	NOUN
ap-662	6	31	,	,	PUNCT
ap-662	6	32	observed	observed	ADJ
ap-662	6	33	coordinates	coordinate	NOUN
ap-662	6	34	(	(	PUNCT
ap-662	6	35	used	use	VERB
ap-662	6	36	in	in	ADP
ap-662	6	37	sequential	sequential	ADJ
ap-662	6	38	adjustment	adjustment	NOUN
ap-662	6	39	,	,	PUNCT
ap-662	6	40	etc	etc	X
ap-662	6	41	.	.	X
ap-662	6	42	)	)	PUNCT
ap-662	6	43	and	and	CCONJ
ap-662	6	44	observed	observe	VERB
ap-662	6	45	coordinate	coordinate	NOUN
ap-662	6	46	differences	difference	NOUN
ap-662	6	47	(	(	PUNCT
ap-662	6	48	vectors	vector	NOUN
ap-662	6	49	)	)	PUNCT
ap-662	6	50	.	.	PUNCT
ap-662	7	1	although	although	SCONJ
ap-662	7	2	such	such	DET
ap-662	7	3	an	an	DET
ap-662	7	4	adjustment	adjustment	NOUN
ap-662	7	5	model	model	NOUN
ap-662	7	6	has	have	AUX
ap-662	7	7	now	now	ADV
ap-662	7	8	been	be	AUX
ap-662	7	9	made	make	VERB
ap-662	7	10	obsolete	obsolete	ADJ
ap-662	7	11	by	by	ADP
ap-662	7	12	global	global	ADJ
ap-662	7	13	positioning	positioning	NOUN
ap-662	7	14	systems	system	NOUN
ap-662	7	15	,	,	PUNCT
ap-662	7	16	it	it	PRON
ap-662	7	17	can	can	AUX
ap-662	7	18	still	still	ADV
ap-662	7	19	serve	serve	VERB
ap-662	7	20	as	as	ADP
ap-662	7	21	an	an	DET
ap-662	7	22	educational	educational	ADJ
ap-662	7	23	tool	tool	NOUN
ap-662	7	24	for	for	ADP
ap-662	7	25	demonstrating	demonstrate	VERB
ap-662	7	26	adjustment	adjustment	NOUN
ap-662	7	27	procedures	procedure	NOUN
ap-662	7	28	to	to	ADP
ap-662	7	29	students	student	NOUN
ap-662	7	30	and	and	CCONJ
ap-662	7	31	as	as	ADP
ap-662	7	32	a	a	DET
ap-662	7	33	starting	starting	NOUN
ap-662	7	34	platform	platform	NOUN
ap-662	7	35	for	for	ADP
ap-662	7	36	the	the	DET
ap-662	7	37	developing	develop	VERB
ap-662	7	38	a	a	DET
ap-662	7	39	new	new	ADJ
ap-662	7	40	branch	branch	NOUN
ap-662	7	41	of	of	ADP
ap-662	7	42	the	the	DET
ap-662	7	43	project	project	NOUN
ap-662	7	44	(	(	PUNCT
ap-662	7	45	gama	gama	NOUN
ap-662	7	46	-	-	PUNCT
ap-662	7	47	g3	g3	NOUN
ap-662	7	48	)	)	PUNCT
ap-662	7	49	.	.	PUNCT
ap-662	8	1	numerical	numerical	ADJ
ap-662	8	2	solution	solution	NOUN
ap-662	8	3	of	of	ADP
ap-662	8	4	least	least	ADJ
ap-662	8	5	squares	square	NOUN
ap-662	8	6	adjustment	adjustment	NOUN
ap-662	8	7	in	in	ADP
ap-662	8	8	geodesy	geodesy	PROPN
ap-662	8	9	is	be	AUX
ap-662	8	10	most	most	ADV
ap-662	8	11	commonly	commonly	ADV
ap-662	8	12	based	base	VERB
ap-662	8	13	on	on	ADP
ap-662	8	14	the	the	DET
ap-662	8	15	solution	solution	NOUN
ap-662	8	16	of	of	ADP
ap-662	8	17	normal	normal	ADJ
ap-662	8	18	equations	equation	NOUN
ap-662	8	19	.	.	PUNCT
ap-662	9	1	as	as	SCONJ
ap-662	9	2	the	the	DET
ap-662	9	3	gama	gama	NOUN
ap-662	9	4	project	project	NOUN
ap-662	9	5	was	be	AUX
ap-662	9	6	also	also	ADV
ap-662	9	7	meant	mean	VERB
ap-662	9	8	to	to	PART
ap-662	9	9	be	be	AUX
ap-662	9	10	a	a	DET
ap-662	9	11	comparison	comparison	NOUN
ap-662	9	12	tool	tool	NOUN
ap-662	9	13	,	,	PUNCT
ap-662	9	14	it	it	PRON
ap-662	9	15	was	be	AUX
ap-662	9	16	desirable	desirable	ADJ
ap-662	9	17	to	to	PART
ap-662	9	18	use	use	VERB
ap-662	9	19	a	a	DET
ap-662	9	20	different	different	ADJ
ap-662	9	21	method	method	NOUN
ap-662	9	22	,	,	PUNCT
ap-662	9	23	and	and	CCONJ
ap-662	9	24	singular	singular	ADJ
ap-662	9	25	value	value	NOUN
ap-662	9	26	decomposition	decomposition	NOUN
ap-662	9	27	(	(	PUNCT
ap-662	9	28	svd	svd	PROPN
ap-662	9	29	)	)	PUNCT
ap-662	9	30	was	be	AUX
ap-662	9	31	implemented	implement	VERB
ap-662	9	32	as	as	ADP
ap-662	9	33	the	the	DET
ap-662	9	34	main	main	ADJ
ap-662	9	35	numerical	numerical	ADJ
ap-662	9	36	algorithm	algorithm	NOUN
ap-662	9	37	.	.	PUNCT
ap-662	10	1	as	as	ADP
ap-662	10	2	an	an	DET
ap-662	10	3	testing	testing	NOUN
ap-662	10	4	alternative	alternative	NOUN
ap-662	10	5	,	,	PUNCT
ap-662	10	6	gama	gama	NOUN
ap-662	10	7	implements	implement	VERB
ap-662	10	8	another	another	DET
ap-662	10	9	algorithm	algorithm	NOUN
ap-662	10	10	from	from	ADP
ap-662	10	11	the	the	DET
ap-662	10	12	family	family	NOUN
ap-662	10	13	of	of	ADP
ap-662	10	14	orthogonal	orthogonal	ADJ
ap-662	10	15	decompositions	decomposition	NOUN
ap-662	10	16	based	base	VERB
ap-662	10	17	on	on	ADP
ap-662	10	18	gram	gram	NOUN
ap-662	10	19	-	-	PUNCT
ap-662	10	20	schmidt	schmidt	NOUN
ap-662	10	21	orthogonalization	orthogonalization	NOUN
ap-662	10	22	(	(	PUNCT
ap-662	10	23	gso	gso	PROPN
ap-662	10	24	)	)	PUNCT
ap-662	10	25	.	.	PUNCT
ap-662	11	1	practical	practical	ADJ
ap-662	11	2	experience	experience	NOUN
ap-662	11	3	with	with	ADP
ap-662	11	4	both	both	DET
ap-662	11	5	algorithms	algorithm	NOUN
ap-662	11	6	is	be	AUX
ap-662	11	7	discussed	discuss	VERB
ap-662	11	8	.	.	PUNCT
ap-662	12	1	in	in	ADP
ap-662	12	2	the	the	DET
ap-662	12	3	gama	gama	NOUN
ap-662	12	4	project	project	NOUN
ap-662	12	5	,	,	PUNCT
ap-662	12	6	the	the	DET
ap-662	12	7	geodetic	geodetic	ADJ
ap-662	12	8	input	input	NOUN
ap-662	12	9	data	datum	NOUN
ap-662	12	10	are	be	AUX
ap-662	12	11	described	describe	VERB
ap-662	12	12	in	in	ADP
ap-662	12	13	extensible	extensible	ADJ
ap-662	12	14	markup	markup	NOUN
ap-662	12	15	language	language	NOUN
ap-662	12	16	(	(	PUNCT
ap-662	12	17	xml	xml	NOUN
ap-662	12	18	)	)	PUNCT
ap-662	12	19	.	.	PUNCT
ap-662	13	1	the	the	DET
ap-662	13	2	primary	primary	ADJ
ap-662	13	3	motivation	motivation	NOUN
ap-662	13	4	for	for	ADP
ap-662	13	5	using	use	VERB
ap-662	13	6	xml	xml	NOUN
ap-662	13	7	was	be	AUX
ap-662	13	8	to	to	PART
ap-662	13	9	define	define	VERB
ap-662	13	10	structured	structured	ADJ
ap-662	13	11	input	input	NOUN
ap-662	13	12	data	datum	NOUN
ap-662	13	13	for	for	ADP
ap-662	13	14	adjustment	adjustment	NOUN
ap-662	13	15	of	of	ADP
ap-662	13	16	a	a	DET
ap-662	13	17	local	local	ADJ
ap-662	13	18	geodetic	geodetic	ADJ
ap-662	13	19	network	network	NOUN
ap-662	13	20	.	.	PUNCT
ap-662	14	1	the	the	DET
ap-662	14	2	most	most	ADV
ap-662	14	3	important	important	ADJ
ap-662	14	4	feature	feature	NOUN
ap-662	14	5	of	of	ADP
ap-662	14	6	xml	xml	NOUN
ap-662	14	7	is	be	AUX
ap-662	14	8	probably	probably	ADV
ap-662	14	9	the	the	DET
ap-662	14	10	ease	ease	NOUN
ap-662	14	11	of	of	ADP
ap-662	14	12	defining	define	VERB
ap-662	14	13	a	a	DET
ap-662	14	14	grammar	grammar	NOUN
ap-662	14	15	for	for	ADP
ap-662	14	16	user	user	NOUN
ap-662	14	17	data	datum	NOUN
ap-662	14	18	(	(	PUNCT
ap-662	14	19	a	a	DET
ap-662	14	20	class	class	NOUN
ap-662	14	21	of	of	ADP
ap-662	14	22	xml	xml	NOUN
ap-662	14	23	documents	document	NOUN
ap-662	14	24	)	)	PUNCT
ap-662	14	25	that	that	PRON
ap-662	14	26	consequently	consequently	ADV
ap-662	14	27	can	can	AUX
ap-662	14	28	be	be	AUX
ap-662	14	29	validated	validate	VERB
ap-662	14	30	even	even	ADV
ap-662	14	31	independently	independently	ADV
ap-662	14	32	of	of	ADP
ap-662	14	33	our	our	PRON
ap-662	14	34	applications	application	NOUN
ap-662	14	35	.	.	PUNCT
ap-662	15	1	one	one	NUM
ap-662	15	2	of	of	ADP
ap-662	15	3	the	the	DET
ap-662	15	4	goals	goal	NOUN
ap-662	15	5	of	of	ADP
ap-662	15	6	the	the	DET
ap-662	15	7	gama	gama	NOUN
ap-662	15	8	project	project	NOUN
ap-662	15	9	is	be	AUX
ap-662	15	10	to	to	PART
ap-662	15	11	build	build	VERB
ap-662	15	12	a	a	DET
ap-662	15	13	collection	collection	NOUN
ap-662	15	14	of	of	ADP
ap-662	15	15	model	model	NOUN
ap-662	15	16	geodetic	geodetic	ADJ
ap-662	15	17	networks	network	NOUN
ap-662	15	18	described	describe	VERB
ap-662	15	19	in	in	ADP
ap-662	15	20	xml	xml	PROPN
ap-662	15	21	.	.	PUNCT
ap-662	16	1	the	the	DET
ap-662	16	2	lack	lack	NOUN
ap-662	16	3	of	of	ADP
ap-662	16	4	reliable	reliable	ADJ
ap-662	16	5	testing	testing	NOUN
ap-662	16	6	data	datum	NOUN
ap-662	16	7	was	be	AUX
ap-662	16	8	one	one	NUM
ap-662	16	9	of	of	ADP
ap-662	16	10	major	major	ADJ
ap-662	16	11	obstacles	obstacle	NOUN
ap-662	16	12	when	when	SCONJ
ap-662	16	13	testing	test	VERB
ap-662	16	14	the	the	DET
ap-662	16	15	implementation	implementation	NOUN
ap-662	16	16	of	of	ADP
ap-662	16	17	the	the	DET
ap-662	16	18	numerical	numerical	ADJ
ap-662	16	19	solution	solution	NOUN
ap-662	16	20	of	of	ADP
ap-662	16	21	the	the	DET
ap-662	16	22	geodetic	geodetic	ADJ
ap-662	16	23	network	network	NOUN
ap-662	16	24	adjustment	adjustment	NOUN
ap-662	16	25	.	.	PUNCT
ap-662	17	1	2	2	NUM
ap-662	17	2	adjustment	adjustment	NOUN
ap-662	17	3	and	and	CCONJ
ap-662	17	4	analysis	analysis	NOUN
ap-662	17	5	of	of	ADP
ap-662	17	6	observations	observation	NOUN
ap-662	17	7	geodesy	geodesy	NOUN
ap-662	17	8	as	as	ADP
ap-662	17	9	a	a	DET
ap-662	17	10	scientific	scientific	ADJ
ap-662	17	11	discipline	discipline	NOUN
ap-662	17	12	studies	study	NOUN
ap-662	17	13	the	the	DET
ap-662	17	14	geometry	geometry	NOUN
ap-662	17	15	of	of	ADP
ap-662	17	16	the	the	DET
ap-662	17	17	earth	earth	NOUN
ap-662	17	18	or	or	CCONJ
ap-662	17	19	,	,	PUNCT
ap-662	17	20	from	from	ADP
ap-662	17	21	the	the	DET
ap-662	17	22	practical	practical	ADJ
ap-662	17	23	point	point	NOUN
ap-662	17	24	of	of	ADP
ap-662	17	25	view	view	NOUN
ap-662	17	26	,	,	PUNCT
ap-662	17	27	the	the	DET
ap-662	17	28	positioning	positioning	NOUN
ap-662	17	29	of	of	ADP
ap-662	17	30	objects	object	NOUN
ap-662	17	31	located	locate	VERB
ap-662	17	32	on	on	ADP
ap-662	17	33	the	the	DET
ap-662	17	34	earth	earth	NOUN
ap-662	17	35	’s	’s	PART
ap-662	17	36	surface	surface	NOUN
ap-662	17	37	or	or	CCONJ
ap-662	17	38	in	in	ADP
ap-662	17	39	zones	zone	NOUN
ap-662	17	40	relatively	relatively	ADV
ap-662	17	41	close	close	ADJ
ap-662	17	42	to	to	ADP
ap-662	17	43	it	it	PRON
ap-662	17	44	.	.	PUNCT
ap-662	18	1	the	the	DET
ap-662	18	2	input	input	NOUN
ap-662	18	3	information	information	NOUN
ap-662	18	4	consists	consist	VERB
ap-662	18	5	of	of	ADP
ap-662	18	6	geodetic	geodetic	ADJ
ap-662	18	7	observations	observation	NOUN
ap-662	18	8	.	.	PUNCT
ap-662	19	1	the	the	DET
ap-662	19	2	spectrum	spectrum	NOUN
ap-662	19	3	of	of	ADP
ap-662	19	4	observation	observation	NOUN
ap-662	19	5	types	type	NOUN
ap-662	19	6	dealt	deal	VERB
ap-662	19	7	with	with	ADP
ap-662	19	8	by	by	ADP
ap-662	19	9	geodesy	geodesy	NOUN
ap-662	19	10	is	be	AUX
ap-662	19	11	very	very	ADV
ap-662	19	12	wide	wide	ADJ
ap-662	19	13	,	,	PUNCT
ap-662	19	14	and	and	CCONJ
ap-662	19	15	ranges	range	VERB
ap-662	19	16	from	from	ADP
ap-662	19	17	classical	classical	ADJ
ap-662	19	18	astro	astro	NOUN
ap-662	19	19	-	-	PUNCT
ap-662	19	20	geodetic	geodetic	ADJ
ap-662	19	21	observations	observation	NOUN
ap-662	19	22	(	(	PUNCT
ap-662	19	23	astronomical	astronomical	ADJ
ap-662	19	24	longitude	longitude	NOUN
ap-662	19	25	and	and	CCONJ
ap-662	19	26	latitude	latitude	NOUN
ap-662	19	27	,	,	PUNCT
ap-662	19	28	variations	variation	NOUN
ap-662	19	29	and	and	CCONJ
ap-662	19	30	position	position	NOUN
ap-662	19	31	of	of	ADP
ap-662	19	32	the	the	DET
ap-662	19	33	earth	earth	NOUN
ap-662	19	34	’s	’s	PART
ap-662	19	35	pole	pole	NOUN
ap-662	19	36	)	)	PUNCT
ap-662	19	37	,	,	PUNCT
ap-662	19	38	measurements	measurement	NOUN
ap-662	19	39	of	of	ADP
ap-662	19	40	geophysical	geophysical	ADJ
ap-662	19	41	quantities	quantity	NOUN
ap-662	19	42	(	(	PUNCT
ap-662	19	43	gravity	gravity	NOUN
ap-662	19	44	acceleration	acceleration	NOUN
ap-662	19	45	and	and	CCONJ
ap-662	19	46	its	its	PRON
ap-662	19	47	local	local	ADJ
ap-662	19	48	anomalies	anomaly	NOUN
ap-662	19	49	)	)	PUNCT
ap-662	19	50	,	,	PUNCT
ap-662	19	51	through	through	ADP
ap-662	19	52	traditional	traditional	ADJ
ap-662	19	53	geometric	geometric	ADJ
ap-662	19	54	observables	observable	NOUN
ap-662	19	55	like	like	ADP
ap-662	19	56	directions	direction	NOUN
ap-662	19	57	,	,	PUNCT
ap-662	19	58	angles	angle	NOUN
ap-662	19	59	and	and	CCONJ
ap-662	19	60	distances	distance	NOUN
ap-662	19	61	to	to	ADP
ap-662	19	62	photogrammetric	photogrammetric	ADJ
ap-662	19	63	measurements	measurement	NOUN
ap-662	19	64	of	of	ADP
ap-662	19	65	historical	historical	ADJ
ap-662	19	66	monuments	monument	NOUN
ap-662	19	67	.	.	PUNCT
ap-662	20	1	however	however	ADV
ap-662	20	2	,	,	PUNCT
ap-662	20	3	the	the	DET
ap-662	20	4	main	main	ADJ
ap-662	20	5	importance	importance	NOUN
ap-662	20	6	in	in	ADP
ap-662	20	7	geodesy	geodesy	NOUN
ap-662	20	8	today	today	NOUN
ap-662	20	9	is	be	AUX
ap-662	20	10	given	give	VERB
ap-662	20	11	to	to	ADP
ap-662	20	12	satellite	satellite	NOUN
ap-662	20	13	global	global	ADJ
ap-662	20	14	positioning	positioning	NOUN
ap-662	20	15	systems	system	NOUN
ap-662	20	16	(	(	PUNCT
ap-662	20	17	first	first	ADV
ap-662	20	18	of	of	ADP
ap-662	20	19	all	all	DET
ap-662	20	20	navstar	navstar	NOUN
ap-662	20	21	gps	gps	PROPN
ap-662	20	22	and	and	CCONJ
ap-662	20	23	other	other	ADJ
ap-662	20	24	complementary	complementary	ADJ
ap-662	20	25	systems	system	NOUN
ap-662	20	26	like	like	ADP
ap-662	20	27	doris	doris	PROPN
ap-662	20	28	or	or	CCONJ
ap-662	20	29	glonass	glonass	NOUN
ap-662	20	30	)	)	PUNCT
ap-662	20	31	.	.	PUNCT
ap-662	21	1	the	the	DET
ap-662	21	2	key	key	ADJ
ap-662	21	3	role	role	NOUN
ap-662	21	4	in	in	ADP
ap-662	21	5	processing	process	VERB
ap-662	21	6	geodetic	geodetic	ADJ
ap-662	21	7	data	datum	NOUN
ap-662	21	8	belongs	belong	VERB
ap-662	21	9	to	to	ADP
ap-662	21	10	the	the	DET
ap-662	21	11	sphere	sphere	NOUN
ap-662	21	12	of	of	ADP
ap-662	21	13	applied	apply	VERB
ap-662	21	14	statistics	statistic	NOUN
ap-662	21	15	in	in	ADP
ap-662	21	16	geodesy	geodesy	PROPN
ap-662	21	17	,	,	PUNCT
ap-662	21	18	traditionally	traditionally	ADV
ap-662	21	19	called	call	VERB
ap-662	21	20	adjustment	adjustment	NOUN
ap-662	21	21	of	of	ADP
ap-662	21	22	observations	observation	NOUN
ap-662	21	23	.	.	PUNCT
ap-662	22	1	the	the	DET
ap-662	22	2	processing	processing	NOUN
ap-662	22	3	of	of	ADP
ap-662	22	4	geodetic	geodetic	ADJ
ap-662	22	5	observations	observation	NOUN
ap-662	22	6	is	be	AUX
ap-662	22	7	determined	determine	VERB
ap-662	22	8	by	by	ADP
ap-662	22	9	the	the	DET
ap-662	22	10	choice	choice	NOUN
ap-662	22	11	of	of	ADP
ap-662	22	12	an	an	DET
ap-662	22	13	appropriate	appropriate	ADJ
ap-662	22	14	mathematical	mathematical	ADJ
ap-662	22	15	model	model	NOUN
ap-662	22	16	,	,	PUNCT
ap-662	22	17	which	which	PRON
ap-662	22	18	can	can	AUX
ap-662	22	19	be	be	AUX
ap-662	22	20	symbolically	symbolically	ADV
ap-662	22	21	expressed	express	VERB
ap-662	22	22	as	as	ADP
ap-662	22	23	f	f	PROPN
ap-662	22	24	c	c	PROPN
ap-662	22	25	x	x	PROPN
ap-662	22	26	l	l	NOUN
ap-662	22	27	(	(	PUNCT
ap-662	22	28	)	)	PUNCT
ap-662	22	29	,	,	PUNCT
ap-662	22	30	,	,	PUNCT
ap-662	22	31	�	�	PROPN
ap-662	22	32	0	0	NUM
ap-662	22	33	,	,	PUNCT
ap-662	22	34	(	(	PUNCT
ap-662	22	35	1	1	X
ap-662	22	36	)	)	PUNCT
ap-662	22	37	where	where	SCONJ
ap-662	22	38	f	f	PROPN
ap-662	22	39	is	be	AUX
ap-662	22	40	a	a	DET
ap-662	22	41	vector	vector	NOUN
ap-662	22	42	of	of	ADP
ap-662	22	43	functions	function	NOUN
ap-662	22	44	describing	describe	VERB
ap-662	22	45	the	the	DET
ap-662	22	46	relations	relation	NOUN
ap-662	22	47	between	between	ADP
ap-662	22	48	constants	constant	NOUN
ap-662	22	49	c	c	PROPN
ap-662	22	50	,	,	PUNCT
ap-662	22	51	unknown	unknown	ADJ
ap-662	22	52	parameters	parameter	NOUN
ap-662	22	53	x	x	PUNCT
ap-662	22	54	and	and	CCONJ
ap-662	22	55	observed	observe	VERB
ap-662	22	56	quantities	quantity	NOUN
ap-662	22	57	l.	l.	PROPN
ap-662	22	58	corresponding	correspond	VERB
ap-662	22	59	to	to	ADP
ap-662	22	60	the	the	DET
ap-662	22	61	three	three	NUM
ap-662	22	62	components	component	NOUN
ap-662	22	63	of	of	ADP
ap-662	22	64	this	this	DET
ap-662	22	65	model	model	NOUN
ap-662	22	66	are	be	AUX
ap-662	22	67	three	three	NUM
ap-662	22	68	mathematical	mathematical	ADJ
ap-662	22	69	spaces	space	NOUN
ap-662	22	70	:	:	PUNCT
ap-662	22	71	parameter	parameter	NOUN
ap-662	22	72	,	,	PUNCT
ap-662	22	73	observation	observation	NOUN
ap-662	22	74	and	and	CCONJ
ap-662	22	75	model	model	NOUN
ap-662	22	76	space	space	NOUN
ap-662	23	1	[	[	X
ap-662	23	2	1	1	NUM
ap-662	23	3	]	]	PUNCT
ap-662	23	4	.	.	PUNCT
ap-662	24	1	the	the	DET
ap-662	24	2	three	three	NUM
ap-662	24	3	basic	basic	ADJ
ap-662	24	4	components	component	NOUN
ap-662	24	5	of	of	ADP
ap-662	24	6	the	the	DET
ap-662	24	7	mathematical	mathematical	ADJ
ap-662	24	8	model	model	NOUN
ap-662	24	9	(	(	PUNCT
ap-662	24	10	1	1	X
ap-662	24	11	)	)	PUNCT
ap-662	24	12	are	be	AUX
ap-662	24	13	depicted	depict	VERB
ap-662	24	14	in	in	ADP
ap-662	24	15	fig	fig	NOUN
ap-662	24	16	.	.	PUNCT
ap-662	25	1	1	1	NUM
ap-662	25	2	,	,	PUNCT
ap-662	25	3	where	where	SCONJ
ap-662	25	4	a	a	DET
ap-662	25	5	,	,	PUNCT
ap-662	25	6	b	b	NOUN
ap-662	25	7	,	,	PUNCT
ap-662	25	8	g	g	PROPN
ap-662	25	9	and	and	CCONJ
ap-662	25	10	h	h	NOUN
ap-662	25	11	are	be	AUX
ap-662	25	12	the	the	DET
ap-662	25	13	matrices	matrix	NOUN
ap-662	25	14	of	of	ADP
ap-662	25	15	corresponding	corresponding	ADJ
ap-662	25	16	linearized	linearize	VERB
ap-662	25	17	relations	relation	NOUN
ap-662	25	18	(	(	PUNCT
ap-662	25	19	values	value	NOUN
ap-662	25	20	of	of	ADP
ap-662	25	21	constants	constant	NOUN
ap-662	25	22	c	c	NOUN
ap-662	25	23	are	be	AUX
ap-662	25	24	not	not	PART
ap-662	25	25	estimated	estimate	VERB
ap-662	25	26	in	in	ADP
ap-662	25	27	geodesy	geodesy	PROPN
ap-662	25	28	and	and	CCONJ
ap-662	25	29	we	we	PRON
ap-662	25	30	can	can	AUX
ap-662	25	31	consider	consider	VERB
ap-662	25	32	them	they	PRON
ap-662	25	33	to	to	PART
ap-662	25	34	be	be	AUX
ap-662	25	35	a	a	DET
ap-662	25	36	part	part	NOUN
ap-662	25	37	of	of	ADP
ap-662	25	38	model	model	NOUN
ap-662	25	39	space	space	NOUN
ap-662	25	40	)	)	PUNCT
ap-662	25	41	.	.	PUNCT
ap-662	26	1	models	model	NOUN
ap-662	26	2	can	can	AUX
ap-662	26	3	be	be	AUX
ap-662	26	4	direct	direct	ADJ
ap-662	26	5	,	,	PUNCT
ap-662	26	6	indirect	indirect	ADJ
ap-662	26	7	or	or	CCONJ
ap-662	26	8	12	12	NUM
ap-662	26	9	©	©	PROPN
ap-662	26	10	czech	czech	PROPN
ap-662	26	11	technical	technical	PROPN
ap-662	26	12	university	university	PROPN
ap-662	26	13	publishing	publishing	NOUN
ap-662	26	14	house	house	NOUN
ap-662	26	15	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-662	26	16	acta	acta	PROPN
ap-662	26	17	polytechnica	polytechnica	PROPN
ap-662	26	18	vol	vol	NOUN
ap-662	26	19	.	.	PROPN
ap-662	27	1	45	45	NUM
ap-662	27	2	no	no	NOUN
ap-662	27	3	.	.	PUNCT
ap-662	28	1	1/2005	1/2005	NUM
ap-662	28	2	czech	czech	PROPN
ap-662	28	3	technical	technical	PROPN
ap-662	28	4	university	university	PROPN
ap-662	28	5	in	in	ADP
ap-662	28	6	prague	prague	PROPN
ap-662	28	7	a	a	DET
ap-662	28	8	progress	progress	NOUN
ap-662	28	9	report	report	NOUN
ap-662	28	10	on	on	ADP
ap-662	28	11	numerical	numerical	ADJ
ap-662	28	12	solutions	solution	NOUN
ap-662	28	13	of	of	ADP
ap-662	28	14	least	least	ADJ
ap-662	28	15	squares	square	NOUN
ap-662	28	16	adjustment	adjustment	NOUN
ap-662	28	17	in	in	ADP
ap-662	28	18	gnu	gnu	PROPN
ap-662	28	19	project	project	PROPN
ap-662	28	20	gama	gama	PROPN
ap-662	28	21	a.	a.	NOUN
ap-662	28	22	čepek	čepek	PROPN
ap-662	28	23	,	,	PUNCT
ap-662	28	24	j.	j.	PROPN
ap-662	28	25	pytel	pytel	PROPN
ap-662	28	26	gnu	gnu	PROPN
ap-662	28	27	project	project	NOUN
ap-662	28	28	gama	gama	NOUN
ap-662	28	29	for	for	ADP
ap-662	28	30	adjustment	adjustment	NOUN
ap-662	28	31	of	of	ADP
ap-662	28	32	geodetic	geodetic	ADJ
ap-662	28	33	networks	network	NOUN
ap-662	28	34	is	be	AUX
ap-662	28	35	presented	present	VERB
ap-662	28	36	.	.	PUNCT
ap-662	29	1	numerical	numerical	ADJ
ap-662	29	2	solution	solution	NOUN
ap-662	29	3	of	of	ADP
ap-662	29	4	least	least	ADJ
ap-662	29	5	squares	square	NOUN
ap-662	29	6	adjustment	adjustment	NOUN
ap-662	29	7	in	in	ADP
ap-662	29	8	the	the	DET
ap-662	29	9	project	project	NOUN
ap-662	29	10	is	be	AUX
ap-662	29	11	based	base	VERB
ap-662	29	12	on	on	ADP
ap-662	29	13	singular	singular	ADJ
ap-662	29	14	value	value	NOUN
ap-662	29	15	decomposition	decomposition	NOUN
ap-662	29	16	(	(	PUNCT
ap-662	29	17	svd	svd	PROPN
ap-662	29	18	)	)	PUNCT
ap-662	29	19	and	and	CCONJ
ap-662	29	20	general	general	ADJ
ap-662	29	21	orthogonalization	orthogonalization	NOUN
ap-662	29	22	algorithm	algorithm	NOUN
ap-662	29	23	(	(	PUNCT
ap-662	29	24	gso	gso	PROPN
ap-662	29	25	)	)	PUNCT
ap-662	29	26	.	.	PUNCT
ap-662	30	1	both	both	DET
ap-662	30	2	algorithms	algorithm	NOUN
ap-662	30	3	enable	enable	VERB
ap-662	30	4	solution	solution	NOUN
ap-662	30	5	of	of	ADP
ap-662	30	6	singular	singular	ADJ
ap-662	30	7	systems	system	NOUN
ap-662	30	8	resulting	result	VERB
ap-662	30	9	from	from	ADP
ap-662	30	10	adjustment	adjustment	NOUN
ap-662	30	11	of	of	ADP
ap-662	30	12	free	free	ADJ
ap-662	30	13	geodetic	geodetic	ADJ
ap-662	30	14	networks	network	NOUN
ap-662	30	15	.	.	PUNCT
ap-662	31	1	keywords	keyword	NOUN
ap-662	31	2	:	:	PUNCT
ap-662	31	3	geodesy	geodesy	NOUN
ap-662	31	4	,	,	PUNCT
ap-662	31	5	least	least	ADJ
ap-662	31	6	square	square	ADJ
ap-662	31	7	adjustment	adjustment	NOUN
ap-662	31	8	,	,	PUNCT
ap-662	31	9	local	local	ADJ
ap-662	31	10	geodetic	geodetic	ADJ
ap-662	31	11	network	network	NOUN
ap-662	31	12	.	.	PUNCT
ap-662	32	1	implicit;	implicit;	X
ap-662	33	1	linear	linear	ADJ
ap-662	33	2	or	or	CCONJ
ap-662	33	3	nonlinear;	nonlinear;	PRON
ap-662	33	4	can	can	AUX
ap-662	33	5	occur	occur	VERB
ap-662	33	6	individually	individually	ADV
ap-662	33	7	or	or	CCONJ
ap-662	33	8	in	in	ADP
ap-662	33	9	combinations	combination	NOUN
ap-662	33	10	model	model	NOUN
ap-662	33	11	explicit	explicit	ADJ
ap-662	33	12	in	in	ADP
ap-662	33	13	x	x	NOUN
ap-662	33	14	:	:	PUNCT
ap-662	33	15	x	x	SYM
ap-662	33	16	g	g	PROPN
ap-662	33	17	l	l	PROPN
ap-662	33	18	�	�	PROPN
ap-662	33	19	(	(	PUNCT
ap-662	33	20	)	)	PUNCT
ap-662	33	21	,	,	PUNCT
ap-662	33	22	x	x	X
ap-662	33	23	gl	gl	PROPN
ap-662	33	24	v	v	PROPN
ap-662	33	25	�	�	PROPN
ap-662	33	26	�	�	PROPN
ap-662	33	27	,	,	PUNCT
ap-662	33	28	model	model	NOUN
ap-662	33	29	explicit	explicit	ADJ
ap-662	33	30	in	in	ADP
ap-662	33	31	l	l	NOUN
ap-662	33	32	:	:	PUNCT
ap-662	33	33	l	l	NOUN
ap-662	33	34	h	h	NOUN
ap-662	33	35	x	x	X
ap-662	33	36	�	�	PROPN
ap-662	33	37	(	(	PUNCT
ap-662	33	38	)	)	PUNCT
ap-662	33	39	,	,	PUNCT
ap-662	33	40	l	l	PROPN
ap-662	33	41	hx	hx	PROPN
ap-662	33	42	v	v	PROPN
ap-662	33	43	�	�	PROPN
ap-662	33	44	�	�	PROPN
ap-662	33	45	,	,	PUNCT
ap-662	33	46	implicit	implicit	ADJ
ap-662	33	47	model	model	NOUN
ap-662	33	48	:	:	PUNCT
ap-662	33	49	f	f	PROPN
ap-662	33	50	x	x	PROPN
ap-662	33	51	,	,	PUNCT
ap-662	33	52	l	l	PROPN
ap-662	33	53	(	(	PUNCT
ap-662	33	54	)	)	PUNCT
ap-662	33	55	�	�	PROPN
ap-662	33	56	0	0	NUM
ap-662	33	57	,	,	PUNCT
ap-662	33	58	ax	ax	PROPN
ap-662	33	59	gl	gl	PROPN
ap-662	33	60	v	v	PROPN
ap-662	33	61	�	�	PROPN
ap-662	33	62	�	�	PROPN
ap-662	33	63	�	�	PROPN
ap-662	33	64	0	0	NUM
ap-662	33	65	.	.	NOUN
ap-662	33	66	3	3	NUM
ap-662	33	67	least	least	ADJ
ap-662	33	68	squares	square	NOUN
ap-662	33	69	and	and	CCONJ
ap-662	33	70	singular	singular	NOUN
ap-662	33	71	systems	system	NOUN
ap-662	33	72	when	when	SCONJ
ap-662	33	73	adjusting	adjust	VERB
ap-662	33	74	geodetic	geodetic	ADJ
ap-662	33	75	observations	observation	NOUN
ap-662	33	76	we	we	PRON
ap-662	33	77	are	be	AUX
ap-662	33	78	relatively	relatively	ADV
ap-662	33	79	often	often	ADV
ap-662	33	80	faced	face	VERB
ap-662	33	81	with	with	ADP
ap-662	33	82	models	model	NOUN
ap-662	33	83	leading	lead	VERB
ap-662	33	84	to	to	ADP
ap-662	33	85	singular	singular	ADJ
ap-662	33	86	sets	set	NOUN
ap-662	33	87	of	of	ADP
ap-662	33	88	linear	linear	PROPN
ap-662	33	89	equations	equation	NOUN
ap-662	33	90	.	.	PUNCT
ap-662	34	1	typically	typically	ADV
ap-662	34	2	these	these	PRON
ap-662	34	3	are	be	AUX
ap-662	34	4	models	model	NOUN
ap-662	34	5	without	without	ADP
ap-662	34	6	fixed	fix	VERB
ap-662	34	7	points	point	NOUN
ap-662	34	8	,	,	PUNCT
ap-662	34	9	ie	ie	X
ap-662	34	10	.	.	PROPN
ap-662	34	11	,	,	PUNCT
ap-662	34	12	no	no	DET
ap-662	34	13	points	point	NOUN
ap-662	34	14	with	with	ADP
ap-662	34	15	fixed	fix	VERB
ap-662	34	16	coordinates	coordinate	NOUN
ap-662	34	17	are	be	AUX
ap-662	34	18	given	give	VERB
ap-662	34	19	,	,	PUNCT
ap-662	34	20	or	or	CCONJ
ap-662	34	21	the	the	DET
ap-662	34	22	number	number	NOUN
ap-662	34	23	of	of	ADP
ap-662	34	24	fixed	fix	VERB
ap-662	34	25	points	point	NOUN
ap-662	34	26	is	be	AUX
ap-662	34	27	not	not	PART
ap-662	34	28	sufficient	sufficient	ADJ
ap-662	34	29	(	(	PUNCT
ap-662	34	30	free	free	ADJ
ap-662	34	31	networks	network	NOUN
ap-662	34	32	,	,	PUNCT
ap-662	34	33	see	see	VERB
ap-662	34	34	[	[	X
ap-662	34	35	6	6	X
ap-662	34	36	]	]	PUNCT
ap-662	34	37	for	for	ADP
ap-662	34	38	more	more	ADJ
ap-662	34	39	information	information	NOUN
ap-662	34	40	)	)	PUNCT
ap-662	34	41	.	.	PUNCT
ap-662	35	1	let	let	VERB
ap-662	35	2	us	we	PRON
ap-662	35	3	take	take	VERB
ap-662	35	4	as	as	ADP
ap-662	35	5	an	an	DET
ap-662	35	6	example	example	NOUN
ap-662	35	7	the	the	DET
ap-662	35	8	local	local	ADJ
ap-662	35	9	network	network	NOUN
ap-662	35	10	with	with	ADP
ap-662	35	11	observed	observed	ADJ
ap-662	35	12	directions	direction	NOUN
ap-662	35	13	and	and	CCONJ
ap-662	35	14	distances	distance	NOUN
ap-662	35	15	from	from	ADP
ap-662	35	16	fig	fig	NOUN
ap-662	35	17	.	.	PUNCT
ap-662	36	1	2	2	X
ap-662	36	2	.	.	X
ap-662	36	3	the	the	DET
ap-662	36	4	relationship	relationship	NOUN
ap-662	36	5	between	between	ADP
ap-662	36	6	the	the	DET
ap-662	36	7	unknown	unknown	ADJ
ap-662	36	8	adjusted	adjust	VERB
ap-662	36	9	coordinates	coordinate	NOUN
ap-662	36	10	and	and	CCONJ
ap-662	36	11	observations	observation	NOUN
ap-662	36	12	can	can	AUX
ap-662	36	13	be	be	AUX
ap-662	36	14	expressed	express	VERB
ap-662	36	15	after	after	ADP
ap-662	36	16	linearization	linearization	NOUN
ap-662	36	17	as	as	ADP
ap-662	36	18	the	the	DET
ap-662	36	19	project	project	NOUN
ap-662	36	20	equations	equation	NOUN
ap-662	36	21	ax	ax	NOUN
ap-662	36	22	l	l	PROPN
ap-662	36	23	v	v	PROPN
ap-662	36	24	�	�	PROPN
ap-662	36	25	�	�	PROPN
ap-662	36	26	,	,	PUNCT
ap-662	36	27	(	(	PUNCT
ap-662	36	28	2	2	X
ap-662	36	29	)	)	PUNCT
ap-662	36	30	where	where	SCONJ
ap-662	36	31	a	a	PRON
ap-662	36	32	is	be	AUX
ap-662	36	33	design	design	NOUN
ap-662	36	34	matrix	matrix	NOUN
ap-662	36	35	,	,	PUNCT
ap-662	36	36	x	x	SYM
ap-662	36	37	vector	vector	NOUN
ap-662	36	38	of	of	ADP
ap-662	36	39	unknowns	unknown	NOUN
ap-662	36	40	,	,	PUNCT
ap-662	36	41	l	l	NOUN
ap-662	36	42	vector	vector	NOUN
ap-662	36	43	of	of	ADP
ap-662	36	44	reduced	reduce	VERB
ap-662	36	45	observations	observation	NOUN
ap-662	36	46	and	and	CCONJ
ap-662	36	47	v	v	ADP
ap-662	36	48	vector	vector	NOUN
ap-662	36	49	of	of	ADP
ap-662	36	50	residuals	residual	NOUN
ap-662	36	51	(	(	PUNCT
ap-662	36	52	misclosure	misclosure	NOUN
ap-662	36	53	vector	vector	NOUN
ap-662	36	54	)	)	PUNCT
ap-662	36	55	.	.	PUNCT
ap-662	37	1	in	in	ADP
ap-662	37	2	geodesy	geodesy	PROPN
ap-662	37	3	,	,	PUNCT
ap-662	37	4	the	the	DET
ap-662	37	5	number	number	NOUN
ap-662	37	6	of	of	ADP
ap-662	37	7	observations	observation	NOUN
ap-662	37	8	is	be	AUX
ap-662	37	9	always	always	ADV
ap-662	37	10	higher	high	ADJ
ap-662	37	11	than	than	ADP
ap-662	37	12	the	the	DET
ap-662	37	13	number	number	NOUN
ap-662	37	14	of	of	ADP
ap-662	37	15	unknowns	unknown	NOUN
ap-662	37	16	.	.	PUNCT
ap-662	38	1	project	project	NOUN
ap-662	38	2	equations	equation	NOUN
ap-662	38	3	(	(	PUNCT
ap-662	38	4	2	2	X
ap-662	38	5	)	)	PUNCT
ap-662	38	6	thus	thus	ADV
ap-662	38	7	represent	represent	VERB
ap-662	38	8	an	an	DET
ap-662	38	9	overdetermined	overdetermined	ADJ
ap-662	38	10	system	system	NOUN
ap-662	38	11	,	,	PUNCT
ap-662	38	12	and	and	CCONJ
ap-662	38	13	matrix	matrix	VERB
ap-662	38	14	a	a	PRON
ap-662	38	15	has	have	AUX
ap-662	38	16	more	more	ADJ
ap-662	38	17	rows	row	NOUN
ap-662	38	18	than	than	ADP
ap-662	38	19	columns	column	NOUN
ap-662	38	20	.	.	PUNCT
ap-662	39	1	least	least	ADJ
ap-662	39	2	squares	square	NOUN
ap-662	39	3	is	be	AUX
ap-662	39	4	the	the	DET
ap-662	39	5	basic	basic	ADJ
ap-662	39	6	method	method	NOUN
ap-662	39	7	used	use	VERB
ap-662	39	8	in	in	ADP
ap-662	39	9	geodesy	geodesy	NOUN
ap-662	39	10	for	for	ADP
ap-662	39	11	observation	observation	NOUN
ap-662	39	12	adjustment	adjustment	NOUN
ap-662	39	13	.	.	PUNCT
ap-662	40	1	it	it	PRON
ap-662	40	2	gives	give	VERB
ap-662	40	3	us	we	PRON
ap-662	40	4	the	the	DET
ap-662	40	5	unique	unique	ADJ
ap-662	40	6	solution	solution	NOUN
ap-662	40	7	x	x	PUNCT
ap-662	40	8	of	of	ADP
ap-662	40	9	system	system	NOUN
ap-662	40	10	(	(	PUNCT
ap-662	40	11	2	2	NUM
ap-662	40	12	)	)	PUNCT
ap-662	40	13	that	that	PRON
ap-662	40	14	minimizes	minimize	VERB
ap-662	40	15	the	the	DET
ap-662	40	16	euclidean	euclidean	ADJ
ap-662	40	17	norm	norm	NOUN
ap-662	40	18	of	of	ADP
ap-662	40	19	the	the	DET
ap-662	40	20	residual	residual	ADJ
ap-662	40	21	vector	vector	NOUN
ap-662	40	22	min	min	PROPN
ap-662	40	23	�	�	PROPN
ap-662	40	24	v	v	NOUN
ap-662	40	25	v	v	NOUN
ap-662	40	26	.	.	PUNCT
ap-662	41	1	(	(	PUNCT
ap-662	41	2	3	3	X
ap-662	41	3	)	)	PUNCT
ap-662	41	4	a	a	DET
ap-662	41	5	method	method	NOUN
ap-662	41	6	commonly	commonly	ADV
ap-662	41	7	used	use	VERB
ap-662	41	8	for	for	ADP
ap-662	41	9	solving	solve	VERB
ap-662	41	10	projects	project	NOUN
ap-662	41	11	equations	equation	NOUN
ap-662	41	12	(	(	PUNCT
ap-662	41	13	2	2	NUM
ap-662	41	14	)	)	PUNCT
ap-662	41	15	(	(	PUNCT
ap-662	41	16	model	model	NOUN
ap-662	41	17	explicit	explicit	ADJ
ap-662	41	18	in	in	ADP
ap-662	41	19	observations	observation	NOUN
ap-662	41	20	)	)	PUNCT
ap-662	41	21	is	be	AUX
ap-662	41	22	based	base	VERB
ap-662	41	23	on	on	ADP
ap-662	41	24	normal	normal	ADJ
ap-662	41	25	equations	equation	NOUN
ap-662	41	26	n	n	ADP
ap-662	41	27	a	a	DET
ap-662	41	28	a	a	PRON
ap-662	41	29	n	n	NOUN
ap-662	41	30	a	a	DET
ap-662	41	31	l	l	NOUN
ap-662	41	32	x	x	SYM
ap-662	41	33	n	n	CCONJ
ap-662	41	34	n	n	CCONJ
ap-662	41	35	�	�	PROPN
ap-662	41	36	�	�	PROPN
ap-662	41	37	�	�	PROPN
ap-662	41	38	�	�	PROPN
ap-662	41	39	�	�	PROPN
ap-662	41	40	�	�	PROPN
ap-662	41	41	,	,	PUNCT
ap-662	41	42	,	,	PUNCT
ap-662	41	43	.1	.1	NUM
ap-662	41	44	(	(	PUNCT
ap-662	41	45	4	4	X
ap-662	41	46	)	)	PUNCT
ap-662	41	47	©	©	PROPN
ap-662	41	48	czech	czech	PROPN
ap-662	41	49	technical	technical	PROPN
ap-662	41	50	university	university	PROPN
ap-662	41	51	publishing	publishing	NOUN
ap-662	41	52	house	house	NOUN
ap-662	41	53	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-662	41	54	13	13	NUM
ap-662	41	55	czech	czech	PROPN
ap-662	41	56	technical	technical	PROPN
ap-662	41	57	university	university	PROPN
ap-662	41	58	in	in	ADP
ap-662	41	59	prague	prague	PROPN
ap-662	41	60	acta	acta	PROPN
ap-662	41	61	polytechnica	polytechnica	PROPN
ap-662	41	62	vol	vol	NOUN
ap-662	41	63	.	.	PROPN
ap-662	42	1	45	45	NUM
ap-662	42	2	no	no	NOUN
ap-662	42	3	.	.	PUNCT
ap-662	43	1	1/2005	1/2005	NUM
ap-662	43	2	fig	fig	NOUN
ap-662	43	3	.	.	PUNCT
ap-662	44	1	1	1	NUM
ap-662	44	2	:	:	PUNCT
ap-662	44	3	linear	linear	ADJ
ap-662	44	4	relations	relation	NOUN
ap-662	44	5	between	between	ADP
ap-662	44	6	parameter	parameter	NOUN
ap-662	44	7	,	,	PUNCT
ap-662	44	8	observation	observation	NOUN
ap-662	44	9	and	and	CCONJ
ap-662	44	10	model	model	NOUN
ap-662	44	11	spaces	space	NOUN
ap-662	44	12	fig	fig	NOUN
ap-662	44	13	.	.	PUNCT
ap-662	45	1	2	2	NUM
ap-662	45	2	:	:	PUNCT
ap-662	45	3	example	example	NOUN
ap-662	45	4	of	of	ADP
ap-662	45	5	a	a	DET
ap-662	45	6	local	local	ADJ
ap-662	45	7	geodetic	geodetic	ADJ
ap-662	45	8	free	free	ADJ
ap-662	45	9	network	network	NOUN
ap-662	45	10	apart	apart	ADV
ap-662	45	11	from	from	ADP
ap-662	45	12	unknown	unknown	ADJ
ap-662	45	13	vector	vector	NOUN
ap-662	45	14	x	x	X
ap-662	45	15	(	(	PUNCT
ap-662	45	16	and	and	CCONJ
ap-662	45	17	residuals	residual	NOUN
ap-662	45	18	v	v	NOUN
ap-662	45	19	)	)	PUNCT
ap-662	45	20	we	we	PRON
ap-662	45	21	are	be	AUX
ap-662	45	22	always	always	ADV
ap-662	45	23	interested	interested	ADJ
ap-662	45	24	in	in	ADP
ap-662	45	25	geodesy	geodesy	NOUN
ap-662	45	26	in	in	ADP
ap-662	45	27	estimates	estimate	NOUN
ap-662	45	28	of	of	ADP
ap-662	45	29	the	the	DET
ap-662	45	30	precision	precision	NOUN
ap-662	45	31	of	of	ADP
ap-662	45	32	the	the	DET
ap-662	45	33	adjusted	adjust	VERB
ap-662	45	34	quantities	quantity	NOUN
ap-662	45	35	,	,	PUNCT
ap-662	45	36	in	in	ADP
ap-662	45	37	geodetic	geodetic	ADJ
ap-662	45	38	practice	practice	NOUN
ap-662	45	39	represented	represent	VERB
ap-662	45	40	by	by	ADP
ap-662	45	41	the	the	DET
ap-662	45	42	variance	variance	NOUN
ap-662	45	43	-	-	PUNCT
ap-662	45	44	covariance	covariance	NOUN
ap-662	45	45	matrix	matrix	NOUN
ap-662	45	46	of	of	ADP
ap-662	45	47	adjusted	adjust	VERB
ap-662	45	48	unknowns	unknown	NOUN
ap-662	45	49	cxx	cxx	NOUN
ap-662	45	50	and	and	CCONJ
ap-662	45	51	adjusted	adjust	VERB
ap-662	45	52	observations	observation	NOUN
ap-662	45	53	cll	cll	PROPN
ap-662	45	54	c	c	PROPN
ap-662	45	55	nxx	nxx	PROPN
ap-662	45	56	m	m	PROPN
ap-662	45	57	�	�	PROPN
ap-662	45	58	�	�	PROPN
ap-662	45	59	�	�	PROPN
ap-662	45	60	0	0	NUM
ap-662	45	61	1	1	NUM
ap-662	45	62	,	,	PUNCT
ap-662	45	63	(	(	PUNCT
ap-662	45	64	5	5	NUM
ap-662	45	65	)	)	PUNCT
ap-662	45	66	c	c	NOUN
ap-662	45	67	ac	ac	VERB
ap-662	45	68	all	all	DET
ap-662	45	69	xx	xx	NUM
ap-662	45	70	�	�	PROPN
ap-662	45	71	�	�	PROPN
ap-662	45	72	.	.	PUNCT
ap-662	46	1	(	(	PUNCT
ap-662	46	2	6	6	NUM
ap-662	46	3	)	)	PUNCT
ap-662	46	4	the	the	DET
ap-662	46	5	geometric	geometric	ADJ
ap-662	46	6	shape	shape	NOUN
ap-662	46	7	of	of	ADP
ap-662	46	8	our	our	PRON
ap-662	46	9	adjusted	adjust	VERB
ap-662	46	10	network	network	NOUN
ap-662	46	11	is	be	AUX
ap-662	46	12	defined	define	VERB
ap-662	46	13	by	by	ADP
ap-662	46	14	observed	observed	ADJ
ap-662	46	15	directions	direction	NOUN
ap-662	46	16	(	(	PUNCT
ap-662	46	17	or	or	CCONJ
ap-662	46	18	angles	angle	NOUN
ap-662	46	19	)	)	PUNCT
ap-662	46	20	and	and	CCONJ
ap-662	46	21	directions	direction	NOUN
ap-662	46	22	.	.	PUNCT
ap-662	47	1	if	if	SCONJ
ap-662	47	2	we	we	PRON
ap-662	47	3	fixed	fix	VERB
ap-662	47	4	the	the	DET
ap-662	47	5	coordinates	coordinate	NOUN
ap-662	47	6	of	of	ADP
ap-662	47	7	two	two	NUM
ap-662	47	8	or	or	CCONJ
ap-662	47	9	more	more	ADJ
ap-662	47	10	points	point	NOUN
ap-662	47	11	the	the	DET
ap-662	47	12	network	network	NOUN
ap-662	47	13	shape	shape	NOUN
ap-662	47	14	would	would	AUX
ap-662	47	15	necessarily	necessarily	ADV
ap-662	47	16	be	be	AUX
ap-662	47	17	distorted	distort	VERB
ap-662	47	18	.	.	PUNCT
ap-662	48	1	normal	normal	ADJ
ap-662	48	2	equations	equation	NOUN
ap-662	48	3	would	would	AUX
ap-662	48	4	lead	lead	VERB
ap-662	48	5	to	to	ADP
ap-662	48	6	an	an	DET
ap-662	48	7	adjustment	adjustment	NOUN
ap-662	48	8	solution	solution	NOUN
ap-662	48	9	in	in	ADP
ap-662	48	10	which	which	PRON
ap-662	48	11	the	the	DET
ap-662	48	12	residuals	residual	NOUN
ap-662	48	13	would	would	AUX
ap-662	48	14	be	be	AUX
ap-662	48	15	dependent	dependent	ADJ
ap-662	48	16	on	on	ADP
ap-662	48	17	the	the	DET
ap-662	48	18	coordinates	coordinate	NOUN
ap-662	48	19	of	of	ADP
ap-662	48	20	the	the	DET
ap-662	48	21	fixed	fix	VERB
ap-662	48	22	points	point	NOUN
ap-662	48	23	.	.	PUNCT
ap-662	49	1	this	this	DET
ap-662	49	2	way	way	NOUN
ap-662	49	3	we	we	PRON
ap-662	49	4	would	would	AUX
ap-662	49	5	degrade	degrade	VERB
ap-662	49	6	our	our	PRON
ap-662	49	7	observations	observation	NOUN
ap-662	49	8	in	in	ADP
ap-662	49	9	cases	case	NOUN
ap-662	49	10	when	when	SCONJ
ap-662	49	11	the	the	DET
ap-662	49	12	coordinates	coordinate	NOUN
ap-662	49	13	of	of	ADP
ap-662	49	14	the	the	DET
ap-662	49	15	network	network	NOUN
ap-662	49	16	points	point	NOUN
ap-662	49	17	are	be	AUX
ap-662	49	18	either	either	CCONJ
ap-662	49	19	unknown	unknown	ADJ
ap-662	49	20	or	or	CCONJ
ap-662	49	21	known	know	VERB
ap-662	49	22	with	with	ADP
ap-662	49	23	lower	low	ADJ
ap-662	49	24	precision	precision	NOUN
ap-662	49	25	.	.	PUNCT
ap-662	50	1	on	on	ADP
ap-662	50	2	the	the	DET
ap-662	50	3	other	other	ADJ
ap-662	50	4	hand	hand	NOUN
ap-662	50	5	if	if	SCONJ
ap-662	50	6	we	we	PRON
ap-662	50	7	consider	consider	VERB
ap-662	50	8	the	the	DET
ap-662	50	9	coordinates	coordinate	NOUN
ap-662	50	10	of	of	ADP
ap-662	50	11	all	all	DET
ap-662	50	12	points	point	NOUN
ap-662	50	13	to	to	PART
ap-662	50	14	be	be	AUX
ap-662	50	15	free	free	ADJ
ap-662	50	16	,	,	PUNCT
ap-662	50	17	the	the	DET
ap-662	50	18	corresponding	correspond	VERB
ap-662	50	19	matrix	matrix	NOUN
ap-662	50	20	n	n	CCONJ
ap-662	50	21	is	be	AUX
ap-662	50	22	inevitably	inevitably	ADV
ap-662	50	23	singular;	singular;	VERB
ap-662	50	24	the	the	DET
ap-662	50	25	columns	column	NOUN
ap-662	50	26	of	of	ADP
ap-662	50	27	matrix	matrix	NOUN
ap-662	50	28	a	a	PRON
ap-662	50	29	are	be	AUX
ap-662	50	30	linearly	linearly	ADV
ap-662	50	31	dependent	dependent	ADJ
ap-662	50	32	(	(	PUNCT
ap-662	50	33	the	the	DET
ap-662	50	34	network	network	NOUN
ap-662	50	35	can	can	AUX
ap-662	50	36	float	float	VERB
ap-662	50	37	freely	freely	ADV
ap-662	50	38	in	in	ADP
ap-662	50	39	the	the	DET
ap-662	50	40	coordinate	coordinate	NOUN
ap-662	50	41	system	system	NOUN
ap-662	50	42	)	)	PUNCT
ap-662	50	43	and	and	CCONJ
ap-662	50	44	normal	normal	ADJ
ap-662	50	45	equation	equation	NOUN
ap-662	50	46	matrix	matrix	NOUN
ap-662	50	47	n	n	NOUN
ap-662	50	48	is	be	AUX
ap-662	50	49	positive	positive	ADJ
ap-662	50	50	-	-	PUNCT
ap-662	50	51	semidefinite	semidefinite	NOUN
ap-662	50	52	�	�	PROPN
ap-662	50	53	�	�	PROPN
ap-662	50	54	�	�	PROPN
ap-662	50	55	p	p	NOUN
ap-662	50	56	np	np	NOUN
ap-662	50	57	p0	p0	NOUN
ap-662	50	58	,	,	PUNCT
ap-662	50	59	0	0	NUM
ap-662	50	60	.	.	PUNCT
ap-662	51	1	to	to	PART
ap-662	51	2	get	get	VERB
ap-662	51	3	a	a	DET
ap-662	51	4	unique	unique	ADJ
ap-662	51	5	solution	solution	NOUN
ap-662	51	6	we	we	PRON
ap-662	51	7	have	have	VERB
ap-662	51	8	to	to	PART
ap-662	51	9	define	define	VERB
ap-662	51	10	additional	additional	ADJ
ap-662	51	11	constraints	constraint	NOUN
ap-662	51	12	regularizing	regularize	VERB
ap-662	51	13	the	the	DET
ap-662	51	14	system	system	NOUN
ap-662	51	15	,	,	PUNCT
ap-662	51	16	preferably	preferably	ADV
ap-662	51	17	without	without	ADP
ap-662	51	18	deforming	deform	VERB
ap-662	51	19	of	of	ADP
ap-662	51	20	the	the	DET
ap-662	51	21	network	network	NOUN
ap-662	51	22	shape	shape	NOUN
ap-662	51	23	.	.	PUNCT
ap-662	52	1	in	in	ADP
ap-662	52	2	geodetic	geodetic	ADJ
ap-662	52	3	practice	practice	NOUN
ap-662	52	4	we	we	PRON
ap-662	52	5	most	most	ADV
ap-662	52	6	often	often	ADV
ap-662	52	7	meet	meet	VERB
ap-662	52	8	the	the	DET
ap-662	52	9	following	follow	VERB
ap-662	52	10	approaches	approach	NOUN
ap-662	52	11	:	:	PUNCT
ap-662	52	12	�	�	PROPN
ap-662	52	13	a	a	DET
ap-662	52	14	singular	singular	ADJ
ap-662	52	15	system	system	NOUN
ap-662	52	16	is	be	AUX
ap-662	52	17	regularized	regularize	VERB
ap-662	52	18	by	by	ADP
ap-662	52	19	introducing	introduce	VERB
ap-662	52	20	pseudo	pseudo	NOUN
ap-662	52	21	-	-	NOUN
ap-662	52	22	observations	observation	NOUN
ap-662	52	23	,	,	PUNCT
ap-662	52	24	typically	typically	ADV
ap-662	52	25	with	with	ADP
ap-662	52	26	huge	huge	ADJ
ap-662	52	27	weights	weight	NOUN
ap-662	52	28	,	,	PUNCT
ap-662	52	29	that	that	PRON
ap-662	52	30	play	play	VERB
ap-662	52	31	a	a	DET
ap-662	52	32	similar	similar	ADJ
ap-662	52	33	role	role	NOUN
ap-662	52	34	as	as	ADP
ap-662	52	35	a	a	DET
ap-662	52	36	set	set	NOUN
ap-662	52	37	of	of	ADP
ap-662	52	38	constraint	constraint	NOUN
ap-662	52	39	equations	equation	NOUN
ap-662	52	40	.	.	PUNCT
ap-662	53	1	�	�	PROPN
ap-662	53	2	an	an	DET
ap-662	53	3	explicit	explicit	ADJ
ap-662	53	4	system	system	NOUN
ap-662	53	5	of	of	ADP
ap-662	53	6	constraint	constraint	NOUN
ap-662	53	7	equations	equation	NOUN
ap-662	53	8	is	be	AUX
ap-662	53	9	defined	define	VERB
ap-662	53	10	to	to	PART
ap-662	53	11	make	make	VERB
ap-662	53	12	the	the	DET
ap-662	53	13	given	give	VERB
ap-662	53	14	system	system	NOUN
ap-662	53	15	regular	regular	ADJ
ap-662	53	16	cx	cx	PROPN
ap-662	53	17	c	c	PROPN
ap-662	53	18	�	�	PROPN
ap-662	53	19	.	.	PUNCT
ap-662	54	1	(	(	PUNCT
ap-662	54	2	7	7	X
ap-662	54	3	)	)	PUNCT
ap-662	54	4	normal	normal	ADJ
ap-662	54	5	equations	equation	NOUN
ap-662	54	6	then	then	ADV
ap-662	54	7	become	become	VERB
ap-662	54	8	n	n	PRON
ap-662	54	9	c	c	NOUN
ap-662	54	10	c	c	NOUN
ap-662	54	11	x	x	X
ap-662	54	12	l	l	NOUN
ap-662	54	13	c	c	X
ap-662	54	14	�	�	PROPN
ap-662	54	15	�	�	PROPN
ap-662	54	16	�	�	PROPN
ap-662	54	17	�	�	PROPN
ap-662	54	18	�	�	PROPN
ap-662	54	19	�	�	PROPN
ap-662	54	20	�	�	PROPN
ap-662	54	21	�	�	PROPN
ap-662	54	22	�	�	PROPN
ap-662	54	23	�	�	PROPN
ap-662	54	24	�	�	PROPN
ap-662	54	25	0	0	NUM
ap-662	54	26	�	�	PROPN
ap-662	54	27	,	,	PUNCT
ap-662	54	28	(	(	PUNCT
ap-662	54	29	8)	8)	NUM
ap-662	54	30	where	where	SCONJ
ap-662	54	31	�	�	PROPN
ap-662	54	32	is	be	AUX
ap-662	54	33	the	the	DET
ap-662	54	34	vector	vector	NOUN
ap-662	54	35	of	of	ADP
ap-662	54	36	lagrange	lagrange	NOUN
ap-662	54	37	multipliers	multiplier	NOUN
ap-662	54	38	.	.	PUNCT
ap-662	55	1	in	in	ADP
ap-662	55	2	this	this	DET
ap-662	55	3	case	case	NOUN
ap-662	55	4	matrix	matrix	NOUN
ap-662	55	5	c	c	NOUN
ap-662	55	6	is	be	AUX
ap-662	55	7	problem	problem	NOUN
ap-662	55	8	dependent	dependent	ADJ
ap-662	55	9	and	and	CCONJ
ap-662	55	10	needs	need	VERB
ap-662	55	11	to	to	PART
ap-662	55	12	be	be	AUX
ap-662	55	13	known	know	VERB
ap-662	55	14	explicitly	explicitly	ADV
ap-662	55	15	in	in	ADP
ap-662	55	16	advance	advance	NOUN
ap-662	55	17	.	.	PUNCT
ap-662	56	1	�	�	PROPN
ap-662	56	2	the	the	DET
ap-662	56	3	euclidean	euclidean	ADJ
ap-662	56	4	norm	norm	NOUN
ap-662	56	5	of	of	ADP
ap-662	56	6	a	a	DET
ap-662	56	7	certain	certain	ADJ
ap-662	56	8	subset	subset	NOUN
ap-662	56	9	of	of	ADP
ap-662	56	10	unknown	unknown	ADJ
ap-662	56	11	parameters	parameter	NOUN
ap-662	56	12	vector	vector	NOUN
ap-662	56	13	x	x	VERB
ap-662	56	14	is	be	AUX
ap-662	56	15	minimized	minimize	VERB
ap-662	56	16	min	min	NOUN
ap-662	56	17	,	,	PUNCT
ap-662	56	18	x	x	PROPN
ap-662	57	1	i	i	PRON
ap-662	57	2	i	i	PROPN
ap-662	57	3	x	x	PROPN
ap-662	57	4	i2	i2	PROPN
ap-662	57	5	�	�	PROPN
ap-662	57	6	�	�	PROPN
ap-662	57	7	�	�	PROPN
ap-662	57	8	.	.	PUNCT
ap-662	58	1	(	(	PUNCT
ap-662	58	2	9	9	X
ap-662	58	3	)	)	PUNCT
ap-662	58	4	the	the	DET
ap-662	58	5	set	set	NOUN
ap-662	58	6	of	of	ADP
ap-662	58	7	indices	index	NOUN
ap-662	58	8	�	�	PROPN
ap-662	58	9	can	can	AUX
ap-662	58	10	contain	contain	VERB
ap-662	58	11	all	all	DET
ap-662	58	12	elements	element	NOUN
ap-662	58	13	,	,	PUNCT
ap-662	58	14	but	but	CCONJ
ap-662	58	15	more	more	ADV
ap-662	58	16	often	often	ADV
ap-662	58	17	only	only	ADV
ap-662	58	18	selected	select	VERB
ap-662	58	19	elements	element	NOUN
ap-662	58	20	of	of	ADP
ap-662	58	21	x.	x.	NOUN
ap-662	58	22	in	in	ADP
ap-662	58	23	the	the	DET
ap-662	58	24	case	case	NOUN
ap-662	58	25	of	of	ADP
ap-662	58	26	a	a	DET
ap-662	58	27	plane	plane	NOUN
ap-662	58	28	geodetic	geodetic	ADJ
ap-662	58	29	free	free	ADJ
ap-662	58	30	network	network	NOUN
ap-662	58	31	we	we	PRON
ap-662	58	32	can	can	AUX
ap-662	58	33	geometrically	geometrically	ADV
ap-662	58	34	interpret	interpret	VERB
ap-662	58	35	the	the	DET
ap-662	58	36	last	last	ADJ
ap-662	58	37	constraint	constraint	NOUN
ap-662	58	38	(	(	PUNCT
ap-662	58	39	9	9	NUM
ap-662	58	40	)	)	PUNCT
ap-662	58	41	as	as	SCONJ
ap-662	58	42	follows	follow	VERB
ap-662	58	43	.	.	PUNCT
ap-662	59	1	by	by	ADP
ap-662	59	2	minimizing	minimize	VERB
ap-662	59	3	of	of	ADP
ap-662	59	4	the	the	DET
ap-662	59	5	euclidean	euclidean	ADJ
ap-662	59	6	norm	norm	NOUN
ap-662	59	7	of	of	ADP
ap-662	59	8	the	the	DET
ap-662	59	9	residual	residual	ADJ
ap-662	59	10	vector	vector	NOUN
ap-662	59	11	(	(	PUNCT
ap-662	59	12	3	3	NUM
ap-662	59	13	)	)	PUNCT
ap-662	59	14	the	the	DET
ap-662	59	15	shape	shape	NOUN
ap-662	59	16	and	and	CCONJ
ap-662	59	17	scale	scale	NOUN
ap-662	59	18	(	(	PUNCT
ap-662	59	19	if	if	SCONJ
ap-662	59	20	at	at	ADV
ap-662	59	21	least	least	ADV
ap-662	59	22	one	one	NUM
ap-662	59	23	distance	distance	NOUN
ap-662	59	24	is	be	AUX
ap-662	59	25	available	available	ADJ
ap-662	59	26	)	)	PUNCT
ap-662	59	27	of	of	ADP
ap-662	59	28	the	the	DET
ap-662	59	29	adjusted	adjusted	ADJ
ap-662	59	30	network	network	NOUN
ap-662	59	31	together	together	ADV
ap-662	59	32	with	with	ADP
ap-662	59	33	the	the	DET
ap-662	59	34	covariances	covariance	NOUN
ap-662	59	35	of	of	ADP
ap-662	59	36	the	the	DET
ap-662	59	37	adjusted	adjust	VERB
ap-662	59	38	observations	observation	NOUN
ap-662	59	39	are	be	AUX
ap-662	59	40	uniquely	uniquely	ADV
ap-662	59	41	defined	define	VERB
ap-662	59	42	.	.	PUNCT
ap-662	60	1	the	the	DET
ap-662	60	2	second	second	ADJ
ap-662	60	3	additional	additional	ADJ
ap-662	60	4	constraint	constraint	NOUN
ap-662	60	5	(	(	PUNCT
ap-662	60	6	9	9	NUM
ap-662	60	7	)	)	PUNCT
ap-662	60	8	then	then	ADV
ap-662	60	9	defines	define	VERB
ap-662	60	10	the	the	DET
ap-662	60	11	localization	localization	NOUN
ap-662	60	12	of	of	ADP
ap-662	60	13	the	the	DET
ap-662	60	14	network	network	NOUN
ap-662	60	15	in	in	ADP
ap-662	60	16	the	the	DET
ap-662	60	17	coordinate	coordinate	NOUN
ap-662	60	18	system	system	NOUN
ap-662	60	19	.	.	PUNCT
ap-662	61	1	apart	apart	ADV
ap-662	61	2	from	from	ADP
ap-662	61	3	the	the	DET
ap-662	61	4	adjusted	adjust	VERB
ap-662	61	5	network	network	NOUN
ap-662	61	6	shape	shape	NOUN
ap-662	61	7	we	we	PRON
ap-662	61	8	simultaneously	simultaneously	ADV
ap-662	61	9	define	define	VERB
ap-662	61	10	its	its	PRON
ap-662	61	11	shift	shift	NOUN
ap-662	61	12	and	and	CCONJ
ap-662	61	13	rotation	rotation	NOUN
ap-662	61	14	in	in	ADP
ap-662	61	15	the	the	DET
ap-662	61	16	coordinate	coordinate	NOUN
ap-662	61	17	system	system	NOUN
ap-662	61	18	.	.	PUNCT
ap-662	62	1	another	another	DET
ap-662	62	2	equivalent	equivalent	ADJ
ap-662	62	3	interpretation	interpretation	NOUN
ap-662	62	4	is	be	AUX
ap-662	62	5	that	that	PRON
ap-662	62	6	constraint	constraint	NOUN
ap-662	62	7	(	(	PUNCT
ap-662	62	8	9	9	NUM
ap-662	62	9	)	)	PUNCT
ap-662	62	10	defines	define	VERB
ap-662	62	11	the	the	DET
ap-662	62	12	particular	particular	ADJ
ap-662	62	13	solution	solution	NOUN
ap-662	62	14	of	of	ADP
ap-662	62	15	(	(	PUNCT
ap-662	62	16	2	2	NUM
ap-662	62	17	)	)	PUNCT
ap-662	62	18	in	in	ADP
ap-662	62	19	which	which	PRON
ap-662	62	20	the	the	DET
ap-662	62	21	trace	trace	NOUN
ap-662	62	22	of	of	ADP
ap-662	62	23	the	the	DET
ap-662	62	24	variance	variance	NOUN
ap-662	62	25	-	-	PUNCT
ap-662	62	26	covariance	covariance	NOUN
ap-662	62	27	submatrix	submatrix	NOUN
ap-662	62	28	corresponding	correspond	VERB
ap-662	62	29	to	to	ADP
ap-662	62	30	indices	index	NOUN
ap-662	62	31	i	i	PRON
ap-662	62	32	�	�	NOUN
ap-662	62	33	�	�	PROPN
ap-662	62	34	is	be	AUX
ap-662	62	35	minimal	minimal	ADJ
ap-662	62	36	.	.	PUNCT
ap-662	63	1	4	4	NUM
ap-662	63	2	normal	normal	ADJ
ap-662	63	3	equations	equation	NOUN
ap-662	63	4	and	and	CCONJ
ap-662	63	5	numerical	numerical	ADJ
ap-662	63	6	stability	stability	PROPN
ap-662	63	7	the	the	DET
ap-662	63	8	numerical	numerical	ADJ
ap-662	63	9	solution	solution	NOUN
ap-662	63	10	of	of	ADP
ap-662	63	11	the	the	DET
ap-662	63	12	adjustment	adjustment	NOUN
ap-662	63	13	of	of	ADP
ap-662	63	14	observed	observed	ADJ
ap-662	63	15	quantities	quantity	NOUN
ap-662	63	16	based	base	VERB
ap-662	63	17	on	on	ADP
ap-662	63	18	normal	normal	ADJ
ap-662	63	19	equations	equation	NOUN
ap-662	63	20	can	can	AUX
ap-662	63	21	be	be	AUX
ap-662	63	22	numerically	numerically	ADV
ap-662	63	23	unstable	unstable	ADJ
ap-662	63	24	and	and	CCONJ
ap-662	63	25	in	in	ADP
ap-662	63	26	certain	certain	ADJ
ap-662	63	27	cases	case	NOUN
ap-662	63	28	we	we	PRON
ap-662	63	29	should	should	AUX
ap-662	63	30	prefer	prefer	VERB
ap-662	63	31	other	other	ADJ
ap-662	63	32	numerical	numerical	ADJ
ap-662	63	33	algorithms	algorithm	NOUN
ap-662	63	34	that	that	PRON
ap-662	63	35	directly	directly	ADV
ap-662	63	36	solve	solve	VERB
ap-662	63	37	the	the	DET
ap-662	63	38	project	project	NOUN
ap-662	63	39	equations	equation	NOUN
ap-662	63	40	(	(	PUNCT
ap-662	63	41	2	2	NUM
ap-662	63	42	)	)	PUNCT
ap-662	63	43	.	.	PUNCT
ap-662	64	1	a	a	DET
ap-662	64	2	possible	possible	ADJ
ap-662	64	3	source	source	NOUN
ap-662	64	4	of	of	ADP
ap-662	64	5	troubles	trouble	NOUN
ap-662	64	6	are	be	AUX
ap-662	64	7	the	the	DET
ap-662	64	8	normal	normal	ADJ
ap-662	64	9	equations	equation	NOUN
ap-662	64	10	themselves	themselves	PRON
ap-662	64	11	,	,	PUNCT
ap-662	64	12	or	or	CCONJ
ap-662	64	13	more	more	ADV
ap-662	64	14	precisely	precisely	ADV
ap-662	64	15	the	the	DET
ap-662	64	16	condition	condition	NOUN
ap-662	64	17	number	number	NOUN
ap-662	64	18	of	of	ADP
ap-662	64	19	normal	normal	ADJ
ap-662	64	20	equations	equation	NOUN
ap-662	64	21	.	.	PUNCT
ap-662	65	1	let	let	VERB
ap-662	65	2	us	we	PRON
ap-662	65	3	restrict	restrict	VERB
ap-662	65	4	our	our	PRON
ap-662	65	5	discussion	discussion	NOUN
ap-662	65	6	here	here	ADV
ap-662	65	7	to	to	ADP
ap-662	65	8	the	the	DET
ap-662	65	9	simple	simple	ADJ
ap-662	65	10	case	case	NOUN
ap-662	65	11	when	when	SCONJ
ap-662	65	12	matrix	matrix	NOUN
ap-662	65	13	a	a	PRON
ap-662	65	14	does	do	AUX
ap-662	65	15	not	not	PART
ap-662	65	16	contain	contain	VERB
ap-662	65	17	linearly	linearly	ADV
ap-662	65	18	dependent	dependent	ADJ
ap-662	65	19	columns	column	NOUN
ap-662	65	20	and	and	CCONJ
ap-662	65	21	matrix	matrix	NOUN
ap-662	65	22	n	n	PRON
ap-662	65	23	is	be	AUX
ap-662	65	24	positive	positive	ADJ
ap-662	65	25	-	-	PUNCT
ap-662	65	26	definite	definite	ADJ
ap-662	65	27	.	.	PUNCT
ap-662	66	1	the	the	DET
ap-662	66	2	condition	condition	NOUN
ap-662	66	3	number	number	NOUN
ap-662	66	4	of	of	ADP
ap-662	66	5	matrix	matrix	NOUN
ap-662	66	6	a	a	PRON
ap-662	66	7	is	be	AUX
ap-662	66	8	defined	define	VERB
ap-662	66	9	as	as	ADP
ap-662	66	10	�	�	PROPN
ap-662	66	11	�	�	PROPN
ap-662	66	12	�	�	PROPN
ap-662	66	13	(	(	PUNCT
ap-662	66	14	)	)	PUNCT
ap-662	66	15	(	(	PUNCT
ap-662	66	16	)	)	PUNCT
ap-662	66	17	(	(	PUNCT
ap-662	66	18	)	)	PUNCT
ap-662	66	19	max	max	PROPN
ap-662	66	20	min	min	PROPN
ap-662	66	21	a	a	DET
ap-662	66	22	a	a	DET
ap-662	66	23	a	a	DET
ap-662	66	24	a	a	DET
ap-662	66	25	a	a	DET
ap-662	66	26	�	�	PROPN
ap-662	66	27	�	�	PROPN
ap-662	66	28	�	�	PROPN
ap-662	66	29	,	,	PUNCT
ap-662	66	30	(	(	PUNCT
ap-662	66	31	10	10	NUM
ap-662	66	32	)	)	PUNCT
ap-662	66	33	where	where	SCONJ
ap-662	66	34	�	�	PROPN
ap-662	66	35	(	(	PUNCT
ap-662	66	36	)	)	PUNCT
ap-662	66	37	*	*	PUNCT
ap-662	66	38	�	�	PROPN
ap-662	66	39	a	a	DET
ap-662	66	40	a	a	DET
ap-662	66	41	denotes	denote	NOUN
ap-662	66	42	the	the	DET
ap-662	66	43	maximal	maximal	ADJ
ap-662	66	44	and	and	CCONJ
ap-662	66	45	minimal	minimal	ADJ
ap-662	66	46	eigenvalue	eigenvalue	NOUN
ap-662	66	47	of	of	ADP
ap-662	66	48	matrix	matrix	NOUN
ap-662	66	49	�	�	PROPN
ap-662	66	50	a	a	DET
ap-662	66	51	a	a	NOUN
ap-662	66	52	.	.	PUNCT
ap-662	67	1	if	if	SCONJ
ap-662	67	2	we	we	PRON
ap-662	67	3	solve	solve	VERB
ap-662	67	4	a	a	DET
ap-662	67	5	linear	linear	ADJ
ap-662	67	6	set	set	NOUN
ap-662	67	7	of	of	ADP
ap-662	67	8	equations	equation	NOUN
ap-662	67	9	then	then	ADV
ap-662	67	10	its	its	PRON
ap-662	67	11	condition	condition	NOUN
ap-662	67	12	number	number	NOUN
ap-662	67	13	represents	represent	VERB
ap-662	67	14	the	the	DET
ap-662	67	15	minimal	minimal	ADJ
ap-662	67	16	upper	upper	ADJ
ap-662	67	17	estimate	estimate	NOUN
ap-662	67	18	of	of	ADP
ap-662	67	19	ratio	ratio	NOUN
ap-662	67	20	of	of	ADP
ap-662	67	21	relative	relative	ADJ
ap-662	67	22	error	error	NOUN
ap-662	67	23	of	of	ADP
ap-662	67	24	x	x	PUNCT
ap-662	67	25	and	and	CCONJ
ap-662	67	26	the	the	DET
ap-662	67	27	relative	relative	ADJ
ap-662	67	28	error	error	NOUN
ap-662	67	29	of	of	ADP
ap-662	67	30	the	the	DET
ap-662	67	31	right	right	ADJ
ap-662	67	32	hand	hand	NOUN
ap-662	67	33	side	side	NOUN
ap-662	67	34	l.	l.	NOUN
ap-662	67	35	from	from	ADP
ap-662	67	36	equation	equation	NOUN
ap-662	67	37	(	(	PUNCT
ap-662	67	38	10	10	NUM
ap-662	67	39	)	)	PUNCT
ap-662	67	40	it	it	PRON
ap-662	67	41	directly	directly	ADV
ap-662	67	42	follows	follow	VERB
ap-662	67	43	that	that	SCONJ
ap-662	67	44	the	the	DET
ap-662	67	45	condition	condition	NOUN
ap-662	67	46	number	number	NOUN
ap-662	67	47	of	of	ADP
ap-662	67	48	normal	normal	ADJ
ap-662	67	49	equation	equation	NOUN
ap-662	67	50	matrix	matrix	NOUN
ap-662	67	51	n	n	NOUN
ap-662	67	52	is	be	AUX
ap-662	67	53	the	the	DET
ap-662	67	54	square	square	NOUN
ap-662	67	55	of	of	ADP
ap-662	67	56	the	the	DET
ap-662	67	57	condition	condition	NOUN
ap-662	67	58	number	number	NOUN
ap-662	67	59	of	of	ADP
ap-662	67	60	the	the	DET
ap-662	67	61	project	project	NOUN
ap-662	67	62	equation	equation	NOUN
ap-662	67	63	matrix	matrix	NOUN
ap-662	67	64	a	a	DET
ap-662	67	65	�	�	PROPN
ap-662	67	66	�	�	PROPN
ap-662	67	67	�	�	PROPN
ap-662	67	68	�	�	PROPN
ap-662	67	69	(	(	PUNCT
ap-662	67	70	)	)	PUNCT
ap-662	67	71	(	(	PUNCT
ap-662	67	72	)	)	PUNCT
ap-662	67	73	n	n	CCONJ
ap-662	67	74	a	a	DET
ap-662	67	75	�	�	PROPN
ap-662	67	76	2	2	NUM
ap-662	67	77	.	.	PUNCT
ap-662	68	1	(	(	PUNCT
ap-662	68	2	11	11	NUM
ap-662	68	3	)	)	PUNCT
ap-662	68	4	we	we	PRON
ap-662	68	5	can	can	AUX
ap-662	68	6	say	say	VERB
ap-662	68	7	that	that	SCONJ
ap-662	68	8	when	when	SCONJ
ap-662	68	9	solving	solve	VERB
ap-662	68	10	poorly	poorly	ADV
ap-662	68	11	conditioned	condition	VERB
ap-662	68	12	normal	normal	ADJ
ap-662	68	13	equations	equation	NOUN
ap-662	68	14	we	we	PRON
ap-662	68	15	lose	lose	VERB
ap-662	68	16	twice	twice	ADV
ap-662	68	17	as	as	ADV
ap-662	68	18	many	many	ADJ
ap-662	68	19	of	of	ADP
ap-662	68	20	correct	correct	ADJ
ap-662	68	21	decimal	decimal	ADJ
ap-662	68	22	digits	digit	NOUN
ap-662	68	23	in	in	ADP
ap-662	68	24	a	a	DET
ap-662	68	25	solution	solution	NOUN
ap-662	68	26	x	x	PUNCT
ap-662	68	27	as	as	ADP
ap-662	68	28	in	in	ADP
ap-662	68	29	any	any	DET
ap-662	68	30	direct	direct	ADJ
ap-662	68	31	solution	solution	NOUN
ap-662	68	32	of	of	ADP
ap-662	68	33	project	project	NOUN
ap-662	68	34	equations	equation	NOUN
ap-662	68	35	.	.	PUNCT
ap-662	69	1	probably	probably	ADV
ap-662	69	2	the	the	DET
ap-662	69	3	most	most	ADV
ap-662	69	4	important	important	ADJ
ap-662	69	5	class	class	NOUN
ap-662	69	6	of	of	ADP
ap-662	69	7	algorithms	algorithm	NOUN
ap-662	69	8	for	for	ADP
ap-662	69	9	direct	direct	ADJ
ap-662	69	10	solution	solution	NOUN
ap-662	69	11	of	of	ADP
ap-662	69	12	project	project	NOUN
ap-662	69	13	equations	equation	NOUN
ap-662	69	14	(	(	PUNCT
ap-662	69	15	2	2	X
ap-662	69	16	)	)	PUNCT
ap-662	69	17	is	be	AUX
ap-662	69	18	the	the	DET
ap-662	69	19	family	family	NOUN
ap-662	69	20	of	of	ADP
ap-662	69	21	orthogonal	orthogonal	ADJ
ap-662	69	22	decomposition	decomposition	NOUN
ap-662	69	23	algorithms	algorithm	NOUN
ap-662	69	24	.	.	PUNCT
ap-662	70	1	apart	apart	ADV
ap-662	70	2	from	from	ADP
ap-662	70	3	other	other	ADJ
ap-662	70	4	goals	goal	NOUN
ap-662	70	5	,	,	PUNCT
ap-662	70	6	gnu	gnu	PROPN
ap-662	70	7	project	project	NOUN
ap-662	70	8	gama	gama	NOUN
ap-662	70	9	has	have	AUX
ap-662	70	10	been	be	AUX
ap-662	70	11	planned	plan	VERB
ap-662	70	12	to	to	PART
ap-662	70	13	be	be	AUX
ap-662	70	14	a	a	DET
ap-662	70	15	kind	kind	NOUN
ap-662	70	16	of	of	ADP
ap-662	70	17	benchmark	benchmark	NOUN
ap-662	70	18	,	,	PUNCT
ap-662	70	19	ie	ie	X
ap-662	70	20	.	.	PROPN
ap-662	70	21	,	,	PUNCT
ap-662	70	22	a	a	DET
ap-662	70	23	tool	tool	NOUN
ap-662	70	24	for	for	ADP
ap-662	70	25	checking	check	VERB
ap-662	70	26	adjustment	adjustment	NOUN
ap-662	70	27	results	result	NOUN
ap-662	70	28	from	from	ADP
ap-662	70	29	other	other	ADJ
ap-662	70	30	software	software	NOUN
ap-662	70	31	products	product	NOUN
ap-662	70	32	.	.	PUNCT
ap-662	71	1	for	for	ADP
ap-662	71	2	this	this	DET
ap-662	71	3	reason	reason	NOUN
ap-662	71	4	it	it	PRON
ap-662	71	5	was	be	AUX
ap-662	71	6	desirable	desirable	ADJ
ap-662	71	7	to	to	PART
ap-662	71	8	have	have	VERB
ap-662	71	9	the	the	DET
ap-662	71	10	adjustment	adjustment	NOUN
ap-662	71	11	based	base	VERB
ap-662	71	12	on	on	ADP
ap-662	71	13	a	a	DET
ap-662	71	14	different	different	ADJ
ap-662	71	15	numerical	numerical	ADJ
ap-662	71	16	method	method	NOUN
ap-662	71	17	other	other	ADJ
ap-662	71	18	than	than	ADP
ap-662	71	19	the	the	DET
ap-662	71	20	traditional	traditional	ADJ
ap-662	71	21	solution	solution	NOUN
ap-662	71	22	of	of	ADP
ap-662	71	23	normal	normal	ADJ
ap-662	71	24	equations	equation	NOUN
ap-662	71	25	,	,	PUNCT
ap-662	71	26	and	and	CCONJ
ap-662	71	27	singular	singular	ADJ
ap-662	71	28	value	value	NOUN
ap-662	71	29	decomposition	decomposition	NOUN
ap-662	71	30	(	(	PUNCT
ap-662	71	31	svd	svd	PROPN
ap-662	71	32	)	)	PUNCT
ap-662	71	33	was	be	AUX
ap-662	71	34	implemented	implement	VERB
ap-662	71	35	as	as	ADP
ap-662	71	36	the	the	DET
ap-662	71	37	main	main	ADJ
ap-662	71	38	numerical	numerical	ADJ
ap-662	71	39	algorithm	algorithm	NOUN
ap-662	71	40	.	.	PUNCT
ap-662	72	1	as	as	ADP
ap-662	72	2	an	an	DET
ap-662	72	3	alternative	alternative	NOUN
ap-662	72	4	,	,	PUNCT
ap-662	72	5	another	another	DET
ap-662	72	6	orthogonal	orthogonal	ADJ
ap-662	72	7	decomposition	decomposition	NOUN
ap-662	72	8	adjustment	adjustment	NOUN
ap-662	72	9	algorithm	algorithm	NOUN
ap-662	72	10	gso	gso	PROPN
ap-662	72	11	(	(	PUNCT
ap-662	72	12	based	base	VERB
ap-662	72	13	on	on	ADP
ap-662	72	14	gram	gram	NOUN
ap-662	72	15	-	-	PUNCT
ap-662	72	16	schmidt	schmidt	NOUN
ap-662	72	17	orthogonalization	orthogonalization	NOUN
ap-662	72	18	)	)	PUNCT
ap-662	72	19	is	be	AUX
ap-662	72	20	also	also	ADV
ap-662	72	21	available	available	ADJ
ap-662	72	22	.	.	PUNCT
ap-662	73	1	we	we	PRON
ap-662	73	2	give	give	VERB
ap-662	73	3	a	a	DET
ap-662	73	4	brief	brief	ADJ
ap-662	73	5	description	description	NOUN
ap-662	73	6	of	of	ADP
ap-662	73	7	both	both	DET
ap-662	73	8	algorithms	algorithm	NOUN
ap-662	73	9	in	in	ADP
ap-662	73	10	the	the	DET
ap-662	73	11	following	follow	VERB
ap-662	73	12	section	section	NOUN
ap-662	73	13	.	.	PUNCT
ap-662	74	1	5	5	NUM
ap-662	74	2	gram	gram	NOUN
ap-662	74	3	-	-	PUNCT
ap-662	74	4	schmidt	schmidt	NOUN
ap-662	74	5	orthogonalization	orthogonalization	NOUN
ap-662	74	6	the	the	DET
ap-662	74	7	gram	gram	NOUN
ap-662	74	8	-	-	PUNCT
ap-662	74	9	schmidt	schmidt	NOUN
ap-662	74	10	orthogonal	orthogonal	ADJ
ap-662	74	11	decomposition	decomposition	NOUN
ap-662	74	12	is	be	AUX
ap-662	74	13	an	an	DET
ap-662	74	14	algorithm	algorithm	NOUN
ap-662	74	15	for	for	ADP
ap-662	74	16	computing	compute	VERB
ap-662	74	17	factorization	factorization	NOUN
ap-662	74	18	a	a	DET
ap-662	74	19	qr	qr	NOUN
ap-662	74	20	q	q	NOUN
ap-662	74	21	q	q	PROPN
ap-662	74	22	�	�	PROPN
ap-662	74	23	�	�	PROPN
ap-662	74	24	�	�	PROPN
ap-662	74	25	,	,	PUNCT
ap-662	74	26	1	1	NUM
ap-662	74	27	,	,	PUNCT
ap-662	74	28	(	(	PUNCT
ap-662	74	29	12	12	NUM
ap-662	74	30	)	)	PUNCT
ap-662	74	31	where	where	SCONJ
ap-662	74	32	q	q	NOUN
ap-662	74	33	is	be	AUX
ap-662	74	34	the	the	DET
ap-662	74	35	orthogonal	orthogonal	ADJ
ap-662	74	36	matrix	matrix	NOUN
ap-662	74	37	and	and	CCONJ
ap-662	74	38	r	r	NOUN
ap-662	74	39	is	be	AUX
ap-662	74	40	the	the	DET
ap-662	74	41	upper	upper	ADJ
ap-662	74	42	triangular	triangular	NOUN
ap-662	74	43	matrix	matrix	NOUN
ap-662	74	44	.	.	PUNCT
ap-662	75	1	matrix	matrix	NOUN
ap-662	75	2	r	r	NOUN
ap-662	75	3	here	here	ADV
ap-662	75	4	is	be	AUX
ap-662	75	5	identical	identical	ADJ
ap-662	75	6	to	to	ADP
ap-662	75	7	the	the	DET
ap-662	75	8	upper	upper	ADJ
ap-662	75	9	triangular	triangular	NOUN
ap-662	75	10	matrix	matrix	NOUN
ap-662	75	11	of	of	ADP
ap-662	75	12	the	the	DET
ap-662	75	13	cholesky	cholesky	ADJ
ap-662	75	14	decomposition	decomposition	NOUN
ap-662	75	15	of	of	ADP
ap-662	75	16	normal	normal	ADJ
ap-662	75	17	equations	equation	NOUN
ap-662	75	18	n	n	ADP
ap-662	75	19	a	a	DET
ap-662	75	20	a	a	DET
ap-662	75	21	r	r	NOUN
ap-662	75	22	q	q	NOUN
ap-662	75	23	qr	qr	NOUN
ap-662	75	24	r	r	NOUN
ap-662	75	25	r	r	PROPN
ap-662	75	26	�	�	PROPN
ap-662	75	27	�	�	PROPN
ap-662	75	28	�	�	PROPN
ap-662	75	29	�	�	PROPN
ap-662	75	30	�	�	PROPN
ap-662	75	31	�	�	PROPN
ap-662	75	32	�	�	PROPN
ap-662	75	33	.	.	PUNCT
ap-662	76	1	(	(	PUNCT
ap-662	76	2	13	13	NUM
ap-662	76	3	)	)	PUNCT
ap-662	76	4	gram	gram	PROPN
ap-662	76	5	-	-	PUNCT
ap-662	76	6	schmidt	schmidt	NOUN
ap-662	76	7	orthogonalization	orthogonalization	NOUN
ap-662	76	8	is	be	AUX
ap-662	76	9	a	a	DET
ap-662	76	10	very	very	ADV
ap-662	76	11	straightforward	straightforward	ADJ
ap-662	76	12	and	and	CCONJ
ap-662	76	13	relatively	relatively	ADV
ap-662	76	14	simple	simple	ADJ
ap-662	76	15	algorithm	algorithm	NOUN
ap-662	76	16	that	that	PRON
ap-662	76	17	can	can	AUX
ap-662	76	18	be	be	AUX
ap-662	76	19	implemented	implement	VERB
ap-662	76	20	in	in	ADP
ap-662	76	21	several	several	ADJ
ap-662	76	22	variants	variant	NOUN
ap-662	76	23	differing	differ	VERB
ap-662	76	24	in	in	ADP
ap-662	76	25	the	the	DET
ap-662	76	26	order	order	NOUN
ap-662	76	27	in	in	ADP
ap-662	76	28	which	which	PRON
ap-662	76	29	the	the	DET
ap-662	76	30	vectors	vector	NOUN
ap-662	76	31	are	be	AUX
ap-662	76	32	orthogonalized	orthogonalize	VERB
ap-662	76	33	.	.	PUNCT
ap-662	77	1	the	the	DET
ap-662	77	2	following	follow	VERB
ap-662	77	3	three	three	NUM
ap-662	77	4	algorithms	algorithm	NOUN
ap-662	77	5	are	be	AUX
ap-662	77	6	adopted	adopt	VERB
ap-662	77	7	from	from	ADP
ap-662	77	8	[	[	X
ap-662	77	9	2	2	NUM
ap-662	77	10	,	,	PUNCT
ap-662	77	11	p.	p.	NOUN
ap-662	77	12	300–301	300–301	NUM
ap-662	77	13	]	]	X
ap-662	77	14	.	.	PUNCT
ap-662	78	1	14	14	NUM
ap-662	79	1	©	©	PROPN
ap-662	79	2	czech	czech	PROPN
ap-662	79	3	technical	technical	PROPN
ap-662	79	4	university	university	PROPN
ap-662	79	5	publishing	publishing	NOUN
ap-662	79	6	house	house	NOUN
ap-662	79	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-662	79	8	acta	acta	PROPN
ap-662	79	9	polytechnica	polytechnica	PROPN
ap-662	79	10	vol	vol	NOUN
ap-662	79	11	.	.	PROPN
ap-662	80	1	45	45	NUM
ap-662	80	2	no	no	NOUN
ap-662	80	3	.	.	PUNCT
ap-662	81	1	1/2005	1/2005	NUM
ap-662	81	2	czech	czech	PROPN
ap-662	81	3	technical	technical	PROPN
ap-662	81	4	university	university	PROPN
ap-662	81	5	in	in	ADP
ap-662	81	6	prague	prague	PROPN
ap-662	81	7	algorithm	algorithm	PROPN
ap-662	81	8	1.1	1.1	NUM
ap-662	82	1	[	[	X
ap-662	82	2	modified	modify	VERB
ap-662	82	3	gram	gram	NOUN
ap-662	82	4	–	–	PUNCT
ap-662	82	5	schmidt	schmidt	NOUN
ap-662	82	6	(	(	PUNCT
ap-662	82	7	mgs	mgs	PROPN
ap-662	82	8	)	)	PUNCT
ap-662	82	9	row	row	NOUN
ap-662	82	10	version	version	NOUN
ap-662	82	11	]	]	PUNCT
ap-662	82	12	for	for	ADP
ap-662	82	13	k	k	PROPN
ap-662	82	14	�	�	PROPN
ap-662	82	15	1	1	NUM
ap-662	82	16	2	2	NUM
ap-662	82	17	,	,	PUNCT
ap-662	82	18	,	,	PUNCT
ap-662	82	19	,	,	PUNCT
ap-662	82	20	�	�	PROPN
ap-662	82	21	n	n	PRON
ap-662	82	22	�	�	PROPN
ap-662	82	23	:	:	PUNCT
ap-662	82	24	;	;	NOUN
ap-662	82	25	:	:	PUNCT
ap-662	82	26	(	(	PUNCT
ap-662	82	27	�	�	PROPN
ap-662	82	28	�	�	PROPN
ap-662	82	29	)	)	PUNCT
ap-662	82	30	;	;	PROPN
ap-662	82	31	(	(	PUNCT
ap-662	82	32	)	)	PUNCT
ap-662	82	33	q	q	PROPN
ap-662	82	34	a	a	DET
ap-662	82	35	r	r	NOUN
ap-662	82	36	q	q	NOUN
ap-662	82	37	qk	qk	NOUN
ap-662	82	38	k	k	PROPN
ap-662	82	39	k	k	PROPN
ap-662	82	40	kk	kk	PROPN
ap-662	82	41	k	k	PROPN
ap-662	82	42	t	t	PROPN
ap-662	82	43	k	k	PROPN
ap-662	82	44	�	�	PROPN
ap-662	82	45	�	�	PROPN
ap-662	82	46	1	1	NUM
ap-662	82	47	2	2	NUM
ap-662	82	48	q	q	NOUN
ap-662	82	49	q	q	NOUN
ap-662	82	50	rk	rk	NOUN
ap-662	82	51	k	k	PROPN
ap-662	82	52	kk	kk	PROPN
ap-662	82	53	:	:	PUNCT
ap-662	82	54	�	�	PROPN
ap-662	82	55	;	;	NOUN
ap-662	82	56	�	�	PROPN
ap-662	82	57	for	for	ADP
ap-662	82	58	i	i	PROPN
ap-662	82	59	k	k	PROPN
ap-662	82	60	n	n	CCONJ
ap-662	82	61	�	�	PROPN
ap-662	82	62	�	�	PROPN
ap-662	82	63	1	1	NUM
ap-662	82	64	,	,	PUNCT
ap-662	82	65	,	,	PUNCT
ap-662	82	66	�	�	PROPN
ap-662	82	67	r	r	NOUN
ap-662	82	68	q	q	PROPN
ap-662	82	69	a	a	PRON
ap-662	82	70	a	a	PRON
ap-662	82	71	a	a	DET
ap-662	82	72	r	r	NOUN
ap-662	82	73	qki	qki	NOUN
ap-662	83	1	k	k	NOUN
ap-662	83	2	t	t	PROPN
ap-662	84	1	i	i	PRON
ap-662	84	2	k	k	INTJ
ap-662	85	1	i	i	PRON
ap-662	85	2	k	k	INTJ
ap-662	86	1	i	i	PRON
ap-662	86	2	k	k	PROPN
ap-662	87	1	ki	ki	PROPN
ap-662	87	2	k	k	NOUN
ap-662	87	3	:	:	PUNCT
ap-662	87	4	(	(	PUNCT
ap-662	87	5	)	)	PUNCT
ap-662	87	6	(	(	PUNCT
ap-662	87	7	)	)	PUNCT
ap-662	87	8	(	(	PUNCT
ap-662	87	9	)	)	PUNCT
ap-662	87	10	;	;	NOUN
ap-662	87	11	:	:	PUNCT
ap-662	87	12	;	;	PROPN
ap-662	87	13	�	�	PROPN
ap-662	87	14	�	�	PROPN
ap-662	87	15	�	�	PROPN
ap-662	87	16	�	�	PROPN
ap-662	87	17	1	1	NUM
ap-662	87	18	end	end	NOUN
ap-662	87	19	end	end	NOUN
ap-662	87	20	algorithm	algorithm	NOUN
ap-662	87	21	1.2	1.2	NUM
ap-662	87	22	[	[	X
ap-662	87	23	modified	modify	VERB
ap-662	87	24	gram	gram	NOUN
ap-662	87	25	–	–	PUNCT
ap-662	87	26	schmidt	schmidt	NOUN
ap-662	87	27	(	(	PUNCT
ap-662	87	28	mgs	mgs	PROPN
ap-662	87	29	)	)	PUNCT
ap-662	87	30	column	column	NOUN
ap-662	87	31	version	version	NOUN
ap-662	87	32	]	]	PUNCT
ap-662	87	33	for	for	ADP
ap-662	87	34	k	k	PROPN
ap-662	87	35	�	�	PROPN
ap-662	87	36	1	1	NUM
ap-662	87	37	2	2	NUM
ap-662	87	38	,	,	PUNCT
ap-662	87	39	,	,	PUNCT
ap-662	87	40	,	,	PUNCT
ap-662	87	41	�	�	PROPN
ap-662	87	42	n	n	CCONJ
ap-662	87	43	for	for	ADP
ap-662	87	44	i	i	PROPN
ap-662	87	45	k	k	PROPN
ap-662	87	46	�	�	PROPN
ap-662	87	47	�	�	PROPN
ap-662	87	48	1	1	NUM
ap-662	87	49	2	2	NUM
ap-662	87	50	1	1	NUM
ap-662	87	51	,	,	PUNCT
ap-662	87	52	,	,	PUNCT
ap-662	87	53	,	,	PUNCT
ap-662	87	54	�	�	PROPN
ap-662	87	55	r	r	NOUN
ap-662	87	56	q	q	PROPN
ap-662	87	57	a	a	DET
ap-662	87	58	a	a	DET
ap-662	87	59	a	a	DET
ap-662	87	60	r	r	NOUN
ap-662	87	61	qik	qik	NOUN
ap-662	88	1	k	k	PROPN
ap-662	88	2	t	t	PROPN
ap-662	89	1	k	k	NOUN
ap-662	90	1	i	i	PRON
ap-662	90	2	k	k	INTJ
ap-662	91	1	i	i	PRON
ap-662	91	2	k	k	VERB
ap-662	92	1	i	i	PRON
ap-662	92	2	ik	ik	PROPN
ap-662	92	3	i	i	PRON
ap-662	92	4	:	:	PUNCT
ap-662	92	5	;	;	NOUN
ap-662	92	6	:	:	PUNCT
ap-662	92	7	;	;	PROPN
ap-662	92	8	(	(	PUNCT
ap-662	92	9	)	)	PUNCT
ap-662	92	10	(	(	PUNCT
ap-662	92	11	)	)	PUNCT
ap-662	92	12	(	(	PUNCT
ap-662	92	13	)	)	PUNCT
ap-662	92	14	�	�	PROPN
ap-662	92	15	�	�	PROPN
ap-662	92	16	�	�	PROPN
ap-662	92	17	�	�	PROPN
ap-662	92	18	1	1	NUM
ap-662	92	19	end	end	NOUN
ap-662	92	20	�	�	PROPN
ap-662	92	21	:	:	PUNCT
ap-662	92	22	;	;	NOUN
ap-662	92	23	:	:	PUNCT
ap-662	92	24	(	(	PUNCT
ap-662	92	25	�	�	PROPN
ap-662	92	26	�	�	PROPN
ap-662	92	27	)	)	PUNCT
ap-662	92	28	;	;	PROPN
ap-662	92	29	(	(	PUNCT
ap-662	92	30	)	)	PUNCT
ap-662	92	31	q	q	PROPN
ap-662	93	1	a	a	DET
ap-662	93	2	r	r	NOUN
ap-662	93	3	q	q	NOUN
ap-662	93	4	qk	qk	NOUN
ap-662	93	5	k	k	PROPN
ap-662	93	6	k	k	PROPN
ap-662	93	7	kk	kk	PROPN
ap-662	93	8	k	k	PROPN
ap-662	93	9	t	t	PROPN
ap-662	93	10	k	k	PROPN
ap-662	93	11	�	�	PROPN
ap-662	93	12	�	�	PROPN
ap-662	93	13	1	1	NUM
ap-662	93	14	2	2	NUM
ap-662	93	15	q	q	NOUN
ap-662	93	16	q	q	NOUN
ap-662	93	17	rk	rk	NOUN
ap-662	93	18	k	k	PROPN
ap-662	93	19	kk	kk	PROPN
ap-662	93	20	:	:	PUNCT
ap-662	93	21	�	�	PROPN
ap-662	93	22	;	;	PUNCT
ap-662	93	23	�	�	PROPN
ap-662	93	24	end	end	VERB
ap-662	93	25	algorithms	algorithms	NOUN
ap-662	93	26	1.3	1.3	NUM
ap-662	93	27	[	[	NOUN
ap-662	93	28	classical	classical	ADJ
ap-662	93	29	gram	gram	NOUN
ap-662	93	30	–	–	PUNCT
ap-662	93	31	schmidt	schmidt	NOUN
ap-662	93	32	(	(	PUNCT
ap-662	93	33	cgs	cgs	PROPN
ap-662	93	34	)	)	PUNCT
ap-662	93	35	]	]	PUNCT
ap-662	93	36	for	for	ADP
ap-662	93	37	k	k	PROPN
ap-662	93	38	�	�	PROPN
ap-662	93	39	1	1	NUM
ap-662	93	40	2	2	NUM
ap-662	93	41	,	,	PUNCT
ap-662	93	42	,	,	PUNCT
ap-662	93	43	,	,	PUNCT
ap-662	93	44	�	�	PROPN
ap-662	93	45	n	n	CCONJ
ap-662	93	46	for	for	ADP
ap-662	93	47	i	i	PROPN
ap-662	93	48	k	k	PROPN
ap-662	93	49	�	�	PROPN
ap-662	93	50	�	�	PROPN
ap-662	93	51	1	1	NUM
ap-662	93	52	2	2	NUM
ap-662	93	53	1	1	NUM
ap-662	93	54	,	,	PUNCT
ap-662	93	55	,	,	PUNCT
ap-662	93	56	,	,	PUNCT
ap-662	93	57	�	�	PROPN
ap-662	93	58	r	r	NOUN
ap-662	93	59	q	q	NOUN
ap-662	94	1	aik	aik	NOUN
ap-662	95	1	i	i	PRON
ap-662	95	2	t	t	PROPN
ap-662	96	1	k	k	NOUN
ap-662	96	2	:	:	PUNCT
ap-662	96	3	;	;	PROPN
ap-662	96	4	�	�	PROPN
ap-662	96	5	end	end	PROPN
ap-662	96	6	�	�	PROPN
ap-662	96	7	:	:	PUNCT
ap-662	96	8	q	q	X
ap-662	96	9	a	a	DET
ap-662	96	10	r	r	NOUN
ap-662	96	11	qk	qk	NOUN
ap-662	96	12	k	k	PROPN
ap-662	96	13	ik	ik	PROPN
ap-662	96	14	ii	ii	PROPN
ap-662	96	15	k	k	PROPN
ap-662	96	16	�	�	PROPN
ap-662	96	17	�	�	PROPN
ap-662	96	18	�	�	PROPN
ap-662	96	19	�	�	PROPN
ap-662	96	20	�	�	PROPN
ap-662	96	21	1	1	NUM
ap-662	96	22	1	1	NUM
ap-662	96	23	r	r	NOUN
ap-662	96	24	q	q	NOUN
ap-662	96	25	q	q	X
ap-662	96	26	q	q	X
ap-662	96	27	q	q	X
ap-662	96	28	rkk	rkk	NOUN
ap-662	96	29	k	k	PROPN
ap-662	96	30	t	t	PROPN
ap-662	97	1	k	k	PROPN
ap-662	97	2	k	k	PROPN
ap-662	97	3	k	k	PROPN
ap-662	97	4	kk	kk	PROPN
ap-662	97	5	:	:	PUNCT
ap-662	97	6	(	(	PUNCT
ap-662	97	7	�	�	PROPN
ap-662	97	8	�	�	PROPN
ap-662	97	9	)	)	PUNCT
ap-662	97	10	;	;	NOUN
ap-662	97	11	:	:	PUNCT
ap-662	97	12	�	�	PROPN
ap-662	97	13	;	;	NOUN
ap-662	97	14	�	�	PROPN
ap-662	97	15	�	�	PROPN
ap-662	97	16	1	1	NUM
ap-662	97	17	2	2	NUM
ap-662	97	18	end	end	NOUN
ap-662	97	19	it	it	PRON
ap-662	97	20	should	should	AUX
ap-662	97	21	not	not	PART
ap-662	97	22	be	be	AUX
ap-662	97	23	forgotten	forget	VERB
ap-662	97	24	that	that	SCONJ
ap-662	97	25	the	the	DET
ap-662	97	26	variant	variant	NOUN
ap-662	97	27	known	know	VERB
ap-662	97	28	as	as	ADP
ap-662	97	29	classical	classical	ADJ
ap-662	97	30	gram	gram	NOUN
ap-662	97	31	–	–	PUNCT
ap-662	97	32	schmidt	schmidt	PROPN
ap-662	97	33	has	have	VERB
ap-662	97	34	very	very	ADV
ap-662	97	35	poor	poor	ADJ
ap-662	97	36	numerical	numerical	ADJ
ap-662	97	37	properties	property	NOUN
ap-662	97	38	in	in	ADP
ap-662	97	39	that	that	SCONJ
ap-662	97	40	there	there	PRON
ap-662	97	41	is	be	VERB
ap-662	97	42	typically	typically	ADV
ap-662	97	43	a	a	DET
ap-662	97	44	severe	severe	ADJ
ap-662	97	45	loss	loss	NOUN
ap-662	97	46	of	of	ADP
ap-662	97	47	orthogonality	orthogonality	NOUN
ap-662	97	48	among	among	ADP
ap-662	97	49	the	the	DET
ap-662	97	50	computed	computed	ADJ
ap-662	97	51	qi	qi	PROPN
ap-662	97	52	.	.	PUNCT
ap-662	98	1	a	a	DET
ap-662	98	2	rearrangement	rearrangement	NOUN
ap-662	98	3	of	of	ADP
ap-662	98	4	the	the	DET
ap-662	98	5	calculation	calculation	NOUN
ap-662	98	6	,	,	PUNCT
ap-662	98	7	known	know	VERB
ap-662	98	8	as	as	ADP
ap-662	98	9	modified	modify	VERB
ap-662	98	10	gram	gram	NOUN
ap-662	98	11	–	–	PUNCT
ap-662	98	12	schmidt	schmidt	NOUN
ap-662	98	13	,	,	PUNCT
ap-662	98	14	yields	yield	VERB
ap-662	98	15	a	a	DET
ap-662	98	16	much	much	ADV
ap-662	98	17	sounder	sounder	ADJ
ap-662	98	18	computational	computational	ADJ
ap-662	98	19	procedure	procedure	NOUN
ap-662	98	20	[	[	X
ap-662	98	21	3	3	NUM
ap-662	98	22	,	,	PUNCT
ap-662	98	23	p.	p.	NOUN
ap-662	98	24	230–232	230–232	NUM
ap-662	98	25	]	]	X
ap-662	98	26	.	.	PUNCT
ap-662	99	1	5.1	5.1	NUM
ap-662	99	2	generalized	generalized	ADJ
ap-662	99	3	orthogonalization	orthogonalization	NOUN
ap-662	99	4	algorithm	algorithm	NOUN
ap-662	99	5	(	(	PUNCT
ap-662	99	6	gso	gso	PROPN
ap-662	99	7	)	)	PUNCT
ap-662	99	8	the	the	DET
ap-662	99	9	generalized	generalized	ADJ
ap-662	99	10	orthogonalization	orthogonalization	NOUN
ap-662	99	11	algorithm	algorithm	NOUN
ap-662	99	12	(	(	PUNCT
ap-662	99	13	gso	gso	PROPN
ap-662	99	14	)	)	PUNCT
ap-662	99	15	,	,	PUNCT
ap-662	99	16	a	a	DET
ap-662	99	17	method	method	NOUN
ap-662	99	18	based	base	VERB
ap-662	99	19	on	on	ADP
ap-662	99	20	gram	gram	NOUN
ap-662	99	21	-	-	PUNCT
ap-662	99	22	schmidt	schmidt	NOUN
ap-662	99	23	orthogonalization	orthogonalization	NOUN
ap-662	99	24	,	,	PUNCT
ap-662	99	25	for	for	ADP
ap-662	99	26	numerical	numerical	ADJ
ap-662	99	27	solution	solution	NOUN
ap-662	99	28	of	of	ADP
ap-662	99	29	various	various	ADJ
ap-662	99	30	adjustment	adjustment	NOUN
ap-662	99	31	models	model	NOUN
ap-662	99	32	in	in	ADP
ap-662	99	33	geodesy	geodesy	PROPN
ap-662	99	34	was	be	AUX
ap-662	99	35	elaborated	elaborate	VERB
ap-662	99	36	by	by	ADP
ap-662	99	37	františek	františek	NOUN
ap-662	99	38	charamza	charamza	NOUN
ap-662	99	39	[	[	X
ap-662	99	40	4	4	NUM
ap-662	99	41	,	,	PUNCT
ap-662	99	42	5	5	NUM
ap-662	99	43	]	]	PUNCT
ap-662	99	44	.	.	PUNCT
ap-662	100	1	gso	gso	PROPN
ap-662	100	2	was	be	AUX
ap-662	100	3	implemented	implement	VERB
ap-662	100	4	in	in	ADP
ap-662	100	5	gnu	gnu	PROPN
ap-662	100	6	gama	gama	NOUN
ap-662	100	7	to	to	PART
ap-662	100	8	conserve	conserve	VERB
ap-662	100	9	this	this	DET
ap-662	100	10	rarely	rarely	ADV
ap-662	100	11	used	used	ADJ
ap-662	100	12	but	but	CCONJ
ap-662	100	13	interesting	interesting	ADJ
ap-662	100	14	method	method	NOUN
ap-662	100	15	,	,	PUNCT
ap-662	100	16	and	and	CCONJ
ap-662	100	17	to	to	PART
ap-662	100	18	offer	offer	VERB
ap-662	100	19	an	an	DET
ap-662	100	20	alternative	alternative	ADJ
ap-662	100	21	numerical	numerical	ADJ
ap-662	100	22	algorithm	algorithm	NOUN
ap-662	100	23	to	to	ADP
ap-662	100	24	svd	svd	PROPN
ap-662	100	25	(	(	PUNCT
ap-662	100	26	which	which	PRON
ap-662	100	27	we	we	PRON
ap-662	100	28	expected	expect	VERB
ap-662	100	29	to	to	PART
ap-662	100	30	give	give	VERB
ap-662	100	31	better	well	ADJ
ap-662	100	32	numerical	numerical	ADJ
ap-662	100	33	results	result	NOUN
ap-662	100	34	for	for	ADP
ap-662	100	35	numerically	numerically	ADV
ap-662	100	36	unstable	unstable	ADJ
ap-662	100	37	systems	system	NOUN
ap-662	100	38	)	)	PUNCT
ap-662	100	39	.	.	PUNCT
ap-662	101	1	algorithm	algorithm	PROPN
ap-662	101	2	gso	gso	PROPN
ap-662	101	3	operates	operate	VERB
ap-662	101	4	on	on	ADP
ap-662	101	5	a	a	DET
ap-662	101	6	block	block	NOUN
ap-662	101	7	matrix	matrix	NOUN
ap-662	101	8	structure	structure	NOUN
ap-662	101	9	m	m	NOUN
ap-662	101	10	m	m	VERB
ap-662	101	11	m	m	VERB
ap-662	101	12	m	m	VERB
ap-662	101	13	q	q	X
ap-662	101	14	q	q	X
ap-662	101	15	qv	qv	INTJ
ap-662	101	16	q	q	PROPN
ap-662	101	17	1	1	NUM
ap-662	101	18	2	2	NUM
ap-662	101	19	3	3	NUM
ap-662	101	20	4	4	NUM
ap-662	101	21	1	1	NUM
ap-662	101	22	2	2	NUM
ap-662	101	23	3	3	NUM
ap-662	101	24	4	4	NUM
ap-662	101	25	�	�	PROPN
ap-662	101	26	�	�	PROPN
ap-662	101	27	�	�	PROPN
ap-662	101	28	�	�	PROPN
ap-662	101	29	�	�	PROPN
ap-662	101	30	�	�	PROPN
ap-662	101	31	�	�	PROPN
ap-662	101	32	,	,	PUNCT
ap-662	101	33	(	(	PUNCT
ap-662	101	34	14	14	NUM
ap-662	101	35	)	)	PUNCT
ap-662	101	36	where	where	SCONJ
ap-662	101	37	the	the	DET
ap-662	101	38	transition	transition	NOUN
ap-662	101	39	from	from	ADP
ap-662	101	40	m	m	PROPN
ap-662	101	41	to	to	PART
ap-662	101	42	q	q	NOUN
ap-662	101	43	is	be	AUX
ap-662	101	44	defined	define	VERB
ap-662	101	45	by	by	ADP
ap-662	101	46	the	the	DET
ap-662	101	47	equations	equation	NOUN
ap-662	101	48	�	�	PROPN
ap-662	101	49	�	�	PROPN
ap-662	101	50	q	q	PROPN
ap-662	101	51	q1	q1	PROPN
ap-662	101	52	1	1	NUM
ap-662	101	53	1	1	NUM
ap-662	101	54	,	,	PUNCT
ap-662	101	55	(	(	PUNCT
ap-662	101	56	15	15	NUM
ap-662	101	57	)	)	PUNCT
ap-662	101	58	m	m	VERB
ap-662	101	59	q	q	PROPN
ap-662	101	60	r1	r1	PROPN
ap-662	101	61	1	1	NUM
ap-662	101	62	�	�	PROPN
ap-662	101	63	,	,	PUNCT
ap-662	101	64	(	(	PUNCT
ap-662	101	65	16	16	NUM
ap-662	101	66	)	)	PUNCT
ap-662	101	67	q	q	PUNCT
ap-662	102	1	m	m	PROPN
ap-662	102	2	r1	r1	NOUN
ap-662	102	3	1	1	NUM
ap-662	102	4	1	1	NUM
ap-662	102	5	�	�	PROPN
ap-662	102	6	�	�	PROPN
ap-662	102	7	,	,	PUNCT
ap-662	102	8	q	q	PROPN
ap-662	102	9	m	m	VERB
ap-662	102	10	q	q	X
ap-662	102	11	q	q	PROPN
ap-662	102	12	m2	m2	PROPN
ap-662	102	13	2	2	NUM
ap-662	102	14	1	1	NUM
ap-662	102	15	1	1	NUM
ap-662	102	16	2	2	NUM
ap-662	102	17	�	�	PROPN
ap-662	102	18	�	�	PROPN
ap-662	102	19	�	�	PROPN
ap-662	102	20	,	,	PUNCT
ap-662	102	21	(	(	PUNCT
ap-662	102	22	17	17	NUM
ap-662	102	23	)	)	PUNCT
ap-662	102	24	q	q	NOUN
ap-662	102	25	m	m	PROPN
ap-662	102	26	r3	r3	PROPN
ap-662	102	27	3	3	NUM
ap-662	102	28	1	1	NUM
ap-662	102	29	�	�	PROPN
ap-662	102	30	�	�	PROPN
ap-662	102	31	,	,	PUNCT
ap-662	102	32	q	q	PROPN
ap-662	102	33	m	m	ADJ
ap-662	102	34	q	q	X
ap-662	102	35	q	q	PUNCT
ap-662	102	36	m4	m4	PROPN
ap-662	102	37	4	4	NUM
ap-662	102	38	3	3	NUM
ap-662	102	39	1	1	NUM
ap-662	102	40	2	2	NUM
ap-662	102	41	�	�	PROPN
ap-662	102	42	�	�	PROPN
ap-662	102	43	�	�	PROPN
ap-662	102	44	,	,	PUNCT
ap-662	102	45	(	(	PUNCT
ap-662	102	46	18	18	NUM
ap-662	102	47	)	)	PUNCT
ap-662	102	48	and	and	CCONJ
ap-662	102	49	r	r	NOUN
ap-662	102	50	is	be	AUX
ap-662	102	51	the	the	DET
ap-662	102	52	upper	upper	ADJ
ap-662	102	53	triangular	triangular	NOUN
ap-662	102	54	matrix	matrix	NOUN
ap-662	102	55	.	.	PUNCT
ap-662	103	1	algorithm	algorithm	NOUN
ap-662	103	2	mgs	mgs	PROPN
ap-662	103	3	is	be	AUX
ap-662	103	4	applied	apply	VERB
ap-662	103	5	to	to	ADP
ap-662	103	6	block	block	NOUN
ap-662	103	7	matrix	matrix	NOUN
ap-662	103	8	m	m	VERB
ap-662	103	9	so	so	SCONJ
ap-662	103	10	that	that	SCONJ
ap-662	103	11	the	the	DET
ap-662	103	12	column	column	NOUN
ap-662	103	13	dot	dot	NOUN
ap-662	103	14	products	product	NOUN
ap-662	103	15	are	be	AUX
ap-662	103	16	computed	compute	VERB
ap-662	103	17	only	only	ADV
ap-662	103	18	for	for	ADP
ap-662	103	19	submatrices	submatrice	NOUN
ap-662	103	20	(	(	PUNCT
ap-662	103	21	m1	m1	PROPN
ap-662	103	22	,	,	PUNCT
ap-662	103	23	m2	m2	PROPN
ap-662	103	24	)	)	PUNCT
ap-662	103	25	,	,	PUNCT
ap-662	103	26	the	the	DET
ap-662	103	27	projections	projection	NOUN
ap-662	103	28	rkiqk	rkiqk	NOUN
ap-662	103	29	are	be	AUX
ap-662	103	30	computed	compute	VERB
ap-662	103	31	for	for	ADP
ap-662	103	32	full	full	ADJ
ap-662	103	33	columns	column	NOUN
ap-662	103	34	of	of	ADP
ap-662	103	35	m	m	PROPN
ap-662	103	36	and	and	CCONJ
ap-662	103	37	the	the	DET
ap-662	103	38	whole	whole	ADJ
ap-662	103	39	process	process	NOUN
ap-662	103	40	is	be	AUX
ap-662	103	41	terminated	terminate	VERB
ap-662	103	42	after	after	ADP
ap-662	103	43	of	of	ADP
ap-662	103	44	all	all	DET
ap-662	103	45	columns	column	NOUN
ap-662	103	46	of	of	ADP
ap-662	103	47	submatrix	submatrix	NOUN
ap-662	103	48	(	(	PUNCT
ap-662	103	49	m1	m1	NOUN
ap-662	103	50	,	,	PUNCT
ap-662	103	51	m3	m3	PROPN
ap-662	103	52	�	�	PROPN
ap-662	103	53	)	)	PUNCT
ap-662	103	54	have	have	AUX
ap-662	103	55	been	be	AUX
ap-662	103	56	processed	process	VERB
ap-662	103	57	.	.	PUNCT
ap-662	104	1	this	this	DET
ap-662	104	2	step	step	NOUN
ap-662	104	3	is	be	AUX
ap-662	104	4	called	call	VERB
ap-662	104	5	the	the	DET
ap-662	104	6	first	first	ADJ
ap-662	104	7	orthogonalization	orthogonalization	NOUN
ap-662	104	8	in	in	ADP
ap-662	104	9	algorithm	algorithm	PROPN
ap-662	104	10	gso	gso	PROPN
ap-662	104	11	.	.	PUNCT
ap-662	105	1	let	let	VERB
ap-662	105	2	us	we	PRON
ap-662	105	3	take	take	VERB
ap-662	105	4	as	as	ADP
ap-662	105	5	an	an	DET
ap-662	105	6	example	example	NOUN
ap-662	105	7	the	the	DET
ap-662	105	8	linear	linear	ADJ
ap-662	105	9	system	system	NOUN
ap-662	105	10	of	of	ADP
ap-662	105	11	project	project	NOUN
ap-662	105	12	equations	equation	NOUN
ap-662	105	13	(	(	PUNCT
ap-662	105	14	2	2	X
ap-662	105	15	)	)	PUNCT
ap-662	105	16	ax	ax	NOUN
ap-662	105	17	l	l	PROPN
ap-662	105	18	v	v	PROPN
ap-662	105	19	�	�	PROPN
ap-662	105	20	�	�	PROPN
ap-662	105	21	and	and	CCONJ
ap-662	105	22	apply	apply	VERB
ap-662	105	23	algorithm	algorithm	NOUN
ap-662	105	24	gso	gso	PROPN
ap-662	105	25	to	to	ADP
ap-662	105	26	the	the	DET
ap-662	105	27	block	block	NOUN
ap-662	105	28	matrix	matrix	NOUN
ap-662	105	29	a	a	DET
ap-662	105	30	l	l	NOUN
ap-662	105	31	q	q	X
ap-662	105	32	v	v	NOUN
ap-662	105	33	r	r	NOUN
ap-662	105	34	x	x	SYM
ap-662	105	35	�	�	PROPN
ap-662	105	36	�	�	PROPN
ap-662	105	37	�	�	PROPN
ap-662	105	38	�	�	PROPN
ap-662	105	39	�	�	PROPN
ap-662	105	40	�	�	PROPN
ap-662	105	41	�	�	PROPN
ap-662	105	42	�	�	PROPN
ap-662	105	43	�	�	PROPN
ap-662	105	44	1	1	NUM
ap-662	105	45	0	0	NUM
ap-662	105	46	1	1	NUM
ap-662	105	47	.	.	PUNCT
ap-662	106	1	the	the	DET
ap-662	106	2	result	result	NOUN
ap-662	106	3	is	be	AUX
ap-662	106	4	directly	directly	ADV
ap-662	106	5	the	the	DET
ap-662	106	6	vector	vector	NOUN
ap-662	106	7	of	of	ADP
ap-662	106	8	unknown	unknown	ADJ
ap-662	106	9	parameters	parameter	NOUN
ap-662	106	10	x	x	PUNCT
ap-662	106	11	and	and	CCONJ
ap-662	106	12	the	the	DET
ap-662	106	13	vector	vector	NOUN
ap-662	106	14	of	of	ADP
ap-662	106	15	residuals	residual	NOUN
ap-662	106	16	v.	v.	ADP
ap-662	106	17	the	the	DET
ap-662	106	18	cofactors	cofactor	NOUN
ap-662	106	19	(	(	PUNCT
ap-662	106	20	weight	weight	NOUN
ap-662	106	21	coefficients	coefficient	NOUN
ap-662	106	22	)	)	PUNCT
ap-662	106	23	of	of	ADP
ap-662	106	24	the	the	DET
ap-662	106	25	adjusted	adjusted	ADJ
ap-662	106	26	parameters	parameter	NOUN
ap-662	106	27	qx	qx	INTJ
ap-662	106	28	xi	xi	X
ap-662	106	29	j	j	PROPN
ap-662	106	30	are	be	AUX
ap-662	106	31	available	available	ADJ
ap-662	106	32	as	as	ADP
ap-662	106	33	the	the	DET
ap-662	106	34	dot	dot	NOUN
ap-662	106	35	products	product	NOUN
ap-662	106	36	of	of	ADP
ap-662	106	37	rows	row	NOUN
ap-662	106	38	i	i	PRON
ap-662	106	39	and	and	CCONJ
ap-662	106	40	j	j	PROPN
ap-662	106	41	of	of	ADP
ap-662	106	42	submatrix	submatrix	NOUN
ap-662	106	43	r	r	NOUN
ap-662	106	44	�	�	PROPN
ap-662	106	45	1	1	NUM
ap-662	106	46	,	,	PUNCT
ap-662	106	47	the	the	DET
ap-662	106	48	cofactors	cofactor	NOUN
ap-662	106	49	of	of	ADP
ap-662	106	50	the	the	DET
ap-662	106	51	adjusted	adjust	VERB
ap-662	106	52	observations	observation	NOUN
ap-662	106	53	ql	ql	INTJ
ap-662	107	1	lm	lm	X
ap-662	107	2	n	n	NOUN
ap-662	107	3	are	be	AUX
ap-662	107	4	computed	compute	VERB
ap-662	107	5	as	as	ADP
ap-662	107	6	the	the	DET
ap-662	107	7	dot	dot	NOUN
ap-662	107	8	products	product	NOUN
ap-662	107	9	of	of	ADP
ap-662	107	10	rows	row	NOUN
ap-662	107	11	m	m	PROPN
ap-662	107	12	and	and	CCONJ
ap-662	107	13	n	n	PROPN
ap-662	107	14	of	of	ADP
ap-662	107	15	submatrix	submatrix	NOUN
ap-662	107	16	q	q	NOUN
ap-662	107	17	and	and	CCONJ
ap-662	107	18	the	the	DET
ap-662	107	19	mixed	mixed	ADJ
ap-662	107	20	cofactors	cofactor	NOUN
ap-662	107	21	qx	qx	PROPN
ap-662	107	22	li	li	NOUN
ap-662	107	23	n	n	X
ap-662	107	24	similarly	similarly	ADV
ap-662	107	25	as	as	ADP
ap-662	107	26	the	the	DET
ap-662	107	27	dot	dot	NOUN
ap-662	107	28	products	product	NOUN
ap-662	107	29	of	of	ADP
ap-662	107	30	the	the	DET
ap-662	107	31	i	i	PROPN
ap-662	107	32	-	-	PUNCT
ap-662	107	33	th	th	X
ap-662	107	34	row	row	NOUN
ap-662	107	35	of	of	ADP
ap-662	107	36	r	r	NOUN
ap-662	107	37	�	�	PROPN
ap-662	107	38	1	1	NUM
ap-662	107	39	and	and	CCONJ
ap-662	107	40	the	the	DET
ap-662	107	41	n	n	CCONJ
ap-662	107	42	-	-	PUNCT
ap-662	107	43	th	th	VERB
ap-662	107	44	row	row	NOUN
ap-662	107	45	of	of	ADP
ap-662	107	46	matrix	matrix	NOUN
ap-662	107	47	q.	q.	NOUN
ap-662	107	48	5.2	5.2	NUM
ap-662	107	49	algorithm	algorithm	NOUN
ap-662	107	50	gso	gso	PROPN
ap-662	107	51	and	and	CCONJ
ap-662	107	52	singular	singular	PROPN
ap-662	107	53	systems	system	NOUN
ap-662	107	54	let	let	VERB
ap-662	107	55	us	we	PRON
ap-662	107	56	suppose	suppose	VERB
ap-662	107	57	now	now	ADV
ap-662	107	58	that	that	SCONJ
ap-662	107	59	project	project	NOUN
ap-662	107	60	equations	equation	NOUN
ap-662	107	61	matrix	matrix	VERB
ap-662	107	62	a	a	DET
ap-662	107	63	contains	contain	VERB
ap-662	107	64	r	r	NOUN
ap-662	107	65	linearly	linearly	ADV
ap-662	107	66	independent	independent	ADJ
ap-662	107	67	columns	column	NOUN
ap-662	107	68	and	and	CCONJ
ap-662	107	69	the	the	DET
ap-662	107	70	remaining	remain	VERB
ap-662	107	71	d	d	NOUN
ap-662	107	72	linearly	linearly	ADV
ap-662	107	73	dependent	dependent	ADJ
ap-662	107	74	columns	column	NOUN
ap-662	107	75	.	.	PUNCT
ap-662	108	1	without	without	ADP
ap-662	108	2	loss	loss	NOUN
ap-662	108	3	of	of	ADP
ap-662	108	4	generality	generality	NOUN
ap-662	108	5	we	we	PRON
ap-662	108	6	can	can	AUX
ap-662	108	7	assume	assume	VERB
ap-662	108	8	that	that	SCONJ
ap-662	108	9	the	the	DET
ap-662	108	10	linearly	linearly	ADV
ap-662	108	11	dependent	dependent	ADJ
ap-662	108	12	columns	column	NOUN
ap-662	108	13	are	be	AUX
ap-662	108	14	located	locate	VERB
ap-662	108	15	in	in	ADP
ap-662	108	16	the	the	DET
ap-662	108	17	right	right	ADJ
ap-662	108	18	part	part	NOUN
ap-662	108	19	of	of	ADP
ap-662	108	20	matrix	matrix	NOUN
ap-662	108	21	a.	a.	NOUN
ap-662	108	22	we	we	PRON
ap-662	108	23	denote	denote	VERB
ap-662	108	24	linearly	linearly	ADV
ap-662	108	25	independent	independent	ADJ
ap-662	108	26	columns	column	NOUN
ap-662	108	27	a1	a1	NOUN
ap-662	108	28	,	,	PUNCT
ap-662	108	29	linearly	linearly	ADV
ap-662	108	30	dependent	dependent	ADJ
ap-662	108	31	columns	column	NOUN
ap-662	108	32	a2	a2	PROPN
ap-662	108	33	and	and	CCONJ
ap-662	108	34	the	the	DET
ap-662	108	35	matrix	matrix	NOUN
ap-662	108	36	of	of	ADP
ap-662	108	37	their	their	PRON
ap-662	108	38	linear	linear	ADJ
ap-662	108	39	combinations	combination	NOUN
ap-662	108	40	�	�	PROPN
ap-662	109	1	a	a	DET
ap-662	109	2	a	a	DET
ap-662	109	3	a	a	DET
ap-662	109	4	a	a	DET
ap-662	109	5	a	a	NOUN
ap-662	109	6	x	x	SYM
ap-662	109	7	x	x	SYM
ap-662	109	8	x	x	SYM
ap-662	109	9	�	�	PROPN
ap-662	109	10	�	�	PROPN
ap-662	109	11	�	�	PROPN
ap-662	109	12	�	�	PROPN
ap-662	109	13	�	�	PROPN
ap-662	109	14	�	�	PROPN
ap-662	109	15	(	(	PUNCT
ap-662	109	16	)	)	PUNCT
ap-662	109	17	,	,	PUNCT
ap-662	109	18	1	1	NUM
ap-662	109	19	2	2	NUM
ap-662	109	20	2	2	NUM
ap-662	109	21	1	1	NUM
ap-662	109	22	1	1	NUM
ap-662	109	23	2	2	NUM
ap-662	109	24	,	,	PUNCT
ap-662	109	25	,	,	PUNCT
ap-662	109	26	�	�	PROPN
ap-662	109	27	.	.	PUNCT
ap-662	110	1	(	(	PUNCT
ap-662	110	2	19	19	NUM
ap-662	110	3	)	)	PUNCT
ap-662	110	4	now	now	ADV
ap-662	110	5	we	we	PRON
ap-662	110	6	can	can	AUX
ap-662	110	7	rewrite	rewrite	VERB
ap-662	110	8	the	the	DET
ap-662	110	9	project	project	NOUN
ap-662	110	10	equations	equation	NOUN
ap-662	110	11	as	as	ADP
ap-662	110	12	v	v	ADP
ap-662	110	13	a	a	PRON
ap-662	110	14	x	x	SYM
ap-662	110	15	a	a	DET
ap-662	110	16	x	x	X
ap-662	110	17	l	l	NOUN
ap-662	110	18	a	a	X
ap-662	110	19	x	x	X
ap-662	110	20	x	x	X
ap-662	110	21	l	l	NOUN
ap-662	110	22	a	a	DET
ap-662	110	23	x	x	X
ap-662	110	24	l	l	X
ap-662	110	25	�	�	PROPN
ap-662	110	26	�	�	PROPN
ap-662	110	27	�	�	PROPN
ap-662	110	28	�	�	PROPN
ap-662	110	29	�	�	PROPN
ap-662	110	30	�	�	PROPN
ap-662	110	31	�	�	PROPN
ap-662	110	32	�	�	PROPN
ap-662	110	33	1	1	NUM
ap-662	110	34	1	1	NUM
ap-662	110	35	2	2	NUM
ap-662	110	36	2	2	NUM
ap-662	110	37	1	1	NUM
ap-662	110	38	1	1	NUM
ap-662	110	39	2	2	NUM
ap-662	110	40	1	1	NUM
ap-662	110	41	(	(	PUNCT
ap-662	110	42	)	)	PUNCT
ap-662	111	1	~	~	PROPN
ap-662	111	2	�	�	X
ap-662	111	3	.	.	PUNCT
ap-662	112	1	(	(	PUNCT
ap-662	112	2	20	20	NUM
ap-662	112	3	)	)	PUNCT
ap-662	112	4	as	as	SCONJ
ap-662	112	5	matrix	matrix	NOUN
ap-662	112	6	a1	a1	NOUN
ap-662	112	7	does	do	AUX
ap-662	112	8	not	not	PART
ap-662	112	9	contain	contain	VERB
ap-662	112	10	linearly	linearly	ADV
ap-662	112	11	dependent	dependent	ADJ
ap-662	112	12	columns	column	NOUN
ap-662	112	13	,	,	PUNCT
ap-662	112	14	a	a	DET
ap-662	112	15	unique	unique	ADJ
ap-662	112	16	solution	solution	NOUN
ap-662	112	17	~x	~x	PUNCT
ap-662	112	18	of	of	ADP
ap-662	112	19	(	(	PUNCT
ap-662	112	20	20	20	NUM
ap-662	112	21	)	)	PUNCT
ap-662	112	22	exists	exist	VERB
ap-662	112	23	that	that	PRON
ap-662	112	24	minimizes	minimize	VERB
ap-662	112	25	the	the	DET
ap-662	112	26	euclidean	euclidean	ADJ
ap-662	112	27	norm	norm	NOUN
ap-662	112	28	of	of	ADP
ap-662	112	29	v.	v.	ADV
ap-662	112	30	if	if	SCONJ
ap-662	112	31	we	we	PRON
ap-662	112	32	know	know	VERB
ap-662	112	33	matrix	matrix	NOUN
ap-662	112	34	�	�	PROPN
ap-662	112	35	and	and	CCONJ
ap-662	112	36	vector	vector	NOUN
ap-662	112	37	~x	~x	PUNCT
ap-662	112	38	then	then	ADV
ap-662	112	39	any	any	DET
ap-662	112	40	solution	solution	NOUN
ap-662	112	41	x	x	PUNCT
ap-662	112	42	of	of	ADP
ap-662	112	43	~	~	PUNCT
ap-662	112	44	(	(	PUNCT
ap-662	112	45	,	,	PUNCT
ap-662	112	46	)	)	PUNCT
ap-662	112	47	x	x	SYM
ap-662	112	48	x	x	PUNCT
ap-662	112	49	x	x	SYM
ap-662	112	50	x	x	SYM
ap-662	112	51	�	�	PROPN
ap-662	112	52	�	�	PROPN
ap-662	112	53	�	�	PROPN
ap-662	112	54	1	1	NUM
ap-662	112	55	2	2	NUM
ap-662	112	56	�	�	PROPN
ap-662	112	57	�	�	PROPN
ap-662	112	58	1	1	NUM
ap-662	112	59	(	(	PUNCT
ap-662	112	60	21	21	NUM
ap-662	112	61	)	)	PUNCT
ap-662	112	62	is	be	AUX
ap-662	112	63	at	at	ADP
ap-662	112	64	the	the	DET
ap-662	112	65	same	same	ADJ
ap-662	112	66	time	time	NOUN
ap-662	112	67	the	the	DET
ap-662	112	68	least	least	ADJ
ap-662	112	69	square	square	ADJ
ap-662	112	70	solution	solution	NOUN
ap-662	112	71	of	of	ADP
ap-662	112	72	(	(	PUNCT
ap-662	112	73	20	20	NUM
ap-662	112	74	)	)	PUNCT
ap-662	112	75	with	with	ADP
ap-662	112	76	the	the	DET
ap-662	112	77	same	same	ADJ
ap-662	112	78	vector	vector	NOUN
ap-662	112	79	of	of	ADP
ap-662	112	80	residuals	residual	NOUN
ap-662	112	81	v.	v.	ADP
ap-662	112	82	if	if	SCONJ
ap-662	112	83	we	we	PRON
ap-662	112	84	apply	apply	VERB
ap-662	112	85	algorithm	algorithm	NOUN
ap-662	112	86	gso	gso	PROPN
ap-662	112	87	to	to	ADP
ap-662	112	88	the	the	DET
ap-662	112	89	matrix	matrix	NOUN
ap-662	112	90	m	m	VERB
ap-662	112	91	m	m	VERB
ap-662	112	92	m	m	VERB
ap-662	112	93	m	m	VERB
ap-662	112	94	m	m	VERB
ap-662	112	95	a	a	PRON
ap-662	112	96	a	a	DET
ap-662	112	97	l	l	NOUN
ap-662	113	1	i	i	NOUN
ap-662	113	2	1	1	NUM
ap-662	113	3	i	i	NOUN
ap-662	113	4	2	2	NUM
ap-662	113	5	i	i	NOUN
ap-662	113	6	3	3	NUM
ap-662	113	7	i	i	NOUN
ap-662	113	8	4	4	NUM
ap-662	113	9	i	i	PRON
ap-662	113	10	�	�	PROPN
ap-662	113	11	�	�	PROPN
ap-662	113	12	�	�	PROPN
ap-662	113	13	�	�	PROPN
ap-662	113	14	�	�	PROPN
ap-662	113	15	�	�	PROPN
ap-662	113	16	�	�	PROPN
ap-662	113	17	�	�	PROPN
ap-662	113	18	�	�	PROPN
ap-662	113	19	1	1	NUM
ap-662	113	20	2	2	NUM
ap-662	113	21	1	1	NUM
ap-662	113	22	0	0	NUM
ap-662	113	23	0	0	NUM
ap-662	113	24	0	0	NUM
ap-662	113	25	1	1	NUM
ap-662	113	26	0	0	NUM
ap-662	113	27	(	(	PUNCT
ap-662	113	28	22	22	NUM
ap-662	113	29	)	)	PUNCT
ap-662	113	30	we	we	PRON
ap-662	113	31	receive	receive	VERB
ap-662	113	32	a	a	DET
ap-662	113	33	block	block	NOUN
ap-662	113	34	matrix	matrix	NOUN
ap-662	113	35	q	q	NOUN
ap-662	113	36	q	q	NOUN
ap-662	113	37	v	v	NOUN
ap-662	113	38	r	r	NOUN
ap-662	113	39	xi	xi	PART
ap-662	113	40	�	�	PROPN
ap-662	113	41	�	�	PROPN
ap-662	113	42	�	�	PROPN
ap-662	113	43	�	�	PROPN
ap-662	113	44	�	�	PROPN
ap-662	113	45	�	�	PROPN
ap-662	113	46	0	0	NUM
ap-662	113	47	0	0	NUM
ap-662	113	48	1	1	NUM
ap-662	113	49	0	0	NUM
ap-662	113	50	1	1	NUM
ap-662	113	51	1	1	NUM
ap-662	113	52	�	�	NOUN
ap-662	113	53	~	~	PUNCT
ap-662	113	54	.	.	PUNCT
ap-662	114	1	(	(	PUNCT
ap-662	114	2	23	23	NUM
ap-662	114	3	)	)	PUNCT
ap-662	114	4	©	©	PROPN
ap-662	114	5	czech	czech	PROPN
ap-662	114	6	technical	technical	PROPN
ap-662	114	7	university	university	PROPN
ap-662	114	8	publishing	publishing	NOUN
ap-662	114	9	house	house	NOUN
ap-662	114	10	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-662	114	11	15	15	NUM
ap-662	114	12	czech	czech	PROPN
ap-662	114	13	technical	technical	PROPN
ap-662	114	14	university	university	PROPN
ap-662	114	15	in	in	ADP
ap-662	114	16	prague	prague	PROPN
ap-662	114	17	acta	acta	PROPN
ap-662	114	18	polytechnica	polytechnica	PROPN
ap-662	114	19	vol	vol	NOUN
ap-662	114	20	.	.	PROPN
ap-662	115	1	45	45	NUM
ap-662	115	2	no	no	NOUN
ap-662	115	3	.	.	PUNCT
ap-662	116	1	1/2005	1/2005	NUM
ap-662	116	2	in	in	ADP
ap-662	116	3	the	the	DET
ap-662	116	4	case	case	NOUN
ap-662	116	5	of	of	ADP
ap-662	116	6	singular	singular	ADJ
ap-662	116	7	systems	system	NOUN
ap-662	116	8	in	in	ADP
ap-662	116	9	gso	gso	PROPN
ap-662	116	10	we	we	PRON
ap-662	116	11	have	have	VERB
ap-662	116	12	the	the	DET
ap-662	116	13	first	first	ADJ
ap-662	116	14	orthogonalization	orthogonalization	NOUN
ap-662	116	15	,	,	PUNCT
ap-662	116	16	which	which	PRON
ap-662	116	17	defines	define	VERB
ap-662	116	18	a	a	DET
ap-662	116	19	particular	particular	ADJ
ap-662	116	20	solution	solution	NOUN
ap-662	116	21	in	in	ADP
ap-662	116	22	which	which	PRON
ap-662	116	23	the	the	DET
ap-662	116	24	unknown	unknown	ADJ
ap-662	116	25	parameters	parameter	NOUN
ap-662	116	26	corresponding	correspond	VERB
ap-662	116	27	to	to	ADP
ap-662	116	28	the	the	DET
ap-662	116	29	linearly	linearly	ADV
ap-662	116	30	dependent	dependent	ADJ
ap-662	116	31	columns	column	NOUN
ap-662	116	32	of	of	ADP
ap-662	116	33	a	a	PRON
ap-662	116	34	are	be	AUX
ap-662	116	35	set	set	VERB
ap-662	116	36	to	to	ADP
ap-662	116	37	zero	zero	NUM
ap-662	116	38	.	.	PUNCT
ap-662	117	1	from	from	ADP
ap-662	117	2	cgs	cgs	NOUN
ap-662	117	3	it	it	PRON
ap-662	117	4	emerges	emerge	VERB
ap-662	117	5	directly	directly	ADV
ap-662	117	6	that	that	DET
ap-662	117	7	matrix	matrix	NOUN
ap-662	117	8	�	�	PROPN
ap-662	117	9	is	be	AUX
ap-662	117	10	the	the	DET
ap-662	117	11	matrix	matrix	NOUN
ap-662	117	12	of	of	ADP
ap-662	117	13	the	the	DET
ap-662	117	14	linear	linear	ADJ
ap-662	117	15	combinations	combination	NOUN
ap-662	117	16	from	from	ADP
ap-662	117	17	(	(	PUNCT
ap-662	117	18	19	19	NUM
ap-662	117	19	)	)	PUNCT
ap-662	117	20	.	.	PUNCT
ap-662	118	1	the	the	DET
ap-662	118	2	cofactors	cofactor	NOUN
ap-662	118	3	are	be	AUX
ap-662	118	4	computed	compute	VERB
ap-662	118	5	the	the	DET
ap-662	118	6	same	same	ADJ
ap-662	118	7	way	way	NOUN
ap-662	118	8	as	as	ADP
ap-662	118	9	in	in	ADP
ap-662	118	10	the	the	DET
ap-662	118	11	case	case	NOUN
ap-662	118	12	of	of	ADP
ap-662	118	13	regular	regular	ADJ
ap-662	118	14	systems	system	NOUN
ap-662	118	15	.	.	PUNCT
ap-662	119	1	when	when	SCONJ
ap-662	119	2	computing	compute	VERB
ap-662	119	3	gso	gso	PROPN
ap-662	119	4	numerically	numerically	ADV
ap-662	119	5	we	we	PRON
ap-662	119	6	naturally	naturally	ADV
ap-662	119	7	do	do	AUX
ap-662	119	8	not	not	PART
ap-662	119	9	obtain	obtain	VERB
ap-662	119	10	exactly	exactly	ADV
ap-662	119	11	zero	zero	NUM
ap-662	119	12	vectors	vector	NOUN
ap-662	119	13	on	on	ADP
ap-662	119	14	the	the	DET
ap-662	119	15	positions	position	NOUN
ap-662	119	16	of	of	ADP
ap-662	119	17	the	the	DET
ap-662	119	18	(	(	PUNCT
ap-662	119	19	almost	almost	ADV
ap-662	119	20	)	)	PUNCT
ap-662	119	21	linearly	linearly	ADV
ap-662	119	22	dependent	dependent	ADJ
ap-662	119	23	columns	column	NOUN
ap-662	119	24	.	.	PUNCT
ap-662	120	1	we	we	PRON
ap-662	120	2	declare	declare	VERB
ap-662	120	3	to	to	PART
ap-662	120	4	be	be	AUX
ap-662	120	5	linearly	linearly	ADV
ap-662	120	6	dependent	dependent	ADJ
ap-662	120	7	those	those	DET
ap-662	120	8	columns	column	NOUN
ap-662	120	9	of	of	ADP
ap-662	120	10	a	a	DET
ap-662	120	11	whose	whose	DET
ap-662	120	12	norms	norm	NOUN
ap-662	120	13	drop	drop	VERB
ap-662	120	14	below	below	ADP
ap-662	120	15	a	a	DET
ap-662	120	16	given	give	VERB
ap-662	120	17	tolerance	tolerance	NOUN
ap-662	120	18	.	.	PUNCT
ap-662	121	1	during	during	ADP
ap-662	121	2	the	the	DET
ap-662	121	3	first	first	ADJ
ap-662	121	4	orthogonalization	orthogonalization	NOUN
ap-662	121	5	we	we	PRON
ap-662	121	6	set	set	VERB
ap-662	121	7	to	to	ADP
ap-662	121	8	zero	zero	NUM
ap-662	121	9	corresponding	corresponding	ADJ
ap-662	121	10	subvectors	subvector	NOUN
ap-662	121	11	in	in	ADP
ap-662	121	12	the	the	DET
ap-662	121	13	area	area	NOUN
ap-662	121	14	of	of	ADP
ap-662	121	15	a2	a2	PROPN
ap-662	121	16	.	.	PUNCT
ap-662	122	1	these	these	DET
ap-662	122	2	values	value	NOUN
ap-662	122	3	can	can	AUX
ap-662	122	4	be	be	AUX
ap-662	122	5	considered	consider	VERB
ap-662	122	6	as	as	ADP
ap-662	122	7	random	random	ADJ
ap-662	122	8	noise	noise	NOUN
ap-662	122	9	that	that	PRON
ap-662	122	10	adds	add	VERB
ap-662	122	11	no	no	DET
ap-662	122	12	information	information	NOUN
ap-662	122	13	to	to	ADP
ap-662	122	14	the	the	DET
ap-662	122	15	whole	whole	ADJ
ap-662	122	16	solution	solution	NOUN
ap-662	122	17	.	.	PUNCT
ap-662	123	1	the	the	DET
ap-662	123	2	result	result	NOUN
ap-662	123	3	of	of	ADP
ap-662	123	4	the	the	DET
ap-662	123	5	first	first	ADJ
ap-662	123	6	orthogonalization	orthogonalization	NOUN
ap-662	123	7	are	be	AUX
ap-662	123	8	first	first	ADV
ap-662	123	9	of	of	ADP
ap-662	123	10	all	all	DET
ap-662	123	11	the	the	DET
ap-662	123	12	vector	vector	NOUN
ap-662	123	13	of	of	ADP
ap-662	123	14	the	the	DET
ap-662	123	15	residuals	residual	NOUN
ap-662	123	16	and	and	CCONJ
ap-662	123	17	cofactors	cofactor	NOUN
ap-662	123	18	of	of	ADP
ap-662	123	19	the	the	DET
ap-662	123	20	adjusted	adjust	VERB
ap-662	123	21	observations	observation	NOUN
ap-662	123	22	.	.	PUNCT
ap-662	124	1	it	it	PRON
ap-662	124	2	now	now	ADV
ap-662	124	3	remains	remain	VERB
ap-662	124	4	to	to	PART
ap-662	124	5	determine	determine	VERB
ap-662	124	6	the	the	DET
ap-662	124	7	vector	vector	NOUN
ap-662	124	8	of	of	ADP
ap-662	124	9	the	the	DET
ap-662	124	10	unknown	unknown	ADJ
ap-662	124	11	parameters	parameter	NOUN
ap-662	124	12	x	x	PUNCT
ap-662	124	13	that	that	SCONJ
ap-662	124	14	satisfies	satisfy	VERB
ap-662	124	15	condition	condition	NOUN
ap-662	124	16	(	(	PUNCT
ap-662	124	17	9	9	NUM
ap-662	124	18	)	)	PUNCT
ap-662	124	19	and	and	CCONJ
ap-662	124	20	its	its	PRON
ap-662	124	21	cofactors	cofactor	NOUN
ap-662	124	22	(	(	PUNCT
ap-662	124	23	weight	weight	NOUN
ap-662	124	24	coefficients	coefficient	NOUN
ap-662	124	25	)	)	PUNCT
ap-662	124	26	.	.	PUNCT
ap-662	125	1	this	this	DET
ap-662	125	2	step	step	NOUN
ap-662	125	3	of	of	ADP
ap-662	125	4	gso	gso	PROPN
ap-662	125	5	is	be	AUX
ap-662	125	6	called	call	VERB
ap-662	125	7	second	second	ADJ
ap-662	125	8	orthogonalization	orthogonalization	NOUN
ap-662	125	9	.	.	PUNCT
ap-662	126	1	by	by	ADP
ap-662	126	2	solving	solve	VERB
ap-662	126	3	the	the	DET
ap-662	126	4	system	system	NOUN
ap-662	126	5	of	of	ADP
ap-662	126	6	linear	linear	PROPN
ap-662	126	7	equations	equation	NOUN
ap-662	126	8	�	�	PROPN
ap-662	126	9	�	�	PROPN
ap-662	126	10	�	�	PROPN
ap-662	126	11	�	�	PROPN
ap-662	126	12	�	�	PROPN
ap-662	126	13	�	�	PROPN
ap-662	126	14	�	�	PROPN
ap-662	126	15	�	�	PROPN
ap-662	126	16	�	�	PROPN
ap-662	126	17	1	1	NUM
ap-662	126	18	0	0	NUM
ap-662	126	19	x	x	SYM
ap-662	126	20	x	x	SYM
ap-662	126	21	2	2	X
ap-662	126	22	~	~	PUNCT
ap-662	126	23	(	(	PUNCT
ap-662	126	24	24	24	NUM
ap-662	126	25	)	)	PUNCT
ap-662	126	26	we	we	PRON
ap-662	126	27	get	get	VERB
ap-662	126	28	,	,	PUNCT
ap-662	126	29	according	accord	VERB
ap-662	126	30	to	to	ADP
ap-662	126	31	(	(	PUNCT
ap-662	126	32	21	21	NUM
ap-662	126	33	)	)	PUNCT
ap-662	126	34	,	,	PUNCT
ap-662	126	35	a	a	DET
ap-662	126	36	vector	vector	NOUN
ap-662	126	37	x	x	PUNCT
ap-662	126	38	with	with	ADP
ap-662	126	39	the	the	DET
ap-662	126	40	minimal	minimal	ADJ
ap-662	126	41	norm	norm	NOUN
ap-662	126	42	.	.	PUNCT
ap-662	127	1	if	if	SCONJ
ap-662	127	2	we	we	PRON
ap-662	127	3	select	select	VERB
ap-662	127	4	from	from	ADP
ap-662	127	5	(	(	PUNCT
ap-662	127	6	24	24	NUM
ap-662	127	7	)	)	PUNCT
ap-662	127	8	only	only	ADV
ap-662	127	9	certain	certain	ADJ
ap-662	127	10	rows	row	NOUN
ap-662	127	11	,	,	PUNCT
ap-662	127	12	we	we	PRON
ap-662	127	13	obtain	obtain	VERB
ap-662	127	14	the	the	DET
ap-662	127	15	solution	solution	NOUN
ap-662	127	16	minimizing	minimize	VERB
ap-662	127	17	the	the	DET
ap-662	127	18	corresponding	corresponding	ADJ
ap-662	127	19	subvector	subvector	NOUN
ap-662	127	20	.	.	PUNCT
ap-662	128	1	this	this	DET
ap-662	128	2	system	system	NOUN
ap-662	128	3	can	can	AUX
ap-662	128	4	naturally	naturally	ADV
ap-662	128	5	be	be	AUX
ap-662	128	6	solved	solve	VERB
ap-662	128	7	using	use	VERB
ap-662	128	8	gso	gso	PROPN
ap-662	128	9	.	.	PUNCT
ap-662	129	1	if	if	SCONJ
ap-662	129	2	we	we	PRON
ap-662	129	3	need	need	VERB
ap-662	129	4	the	the	DET
ap-662	129	5	cofactors	cofactor	NOUN
ap-662	129	6	of	of	ADP
ap-662	129	7	the	the	DET
ap-662	129	8	adjusted	adjust	VERB
ap-662	129	9	unknowns	unknown	NOUN
ap-662	129	10	,	,	PUNCT
ap-662	129	11	as	as	SCONJ
ap-662	129	12	is	be	AUX
ap-662	129	13	the	the	DET
ap-662	129	14	standard	standard	ADJ
ap-662	129	15	case	case	NOUN
ap-662	129	16	with	with	ADP
ap-662	129	17	geodetic	geodetic	ADJ
ap-662	129	18	applications	application	NOUN
ap-662	129	19	,	,	PUNCT
ap-662	129	20	we	we	PRON
ap-662	129	21	have	have	VERB
ap-662	129	22	to	to	PART
ap-662	129	23	process	process	VERB
ap-662	129	24	during	during	ADP
ap-662	129	25	the	the	DET
ap-662	129	26	second	second	ADJ
ap-662	129	27	orthogonalization	orthogonalization	NOUN
ap-662	129	28	the	the	DET
ap-662	129	29	whole	whole	ADV
ap-662	129	30	lower	low	ADJ
ap-662	129	31	submatrix	submatrix	NOUN
ap-662	129	32	that	that	PRON
ap-662	129	33	resulted	result	VERB
ap-662	129	34	from	from	ADP
ap-662	129	35	the	the	DET
ap-662	129	36	first	first	ADJ
ap-662	129	37	orthogonalization	orthogonalization	NOUN
ap-662	129	38	step	step	NOUN
ap-662	129	39	.	.	PUNCT
ap-662	130	1	m	m	VERB
ap-662	130	2	m	m	VERB
ap-662	130	3	m	m	VERB
ap-662	130	4	r	r	NOUN
ap-662	130	5	xii	xii	PROPN
ap-662	130	6	ii	ii	PROPN
ap-662	130	7	ii	ii	PROPN
ap-662	130	8	�	�	PROPN
ap-662	130	9	�	�	PROPN
ap-662	130	10	�	�	PROPN
ap-662	130	11	�	�	PROPN
ap-662	130	12	�	�	PROPN
ap-662	130	13	�	�	PROPN
ap-662	130	14	�	�	PROPN
ap-662	130	15	(	(	PUNCT
ap-662	130	16	)	)	PUNCT
ap-662	130	17	~	~	PUNCT
ap-662	130	18	1	1	NUM
ap-662	130	19	1	1	NUM
ap-662	130	20	1	1	NUM
ap-662	130	21	1	1	NUM
ap-662	130	22	�	�	PROPN
ap-662	130	23	1	1	NUM
ap-662	130	24	0	0	NUM
ap-662	130	25	0	0	NUM
ap-662	130	26	.	.	PUNCT
ap-662	131	1	(	(	PUNCT
ap-662	131	2	25	25	NUM
ap-662	131	3	)	)	PUNCT
ap-662	131	4	during	during	ADP
ap-662	131	5	the	the	DET
ap-662	131	6	first	first	ADJ
ap-662	131	7	orthogonalization	orthogonalization	NOUN
ap-662	131	8	,	,	PUNCT
ap-662	131	9	the	the	DET
ap-662	131	10	linearly	linearly	ADV
ap-662	131	11	dependent	dependent	ADJ
ap-662	131	12	columns	column	NOUN
ap-662	131	13	in	in	ADP
ap-662	131	14	m1	m1	PROPN
ap-662	131	15	are	be	AUX
ap-662	131	16	identified	identify	VERB
ap-662	131	17	and	and	CCONJ
ap-662	131	18	are	be	AUX
ap-662	131	19	explicitly	explicitly	ADV
ap-662	131	20	zeroed	zero	VERB
ap-662	131	21	.	.	PUNCT
ap-662	132	1	the	the	DET
ap-662	132	2	result	result	NOUN
ap-662	132	3	of	of	ADP
ap-662	132	4	the	the	DET
ap-662	132	5	first	first	ADJ
ap-662	132	6	orthogonalization	orthogonalization	NOUN
ap-662	132	7	is	be	AUX
ap-662	132	8	a	a	DET
ap-662	132	9	particular	particular	ADJ
ap-662	132	10	solution	solution	NOUN
ap-662	132	11	in	in	ADP
ap-662	132	12	which	which	PRON
ap-662	132	13	the	the	DET
ap-662	132	14	unknowns	unknown	NOUN
ap-662	132	15	corresponding	correspond	VERB
ap-662	132	16	to	to	ADP
ap-662	132	17	the	the	DET
ap-662	132	18	linearly	linearly	ADV
ap-662	132	19	dependent	dependent	ADJ
ap-662	132	20	columns	column	NOUN
ap-662	132	21	are	be	AUX
ap-662	132	22	all	all	ADV
ap-662	132	23	set	set	VERB
ap-662	132	24	to	to	ADP
ap-662	132	25	zero	zero	NUM
ap-662	132	26	.	.	PUNCT
ap-662	133	1	naturally	naturally	ADV
ap-662	133	2	their	their	PRON
ap-662	133	3	cofactors	cofactor	NOUN
ap-662	133	4	are	be	AUX
ap-662	133	5	zero	zero	NUM
ap-662	133	6	as	as	ADV
ap-662	133	7	well	well	ADV
ap-662	133	8	.	.	PUNCT
ap-662	134	1	during	during	ADP
ap-662	134	2	the	the	DET
ap-662	134	3	second	second	ADJ
ap-662	134	4	orthogonalization	orthogonalization	NOUN
ap-662	134	5	step	step	NOUN
ap-662	134	6	only	only	ADV
ap-662	134	7	the	the	DET
ap-662	134	8	submatrix	submatrix	NOUN
ap-662	134	9	(	(	PUNCT
ap-662	134	10	q	q	NOUN
ap-662	134	11	q3	q3	PROPN
ap-662	134	12	4	4	NUM
ap-662	134	13	i	i	NOUN
ap-662	134	14	i	i	PRON
ap-662	134	15	,	,	PUNCT
ap-662	134	16	)	)	PUNCT
ap-662	134	17	is	be	AUX
ap-662	134	18	influenced	influence	VERB
ap-662	134	19	and	and	CCONJ
ap-662	134	20	the	the	DET
ap-662	134	21	orthogonalization	orthogonalization	NOUN
ap-662	134	22	process	process	NOUN
ap-662	134	23	is	be	AUX
ap-662	134	24	carried	carry	VERB
ap-662	134	25	out	out	ADP
ap-662	134	26	as	as	SCONJ
ap-662	134	27	follows	follow	VERB
ap-662	134	28	�	�	PROPN
ap-662	134	29	gram	gram	PROPN
ap-662	134	30	-	-	PUNCT
ap-662	134	31	schmidt	schmidt	NOUN
ap-662	134	32	orthogonalization	orthogonalization	NOUN
ap-662	134	33	runs	run	VERB
ap-662	134	34	only	only	ADV
ap-662	134	35	through	through	ADP
ap-662	134	36	columns	column	NOUN
ap-662	134	37	corresponding	correspond	VERB
ap-662	134	38	to	to	ADP
ap-662	134	39	the	the	DET
ap-662	134	40	linearly	linearly	ADV
ap-662	134	41	dependent	dependent	ADJ
ap-662	134	42	columns	column	NOUN
ap-662	134	43	of	of	ADP
ap-662	134	44	m1	m1	PROPN
ap-662	134	45	as	as	SCONJ
ap-662	134	46	if	if	SCONJ
ap-662	134	47	they	they	PRON
ap-662	134	48	were	be	AUX
ap-662	134	49	numbered	number	VERB
ap-662	134	50	1	1	NUM
ap-662	134	51	,	,	PUNCT
ap-662	134	52	2	2	NUM
ap-662	134	53	,	,	PUNCT
ap-662	134	54	…	…	PUNCT
ap-662	134	55	,	,	PUNCT
ap-662	134	56	d	d	X
ap-662	134	57	,	,	PUNCT
ap-662	134	58	where	where	SCONJ
ap-662	134	59	d	d	NOUN
ap-662	134	60	is	be	AUX
ap-662	134	61	the	the	DET
ap-662	134	62	nullity	nullity	NOUN
ap-662	134	63	of	of	ADP
ap-662	134	64	m1	m1	PROPN
ap-662	134	65	�	�	NOUN
ap-662	134	66	dot	dot	NOUN
ap-662	134	67	products	product	NOUN
ap-662	134	68	are	be	AUX
ap-662	134	69	computed	compute	VERB
ap-662	134	70	only	only	ADV
ap-662	134	71	for	for	ADP
ap-662	134	72	indices	index	NOUN
ap-662	134	73	i	i	PRON
ap-662	134	74	�	�	PROPN
ap-662	134	75	�	�	PROPN
ap-662	134	76	from	from	ADP
ap-662	134	77	the	the	DET
ap-662	134	78	regularization	regularization	NOUN
ap-662	134	79	condition	condition	NOUN
ap-662	134	80	min	min	NOUN
ap-662	134	81	,	,	PUNCT
ap-662	134	82	x	x	PROPN
ap-662	134	83	i	i	PRON
ap-662	134	84	i	i	PROPN
ap-662	134	85	x	x	PROPN
ap-662	134	86	i2	i2	PROPN
ap-662	134	87	�	�	PROPN
ap-662	134	88	�	�	PROPN
ap-662	134	89	�	�	PROPN
ap-662	134	90	.	.	PUNCT
ap-662	135	1	linearly	linearly	ADV
ap-662	135	2	dependent	dependent	ADJ
ap-662	135	3	columns	column	NOUN
ap-662	135	4	are	be	AUX
ap-662	135	5	zeroed	zero	VERB
ap-662	135	6	during	during	ADP
ap-662	135	7	the	the	DET
ap-662	135	8	second	second	ADJ
ap-662	135	9	orthogonalization	orthogonalization	NOUN
ap-662	135	10	even	even	ADV
ap-662	135	11	in	in	ADP
ap-662	135	12	the	the	DET
ap-662	135	13	region	region	NOUN
ap-662	135	14	of	of	ADP
ap-662	135	15	submatrix	submatrix	NOUN
ap-662	135	16	(	(	PUNCT
ap-662	135	17	q3	q3	PROPN
ap-662	135	18	,	,	PUNCT
ap-662	135	19	q4	q4	PROPN
ap-662	135	20	)	)	PUNCT
ap-662	135	21	.	.	PUNCT
ap-662	136	1	the	the	DET
ap-662	136	2	cofactors	cofactor	NOUN
ap-662	136	3	after	after	SCONJ
ap-662	136	4	the	the	DET
ap-662	136	5	second	second	ADJ
ap-662	136	6	orthogonalization	orthogonalization	NOUN
ap-662	136	7	are	be	AUX
ap-662	136	8	computed	compute	VERB
ap-662	136	9	in	in	ADP
ap-662	136	10	the	the	DET
ap-662	136	11	same	same	ADJ
ap-662	136	12	way	way	NOUN
ap-662	136	13	as	as	ADP
ap-662	136	14	in	in	ADP
ap-662	136	15	the	the	DET
ap-662	136	16	case	case	NOUN
ap-662	136	17	of	of	ADP
ap-662	136	18	regular	regular	ADJ
ap-662	136	19	systems	system	NOUN
ap-662	136	20	.	.	PUNCT
ap-662	137	1	6	6	NUM
ap-662	137	2	singular	singular	ADJ
ap-662	137	3	value	value	NOUN
ap-662	137	4	decomposition	decomposition	NOUN
ap-662	137	5	(	(	PUNCT
ap-662	137	6	svd	svd	PROPN
ap-662	137	7	)	)	PUNCT
ap-662	137	8	for	for	ADP
ap-662	137	9	any	any	DET
ap-662	137	10	real	real	ADJ
ap-662	137	11	m×n	m×n	NOUN
ap-662	137	12	matrix	matrix	NOUN
ap-662	137	13	a	a	DET
ap-662	137	14	,	,	PUNCT
ap-662	137	15	m	m	VERB
ap-662	137	16	�	�	PROPN
ap-662	137	17	n	n	CCONJ
ap-662	137	18	,	,	PUNCT
ap-662	137	19	there	there	PRON
ap-662	137	20	exists	exist	VERB
ap-662	137	21	the	the	DET
ap-662	137	22	singular	singular	ADJ
ap-662	137	23	value	value	NOUN
ap-662	137	24	decomposition	decomposition	NOUN
ap-662	137	25	a	a	DET
ap-662	137	26	uw	uw	PROPN
ap-662	137	27	v	v	PROPN
ap-662	137	28	�	�	PROPN
ap-662	137	29	�	�	PROPN
ap-662	137	30	(	(	PUNCT
ap-662	137	31	26	26	NUM
ap-662	137	32	)	)	PUNCT
ap-662	137	33	�	�	PROPN
ap-662	137	34	�	�	PROPN
ap-662	137	35	�	�	PROPN
ap-662	137	36	�	�	PROPN
ap-662	137	37	�	�	PROPN
ap-662	137	38	�	�	PROPN
ap-662	137	39	u	u	NOUN
ap-662	137	40	u	u	NOUN
ap-662	137	41	vv	vv	ADP
ap-662	137	42	v	v	NUM
ap-662	137	43	v1	v1	NOUN
ap-662	137	44	1	1	NUM
ap-662	137	45	,	,	PUNCT
ap-662	137	46	,	,	PUNCT
ap-662	137	47	where	where	SCONJ
ap-662	137	48	u	u	NOUN
ap-662	137	49	is	be	AUX
ap-662	137	50	an	an	DET
ap-662	137	51	m×n	m×n	ADJ
ap-662	137	52	matrix	matrix	NOUN
ap-662	137	53	with	with	ADP
ap-662	137	54	orthogonal	orthogonal	ADJ
ap-662	137	55	columns	column	NOUN
ap-662	137	56	,	,	PUNCT
ap-662	137	57	w	w	PROPN
ap-662	137	58	is	be	AUX
ap-662	137	59	a	a	DET
ap-662	137	60	diagonal	diagonal	ADJ
ap-662	137	61	matrix	matrix	NOUN
ap-662	137	62	n×n	n×n	PROPN
ap-662	137	63	with	with	ADP
ap-662	137	64	nonnegative	nonnegative	ADJ
ap-662	137	65	elements	element	NOUN
ap-662	137	66	and	and	CCONJ
ap-662	137	67	v	v	NOUN
ap-662	137	68	is	be	AUX
ap-662	137	69	a	a	DET
ap-662	137	70	square	square	ADJ
ap-662	137	71	orthogonal	orthogonal	ADJ
ap-662	137	72	matrix	matrix	NOUN
ap-662	137	73	n×n	n×n	PROPN
ap-662	137	74	,	,	PUNCT
ap-662	137	75	(	(	PUNCT
ap-662	137	76	this	this	DET
ap-662	137	77	variant	variant	NOUN
ap-662	137	78	is	be	AUX
ap-662	137	79	referred	refer	VERB
ap-662	137	80	to	to	ADP
ap-662	137	81	as	as	ADP
ap-662	137	82	the	the	DET
ap-662	137	83	thin	thin	ADJ
ap-662	137	84	svd	svd	PROPN
ap-662	138	1	[	[	X
ap-662	138	2	3	3	NUM
ap-662	138	3	]	]	NUM
ap-662	138	4	)	)	PUNCT
ap-662	138	5	.	.	PUNCT
ap-662	139	1	matrix	matrix	NOUN
ap-662	139	2	w	w	NOUN
ap-662	139	3	is	be	AUX
ap-662	139	4	uniquely	uniquely	ADV
ap-662	139	5	determined	determine	VERB
ap-662	139	6	up	up	ADP
ap-662	139	7	to	to	ADP
ap-662	139	8	the	the	DET
ap-662	139	9	permutation	permutation	NOUN
ap-662	139	10	of	of	ADP
ap-662	139	11	its	its	PRON
ap-662	139	12	diagonal	diagonal	ADJ
ap-662	139	13	elements	element	NOUN
ap-662	139	14	.	.	PUNCT
ap-662	140	1	the	the	DET
ap-662	140	2	diagonal	diagonal	ADJ
ap-662	140	3	elements	element	NOUN
ap-662	140	4	wi	wi	PROPN
ap-662	140	5	are	be	AUX
ap-662	140	6	called	call	VERB
ap-662	140	7	singular	singular	ADJ
ap-662	140	8	values	value	NOUN
ap-662	140	9	of	of	ADP
ap-662	140	10	matrix	matrix	NOUN
ap-662	140	11	a.	a.	NOUN
ap-662	140	12	their	their	PRON
ap-662	140	13	squares	square	NOUN
ap-662	140	14	are	be	AUX
ap-662	140	15	eigenvalues	eigenvalue	NOUN
ap-662	140	16	of	of	ADP
ap-662	140	17	n×n	n×n	PROPN
ap-662	140	18	matrix	matrix	NOUN
ap-662	140	19	�	�	NOUN
ap-662	140	20	a	a	DET
ap-662	140	21	a.	a.	NOUN
ap-662	140	22	thus	thus	ADV
ap-662	140	23	,	,	PUNCT
ap-662	140	24	the	the	DET
ap-662	140	25	condition	condition	NOUN
ap-662	140	26	number	number	NOUN
ap-662	140	27	of	of	ADP
ap-662	140	28	matrix	matrix	NOUN
ap-662	140	29	a	a	PRON
ap-662	140	30	can	can	AUX
ap-662	140	31	be	be	AUX
ap-662	140	32	computed	compute	VERB
ap-662	140	33	as	as	ADP
ap-662	140	34	the	the	DET
ap-662	140	35	ratio	ratio	NOUN
ap-662	140	36	of	of	ADP
ap-662	140	37	the	the	DET
ap-662	140	38	maximal	maximal	ADJ
ap-662	140	39	and	and	CCONJ
ap-662	140	40	minimal	minimal	ADJ
ap-662	140	41	singular	singular	ADJ
ap-662	140	42	value	value	NOUN
ap-662	140	43	.	.	PUNCT
ap-662	141	1	�	�	PROPN
ap-662	141	2	(	(	PUNCT
ap-662	141	3	)	)	PUNCT
ap-662	141	4	max	max	PROPN
ap-662	141	5	min	min	PROPN
ap-662	141	6	a	a	DET
ap-662	141	7	�	�	PROPN
ap-662	141	8	w	w	PROPN
ap-662	141	9	w	w	PROPN
ap-662	141	10	.	.	PUNCT
ap-662	142	1	(	(	PUNCT
ap-662	142	2	27	27	NUM
ap-662	142	3	)	)	PUNCT
ap-662	142	4	with	with	ADP
ap-662	142	5	singular	singular	ADJ
ap-662	142	6	decomposition	decomposition	NOUN
ap-662	142	7	we	we	PRON
ap-662	142	8	can	can	AUX
ap-662	142	9	directly	directly	ADV
ap-662	142	10	express	express	VERB
ap-662	142	11	the	the	DET
ap-662	142	12	vector	vector	NOUN
ap-662	142	13	of	of	ADP
ap-662	142	14	unknown	unknown	ADJ
ap-662	142	15	parameters	parameter	NOUN
ap-662	142	16	x	x	VERB
ap-662	142	17	from	from	ADP
ap-662	142	18	the	the	DET
ap-662	142	19	project	project	NOUN
ap-662	142	20	equations	equation	NOUN
ap-662	142	21	ax	ax	NOUN
ap-662	142	22	l	l	NOUN
ap-662	142	23	x	x	X
ap-662	142	24	vw	vw	PROPN
ap-662	142	25	u	u	PROPN
ap-662	142	26	l	l	PROPN
ap-662	142	27	w	w	PROPN
ap-662	142	28	�	�	PROPN
ap-662	142	29	�	�	PROPN
ap-662	142	30	�	�	PROPN
ap-662	142	31	�	�	PROPN
ap-662	142	32	�	�	PROPN
ap-662	142	33	�	�	PROPN
ap-662	142	34	,	,	PUNCT
ap-662	142	35	,	,	PUNCT
ap-662	142	36	(	(	PUNCT
ap-662	142	37	)	)	SYM
ap-662	142	38	1	1	NUM
ap-662	142	39	1	1	NUM
ap-662	142	40	1diag	1diag	NUM
ap-662	142	41	wi	wi	PROPN
ap-662	142	42	.	.	PUNCT
ap-662	143	1	(	(	PUNCT
ap-662	143	2	28	28	NUM
ap-662	143	3	)	)	PUNCT
ap-662	143	4	if	if	SCONJ
ap-662	143	5	matrix	matrix	NOUN
ap-662	143	6	a	a	PRON
ap-662	143	7	has	have	VERB
ap-662	143	8	more	more	ADJ
ap-662	143	9	rows	row	NOUN
ap-662	143	10	than	than	ADP
ap-662	143	11	columns	column	NOUN
ap-662	143	12	(	(	PUNCT
ap-662	143	13	overdetermined	overdetermine	VERB
ap-662	143	14	system	system	NOUN
ap-662	143	15	)	)	PUNCT
ap-662	143	16	,	,	PUNCT
ap-662	143	17	then	then	ADV
ap-662	143	18	the	the	DET
ap-662	143	19	euclidean	euclidean	ADJ
ap-662	143	20	norm	norm	NOUN
ap-662	143	21	of	of	ADP
ap-662	143	22	the	the	DET
ap-662	143	23	residual	residual	ADJ
ap-662	143	24	vector	vector	NOUN
ap-662	143	25	v	v	ADP
ap-662	143	26	ax	ax	NOUN
ap-662	143	27	l	l	X
ap-662	143	28	�	�	PROPN
ap-662	143	29	�	�	PROPN
ap-662	143	30	is	be	AUX
ap-662	143	31	minimal	minimal	ADJ
ap-662	143	32	and	and	CCONJ
ap-662	143	33	vector	vector	NOUN
ap-662	143	34	x	x	X
ap-662	143	35	is	be	AUX
ap-662	143	36	the	the	DET
ap-662	143	37	least	least	ADJ
ap-662	143	38	squares	square	NOUN
ap-662	143	39	solution	solution	NOUN
ap-662	143	40	to	to	ADP
ap-662	143	41	the	the	DET
ap-662	143	42	project	project	NOUN
ap-662	143	43	equations	equation	NOUN
ap-662	143	44	(	(	PUNCT
ap-662	143	45	2	2	NUM
ap-662	143	46	)	)	PUNCT
ap-662	143	47	.	.	PUNCT
ap-662	144	1	for	for	ADP
ap-662	144	2	a	a	DET
ap-662	144	3	matrix	matrix	NOUN
ap-662	144	4	a	a	PRON
ap-662	144	5	with	with	ADP
ap-662	144	6	linearly	linearly	ADV
ap-662	144	7	dependent	dependent	ADJ
ap-662	144	8	columns	column	NOUN
ap-662	144	9	d	d	ADP
ap-662	144	10	singular	singular	ADJ
ap-662	144	11	values	value	NOUN
ap-662	144	12	are	be	AUX
ap-662	144	13	zero	zero	NUM
ap-662	144	14	(	(	PUNCT
ap-662	144	15	d	d	NOUN
ap-662	144	16	is	be	AUX
ap-662	144	17	the	the	DET
ap-662	144	18	dimension	dimension	NOUN
ap-662	144	19	of	of	ADP
ap-662	144	20	null	null	ADJ
ap-662	144	21	space	space	NOUN
ap-662	144	22	of	of	ADP
ap-662	144	23	a	a	PRON
ap-662	144	24	)	)	PUNCT
ap-662	144	25	.	.	PUNCT
ap-662	145	1	singular	singular	PROPN
ap-662	145	2	value	value	NOUN
ap-662	145	3	decomposition	decomposition	NOUN
ap-662	145	4	explicitly	explicitly	ADV
ap-662	145	5	constructs	construct	VERB
ap-662	145	6	the	the	DET
ap-662	145	7	orthonormal	orthonormal	ADJ
ap-662	145	8	vector	vector	NOUN
ap-662	145	9	basis	basis	NOUN
ap-662	145	10	of	of	ADP
ap-662	145	11	the	the	DET
ap-662	145	12	null	null	ADJ
ap-662	145	13	space	space	NOUN
ap-662	145	14	and	and	CCONJ
ap-662	145	15	the	the	DET
ap-662	145	16	range	range	NOUN
ap-662	145	17	of	of	ADP
ap-662	145	18	a.	a.	NOUN
ap-662	145	19	the	the	DET
ap-662	145	20	columns	column	NOUN
ap-662	145	21	of	of	ADP
ap-662	145	22	matrix	matrix	NOUN
ap-662	145	23	u	u	NOUN
ap-662	145	24	corresponding	correspond	VERB
ap-662	145	25	to	to	ADP
ap-662	145	26	nonzero	nonzero	PROPN
ap-662	145	27	singular	singular	PROPN
ap-662	145	28	values	value	NOUN
ap-662	145	29	wi	wi	PROPN
ap-662	145	30	form	form	VERB
ap-662	145	31	the	the	DET
ap-662	145	32	orthonormal	orthonormal	ADJ
ap-662	145	33	base	base	NOUN
ap-662	145	34	of	of	ADP
ap-662	145	35	the	the	DET
ap-662	145	36	range	range	NOUN
ap-662	145	37	of	of	ADP
ap-662	145	38	a.	a.	NOUN
ap-662	145	39	similarly	similarly	ADV
ap-662	145	40	,	,	PUNCT
ap-662	145	41	the	the	DET
ap-662	145	42	columns	column	NOUN
ap-662	145	43	of	of	ADP
ap-662	145	44	matrix	matrix	NOUN
ap-662	145	45	v	v	ADP
ap-662	145	46	corresponding	correspond	VERB
ap-662	145	47	to	to	ADP
ap-662	145	48	nonzero	nonzero	PROPN
ap-662	145	49	singular	singular	ADJ
ap-662	145	50	values	value	NOUN
ap-662	145	51	form	form	VERB
ap-662	145	52	the	the	DET
ap-662	145	53	orthonormal	orthonormal	ADJ
ap-662	145	54	basis	basis	NOUN
ap-662	145	55	of	of	ADP
ap-662	145	56	the	the	DET
ap-662	145	57	null	null	ADJ
ap-662	145	58	space	space	NOUN
ap-662	145	59	of	of	ADP
ap-662	145	60	a.	a.	PROPN
ap-662	145	61	�	�	PROPN
ap-662	145	62	�	�	PROPN
ap-662	145	63	�	�	PROPN
ap-662	145	64	�	�	PROPN
ap-662	145	65	a	a	DET
ap-662	145	66	x	x	ADJ
ap-662	145	67	ax	ax	ADJ
ap-662	145	68	x	x	PROPN
ap-662	145	69	�	�	PROPN
ap-662	145	70	�	�	PROPN
ap-662	145	71	�	�	PROPN
ap-662	145	72	0	0	NUM
ap-662	145	73	,	,	PUNCT
ap-662	145	74	n	n	PRON
ap-662	145	75	�	�	PROPN
ap-662	145	76	�	�	PROPN
ap-662	145	77	�	�	PROPN
ap-662	145	78	�	�	PROPN
ap-662	145	79	a	a	PROPN
ap-662	145	80	y	y	PROPN
ap-662	145	81	y	y	PROPN
ap-662	145	82	ax	ax	NOUN
ap-662	145	83	x	x	PROPN
ap-662	145	84	�	�	PROPN
ap-662	145	85	�	�	PROPN
ap-662	145	86	�	�	PROPN
ap-662	145	87	,	,	PUNCT
ap-662	145	88	n	n	NOUN
ap-662	145	89	.	.	PUNCT
ap-662	146	1	in	in	ADP
ap-662	146	2	the	the	DET
ap-662	146	3	case	case	NOUN
ap-662	146	4	of	of	ADP
ap-662	146	5	rank	rank	PROPN
ap-662	146	6	deficient	deficient	ADJ
ap-662	146	7	systems	system	NOUN
ap-662	146	8	,	,	PUNCT
ap-662	146	9	we	we	PRON
ap-662	146	10	set	set	VERB
ap-662	146	11	into	into	ADP
ap-662	146	12	the	the	DET
ap-662	146	13	diagonal	diagonal	NOUN
ap-662	146	14	of	of	ADP
ap-662	146	15	inverse	inverse	NOUN
ap-662	146	16	matrix	matrix	NOUN
ap-662	146	17	w	w	PROPN
ap-662	146	18	�	�	PROPN
ap-662	146	19	1	1	NUM
ap-662	146	20	zeros	zero	NOUN
ap-662	146	21	instead	instead	ADV
ap-662	146	22	of	of	ADP
ap-662	146	23	reciprocals	reciprocal	NOUN
ap-662	146	24	for	for	ADP
ap-662	146	25	elements	element	NOUN
ap-662	146	26	corresponding	correspond	VERB
ap-662	146	27	to	to	ADP
ap-662	146	28	linearly	linearly	ADV
ap-662	146	29	dependent	dependent	ADJ
ap-662	146	30	columns	column	NOUN
ap-662	146	31	a	a	DET
ap-662	146	32	w	w	PROPN
ap-662	146	33	�	�	PROPN
ap-662	146	34	�	�	PROPN
ap-662	146	35	�	�	PROPN
ap-662	146	36	�	�	PROPN
ap-662	146	37	�	�	PROPN
ap-662	146	38	�	�	PROPN
ap-662	146	39	�	�	PROPN
ap-662	146	40	1	1	NUM
ap-662	146	41	1	1	NUM
ap-662	146	42	0	0	NUM
ap-662	146	43	0	0	NUM
ap-662	146	44	0	0	NUM
ap-662	146	45	diag	diag	NOUN
ap-662	146	46	for	for	ADP
ap-662	146	47	for	for	ADP
ap-662	146	48	w	w	PROPN
ap-662	146	49	w	w	PROPN
ap-662	146	50	w	w	PROPN
ap-662	147	1	i	i	PRON
ap-662	148	1	i	i	PRON
ap-662	149	1	i	i	INTJ
ap-662	149	2	.	.	PUNCT
ap-662	150	1	(	(	PUNCT
ap-662	150	2	29	29	NUM
ap-662	150	3	)	)	PUNCT
ap-662	150	4	the	the	DET
ap-662	150	5	resulting	result	VERB
ap-662	150	6	particular	particular	ADJ
ap-662	150	7	solution	solution	NOUN
ap-662	150	8	x	x	PRON
ap-662	150	9	minimizes	minimize	VERB
ap-662	150	10	both	both	CCONJ
ap-662	150	11	the	the	DET
ap-662	150	12	euclidean	euclidean	ADJ
ap-662	150	13	norm	norm	NOUN
ap-662	150	14	of	of	ADP
ap-662	150	15	the	the	DET
ap-662	150	16	residuals	residual	NOUN
ap-662	150	17	and	and	CCONJ
ap-662	150	18	at	at	ADP
ap-662	150	19	the	the	DET
ap-662	150	20	same	same	ADJ
ap-662	150	21	time	time	NOUN
ap-662	150	22	the	the	DET
ap-662	150	23	norm	norm	NOUN
ap-662	150	24	of	of	ADP
ap-662	150	25	unknown	unknown	ADJ
ap-662	150	26	parameters	parameter	NOUN
ap-662	150	27	x.	x.	VERB
ap-662	150	28	the	the	DET
ap-662	150	29	rather	rather	ADV
ap-662	150	30	surprising	surprising	ADJ
ap-662	150	31	replacement	replacement	NOUN
ap-662	150	32	of	of	ADP
ap-662	150	33	reciprocal	reciprocal	ADJ
ap-662	150	34	1	1	NUM
ap-662	150	35	0	0	NUM
ap-662	150	36	�	�	PROPN
ap-662	150	37	�	�	PROPN
ap-662	150	38	by	by	ADP
ap-662	150	39	zero	zero	NUM
ap-662	150	40	can	can	AUX
ap-662	150	41	be	be	AUX
ap-662	150	42	explained	explain	VERB
ap-662	150	43	as	as	SCONJ
ap-662	150	44	follows	follow	VERB
ap-662	150	45	.	.	PUNCT
ap-662	151	1	the	the	DET
ap-662	151	2	solution	solution	NOUN
ap-662	151	3	vector	vector	NOUN
ap-662	151	4	x	x	PROPN
ap-662	151	5	of	of	ADP
ap-662	151	6	the	the	DET
ap-662	151	7	overdetermined	overdetermine	VERB
ap-662	151	8	system	system	NOUN
ap-662	151	9	ax	ax	NOUN
ap-662	151	10	l	l	X
ap-662	151	11	�	�	PROPN
ap-662	151	12	can	can	AUX
ap-662	151	13	be	be	AUX
ap-662	151	14	expressed	express	VERB
ap-662	151	15	as	as	ADP
ap-662	151	16	the	the	DET
ap-662	151	17	linear	linear	ADJ
ap-662	151	18	combination	combination	NOUN
ap-662	151	19	of	of	ADP
ap-662	151	20	the	the	DET
ap-662	151	21	columns	column	NOUN
ap-662	151	22	of	of	ADP
ap-662	151	23	matrix	matrix	NOUN
ap-662	151	24	v	v	NOUN
ap-662	151	25	x	x	SYM
ap-662	151	26	u	u	PROPN
ap-662	151	27	l	l	PROPN
ap-662	151	28	v	v	PROPN
ap-662	151	29	�	�	PROPN
ap-662	151	30	�	�	PROPN
ap-662	151	31	�	�	PROPN
ap-662	151	32	�	�	PROPN
ap-662	151	33	�	�	PROPN
ap-662	151	34	�	�	PROPN
ap-662	151	35	1	1	NUM
ap-662	151	36	1	1	NUM
ap-662	151	37	wi	wi	PROPN
ap-662	152	1	i	i	PRON
ap-662	152	2	i	i	PRON
ap-662	153	1	i	i	VERB
ap-662	153	2	n	n	VERB
ap-662	153	3	(	(	PUNCT
ap-662	153	4	)	)	PUNCT
ap-662	153	5	(	(	PUNCT
ap-662	153	6	)	)	PUNCT
ap-662	153	7	.	.	PUNCT
ap-662	154	1	(	(	PUNCT
ap-662	154	2	30	30	NUM
ap-662	154	3	)	)	PUNCT
ap-662	154	4	16	16	NUM
ap-662	154	5	©	©	PROPN
ap-662	154	6	czech	czech	PROPN
ap-662	154	7	technical	technical	PROPN
ap-662	154	8	university	university	PROPN
ap-662	154	9	publishing	publishing	NOUN
ap-662	154	10	house	house	NOUN
ap-662	154	11	e	e	PROPN
ap-662	154	12	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-662	154	13	acta	acta	PROPN
ap-662	154	14	polytechnica	polytechnica	PROPN
ap-662	154	15	vol	vol	NOUN
ap-662	154	16	.	.	PROPN
ap-662	155	1	45	45	NUM
ap-662	155	2	no	no	NOUN
ap-662	155	3	.	.	PUNCT
ap-662	156	1	1/2005	1/2005	NUM
ap-662	156	2	czech	czech	PROPN
ap-662	156	3	technical	technical	PROPN
ap-662	156	4	university	university	PROPN
ap-662	156	5	in	in	ADP
ap-662	156	6	prague	prague	PROPN
ap-662	156	7	the	the	DET
ap-662	156	8	coefficients	coefficient	NOUN
ap-662	156	9	in	in	ADP
ap-662	156	10	parentheses	parenthesis	NOUN
ap-662	156	11	are	be	AUX
ap-662	156	12	dot	dot	NOUN
ap-662	156	13	products	product	NOUN
ap-662	156	14	of	of	ADP
ap-662	156	15	columns	column	NOUN
ap-662	156	16	u	u	NOUN
ap-662	156	17	and	and	CCONJ
ap-662	156	18	right	right	ADJ
ap-662	156	19	hand	hand	NOUN
ap-662	156	20	side	side	NOUN
ap-662	156	21	l	l	NOUN
ap-662	156	22	multiplied	multiply	VERB
ap-662	156	23	by	by	ADP
ap-662	156	24	the	the	DET
ap-662	156	25	reciprocal	reciprocal	ADJ
ap-662	156	26	value	value	NOUN
ap-662	156	27	of	of	ADP
ap-662	156	28	the	the	DET
ap-662	156	29	singular	singular	ADJ
ap-662	156	30	value	value	NOUN
ap-662	156	31	.	.	PUNCT
ap-662	157	1	the	the	DET
ap-662	157	2	zero	zero	NUM
ap-662	157	3	singular	singular	ADJ
ap-662	157	4	values	value	NOUN
ap-662	157	5	correspond	correspond	VERB
ap-662	157	6	to	to	ADP
ap-662	157	7	the	the	DET
ap-662	157	8	linearly	linearly	ADV
ap-662	157	9	dependent	dependent	ADJ
ap-662	157	10	columns	column	NOUN
ap-662	157	11	of	of	ADP
ap-662	157	12	matrix	matrix	NOUN
ap-662	157	13	a	a	PRON
ap-662	157	14	that	that	PRON
ap-662	157	15	add	add	VERB
ap-662	157	16	no	no	DET
ap-662	157	17	other	other	ADJ
ap-662	157	18	information	information	NOUN
ap-662	157	19	to	to	ADP
ap-662	157	20	the	the	DET
ap-662	157	21	given	give	VERB
ap-662	157	22	system	system	NOUN
ap-662	157	23	.	.	PUNCT
ap-662	158	1	setting	set	VERB
ap-662	158	2	corresponding	corresponding	ADJ
ap-662	158	3	diagonal	diagonal	ADJ
ap-662	158	4	elements	element	NOUN
ap-662	158	5	of	of	ADP
ap-662	158	6	matrix	matrix	NOUN
ap-662	158	7	w	w	PROPN
ap-662	158	8	�	�	PROPN
ap-662	158	9	1	1	NUM
ap-662	158	10	to	to	ADP
ap-662	158	11	zeros	zero	NOUN
ap-662	158	12	is	be	AUX
ap-662	158	13	equivalent	equivalent	ADJ
ap-662	158	14	to	to	ADP
ap-662	158	15	eliminating	eliminate	VERB
ap-662	158	16	the	the	DET
ap-662	158	17	linearly	linearly	ADV
ap-662	158	18	dependent	dependent	ADJ
ap-662	158	19	columns	column	NOUN
ap-662	158	20	from	from	ADP
ap-662	158	21	matrix	matrix	NOUN
ap-662	158	22	a.	a.	NOUN
ap-662	158	23	with	with	ADP
ap-662	158	24	matrix	matrix	NOUN
ap-662	158	25	w	w	PROPN
ap-662	158	26	�	�	PROPN
ap-662	158	27	1	1	NUM
ap-662	158	28	defined	define	VERB
ap-662	158	29	according	accord	VERB
ap-662	158	30	to	to	ADP
ap-662	158	31	(	(	PUNCT
ap-662	158	32	29	29	NUM
ap-662	158	33	)	)	PUNCT
ap-662	158	34	,	,	PUNCT
ap-662	158	35	the	the	DET
ap-662	158	36	cofactors	cofactor	NOUN
ap-662	158	37	computed	compute	VERB
ap-662	158	38	the	the	DET
ap-662	158	39	same	same	ADJ
ap-662	158	40	way	way	NOUN
ap-662	158	41	for	for	ADP
ap-662	158	42	regular	regular	ADJ
ap-662	158	43	and	and	CCONJ
ap-662	158	44	singular	singular	PROPN
ap-662	158	45	systems	system	NOUN
ap-662	158	46	q	q	PROPN
ap-662	158	47	n	n	ADP
ap-662	158	48	a	a	DET
ap-662	158	49	a	a	DET
ap-662	158	50	vw	vw	NOUN
ap-662	158	51	u	u	PROPN
ap-662	158	52	uwv	uwv	PROPN
ap-662	158	53	vw	vw	PROPN
ap-662	158	54	w	w	PROPN
ap-662	158	55	vxx	vxx	PROPN
ap-662	158	56	�	�	PROPN
ap-662	158	57	�	�	PROPN
ap-662	158	58	�	�	PROPN
ap-662	158	59	�	�	PROPN
ap-662	158	60	�	�	PROPN
ap-662	158	61	�	�	PROPN
ap-662	158	62	�	�	PROPN
ap-662	158	63	�	�	PROPN
ap-662	158	64	�	�	PROPN
ap-662	158	65	�	�	PROPN
ap-662	158	66	�	�	PROPN
ap-662	158	67	�	�	PROPN
ap-662	158	68	�	�	PROPN
ap-662	158	69	�	�	PROPN
ap-662	158	70	1	1	NUM
ap-662	158	71	1	1	NUM
ap-662	158	72	1	1	NUM
ap-662	158	73	1	1	NUM
ap-662	158	74	(	(	PUNCT
ap-662	158	75	)	)	PUNCT
ap-662	158	76	(	(	PUNCT
ap-662	158	77	)	)	PUNCT
ap-662	158	78	t	t	NOUN
ap-662	158	79	,	,	PUNCT
ap-662	158	80	(	(	PUNCT
ap-662	158	81	31	31	NUM
ap-662	158	82	)	)	PUNCT
ap-662	158	83	q	q	NOUN
ap-662	158	84	aq	aq	VERB
ap-662	158	85	a	a	DET
ap-662	158	86	uwv	uwv	PROPN
ap-662	158	87	vw	vw	PROPN
ap-662	158	88	w	w	PROPN
ap-662	158	89	v	v	PROPN
ap-662	158	90	vw	vw	PROPN
ap-662	158	91	u	u	PROPN
ap-662	158	92	uull	uull	ADJ
ap-662	158	93	xx	xx	NUM
ap-662	158	94	�	�	PROPN
ap-662	158	95	�	�	PROPN
ap-662	158	96	�	�	PROPN
ap-662	158	97	�	�	PROPN
ap-662	158	98	�	�	PROPN
ap-662	158	99	�	�	PROPN
ap-662	158	100	�	�	PROPN
ap-662	158	101	�	�	PROPN
ap-662	158	102	�	�	PROPN
ap-662	158	103	�	�	PROPN
ap-662	158	104	�	�	PROPN
ap-662	158	105	(	(	PUNCT
ap-662	158	106	)	)	PUNCT
ap-662	158	107	)	)	PUNCT
ap-662	158	108	(	(	PUNCT
ap-662	158	109	)	)	PUNCT
ap-662	158	110	(	(	PUNCT
ap-662	158	111	t1	t1	NOUN
ap-662	158	112	,	,	PUNCT
ap-662	158	113	(	(	PUNCT
ap-662	158	114	32	32	NUM
ap-662	158	115	)	)	PUNCT
ap-662	158	116	q	q	NOUN
ap-662	159	1	aq	aq	X
ap-662	159	2	uwv	uwv	PROPN
ap-662	159	3	vw	vw	PROPN
ap-662	159	4	w	w	PROPN
ap-662	159	5	v	v	PROPN
ap-662	159	6	uw	uw	PROPN
ap-662	159	7	vlx	vlx	NOUN
ap-662	159	8	xx	xx	NUM
ap-662	159	9	�	�	PROPN
ap-662	159	10	�	�	PROPN
ap-662	159	11	�	�	PROPN
ap-662	159	12	�	�	PROPN
ap-662	159	13	�	�	PROPN
ap-662	159	14	�	�	PROPN
ap-662	159	15	�	�	PROPN
ap-662	159	16	�	�	PROPN
ap-662	159	17	�	�	PROPN
ap-662	159	18	1	1	NUM
ap-662	159	19	1	1	NUM
ap-662	159	20	t	t	NOUN
ap-662	159	21	.	.	PUNCT
ap-662	160	1	(	(	PUNCT
ap-662	160	2	33	33	NUM
ap-662	160	3	)	)	PUNCT
ap-662	160	4	the	the	DET
ap-662	160	5	cofactors	cofactor	NOUN
ap-662	160	6	(	(	PUNCT
ap-662	160	7	weight	weight	NOUN
ap-662	160	8	coefficients	coefficient	NOUN
ap-662	160	9	)	)	PUNCT
ap-662	160	10	for	for	ADP
ap-662	160	11	the	the	DET
ap-662	160	12	adjusted	adjust	VERB
ap-662	160	13	parameters	parameter	NOUN
ap-662	160	14	,	,	PUNCT
ap-662	160	15	observations	observation	NOUN
ap-662	160	16	and	and	CCONJ
ap-662	160	17	mixed	mixed	ADJ
ap-662	160	18	cofactors	cofactor	NOUN
ap-662	160	19	are	be	AUX
ap-662	160	20	computed	compute	VERB
ap-662	160	21	,	,	PUNCT
ap-662	160	22	similarly	similarly	ADV
ap-662	160	23	as	as	ADP
ap-662	160	24	in	in	ADP
ap-662	160	25	the	the	DET
ap-662	160	26	case	case	NOUN
ap-662	160	27	of	of	ADP
ap-662	160	28	gso	gso	PROPN
ap-662	160	29	,	,	PUNCT
ap-662	160	30	as	as	SCONJ
ap-662	160	31	the	the	DET
ap-662	160	32	dot	dot	NOUN
ap-662	160	33	products	product	NOUN
ap-662	160	34	of	of	ADP
ap-662	160	35	the	the	DET
ap-662	160	36	rows	row	NOUN
ap-662	160	37	of	of	ADP
ap-662	160	38	matrices	matrix	NOUN
ap-662	160	39	u	u	NOUN
ap-662	160	40	and	and	CCONJ
ap-662	160	41	v	v	NOUN
ap-662	160	42	;	;	NOUN
ap-662	160	43	multiplied	multiply	VERB
ap-662	160	44	by	by	ADP
ap-662	160	45	the	the	DET
ap-662	160	46	diagonal	diagonal	ADJ
ap-662	160	47	elements	element	NOUN
ap-662	160	48	of	of	ADP
ap-662	160	49	w	w	PROPN
ap-662	160	50	�	�	PROPN
ap-662	160	51	1	1	NUM
ap-662	160	52	in	in	ADP
ap-662	160	53	the	the	DET
ap-662	160	54	case	case	NOUN
ap-662	160	55	of	of	ADP
ap-662	160	56	cofactors	cofactor	NOUN
ap-662	160	57	of	of	ADP
ap-662	160	58	x.	x.	NOUN
ap-662	160	59	6.1	6.1	NUM
ap-662	160	60	algorithm	algorithm	NOUN
ap-662	160	61	svd	svd	PROPN
ap-662	160	62	and	and	CCONJ
ap-662	160	63	singular	singular	PROPN
ap-662	160	64	systems	system	NOUN
ap-662	160	65	what	what	PRON
ap-662	160	66	now	now	ADV
ap-662	160	67	remains	remain	VERB
ap-662	160	68	is	be	AUX
ap-662	160	69	to	to	PART
ap-662	160	70	show	show	VERB
ap-662	160	71	how	how	SCONJ
ap-662	160	72	to	to	PART
ap-662	160	73	compute	compute	VERB
ap-662	160	74	the	the	DET
ap-662	160	75	particular	particular	ADJ
ap-662	160	76	solution	solution	NOUN
ap-662	160	77	that	that	PRON
ap-662	160	78	minimizes	minimize	VERB
ap-662	160	79	only	only	ADV
ap-662	160	80	a	a	DET
ap-662	160	81	given	give	VERB
ap-662	160	82	subset	subset	NOUN
ap-662	160	83	of	of	ADP
ap-662	160	84	subvector	subvector	NOUN
ap-662	160	85	x	x	PUNCT
ap-662	160	86	according	accord	VERB
ap-662	160	87	to	to	ADP
ap-662	160	88	the	the	DET
ap-662	160	89	second	second	ADJ
ap-662	160	90	regularization	regularization	NOUN
ap-662	160	91	condition	condition	NOUN
ap-662	160	92	(	(	PUNCT
ap-662	160	93	9	9	NUM
ap-662	160	94	)	)	PUNCT
ap-662	160	95	.	.	PUNCT
ap-662	161	1	we	we	PRON
ap-662	161	2	compose	compose	VERB
ap-662	161	3	an	an	DET
ap-662	161	4	overdetermined	overdetermined	ADJ
ap-662	161	5	system	system	NOUN
ap-662	161	6	of	of	ADP
ap-662	161	7	linear	linear	PROPN
ap-662	161	8	equations	equation	NOUN
ap-662	161	9	�	�	PROPN
ap-662	161	10	c	c	NOUN
ap-662	161	11	x	x	SYM
ap-662	161	12	x	x	X
ap-662	161	13	�	�	PROPN
ap-662	161	14	�	�	PROPN
ap-662	161	15	�	�	PROPN
ap-662	161	16	,	,	PUNCT
ap-662	161	17	(	(	PUNCT
ap-662	161	18	34	34	NUM
ap-662	161	19	)	)	PUNCT
ap-662	161	20	where	where	SCONJ
ap-662	161	21	the	the	DET
ap-662	161	22	columns	column	NOUN
ap-662	161	23	of	of	ADP
ap-662	161	24	matrix	matrix	NOUN
ap-662	161	25	�	�	PROPN
ap-662	161	26	are	be	AUX
ap-662	161	27	vectors	vector	NOUN
ap-662	161	28	of	of	ADP
ap-662	161	29	null	null	ADJ
ap-662	161	30	space	space	NOUN
ap-662	161	31	basis	basis	NOUN
ap-662	161	32	�	�	PROPN
ap-662	161	33	�	�	PROPN
ap-662	161	34	�	�	PROPN
ap-662	161	35	(	(	PUNCT
ap-662	161	36	,	,	PUNCT
ap-662	161	37	,	,	PUNCT
ap-662	161	38	,	,	PUNCT
ap-662	161	39	)	)	PUNCT
ap-662	161	40	,	,	PUNCT
ap-662	161	41	,	,	PUNCT
ap-662	161	42	(	(	PUNCT
ap-662	161	43	)	)	PUNCT
ap-662	161	44	(	(	PUNCT
ap-662	161	45	)	)	PUNCT
ap-662	161	46	(	(	PUNCT
ap-662	161	47	)	)	PUNCT
ap-662	161	48	v	v	NOUN
ap-662	161	49	v	v	NOUN
ap-662	161	50	vi	vi	NOUN
ap-662	162	1	i	i	PRON
ap-662	162	2	i	i	PRON
ap-662	163	1	i	i	VERB
ap-662	163	2	d	d	PROPN
ap-662	163	3	n	n	PROPN
ap-662	163	4	w	w	PROPN
ap-662	163	5	1	1	NUM
ap-662	163	6	2	2	NUM
ap-662	163	7	0	0	NUM
ap-662	163	8	�	�	PROPN
ap-662	163	9	and	and	CCONJ
ap-662	163	10	c	c	PROPN
ap-662	163	11	is	be	AUX
ap-662	163	12	the	the	DET
ap-662	163	13	vector	vector	NOUN
ap-662	163	14	of	of	ADP
ap-662	163	15	the	the	DET
ap-662	163	16	coefficients	coefficient	NOUN
ap-662	163	17	of	of	ADP
ap-662	163	18	the	the	DET
ap-662	163	19	linear	linear	ADJ
ap-662	163	20	combination	combination	NOUN
ap-662	163	21	of	of	ADP
ap-662	163	22	null	null	ADJ
ap-662	163	23	space	space	NOUN
ap-662	163	24	basis	basis	NOUN
ap-662	163	25	vectors	vector	NOUN
ap-662	163	26	that	that	PRON
ap-662	163	27	,	,	PUNCT
ap-662	163	28	when	when	SCONJ
ap-662	163	29	added	add	VERB
ap-662	163	30	to	to	ADP
ap-662	163	31	vector	vector	NOUN
ap-662	163	32	x	x	X
ap-662	163	33	,	,	PUNCT
ap-662	163	34	minimizes	minimize	VERB
ap-662	163	35	the	the	DET
ap-662	163	36	selected	select	VERB
ap-662	163	37	subvector	subvector	NOUN
ap-662	163	38	of	of	ADP
ap-662	163	39	unknown	unknown	ADJ
ap-662	163	40	parameters	parameter	NOUN
ap-662	163	41	�	�	VERB
ap-662	163	42	x	x	SYM
ap-662	163	43	(	(	PUNCT
ap-662	163	44	here	here	ADV
ap-662	163	45	they	they	PRON
ap-662	163	46	act	act	VERB
ap-662	163	47	as	as	ADP
ap-662	163	48	residuals	residual	NOUN
ap-662	163	49	)	)	PUNCT
ap-662	163	50	.	.	PUNCT
ap-662	164	1	from	from	ADP
ap-662	164	2	a	a	DET
ap-662	164	3	comparison	comparison	NOUN
ap-662	164	4	of	of	ADP
ap-662	164	5	(	(	PUNCT
ap-662	164	6	34	34	NUM
ap-662	164	7	)	)	PUNCT
ap-662	164	8	with	with	ADP
ap-662	164	9	equations	equation	NOUN
ap-662	164	10	(	(	PUNCT
ap-662	164	11	24	24	NUM
ap-662	164	12	)	)	PUNCT
ap-662	164	13	and	and	CCONJ
ap-662	164	14	(	(	PUNCT
ap-662	164	15	25	25	NUM
ap-662	164	16	)	)	PUNCT
ap-662	164	17	it	it	PRON
ap-662	164	18	is	be	AUX
ap-662	164	19	obvious	obvious	ADJ
ap-662	164	20	that	that	SCONJ
ap-662	164	21	for	for	ADP
ap-662	164	22	computing	compute	VERB
ap-662	164	23	�	�	PROPN
ap-662	164	24	x	x	VERB
ap-662	164	25	we	we	PRON
ap-662	164	26	can	can	AUX
ap-662	164	27	use	use	VERB
ap-662	164	28	the	the	DET
ap-662	164	29	second	second	ADJ
ap-662	164	30	orthogonalization	orthogonalization	NOUN
ap-662	164	31	of	of	ADP
ap-662	164	32	algorithm	algorithm	NOUN
ap-662	164	33	gso	gso	PROPN
ap-662	164	34	.	.	PUNCT
ap-662	165	1	if	if	SCONJ
ap-662	165	2	the	the	DET
ap-662	165	3	gso	gso	PROPN
ap-662	165	4	second	second	ADJ
ap-662	165	5	orthogonalization	orthogonalization	NOUN
ap-662	165	6	is	be	AUX
ap-662	165	7	applied	apply	VERB
ap-662	165	8	to	to	PART
ap-662	165	9	matrix	matrix	VERB
ap-662	165	10	v	v	NOUN
ap-662	165	11	from	from	ADP
ap-662	165	12	the	the	DET
ap-662	165	13	singular	singular	ADJ
ap-662	165	14	decomposition	decomposition	NOUN
ap-662	165	15	m	m	VERB
ap-662	165	16	m	m	VERB
ap-662	165	17	mii	mii	PROPN
ap-662	165	18	ii	ii	PROPN
ap-662	165	19	ii	ii	PROPN
ap-662	165	20	�	�	PROPN
ap-662	165	21	�	�	PROPN
ap-662	165	22	(	(	PUNCT
ap-662	165	23	)	)	PUNCT
ap-662	165	24	(	(	PUNCT
ap-662	165	25	)	)	SYM
ap-662	165	26	1	1	NUM
ap-662	165	27	2	2	NUM
ap-662	165	28	�	�	PROPN
ap-662	165	29	�	�	PROPN
ap-662	165	30	,	,	PUNCT
ap-662	165	31	(	(	PUNCT
ap-662	165	32	35	35	NUM
ap-662	165	33	)	)	PUNCT
ap-662	165	34	we	we	PRON
ap-662	165	35	obtain	obtain	VERB
ap-662	165	36	matrix	matrix	NOUN
ap-662	165	37	�	�	NOUN
ap-662	165	38	v	v	NOUN
ap-662	165	39	.	.	PUNCT
ap-662	166	1	if	if	SCONJ
ap-662	166	2	we	we	PRON
ap-662	166	3	now	now	ADV
ap-662	166	4	replace	replace	VERB
ap-662	166	5	the	the	DET
ap-662	166	6	singular	singular	ADJ
ap-662	166	7	value	value	NOUN
ap-662	166	8	decomposition	decomposition	NOUN
ap-662	166	9	matrix	matrix	NOUN
ap-662	166	10	v	v	NOUN
ap-662	166	11	by	by	ADP
ap-662	166	12	matrix	matrix	NOUN
ap-662	166	13	�	�	PROPN
ap-662	166	14	v	v	NOUN
ap-662	166	15	,	,	PUNCT
ap-662	166	16	we	we	PRON
ap-662	166	17	can	can	AUX
ap-662	166	18	compute	compute	VERB
ap-662	166	19	vector	vector	NOUN
ap-662	166	20	�	�	PROPN
ap-662	166	21	x	x	SYM
ap-662	166	22	and	and	CCONJ
ap-662	166	23	all	all	DET
ap-662	166	24	cofactors	cofactor	NOUN
ap-662	166	25	according	accord	VERB
ap-662	166	26	to	to	ADP
ap-662	166	27	the	the	DET
ap-662	166	28	same	same	ADJ
ap-662	166	29	formulas	formula	NOUN
ap-662	166	30	(	(	PUNCT
ap-662	166	31	30–33	30–33	NUM
ap-662	166	32	)	)	PUNCT
ap-662	166	33	as	as	ADP
ap-662	166	34	in	in	ADP
ap-662	166	35	the	the	DET
ap-662	166	36	case	case	NOUN
ap-662	166	37	of	of	ADP
ap-662	166	38	standard	standard	ADJ
ap-662	166	39	svd	svd	PROPN
ap-662	166	40	solution	solution	NOUN
ap-662	166	41	x.	x.	NOUN
ap-662	166	42	7	7	NUM
ap-662	166	43	network	network	NOUN
ap-662	166	44	adjustment	adjustment	NOUN
ap-662	166	45	in	in	ADP
ap-662	166	46	gnu	gnu	PROPN
ap-662	166	47	gama	gama	PROPN
ap-662	166	48	gama	gama	NOUN
ap-662	166	49	was	be	AUX
ap-662	166	50	started	start	VERB
ap-662	166	51	in	in	ADP
ap-662	166	52	1998	1998	NUM
ap-662	166	53	as	as	ADP
ap-662	166	54	a	a	DET
ap-662	166	55	local	local	ADJ
ap-662	166	56	educational	educational	ADJ
ap-662	166	57	project	project	NOUN
ap-662	166	58	,	,	PUNCT
ap-662	166	59	mainly	mainly	ADV
ap-662	166	60	to	to	PART
ap-662	166	61	demonstrate	demonstrate	VERB
ap-662	166	62	to	to	ADP
ap-662	166	63	our	our	PRON
ap-662	166	64	students	student	NOUN
ap-662	166	65	the	the	DET
ap-662	166	66	power	power	NOUN
ap-662	166	67	and	and	CCONJ
ap-662	166	68	capability	capability	NOUN
ap-662	166	69	of	of	ADP
ap-662	166	70	object	object	NOUN
ap-662	166	71	programming	programming	NOUN
ap-662	166	72	(	(	PUNCT
ap-662	166	73	the	the	DET
ap-662	166	74	project	project	NOUN
ap-662	166	75	is	be	AUX
ap-662	166	76	written	write	VERB
ap-662	166	77	in	in	ADP
ap-662	166	78	c	c	PROPN
ap-662	166	79	�	�	PROPN
ap-662	166	80	�	�	PROPN
ap-662	166	81	)	)	PUNCT
ap-662	166	82	,	,	PUNCT
ap-662	166	83	and	and	CCONJ
ap-662	166	84	at	at	ADP
ap-662	166	85	the	the	DET
ap-662	166	86	same	same	ADJ
ap-662	166	87	time	time	NOUN
ap-662	166	88	to	to	PART
ap-662	166	89	show	show	VERB
ap-662	166	90	some	some	DET
ap-662	166	91	alternatives	alternative	NOUN
ap-662	166	92	to	to	ADP
ap-662	166	93	traditional	traditional	ADJ
ap-662	166	94	approaches	approach	NOUN
ap-662	166	95	to	to	ADP
ap-662	166	96	numerical	numerical	ADJ
ap-662	166	97	solutions	solution	NOUN
ap-662	166	98	of	of	ADP
ap-662	166	99	least	least	ADJ
ap-662	166	100	squares	square	NOUN
ap-662	166	101	adjustments	adjustment	NOUN
ap-662	166	102	based	base	VERB
ap-662	166	103	on	on	ADP
ap-662	166	104	normal	normal	ADJ
ap-662	166	105	equations	equation	NOUN
ap-662	166	106	.	.	PUNCT
ap-662	167	1	project	project	NOUN
ap-662	167	2	gama	gama	NOUN
ap-662	167	3	was	be	AUX
ap-662	167	4	released	release	VERB
ap-662	167	5	under	under	ADP
ap-662	167	6	the	the	DET
ap-662	167	7	terms	term	NOUN
ap-662	167	8	of	of	ADP
ap-662	167	9	the	the	DET
ap-662	167	10	gnu	gnu	PROPN
ap-662	167	11	general	general	ADJ
ap-662	167	12	public	public	ADJ
ap-662	167	13	license	license	NOUN
ap-662	167	14	,	,	PUNCT
ap-662	167	15	and	and	CCONJ
ap-662	167	16	in	in	ADP
ap-662	167	17	2001	2001	NUM
ap-662	167	18	received	receive	VERB
ap-662	167	19	the	the	DET
ap-662	167	20	official	official	ADJ
ap-662	167	21	status	status	NOUN
ap-662	167	22	of	of	ADP
ap-662	167	23	gnu	gnu	PROPN
ap-662	167	24	software	software	PROPN
ap-662	167	25	.	.	PUNCT
ap-662	168	1	numerical	numerical	ADJ
ap-662	168	2	solution	solution	NOUN
ap-662	168	3	of	of	ADP
ap-662	168	4	geodetic	geodetic	ADJ
ap-662	168	5	network	network	NOUN
ap-662	168	6	adjustment	adjustment	NOUN
ap-662	168	7	in	in	ADP
ap-662	168	8	gama	gama	NOUN
ap-662	168	9	is	be	AUX
ap-662	168	10	based	base	VERB
ap-662	168	11	on	on	ADP
ap-662	168	12	an	an	DET
ap-662	168	13	abstract	abstract	ADJ
ap-662	168	14	c	c	PROPN
ap-662	168	15	�	�	NOUN
ap-662	168	16	�	�	PROPN
ap-662	168	17	class	class	NOUN
ap-662	168	18	and	and	CCONJ
ap-662	168	19	currently	currently	ADV
ap-662	168	20	two	two	NUM
ap-662	168	21	derived	derived	ADJ
ap-662	168	22	classes	class	NOUN
ap-662	168	23	are	be	AUX
ap-662	168	24	available	available	ADJ
ap-662	168	25	implementing	implement	VERB
ap-662	168	26	algorithms	algorithm	NOUN
ap-662	168	27	svd	svd	PROPN
ap-662	168	28	and	and	CCONJ
ap-662	168	29	gso	gso	PROPN
ap-662	168	30	.	.	PROPN
ap-662	169	1	svd	svd	PROPN
ap-662	169	2	is	be	AUX
ap-662	169	3	the	the	DET
ap-662	169	4	primary	primary	ADJ
ap-662	169	5	algorithm	algorithm	NOUN
ap-662	169	6	used	use	VERB
ap-662	169	7	in	in	ADP
ap-662	169	8	gama	gama	NOUN
ap-662	169	9	(	(	PUNCT
ap-662	169	10	one	one	NUM
ap-662	169	11	of	of	ADP
ap-662	169	12	our	our	PRON
ap-662	169	13	long	long	ADJ
ap-662	169	14	term	term	NOUN
ap-662	169	15	goals	goal	NOUN
ap-662	169	16	is	be	AUX
ap-662	169	17	to	to	PART
ap-662	169	18	add	add	VERB
ap-662	169	19	more	more	ADJ
ap-662	169	20	numerical	numerical	ADJ
ap-662	169	21	solutions	solution	NOUN
ap-662	169	22	,	,	PUNCT
ap-662	169	23	namely	namely	ADV
ap-662	169	24	solutions	solution	NOUN
ap-662	169	25	exploiting	exploit	VERB
ap-662	169	26	the	the	DET
ap-662	169	27	sparse	sparse	ADJ
ap-662	169	28	structure	structure	NOUN
ap-662	169	29	of	of	ADP
ap-662	169	30	project	project	NOUN
ap-662	169	31	equations	equation	NOUN
ap-662	169	32	)	)	PUNCT
ap-662	169	33	.	.	PUNCT
ap-662	170	1	from	from	ADP
ap-662	170	2	this	this	DET
ap-662	170	3	perspective	perspective	NOUN
ap-662	170	4	,	,	PUNCT
ap-662	170	5	algorithm	algorithm	PROPN
ap-662	170	6	gso	gso	PROPN
ap-662	170	7	was	be	AUX
ap-662	170	8	implemented	implement	VERB
ap-662	170	9	in	in	ADP
ap-662	170	10	gama	gama	NOUN
ap-662	170	11	only	only	ADV
ap-662	170	12	as	as	ADP
ap-662	170	13	an	an	DET
ap-662	170	14	testing	testing	NOUN
ap-662	170	15	alternative	alternative	NOUN
ap-662	170	16	,	,	PUNCT
ap-662	170	17	both	both	PRON
ap-662	170	18	for	for	ADP
ap-662	170	19	comparing	compare	VERB
ap-662	170	20	numerical	numerical	ADJ
ap-662	170	21	results	result	NOUN
ap-662	170	22	and	and	CCONJ
ap-662	170	23	for	for	ADP
ap-662	170	24	testing	test	VERB
ap-662	170	25	the	the	DET
ap-662	170	26	hierarchy	hierarchy	NOUN
ap-662	170	27	of	of	ADP
ap-662	170	28	the	the	DET
ap-662	170	29	adjustment	adjustment	NOUN
ap-662	170	30	classes	class	NOUN
ap-662	170	31	in	in	ADP
ap-662	170	32	practice	practice	NOUN
ap-662	170	33	.	.	PUNCT
ap-662	171	1	it	it	PRON
ap-662	171	2	is	be	AUX
ap-662	171	3	generally	generally	ADV
ap-662	171	4	agreed	agree	VERB
ap-662	171	5	that	that	SCONJ
ap-662	171	6	a	a	DET
ap-662	171	7	bad	bad	ADJ
ap-662	171	8	implementation	implementation	NOUN
ap-662	171	9	of	of	ADP
ap-662	171	10	gso	gso	PROPN
ap-662	171	11	can	can	AUX
ap-662	171	12	produce	produce	VERB
ap-662	171	13	disastrous	disastrous	ADJ
ap-662	171	14	results	result	NOUN
ap-662	171	15	.	.	PUNCT
ap-662	172	1	for	for	ADP
ap-662	172	2	example	example	NOUN
ap-662	172	3	,	,	PUNCT
ap-662	172	4	during	during	ADP
ap-662	172	5	the	the	DET
ap-662	172	6	first	first	ADJ
ap-662	172	7	orthogonalization	orthogonalization	NOUN
ap-662	172	8	step	step	NOUN
ap-662	172	9	of	of	ADP
ap-662	172	10	gso	gso	PROPN
ap-662	172	11	we	we	PRON
ap-662	172	12	set	set	VERB
ap-662	172	13	to	to	ADP
ap-662	172	14	zeros	zero	NOUN
ap-662	172	15	the	the	DET
ap-662	172	16	unknown	unknown	ADJ
ap-662	172	17	parameters	parameter	NOUN
ap-662	172	18	corresponding	correspond	VERB
ap-662	172	19	to	to	ADP
ap-662	172	20	linearly	linearly	ADV
ap-662	172	21	dependent	dependent	ADJ
ap-662	172	22	columns	column	NOUN
ap-662	172	23	.	.	PUNCT
ap-662	173	1	in	in	ADP
ap-662	173	2	the	the	DET
ap-662	173	3	case	case	NOUN
ap-662	173	4	of	of	ADP
ap-662	173	5	a	a	DET
ap-662	173	6	free	free	ADJ
ap-662	173	7	geodetic	geodetic	ADJ
ap-662	173	8	network	network	NOUN
ap-662	173	9	adjustment	adjustment	NOUN
ap-662	173	10	these	these	PRON
ap-662	173	11	are	be	AUX
ap-662	173	12	the	the	DET
ap-662	173	13	coordinates	coordinate	NOUN
ap-662	173	14	of	of	ADP
ap-662	173	15	certain	certain	ADJ
ap-662	173	16	points	point	NOUN
ap-662	173	17	–	–	PUNCT
ap-662	173	18	the	the	DET
ap-662	173	19	whole	whole	ADJ
ap-662	173	20	network	network	NOUN
ap-662	173	21	is	be	AUX
ap-662	173	22	pinned	pin	VERB
ap-662	173	23	on	on	ADP
ap-662	173	24	these	these	DET
ap-662	173	25	points	point	NOUN
ap-662	173	26	and	and	CCONJ
ap-662	173	27	clearly	clearly	ADV
ap-662	173	28	,	,	PUNCT
ap-662	173	29	if	if	SCONJ
ap-662	173	30	close	close	ADJ
ap-662	173	31	points	point	NOUN
ap-662	173	32	are	be	AUX
ap-662	173	33	selected	select	VERB
ap-662	173	34	the	the	DET
ap-662	173	35	regularization	regularization	NOUN
ap-662	173	36	is	be	AUX
ap-662	173	37	unstable	unstable	ADJ
ap-662	173	38	.	.	PUNCT
ap-662	174	1	the	the	DET
ap-662	174	2	order	order	NOUN
ap-662	174	3	of	of	ADP
ap-662	174	4	the	the	DET
ap-662	174	5	columns	column	NOUN
ap-662	174	6	in	in	ADP
ap-662	174	7	the	the	DET
ap-662	174	8	orthogonalization	orthogonalization	NOUN
ap-662	174	9	is	be	AUX
ap-662	174	10	important	important	ADJ
ap-662	174	11	.	.	PUNCT
ap-662	175	1	from	from	ADP
ap-662	175	2	practical	practical	ADJ
ap-662	175	3	experience	experience	NOUN
ap-662	175	4	we	we	PRON
ap-662	175	5	know	know	VERB
ap-662	175	6	that	that	SCONJ
ap-662	175	7	vector	vector	NOUN
ap-662	175	8	norms	norm	NOUN
ap-662	175	9	in	in	ADP
ap-662	175	10	the	the	DET
ap-662	175	11	gso	gso	PROPN
ap-662	175	12	orthogonalization	orthogonalization	NOUN
ap-662	175	13	process	process	NOUN
ap-662	175	14	generally	generally	ADV
ap-662	175	15	tend	tend	VERB
ap-662	175	16	to	to	PART
ap-662	175	17	decrease	decrease	VERB
ap-662	175	18	.	.	PUNCT
ap-662	176	1	as	as	SCONJ
ap-662	176	2	gso	gso	PROPN
ap-662	176	3	is	be	AUX
ap-662	176	4	just	just	ADV
ap-662	176	5	an	an	DET
ap-662	176	6	alternative	alternative	ADJ
ap-662	176	7	algorithm	algorithm	NOUN
ap-662	176	8	in	in	ADP
ap-662	176	9	gama	gama	NOUN
ap-662	176	10	and	and	CCONJ
ap-662	176	11	its	its	PRON
ap-662	176	12	performance	performance	NOUN
ap-662	176	13	is	be	AUX
ap-662	176	14	not	not	PART
ap-662	176	15	a	a	DET
ap-662	176	16	crucial	crucial	ADJ
ap-662	176	17	point	point	NOUN
ap-662	176	18	,	,	PUNCT
ap-662	176	19	we	we	PRON
ap-662	176	20	implemented	implement	VERB
ap-662	176	21	it	it	PRON
ap-662	176	22	with	with	ADP
ap-662	176	23	full	full	ADJ
ap-662	176	24	pivoting	pivoting	NOUN
ap-662	176	25	,	,	PUNCT
ap-662	176	26	i.e.	i.e.	X
ap-662	176	27	,	,	PUNCT
ap-662	176	28	in	in	ADP
ap-662	176	29	each	each	DET
ap-662	176	30	orthogonalization	orthogonalization	NOUN
ap-662	176	31	cycle	cycle	NOUN
ap-662	176	32	the	the	DET
ap-662	176	33	vector	vector	NOUN
ap-662	176	34	with	with	ADP
ap-662	176	35	the	the	DET
ap-662	176	36	maximal	maximal	ADJ
ap-662	176	37	norm	norm	NOUN
ap-662	176	38	is	be	AUX
ap-662	176	39	selected	select	VERB
ap-662	176	40	as	as	ADP
ap-662	176	41	a	a	DET
ap-662	176	42	pivot	pivot	NOUN
ap-662	176	43	(	(	PUNCT
ap-662	176	44	with	with	ADP
ap-662	176	45	this	this	DET
ap-662	176	46	modification	modification	NOUN
ap-662	176	47	gso	gso	NOUN
ap-662	176	48	is	be	AUX
ap-662	176	49	about	about	ADV
ap-662	176	50	twice	twice	ADV
ap-662	176	51	as	as	ADV
ap-662	176	52	slow	slow	ADJ
ap-662	176	53	as	as	ADP
ap-662	176	54	svd	svd	PROPN
ap-662	176	55	for	for	ADP
ap-662	176	56	large	large	ADJ
ap-662	176	57	networks	network	NOUN
ap-662	176	58	)	)	PUNCT
ap-662	176	59	.	.	PUNCT
ap-662	177	1	singular	singular	PROPN
ap-662	177	2	value	value	NOUN
ap-662	177	3	decomposition	decomposition	NOUN
ap-662	177	4	is	be	AUX
ap-662	177	5	a	a	DET
ap-662	177	6	very	very	ADV
ap-662	177	7	robust	robust	ADJ
ap-662	177	8	method	method	NOUN
ap-662	177	9	for	for	ADP
ap-662	177	10	dealing	deal	VERB
ap-662	177	11	with	with	ADP
ap-662	177	12	systems	system	NOUN
ap-662	177	13	that	that	PRON
ap-662	177	14	are	be	AUX
ap-662	177	15	either	either	CCONJ
ap-662	177	16	singular	singular	ADJ
ap-662	177	17	or	or	CCONJ
ap-662	177	18	numerically	numerically	ADV
ap-662	177	19	close	close	ADJ
ap-662	177	20	to	to	ADP
ap-662	177	21	singular	singular	NOUN
ap-662	177	22	.	.	PUNCT
ap-662	178	1	even	even	ADV
ap-662	178	2	with	with	ADP
ap-662	178	3	full	full	ADJ
ap-662	178	4	pivoting	pivoting	NOUN
ap-662	178	5	we	we	PRON
ap-662	178	6	had	have	AUX
ap-662	178	7	expected	expect	VERB
ap-662	178	8	gso	gso	PROPN
ap-662	178	9	to	to	PART
ap-662	178	10	prove	prove	VERB
ap-662	178	11	to	to	PART
ap-662	178	12	be	be	AUX
ap-662	178	13	inferior	inferior	ADJ
ap-662	178	14	to	to	ADP
ap-662	178	15	svd	svd	PROPN
ap-662	178	16	,	,	PUNCT
ap-662	178	17	at	at	ADP
ap-662	178	18	least	least	ADJ
ap-662	178	19	in	in	ADP
ap-662	178	20	cases	case	NOUN
ap-662	178	21	with	with	ADP
ap-662	178	22	illconditioned	illconditione	VERB
ap-662	178	23	matrices	matrix	NOUN
ap-662	178	24	.	.	PUNCT
ap-662	179	1	surprisingly	surprisingly	ADV
ap-662	179	2	,	,	PUNCT
ap-662	179	3	with	with	ADP
ap-662	179	4	all	all	DET
ap-662	179	5	the	the	DET
ap-662	179	6	real	real	ADJ
ap-662	179	7	geodetic	geodetic	ADJ
ap-662	179	8	networks	network	NOUN
ap-662	179	9	that	that	PRON
ap-662	179	10	we	we	PRON
ap-662	179	11	have	have	VERB
ap-662	179	12	available	available	ADJ
ap-662	179	13	this	this	PRON
ap-662	179	14	was	be	AUX
ap-662	179	15	not	not	PART
ap-662	179	16	the	the	DET
ap-662	179	17	case	case	NOUN
ap-662	179	18	.	.	PUNCT
ap-662	180	1	apart	apart	ADV
ap-662	180	2	from	from	ADP
ap-662	180	3	real	real	ADJ
ap-662	180	4	data	datum	NOUN
ap-662	180	5	,	,	PUNCT
ap-662	180	6	we	we	PRON
ap-662	180	7	used	use	VERB
ap-662	180	8	series	series	NOUN
ap-662	180	9	of	of	ADP
ap-662	180	10	randomly	randomly	ADV
ap-662	180	11	generated	generate	VERB
ap-662	180	12	three	three	NUM
ap-662	180	13	-	-	PUNCT
ap-662	180	14	dimensional	dimensional	ADJ
ap-662	180	15	networks	network	NOUN
ap-662	180	16	for	for	ADP
ap-662	180	17	testing	testing	NOUN
ap-662	180	18	.	.	PUNCT
ap-662	181	1	our	our	PRON
ap-662	181	2	implementation	implementation	NOUN
ap-662	181	3	of	of	ADP
ap-662	181	4	svd	svd	PROPN
ap-662	181	5	is	be	AUX
ap-662	181	6	based	base	VERB
ap-662	181	7	on	on	ADP
ap-662	181	8	a	a	DET
ap-662	181	9	classical	classical	ADJ
ap-662	181	10	algorithm	algorithm	NOUN
ap-662	181	11	published	publish	VERB
ap-662	181	12	by	by	ADP
ap-662	181	13	golub	golub	PROPN
ap-662	181	14	and	and	CCONJ
ap-662	181	15	reinsch	reinsch	ADJ
ap-662	181	16	[	[	X
ap-662	181	17	7	7	X
ap-662	181	18	]	]	X
ap-662	181	19	(	(	PUNCT
ap-662	181	20	the	the	DET
ap-662	181	21	algol	algol	NOUN
ap-662	181	22	procedure	procedure	NOUN
ap-662	181	23	svd	svd	PROPN
ap-662	181	24	)	)	PUNCT
ap-662	181	25	.	.	PUNCT
ap-662	182	1	the	the	DET
ap-662	182	2	decomposition	decomposition	NOUN
ap-662	182	3	is	be	AUX
ap-662	182	4	constructed	construct	VERB
ap-662	182	5	in	in	ADP
ap-662	182	6	two	two	NUM
ap-662	182	7	phases	phase	NOUN
ap-662	182	8	.	.	PUNCT
ap-662	183	1	it	it	PRON
ap-662	183	2	starts	start	VERB
ap-662	183	3	with	with	ADP
ap-662	183	4	the	the	DET
ap-662	183	5	householder	householder	ADJ
ap-662	183	6	reduction	reduction	NOUN
ap-662	183	7	to	to	ADP
ap-662	183	8	bidiagonal	bidiagonal	ADJ
ap-662	183	9	form	form	NOUN
ap-662	183	10	,	,	PUNCT
ap-662	183	11	followed	follow	VERB
ap-662	183	12	by	by	ADP
ap-662	183	13	diagonalization	diagonalization	NOUN
ap-662	183	14	.	.	PUNCT
ap-662	184	1	contrary	contrary	ADJ
ap-662	184	2	to	to	ADP
ap-662	184	3	our	our	PRON
ap-662	184	4	expectations	expectation	NOUN
ap-662	184	5	,	,	PUNCT
ap-662	184	6	svd	svd	PROPN
ap-662	184	7	as	as	SCONJ
ap-662	184	8	used	use	VERB
ap-662	184	9	in	in	ADP
ap-662	184	10	gama	gama	NOUN
ap-662	184	11	has	have	AUX
ap-662	184	12	not	not	PART
ap-662	184	13	proved	prove	VERB
ap-662	184	14	to	to	PART
ap-662	184	15	give	give	VERB
ap-662	184	16	numerically	numerically	ADV
ap-662	184	17	better	well	ADJ
ap-662	184	18	results	result	NOUN
ap-662	184	19	and	and	CCONJ
ap-662	184	20	in	in	ADP
ap-662	184	21	some	some	DET
ap-662	184	22	cases	case	NOUN
ap-662	184	23	it	it	PRON
ap-662	184	24	has	have	AUX
ap-662	184	25	even	even	ADV
ap-662	184	26	lost	lose	VERB
ap-662	184	27	convergence	convergence	NOUN
ap-662	184	28	in	in	ADP
ap-662	184	29	the	the	DET
ap-662	184	30	diagonalization	diagonalization	NOUN
ap-662	184	31	phase	phase	NOUN
ap-662	184	32	.	.	PUNCT
ap-662	185	1	a	a	DET
ap-662	185	2	simple	simple	ADJ
ap-662	185	3	and	and	CCONJ
ap-662	185	4	tempting	tempting	ADJ
ap-662	185	5	explanation	explanation	NOUN
ap-662	185	6	that	that	PRON
ap-662	185	7	comes	come	VERB
ap-662	185	8	first	first	ADV
ap-662	185	9	to	to	ADP
ap-662	185	10	mind	mind	NOUN
ap-662	185	11	would	would	AUX
ap-662	185	12	be	be	AUX
ap-662	185	13	that	that	SCONJ
ap-662	185	14	the	the	DET
ap-662	185	15	svd	svd	PROPN
ap-662	185	16	implementation	implementation	NOUN
ap-662	185	17	in	in	ADP
ap-662	185	18	gama	gama	NOUN
ap-662	185	19	is	be	AUX
ap-662	185	20	somehow	somehow	ADV
ap-662	185	21	wrong	wrong	ADJ
ap-662	185	22	.	.	PUNCT
ap-662	186	1	after	after	ADP
ap-662	186	2	all	all	DET
ap-662	186	3	testing	testing	NOUN
ap-662	186	4	and	and	CCONJ
ap-662	186	5	revisions	revision	NOUN
ap-662	186	6	this	this	PRON
ap-662	186	7	does	do	AUX
ap-662	186	8	not	not	PART
ap-662	186	9	seem	seem	VERB
ap-662	186	10	to	to	PART
ap-662	186	11	be	be	AUX
ap-662	186	12	the	the	DET
ap-662	186	13	point	point	NOUN
ap-662	186	14	.	.	PUNCT
ap-662	187	1	a	a	DET
ap-662	187	2	possible	possible	ADJ
ap-662	187	3	explanation	explanation	NOUN
ap-662	187	4	might	might	AUX
ap-662	187	5	be	be	AUX
ap-662	187	6	given	give	VERB
ap-662	187	7	by	by	ADP
ap-662	187	8	the	the	DET
ap-662	187	9	following	follow	VERB
ap-662	187	10	quotation	quotation	NOUN
ap-662	187	11	from	from	ADP
ap-662	187	12	[	[	X
ap-662	187	13	3	3	NUM
ap-662	187	14	]	]	PUNCT
ap-662	187	15	…	…	PUNCT
ap-662	187	16	finally	finally	ADV
ap-662	187	17	,	,	PUNCT
ap-662	187	18	we	we	PRON
ap-662	187	19	mention	mention	VERB
ap-662	187	20	jacobi	jacobi	PROPN
ap-662	187	21	’s	’s	PART
ap-662	187	22	method	method	NOUN
ap-662	187	23	…	…	PUNCT
ap-662	187	24	for	for	ADP
ap-662	187	25	the	the	DET
ap-662	187	26	svd	svd	PROPN
ap-662	187	27	.	.	PUNCT
ap-662	188	1	this	this	DET
ap-662	188	2	transformation	transformation	NOUN
ap-662	188	3	method	method	NOUN
ap-662	188	4	repeatedly	repeatedly	ADV
ap-662	188	5	multiplies	multiply	VERB
ap-662	188	6	a	a	PRON
ap-662	188	7	on	on	ADP
ap-662	188	8	the	the	DET
ap-662	188	9	right	right	NOUN
ap-662	188	10	by	by	ADP
ap-662	188	11	elementary	elementary	ADJ
ap-662	188	12	orthogonal	orthogonal	ADJ
ap-662	188	13	matrices	matrix	NOUN
ap-662	188	14	(	(	PUNCT
ap-662	188	15	jacobi	jacobi	PROPN
ap-662	188	16	rotations	rotation	NOUN
ap-662	188	17	)	)	PUNCT
ap-662	188	18	until	until	SCONJ
ap-662	188	19	a	a	DET
ap-662	188	20	converges	converge	NOUN
ap-662	188	21	to	to	AUX
ap-662	188	22	u	u	NOUN
ap-662	188	23	�	�	PROPN
ap-662	188	24	;	;	NOUN
ap-662	188	25	the	the	DET
ap-662	188	26	product	product	NOUN
ap-662	188	27	of	of	ADP
ap-662	188	28	the	the	DET
ap-662	188	29	jacobi	jacobi	PROPN
ap-662	188	30	rotations	rotation	NOUN
ap-662	188	31	is	be	AUX
ap-662	188	32	v.	v.	ADP
ap-662	188	33	jacobi	jacobi	PROPN
ap-662	188	34	is	be	AUX
ap-662	188	35	slower	slow	ADJ
ap-662	188	36	than	than	ADP
ap-662	188	37	any	any	PRON
ap-662	188	38	of	of	ADP
ap-662	188	39	the	the	DET
ap-662	188	40	above	above	ADJ
ap-662	188	41	transformation	transformation	NOUN
ap-662	188	42	methods	method	NOUN
ap-662	188	43	(	(	PUNCT
ap-662	188	44	it	it	PRON
ap-662	188	45	can	can	AUX
ap-662	188	46	be	be	AUX
ap-662	188	47	made	make	VERB
ap-662	188	48	to	to	PART
ap-662	188	49	run	run	VERB
ap-662	188	50	within	within	ADP
ap-662	188	51	about	about	ADP
ap-662	188	52	twice	twice	DET
ap-662	188	53	the	the	DET
ap-662	188	54	time	time	NOUN
ap-662	188	55	of	of	ADP
ap-662	188	56	qr	qr	NOUN
ap-662	188	57	…	…	PUNCT
ap-662	188	58	)	)	PUNCT
ap-662	188	59	but	but	CCONJ
ap-662	188	60	has	have	VERB
ap-662	188	61	the	the	DET
ap-662	188	62	useful	useful	ADJ
ap-662	188	63	property	property	NOUN
ap-662	188	64	that	that	PRON
ap-662	188	65	for	for	ADP
ap-662	188	66	certain	certain	ADJ
ap-662	188	67	a	a	PRON
ap-662	188	68	it	it	PRON
ap-662	188	69	can	can	AUX
ap-662	188	70	deliver	deliver	VERB
ap-662	188	71	the	the	DET
ap-662	188	72	tiny	tiny	ADJ
ap-662	188	73	singular	singular	ADJ
ap-662	188	74	values	value	NOUN
ap-662	188	75	,	,	PUNCT
ap-662	188	76	and	and	CCONJ
ap-662	188	77	their	their	PRON
ap-662	188	78	singular	singular	ADJ
ap-662	188	79	vectors	vector	NOUN
ap-662	188	80	,	,	PUNCT
ap-662	188	81	much	much	ADV
ap-662	188	82	more	more	ADV
ap-662	188	83	accurately	accurately	ADV
ap-662	188	84	than	than	ADP
ap-662	188	85	any	any	PRON
ap-662	188	86	of	of	ADP
ap-662	188	87	the	the	DET
ap-662	188	88	above	above	ADJ
ap-662	188	89	methods	method	NOUN
ap-662	188	90	provided	provide	VERB
ap-662	188	91	that	that	SCONJ
ap-662	188	92	it	it	PRON
ap-662	188	93	is	be	AUX
ap-662	188	94	properly	properly	ADV
ap-662	188	95	implemented	implement	VERB
ap-662	188	96	…	…	PUNCT
ap-662	188	97	surely	surely	ADV
ap-662	188	98	to	to	PART
ap-662	188	99	have	have	VERB
ap-662	188	100	more	more	ADJ
ap-662	188	101	numerical	numerical	ADJ
ap-662	188	102	methods	method	NOUN
ap-662	188	103	implemented	implement	VERB
ap-662	188	104	in	in	ADP
ap-662	188	105	gama	gama	NOUN
ap-662	188	106	would	would	AUX
ap-662	188	107	be	be	AUX
ap-662	188	108	helpful	helpful	ADJ
ap-662	188	109	,	,	PUNCT
ap-662	188	110	for	for	ADP
ap-662	188	111	example	example	NOUN
ap-662	188	112	the	the	DET
ap-662	188	113	above	above	ADV
ap-662	188	114	mentioned	mention	VERB
ap-662	188	115	jacobi	jacobi	PROPN
ap-662	188	116	method	method	NOUN
ap-662	188	117	for	for	ADP
ap-662	188	118	svd	svd	PROPN
ap-662	188	119	.	.	PUNCT
ap-662	189	1	a	a	DET
ap-662	189	2	practical	practical	ADJ
ap-662	189	3	problem	problem	NOUN
ap-662	189	4	during	during	ADP
ap-662	189	5	testing	testing	NOUN
ap-662	189	6	of	of	ADP
ap-662	189	7	the	the	DET
ap-662	189	8	adjustment	adjustment	NOUN
ap-662	189	9	methods	method	NOUN
ap-662	189	10	in	in	ADP
ap-662	189	11	gama	gama	NOUN
ap-662	189	12	was	be	AUX
ap-662	189	13	the	the	DET
ap-662	189	14	relative	relative	ADJ
ap-662	189	15	shortage	shortage	NOUN
ap-662	189	16	of	of	ADP
ap-662	189	17	reliable	reliable	ADJ
ap-662	189	18	observation	observation	NOUN
ap-662	189	19	data	datum	NOUN
ap-662	189	20	and	and	CCONJ
ap-662	189	21	their	their	PRON
ap-662	189	22	adjustment	adjustment	NOUN
ap-662	189	23	results	result	NOUN
ap-662	189	24	for	for	ADP
ap-662	189	25	testing	testing	NOUN
ap-662	189	26	.	.	PUNCT
ap-662	190	1	to	to	PART
ap-662	190	2	enable	enable	VERB
ap-662	190	3	easy	easy	ADJ
ap-662	190	4	comparison	comparison	NOUN
ap-662	190	5	with	with	ADP
ap-662	190	6	other	other	ADJ
ap-662	190	7	softwares	software	NOUN
ap-662	190	8	we	we	PRON
ap-662	190	9	made	make	VERB
ap-662	190	10	a	a	DET
ap-662	190	11	description	description	NOUN
ap-662	190	12	of	of	ADP
ap-662	190	13	geodetic	geodetic	ADJ
ap-662	190	14	networks	network	NOUN
ap-662	190	15	in	in	ADP
ap-662	190	16	xml	xml	NOUN
ap-662	190	17	(	(	PUNCT
ap-662	190	18	we	we	PRON
ap-662	190	19	use	use	VERB
ap-662	190	20	dtd	dtd	NOUN
ap-662	190	21	for	for	ADP
ap-662	190	22	the	the	DET
ap-662	190	23	definition	definition	NOUN
ap-662	190	24	©	©	PROPN
ap-662	190	25	czech	czech	PROPN
ap-662	190	26	technical	technical	PROPN
ap-662	190	27	university	university	PROPN
ap-662	190	28	publishing	publishing	NOUN
ap-662	190	29	housee	housee	PROPN
ap-662	190	30	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-662	190	31	17	17	NUM
ap-662	190	32	czech	czech	PROPN
ap-662	190	33	technical	technical	PROPN
ap-662	190	34	university	university	PROPN
ap-662	190	35	in	in	ADP
ap-662	190	36	prague	prague	PROPN
ap-662	190	37	acta	acta	PROPN
ap-662	190	38	polytechnica	polytechnica	PROPN
ap-662	190	39	vol	vol	NOUN
ap-662	190	40	.	.	PROPN
ap-662	191	1	45	45	NUM
ap-662	191	2	no	no	NOUN
ap-662	191	3	.	.	PUNCT
ap-662	192	1	1/2005	1/2005	NUM
ap-662	192	2	of	of	ADP
ap-662	192	3	the	the	DET
ap-662	192	4	formal	formal	ADJ
ap-662	192	5	syntax	syntax	NOUN
ap-662	192	6	of	of	ADP
ap-662	192	7	our	our	PRON
ap-662	192	8	structured	structured	ADJ
ap-662	192	9	data	datum	NOUN
ap-662	192	10	)	)	PUNCT
ap-662	192	11	.	.	PUNCT
ap-662	193	1	conversion	conversion	NOUN
ap-662	193	2	from	from	ADP
ap-662	193	3	a	a	DET
ap-662	193	4	well	well	ADV
ap-662	193	5	defined	define	VERB
ap-662	193	6	data	data	NOUN
ap-662	193	7	format	format	NOUN
ap-662	193	8	into	into	ADP
ap-662	193	9	xml	xml	NOUN
ap-662	193	10	is	be	AUX
ap-662	193	11	a	a	DET
ap-662	193	12	relatively	relatively	ADV
ap-662	193	13	simple	simple	ADJ
ap-662	193	14	task	task	NOUN
ap-662	193	15	,	,	PUNCT
ap-662	193	16	but	but	CCONJ
ap-662	193	17	processing	processing	NOUN
ap-662	193	18	of	of	ADP
ap-662	193	19	xml	xml	NOUN
ap-662	193	20	is	be	AUX
ap-662	193	21	not	not	PART
ap-662	193	22	a	a	DET
ap-662	193	23	trivial	trivial	ADJ
ap-662	193	24	task	task	NOUN
ap-662	193	25	and	and	CCONJ
ap-662	193	26	can	can	AUX
ap-662	193	27	not	not	PART
ap-662	193	28	be	be	AUX
ap-662	193	29	done	do	VERB
ap-662	193	30	without	without	ADP
ap-662	193	31	an	an	DET
ap-662	193	32	xml	xml	NOUN
ap-662	193	33	parser	parser	NOUN
ap-662	193	34	.	.	PUNCT
ap-662	194	1	in	in	ADP
ap-662	194	2	the	the	DET
ap-662	194	3	gnu	gnu	PROPN
ap-662	194	4	gama	gama	PROPN
ap-662	194	5	project	project	NOUN
ap-662	194	6	we	we	PRON
ap-662	194	7	use	use	VERB
ap-662	194	8	the	the	DET
ap-662	194	9	xml	xml	NOUN
ap-662	194	10	parser	parser	NOUN
ap-662	194	11	expat	expat	NOUN
ap-662	194	12	by	by	ADP
ap-662	194	13	james	james	PROPN
ap-662	194	14	clark	clark	PROPN
ap-662	194	15	,	,	PUNCT
ap-662	194	16	see	see	VERB
ap-662	194	17	http://expat.sourceforge.net/.	http://expat.sourceforge.net/.	NOUN
ap-662	194	18	we	we	PRON
ap-662	194	19	believe	believe	VERB
ap-662	194	20	that	that	SCONJ
ap-662	194	21	xml	xml	NOUN
ap-662	194	22	is	be	AUX
ap-662	194	23	the	the	DET
ap-662	194	24	best	good	ADJ
ap-662	194	25	data	data	NOUN
ap-662	194	26	format	format	NOUN
ap-662	194	27	for	for	ADP
ap-662	194	28	description	description	NOUN
ap-662	194	29	and	and	CCONJ
ap-662	194	30	exchange	exchange	NOUN
ap-662	194	31	of	of	ADP
ap-662	194	32	structured	structured	ADJ
ap-662	194	33	data	datum	NOUN
ap-662	194	34	in	in	ADP
ap-662	194	35	the	the	DET
ap-662	194	36	gama	gama	NOUN
ap-662	194	37	project	project	NOUN
ap-662	194	38	.	.	PUNCT
ap-662	195	1	one	one	NUM
ap-662	195	2	of	of	ADP
ap-662	195	3	the	the	DET
ap-662	195	4	goals	goal	NOUN
ap-662	195	5	of	of	ADP
ap-662	195	6	our	our	PRON
ap-662	195	7	project	project	NOUN
ap-662	195	8	is	be	AUX
ap-662	195	9	to	to	PART
ap-662	195	10	compile	compile	VERB
ap-662	195	11	a	a	DET
ap-662	195	12	free	free	ADJ
ap-662	195	13	collection	collection	NOUN
ap-662	195	14	of	of	ADP
ap-662	195	15	geodetic	geodetic	ADJ
ap-662	195	16	networks	network	NOUN
ap-662	195	17	described	describe	VERB
ap-662	195	18	in	in	ADP
ap-662	195	19	xml	xml	PROPN
ap-662	195	20	.	.	PUNCT
ap-662	196	1	references	reference	NOUN
ap-662	196	2	[	[	X
ap-662	196	3	1	1	NUM
ap-662	196	4	]	]	X
ap-662	196	5	vaníček	vaníček	NOUN
ap-662	196	6	,	,	PUNCT
ap-662	196	7	p.	p.	NOUN
ap-662	196	8	,	,	PUNCT
ap-662	196	9	krakiwsky	krakiwsky	NOUN
ap-662	196	10	,	,	PUNCT
ap-662	196	11	e.	e.	PROPN
ap-662	196	12	j.	j.	PROPN
ap-662	196	13	:	:	PUNCT
ap-662	196	14	“	"	PUNCT
ap-662	196	15	geodesy	geodesy	NOUN
ap-662	196	16	:	:	PUNCT
ap-662	196	17	the	the	DET
ap-662	196	18	concepts	concept	NOUN
ap-662	196	19	”	"	PUNCT
ap-662	196	20	,	,	PUNCT
ap-662	196	21	north	north	NOUN
ap-662	196	22	-	-	PUNCT
ap-662	196	23	holland	holland	PROPN
ap-662	196	24	,	,	PUNCT
ap-662	196	25	2nd	2nd	PROPN
ap-662	196	26	.	.	PUNCT
ap-662	197	1	ed	ed	NOUN
ap-662	197	2	.	.	PUNCT
ap-662	198	1	(	(	PUNCT
ap-662	198	2	1986	1986	NUM
ap-662	198	3	)	)	PUNCT
ap-662	198	4	,	,	PUNCT
ap-662	198	5	isbn	isbn	ADJ
ap-662	198	6	0	0	NUM
ap-662	198	7	-	-	PUNCT
ap-662	198	8	444	444	NUM
ap-662	198	9	-	-	PUNCT
ap-662	198	10	87775	87775	NUM
ap-662	198	11	-	-	PUNCT
ap-662	198	12	4	4	NUM
ap-662	198	13	.	.	PUNCT
ap-662	199	1	[	[	X
ap-662	199	2	2	2	NUM
ap-662	199	3	]	]	PUNCT
ap-662	199	4	björck	björck	NOUN
ap-662	199	5	,	,	PUNCT
ap-662	199	6	:	:	PUNCT
ap-662	199	7	“	"	PUNCT
ap-662	199	8	numerics	numeric	NOUN
ap-662	199	9	of	of	ADP
ap-662	199	10	gram	gram	NOUN
ap-662	199	11	-	-	PUNCT
ap-662	199	12	schmidt	schmidt	NOUN
ap-662	199	13	orthogonalization	orthogonalization	NOUN
ap-662	199	14	”	"	PUNCT
ap-662	199	15	.	.	PUNCT
ap-662	200	1	linear	linear	PROPN
ap-662	200	2	algebra	algebra	PROPN
ap-662	200	3	and	and	CCONJ
ap-662	200	4	its	its	PRON
ap-662	200	5	applications	application	NOUN
ap-662	200	6	vol	vol	NOUN
ap-662	200	7	.	.	PROPN
ap-662	200	8	197	197	NUM
ap-662	200	9	,	,	PUNCT
ap-662	200	10	198	198	NUM
ap-662	200	11	,	,	PUNCT
ap-662	200	12	(	(	PUNCT
ap-662	200	13	1994	1994	NUM
ap-662	200	14	)	)	PUNCT
ap-662	200	15	,	,	PUNCT
ap-662	201	1	p.	p.	NOUN
ap-662	201	2	297–316	297–316	NUM
ap-662	201	3	.	.	PUNCT
ap-662	202	1	[	[	X
ap-662	202	2	3	3	X
ap-662	202	3	]	]	X
ap-662	202	4	golub	golub	PROPN
ap-662	202	5	,	,	PUNCT
ap-662	202	6	g.	g.	PROPN
ap-662	202	7	h.	h.	PROPN
ap-662	202	8	,	,	PUNCT
ap-662	202	9	van	van	PROPN
ap-662	202	10	loan	loan	PROPN
ap-662	202	11	,	,	PUNCT
ap-662	202	12	c.	c.	PROPN
ap-662	202	13	f.	f.	PROPN
ap-662	202	14	:	:	PUNCT
ap-662	202	15	“	"	PUNCT
ap-662	202	16	matrix	matrix	NOUN
ap-662	202	17	computations	computation	NOUN
ap-662	202	18	”	"	PUNCT
ap-662	202	19	,	,	PUNCT
ap-662	202	20	3rd	3rd	ADJ
ap-662	202	21	edition	edition	NOUN
ap-662	202	22	,	,	PUNCT
ap-662	202	23	the	the	DET
ap-662	202	24	john	john	PROPN
ap-662	202	25	hopkins	hopkins	PROPN
ap-662	202	26	university	university	PROPN
ap-662	202	27	press	press	PROPN
ap-662	202	28	1996	1996	NUM
ap-662	202	29	,	,	PUNCT
ap-662	202	30	isbn	isbn	ADJ
ap-662	202	31	0	0	NUM
ap-662	202	32	-	-	PUNCT
ap-662	202	33	8018	8018	NUM
ap-662	202	34	-	-	SYM
ap-662	202	35	5413	5413	NUM
ap-662	202	36	-	-	PUNCT
ap-662	202	37	x.	x.	NOUN
ap-662	203	1	[	[	X
ap-662	203	2	4	4	NUM
ap-662	203	3	]	]	X
ap-662	203	4	charamza	charamza	NOUN
ap-662	203	5	,	,	PUNCT
ap-662	203	6	f.	f.	PROPN
ap-662	203	7	:	:	PUNCT
ap-662	203	8	“	"	PUNCT
ap-662	203	9	gso	gso	X
ap-662	203	10	–	–	PUNCT
ap-662	203	11	an	an	DET
ap-662	203	12	algorithm	algorithm	NOUN
ap-662	203	13	for	for	ADP
ap-662	203	14	solving	solve	VERB
ap-662	203	15	least	least	ADJ
ap-662	203	16	-	-	PUNCT
ap-662	203	17	squares	square	NOUN
ap-662	203	18	problems	problem	NOUN
ap-662	203	19	with	with	ADP
ap-662	203	20	possibly	possibly	ADV
ap-662	203	21	rank	rank	VERB
ap-662	203	22	deficient	deficient	ADJ
ap-662	203	23	matrices	matrix	NOUN
ap-662	203	24	”	"	PUNCT
ap-662	203	25	.	.	PUNCT
ap-662	204	1	optimization	optimization	NOUN
ap-662	204	2	of	of	ADP
ap-662	204	3	design	design	NOUN
ap-662	204	4	and	and	CCONJ
ap-662	204	5	computation	computation	NOUN
ap-662	204	6	of	of	ADP
ap-662	204	7	control	control	NOUN
ap-662	204	8	networks	network	NOUN
ap-662	204	9	,	,	PUNCT
ap-662	204	10	budapest	budapest	PROPN
ap-662	204	11	,	,	PUNCT
ap-662	204	12	akadémiai	akadémiai	ADJ
ap-662	204	13	kiadó	kiadó	PROPN
ap-662	204	14	,	,	PUNCT
ap-662	204	15	1979	1979	NUM
ap-662	204	16	.	.	PUNCT
ap-662	205	1	[	[	X
ap-662	205	2	5	5	NUM
ap-662	205	3	]	]	PUNCT
ap-662	205	4	charamza	charamza	NOUN
ap-662	205	5	,	,	PUNCT
ap-662	205	6	f.	f.	PROPN
ap-662	205	7	:	:	PUNCT
ap-662	205	8	“	"	PUNCT
ap-662	205	9	an	an	DET
ap-662	205	10	algorithm	algorithm	NOUN
ap-662	205	11	for	for	ADP
ap-662	205	12	the	the	DET
ap-662	205	13	minimum	minimum	ADJ
ap-662	205	14	-	-	PUNCT
ap-662	205	15	length	length	NOUN
ap-662	205	16	least	least	ADJ
ap-662	205	17	-	-	PUNCT
ap-662	205	18	squares	square	NOUN
ap-662	205	19	solution	solution	NOUN
ap-662	205	20	of	of	ADP
ap-662	205	21	a	a	DET
ap-662	205	22	set	set	NOUN
ap-662	205	23	of	of	ADP
ap-662	205	24	observation	observation	NOUN
ap-662	205	25	equations	equation	NOUN
ap-662	205	26	”	"	PUNCT
ap-662	205	27	.	.	PUNCT
ap-662	206	1	studia	studia	PROPN
ap-662	206	2	geoph	geoph	PROPN
ap-662	206	3	.	.	PUNCT
ap-662	207	1	et	et	PROPN
ap-662	207	2	geod	geod	PROPN
ap-662	207	3	.	.	PUNCT
ap-662	207	4	,	,	PUNCT
ap-662	207	5	vol	vol	NOUN
ap-662	207	6	22	22	NUM
ap-662	207	7	,	,	PUNCT
ap-662	207	8	(	(	PUNCT
ap-662	207	9	1978	1978	NUM
ap-662	207	10	)	)	PUNCT
ap-662	207	11	,	,	PUNCT
ap-662	207	12	p.	p.	NOUN
ap-662	207	13	129–139	129–139	NUM
ap-662	207	14	.	.	PUNCT
ap-662	208	1	[	[	X
ap-662	208	2	6	6	NUM
ap-662	208	3	]	]	X
ap-662	208	4	koch	koch	PROPN
ap-662	208	5	,	,	PUNCT
ap-662	208	6	k.	k.	PROPN
ap-662	208	7	r.	r.	PROPN
ap-662	208	8	:	:	PUNCT
ap-662	208	9	“	"	PUNCT
ap-662	208	10	parameter	parameter	NOUN
ap-662	208	11	estimation	estimation	NOUN
ap-662	208	12	and	and	CCONJ
ap-662	208	13	hypothesis	hypothesis	NOUN
ap-662	208	14	testing	testing	NOUN
ap-662	208	15	in	in	ADP
ap-662	208	16	linear	linear	PROPN
ap-662	208	17	models	model	NOUN
ap-662	208	18	”	"	PUNCT
ap-662	208	19	.	.	PUNCT
ap-662	209	1	2nd	2nd	ADJ
ap-662	209	2	ed	ed	NOUN
ap-662	209	3	.	.	PUNCT
ap-662	209	4	springer	springer	NOUN
ap-662	209	5	-	-	PUNCT
ap-662	209	6	verlag	verlag	PROPN
ap-662	209	7	(	(	PUNCT
ap-662	209	8	1999	1999	NUM
ap-662	209	9	)	)	PUNCT
ap-662	209	10	,	,	PUNCT
ap-662	209	11	isbn	isbn	ADJ
ap-662	209	12	3	3	NUM
ap-662	209	13	-	-	SYM
ap-662	209	14	540	540	NUM
ap-662	209	15	-	-	PUNCT
ap-662	209	16	65257	65257	NUM
ap-662	209	17	-	-	PUNCT
ap-662	209	18	4	4	NUM
ap-662	209	19	.	.	PUNCT
ap-662	210	1	[	[	X
ap-662	210	2	7	7	X
ap-662	210	3	]	]	X
ap-662	210	4	golub	golub	PROPN
ap-662	210	5	,	,	PUNCT
ap-662	210	6	g.	g.	PROPN
ap-662	210	7	h.	h.	PROPN
ap-662	210	8	,	,	PUNCT
ap-662	210	9	reinsch	reinsch	ADJ
ap-662	210	10	,	,	PUNCT
ap-662	210	11	c.	c.	NOUN
ap-662	210	12	:	:	PUNCT
ap-662	210	13	“	"	PUNCT
ap-662	210	14	singular	singular	ADJ
ap-662	210	15	value	value	NOUN
ap-662	210	16	decomposition	decomposition	NOUN
ap-662	210	17	and	and	CCONJ
ap-662	210	18	least	least	ADJ
ap-662	210	19	squares	square	NOUN
ap-662	210	20	solutions	solution	NOUN
ap-662	210	21	”	"	PUNCT
ap-662	210	22	.	.	PUNCT
ap-662	211	1	numer	numer	PROPN
ap-662	211	2	.	.	PUNCT
ap-662	211	3	math	math	NOUN
ap-662	211	4	.	.	PUNCT
ap-662	212	1	14	14	NUM
ap-662	212	2	,	,	PUNCT
ap-662	212	3	(	(	PUNCT
ap-662	212	4	1970	1970	NUM
ap-662	212	5	)	)	PUNCT
ap-662	212	6	,	,	PUNCT
ap-662	212	7	p.	p.	NOUN
ap-662	212	8	403–420	403–420	NUM
ap-662	212	9	,	,	PUNCT
ap-662	212	10	handbook	handbook	NOUN
ap-662	212	11	for	for	ADP
ap-662	212	12	auto	auto	NOUN
ap-662	212	13	.	.	PUNCT
ap-662	213	1	comp	comp	PROPN
ap-662	213	2	.	.	PUNCT
ap-662	213	3	,	,	PUNCT
ap-662	213	4	vol	vol	NOUN
ap-662	213	5	.	.	PUNCT
ap-662	214	1	ii	ii	PROPN
ap-662	214	2	–	–	PUNCT
ap-662	214	3	linear	linear	PROPN
ap-662	214	4	algebra	algebra	NOUN
ap-662	214	5	,	,	PUNCT
ap-662	214	6	(	(	PUNCT
ap-662	214	7	1971	1971	NUM
ap-662	214	8	)	)	PUNCT
ap-662	214	9	,	,	PUNCT
ap-662	214	10	p.	p.	NOUN
ap-662	214	11	134–151	134–151	NUM
ap-662	214	12	.	.	PUNCT
ap-662	215	1	[	[	X
ap-662	215	2	8	8	NUM
ap-662	215	3	]	]	X
ap-662	215	4	demmel	demmel	PROPN
ap-662	215	5	,	,	PUNCT
ap-662	215	6	j.	j.	PROPN
ap-662	215	7	w.	w.	PROPN
ap-662	215	8	:	:	PUNCT
ap-662	215	9	“	"	PUNCT
ap-662	215	10	singular	singular	ADJ
ap-662	215	11	value	value	NOUN
ap-662	215	12	decomposition	decomposition	NOUN
ap-662	215	13	”	"	PUNCT
ap-662	215	14	.	.	PUNCT
ap-662	216	1	in	in	ADP
ap-662	216	2	z.	z.	PROPN
ap-662	216	3	bai	bai	PROPN
ap-662	216	4	,	,	PUNCT
ap-662	216	5	j.	j.	PROPN
ap-662	216	6	demmel	demmel	PROPN
ap-662	216	7	,	,	PUNCT
ap-662	216	8	j.	j.	PROPN
ap-662	216	9	dongarra	dongarra	PROPN
ap-662	216	10	,	,	PUNCT
ap-662	216	11	a.	a.	NOUN
ap-662	216	12	ruhe	ruhe	PROPN
ap-662	216	13	,	,	PUNCT
ap-662	216	14	and	and	CCONJ
ap-662	216	15	h.	h.	PROPN
ap-662	216	16	van	van	PROPN
ap-662	216	17	der	der	PROPN
ap-662	216	18	vorst	vorst	PROPN
ap-662	216	19	,	,	PUNCT
ap-662	216	20	editors	editor	NOUN
ap-662	216	21	.	.	PUNCT
ap-662	217	1	templates	template	NOUN
ap-662	217	2	for	for	ADP
ap-662	217	3	the	the	DET
ap-662	217	4	solution	solution	NOUN
ap-662	217	5	of	of	ADP
ap-662	217	6	algebraic	algebraic	PROPN
ap-662	217	7	eigenvalue	eigenvalue	NOUN
ap-662	217	8	problems	problem	NOUN
ap-662	217	9	:	:	PUNCT
ap-662	217	10	a	a	DET
ap-662	217	11	practical	practical	ADJ
ap-662	217	12	guide	guide	NOUN
ap-662	217	13	.	.	PUNCT
ap-662	218	1	siam	siam	PROPN
ap-662	218	2	,	,	PUNCT
ap-662	218	3	philadelphia	philadelphia	PROPN
ap-662	218	4	,	,	PUNCT
ap-662	218	5	2000	2000	NUM
ap-662	218	6	,	,	PUNCT
ap-662	218	7	http://www.cs.utk.edu/~dongarra/etemplates/book.html	http://www.cs.utk.edu/~dongarra/etemplates/book.html	NUM
ap-662	218	8	prof	prof	NOUN
ap-662	218	9	.	.	PUNCT
ap-662	219	1	ing	ing	PROPN
ap-662	219	2	.	.	PUNCT
ap-662	220	1	aleš	aleš	PROPN
ap-662	220	2	čepek	čepek	PROPN
ap-662	220	3	,	,	PUNCT
ap-662	220	4	csc	csc	PROPN
ap-662	220	5	.	.	PROPN
ap-662	220	6	phone	phone	NOUN
ap-662	220	7	:	:	PUNCT
ap-662	220	8	+420	+420	PROPN
ap-662	220	9	224	224	NUM
ap-662	220	10	354	354	NUM
ap-662	220	11	647	647	NUM
ap-662	220	12	e	e	NOUN
ap-662	220	13	-	-	NOUN
ap-662	220	14	mail	mail	NOUN
ap-662	220	15	:	:	PUNCT
ap-662	220	16	cepek@fsv.cvut.cz	cepek@fsv.cvut.cz	NOUN
ap-662	220	17	department	department	NOUN
ap-662	220	18	of	of	ADP
ap-662	220	19	mapping	mapping	NOUN
ap-662	220	20	and	and	CCONJ
ap-662	220	21	cartography	cartography	NOUN
ap-662	220	22	ing	ing	PROPN
ap-662	220	23	.	.	PUNCT
ap-662	221	1	jan	jan	PROPN
ap-662	221	2	pytel	pytel	PROPN
ap-662	221	3	phone	phone	NOUN
ap-662	221	4	:	:	PUNCT
ap-662	221	5	+420	+420	PROPN
ap-662	221	6	224	224	NUM
ap-662	221	7	354	354	NUM
ap-662	221	8	644	644	NUM
ap-662	221	9	e	e	NOUN
ap-662	221	10	-	-	NOUN
ap-662	221	11	mail	mail	NOUN
ap-662	221	12	:	:	PUNCT
ap-662	221	13	pytel@gama.fsv.cvut.cz	pytel@gama.fsv.cvut.cz	PROPN
ap-662	221	14	czech	czech	PROPN
ap-662	221	15	technical	technical	PROPN
ap-662	221	16	university	university	PROPN
ap-662	221	17	in	in	ADP
ap-662	221	18	prague	prague	PROPN
ap-662	221	19	faculty	faculty	NOUN
ap-662	221	20	of	of	ADP
ap-662	221	21	civil	civil	ADJ
ap-662	221	22	engineering	engineering	NOUN
ap-662	221	23	thákurova	thákurova	VERB
ap-662	221	24	7	7	NUM
ap-662	221	25	166	166	NUM
ap-662	221	26	29	29	NUM
ap-662	221	27	prague	prague	NOUN
ap-662	221	28	,	,	PUNCT
ap-662	221	29	czech	czech	PROPN
ap-662	221	30	republic	republic	NOUN
ap-662	221	31	18	18	NUM
ap-662	221	32	©	©	PROPN
ap-662	221	33	czech	czech	PROPN
ap-662	221	34	technical	technical	PROPN
ap-662	221	35	university	university	PROPN
ap-662	221	36	publishing	publishing	NOUN
ap-662	221	37	housee	housee	PROPN
ap-662	222	1	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-662	222	2	acta	acta	PROPN
ap-662	222	3	polytechnica	polytechnica	PROPN
ap-662	222	4	vol	vol	NOUN
ap-662	222	5	.	.	PROPN
ap-662	223	1	45	45	NUM
ap-662	223	2	no	no	NOUN
ap-662	223	3	.	.	PUNCT
ap-662	224	1	1/2005	1/2005	NUM
ap-662	224	2	czech	czech	PROPN
ap-662	224	3	technical	technical	PROPN
ap-662	224	4	university	university	PROPN
ap-662	224	5	in	in	ADP
ap-662	224	6	prague	prague	NOUN