QR Solution of Linear Equation for n up to 25.xlsx

	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z	AA	AB	AC	AE	AF	AG	AH	AI	AJ	AK	AL	AM	AN	AO	AP	AQ	AR	AS	AT	AU	AV	AW	AX	AY	AZ	BA	BB	BC	BD	BE	BF	BG	BH	BI	BJ	BK	BL	BM	BN	BO	BP	BQ	BR	BS	BT	BU	BV	BW	BX	BY	BZ	CA	CB	CC	CD
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2		Solving linear equations in up to 25 variables using QR Factorization
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4
5		A an nxn non-singular matrix
6
7		b a nx1 column vector
8
9		Perform a Gram Schmidt procedure of the columns of A
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11
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15
16
17
18
19
20
21
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23
24
25
26
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28
29
30
31
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35
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38
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52
53																													Solution of Ax = b
54																														1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
55
56																													j -->	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
57																													xj	4.000E+00	-3.000E+00	1.000E+00	4.932E-13	6.000E+00	-2.000E+00	5.000E+00	1.000E+00	-7.000E+00	3.0000E+00	3.0000E+00	-2.0000E+00	5.0000E+00	4.0000E+00	9.0000E+00	3.0000E+00	6.0000E+00	-2.0000E+00	1.0000E+00	1.0000E+00	8.0000E+00	5.0000E+00	3.0000E+00	2.0000E+00	2.00000
58		Input Section
59	Enter Value of n --->		25	n + 1 =	26																								Solution Check:
60		b vector		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	Ax	b
61	1	4	A Matrix	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	4	4
62	2	5		2	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	5	5
63	3	21		3	-2	3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	21	21
64	4	-8		0	3	1	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-8	-8
65	5	14		0	0	2	3	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	14	14
66	6	14		0	0	0	-1	3	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	14	14
67	7	10		0	0	0	0	1	3	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	10	10
68	8	-15		0	0	0	0	0	1	-3	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-15	-15
69	9	-8		0	0	0	0	0	0	1	1	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-8	-8
70	10	-12		0	0	0	0	0	0	0	3	3	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	-12	-12
71	11	2		0	0	0	0	0	0	0	0	1	1	2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2	2
72	12	8		0	0	0	0	0	0	0	0	0	1	3	2	0	0	0	0	0	0	0	0	0	0	0	0	0	8	8
73	13	11		0	0	0	0	0	0	0	0	0	0	1	1	2	0	0	0	0	0	0	0	0	0	0	0	0	11	11
74	14	-11		0	0	0	0	0	0	0	0	0	0	0	2	-3	2	0	0	0	0	0	0	0	0	0	0	0	-11	-11
75	15	35		0	0	0	0	0	0	0	0	0	0	0	0	1	3	2	0	0	0	0	0	0	0	0	0	0	35	35
76	16	19		0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	2	0	0	0	0	0	0	0	0	0	19	19
77	17	48		0	0	0	0	0	0	0	0	0	0	0	0	0	0	3	3	2	0	0	0	0	0	0	0	0	48	48
78	18	17		0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	3	2	0	0	0	0	0	0	0	17	17
79	19	2		0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	3	2	0	0	0	0	0	0	2	2
80	20	3		0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	3	2	0	0	0	0	0	3	3
81	21	20		0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	3	2	0	0	0	0	20	20
82	22	35		0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	3	2	0	0	0	35	35
83	23	29		0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	3	2	0	0	29	29
84	24	16		0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	3	1	0	16	16
85	25	7		0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	7	7
86
87
88
89																														Inner Products																										Constructing the C columns
90		C Columns		E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z	AA	AB	AC		F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z	AA	AB	AC			F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z	AA	AB	AC
91				1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25		2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25			2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25
92			1	1	0.2857142857	-0.6333333333	0.5	0.4756097561	-0.004973398103	-0.08002951979	-0.03145348552	0.04537652422	-0.007970821318	-0.0647294848	0.06357253244	0.1212064026	-0.1317909546	0.04089646435	-0.01208950337	-0.0173934968	0.0234096368	-0.02400163558	0.02457696074	-0.0251778737	0.02568413965	-0.02605809636	0.009939040195	-0.01335299777	1	-1.069044968	2.405351177	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	E	1	0.2857142857	-0.6333333333	0.5	0.4756097561	-0.004973398103	-0.08002951979	-0.03145348552	0.04537652422	-0.007970821318	-0.0647294848	0.06357253244	0.1212064026	-0.1317909546	0.04089646435	-0.01208950337	-0.0173934968	0.0234096368	-0.02400163558	0.02457696074	-0.0251778737	0.02568413965	-0.02605809636	0.009939040195	-0.01335299777	1
93			2	2	1.571428571	-1.233333333	0.5	0.7682926829	-0.2131621559	-0.08126523187	0.02982366418	-0.01937508002	-0.005413065493	0.04185054181	-0.03237452519	-0.06586884351	0.0694601042	-0.02072962642	0.005501100439	0.009311276813	-0.01195701385	0.01215184033	-0.01240745698	0.01269646055	-0.01294539282	0.01313090565	-0.005007656488	0.006727272629	2		-0.1195228609	1.673320053	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	F	2	1.571428571	-1.233333333	0.5	0.7682926829	-0.2131621559	-0.08126523187	0.02982366418	-0.01937508002	-0.005413065493	0.04185054181	-0.03237452519	-0.06586884351	0.0694601042	-0.02072962642	0.005501100439	0.009311276813	-0.01195701385	0.01215184033	-0.01240745698	0.01269646055	-0.01294539282	0.01313090565	-0.005007656488	0.006727272629	2
94			3	3	-1.142857143	1.033333333	-0.5	-0.6707317073	0.1437659033	0.08085332784	-0.009397947613	-0.002208788062	0.006265650768	-0.006323866272	0.0003921726468	0.003510428152	-0.002376417929	0.0001875961588	0.0003624341632	-0.0004096856078	0.0001681302984	-0.0001006816933	0.00007931774154	-0.00007168247116	0.00006888199247	-0.00006790497635	0.00002542426015	-0.00003384916205	3			2.863564213	1.396860592	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	G	3	-1.142857143	1.033333333	-0.5	-0.6707317073	0.1437659033	0.08085332784	-0.009397947613	-0.002208788062	0.006265650768	-0.006323866272	0.0003921726468	0.003510428152	-0.002376417929	0.0001875961588	0.0003624341632	-0.0004096856078	0.0001681302984	-0.0001006816933	0.00007931774154	-0.00007168247116	0.00006888199247	-0.00006790497635	0.00002542426015	-0.00003384916205	3
95			4	0	3	1.1	-0.5	-0.7032520325	0.1668979875	0.08099062918	-0.0162065198	0.004985834632	0.005981455677	-0.01816609145	0.01105295683	0.0242965666	-0.02473764669	0.007034939578	-0.001592077371	-0.003376882676	0.004097758148	-0.004117734573	0.004188697488	-0.004279941832	0.004361052267	-0.004422238533	0.001686168336	-0.002264990318	4				-0.5773502692	-1.154700538	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	H	4	3	1.1	-0.5	-0.7032520325	0.1668979875	0.08099062918	-0.0162065198	0.004985834632	0.005981455677	-0.01816609145	0.01105295683	0.0242965666	-0.02473764669	0.007034939578	-0.001592077371	-0.003376882676	0.004097758148	-0.004117734573	0.004188697488	-0.004279941832	0.004361052267	-0.004422238533	0.001686168336	-0.002264990318	4
96			5	0	0	2	1	1.357723577	-0.2990978487	-0.1617753064	0.02220018132	0.0008202647767	-0.01238920399	0.01856884513	-0.006114737384	-0.01741392553	0.01593345024	-0.003798864027	0.0002523874407	0.00230296975	-0.002301074522	0.002209889826	-0.002213325356	0.002247494623	-0.002283849122	0.002312976731	-0.0008812205583	0.001183268902	5					2.434665598	0.5843197436	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	I	5	0	2	1	1.357723577	-0.2990978487	-0.1617753064	0.02220018132	0.0008202647767	-0.01238920399	0.01856884513	-0.006114737384	-0.01741392553	0.01593345024	-0.003798864027	0.0002523874407	0.00230296975	-0.002301074522	0.002209889826	-0.002213325356	0.002247494623	-0.002283849122	0.002312976731	-0.0008812205583	0.001183268902	5
97			6	0	0	0	-1	2.666666667	-0.5634975711	-0.3233446607	0.03418750436	0.01243246359	-0.02520470062	0.0193743525	0.003761701504	-0.003648643383	-0.001674942662	0.002673287074	-0.00242699242	0.000155143897	0.001292292731	-0.001605799666	0.001737418907	-0.001817399796	0.001870557167	-0.001905546873	0.0007286749973	-0.0009801739296	6						0.607624768	0.7704243649	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	J	6	0	0	-1	2.666666667	-0.5634975711	-0.3233446607	0.03418750436	0.01243246359	-0.02520470062	0.0193743525	0.003761701504	-0.003648643383	-0.001674942662	0.002673287074	-0.00242699242	0.000155143897	0.001292292731	-0.001605799666	0.001737418907	-0.001817399796	0.001870557167	-0.001905546873	0.0007286749973	-0.0009801739296	6
98			7	0	0	0	0	1	2.288688411	1.293584595	-0.1469628757	-0.03893792033	0.1003925098	-0.09526074776	0.0009443702572	0.04577378121	-0.02684207249	-0.0004221331684	0.006776202378	-0.00507137119	0.0007252708499	0.0003976193466	-0.0007856060085	0.000957210142	-0.001043973258	0.001090687157	-0.0004235838755	0.000573983985	7							-1.499984151	0.548627939	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	K	7	0	0	0	1	2.288688411	1.293584595	-0.1469628757	-0.03893792033	0.1003925098	-0.09526074776	0.0009443702572	0.04577378121	-0.02684207249	-0.0004221331684	0.006776202378	-0.00507137119	0.0007252708499	0.0003976193466	-0.0007856060085	0.000957210142	-0.001043973258	0.001090687157	-0.0004235838755	0.000573983985	7
99			8	0	0	0	0	0	1	-3.234064463	0.3725136184	0.09194883381	-0.2507681283	0.2470335383	-0.01035651378	-0.1300240569	0.08387610279	-0.004080174643	-0.0154746223	0.01490382578	-0.004760398012	0.002018741293	-0.001118019788	0.0007631691659	-0.0006091945618	0.0005390322756	-0.0001865983682	0.0002383959043	8								3.539658558	1.796335221	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	L	8	0	0	0	0	1	-3.234064463	0.3725136184	0.09194883381	-0.2507681283	0.2470335383	-0.01035651378	-0.1300240569	0.08387610279	-0.004080174643	-0.0154746223	0.01490382578	-0.004760398012	0.002018741293	-0.001118019788	0.0007631691659	-0.0006091945618	0.0005390322756	-0.0001865983682	0.0002383959043	8
100			9	0	0	0	0	0	0	1	1.411466607	0.3537223421	-0.9530894045	0.9316221104	-0.03295828185	-0.481619733	0.3053124533	-0.01139625759	-0.05997627164	0.05485421971	-0.01573173574	0.005260985186	-0.001782847348	0.0003750872136	0.0002603628299	-0.000564277487	0.0002873726463	-0.000432780257	9									0.593191524	1.849139207	0	0	0	0	0	0	0	0	0	0	0	0	0	0	M	9	0	0	0	0	0	1	1.411466607	0.3537223421	-0.9530894045	0.9316221104	-0.03295828185	-0.481619733	0.3053124533	-0.01139625759	-0.05997627164	0.05485421971	-0.01573173574	0.005260985186	-0.001782847348	0.0003750872136	0.0002603628299	-0.000564277487	0.0002873726463	-0.000432780257	9