p4 - I C David Mahen MATH Mes/OR 4816001 3-18-2010 Project...

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Unformatted text preview: I C David Mahen MATH Mes/OR 4816001 3-18-2010 Project 4:: Gaussian Elimination and Ermi- Magnification 1. . - For this problem I created the following matrix A1: 13 Using the code from elimm, I recived the following answer: 1.000000000000000 1.000000000000000 1.000000000000000 1.000000000000000 To test the code I mtfltiplied matrix A1 by the elim result matrix x to get: 16.000000000000000 ' 5.000000000000000 29.999999999999996 13.000000000000002 This shows that there is a lack of accuracy, which will be explored in the subsequent problems. 9-11 2.038613766606126 _ 8-07 2-16 e+08 2.330122273445869 2.310540926594034 6-04 e~15 e+11 _ 0-14 e+13 , e+03 e-14 -- 16 . 3. For this question I am referring to any version of matrix B as A3. This is in line with my matrix naming scheme for the entire project RFE BFE a 1.554312234475219 1.913861775048246 8.121340081814619 e—14 e-15 2.832178935818774 1.147952565305305 24.671565487050245 e 13 10 1.301181384860683 4.703832945972041 27.662151266976938 13 e-15 12 1.072475441787901 2.730820210382667 39.273015400659290 e-15 14 5.654365864315922 1.227653277133541 46.05832908798fi454 e—14 -*’ The difference between matrices A2 and matrices A3 is immediately evident. The A3 series have a much smaller ratio between the RFE and REE, comparing e+01 and e+06 through e+ 16. Using the [mod 1) to remove the integer part of the numbers has a dramatic effect The accuracy appears to increase by many factors. Another observation I made was how much slowiy the RFE grows in A3 than A2. 5 i5 _,_r§f‘37”8’\.. ,. MATLAB Diary: Elm)? A1 = [4 7 3 2:3 1 1 0:5 9 8 0:3 4-61] 1.0000001101000000 1.0000001130000000 A1 = ED” V; Ai’x‘ 4 7 3 2 3 1 1 0 ans = 5 9 B B 2 4 6 1 16.000000000100000 5.0000130000000000 EDU» c = onesfahl) 29.999999999399996 13.000000000000002 C = EDI)» type maloemtrix 1 1 11:6: 1 far i=1m 1 Farj=lm a0-iJ= [(25 + 3577mm»: EDU» 31 = 31": end end 31 = E011» makeman'lx 16 E003) A2 1 = a 5 30 A21 = 13 Cailmms 1 through 3 EDU): n = 4 1.250000000000000 1.222222222222222 1.8125000000001130 5 = 0.777777777777778 0.812500000000000 1.2“'0‘1'300000000010l 0.637500000000000 0.533000000000000 0.972222222222222 4- 0.760000000000000 0.696444444444444 0.877551020400163 0.972222222222222 0.836734693877551 0.921875000000000 EDB>> a =A1; I 136734693017 5510 1.140625000000000 1.123456790123457 EDU» b a BI: EDIT» elim Calms 4 01:0th 6 an; 2 3.320600000000113” 6.805555555555555 14.918367346938776 2.361111111111111 5.040816326530622 11.453125000000000 10000000000000“) 1.016326530612245 3.92187500m00 9.098765432098766 1.000000000000000 1.515625000000000 3.197530864197531 7.4500000000111000 1.395061720395062 2.750000000000000 6.289255198347103 1.450000000000000 2.537190032644623 5.506946144444445 EDUb: c = ones[n.1) c: u H H M H M E00» B21 = AZI‘C 3321 = 293236-1512 $7 165 52 21.685330215419501 17.176689184933231 1.4.4951 5 1329050 13 8 13.165149842841942 13.125563255938039 E0113) 1) = 321 b = 29.3 236451 211-7 16 552 21.68533 021541-19 501 17.176689184933231 14.495151329050130 13.165149812841942 13.125516132559880 39 EDU >5 eJln‘: ans: 0999999999999551 L000000000007053 0999999999954769 1.000000000076782 0.999999999954496 1.000000000008626 £00» RFE = (max{ahs{x'-c]]jfmax[abs[c]] RFE r 7.6781692115446282-11 E00» REE =[maxfabsg321 -[821‘x'))}]fmax[abs(821j] RBE= 6.0 56729971 117681917 EDU>> EMF = RFEfRBE EMF = 1.267703609032029H06 E00» t3: p2 Tn a'immarrix IFS: for i: :n for ] 1m a0-0= {[20 4‘ 3"]H[[i+0"2])= end and 500 >> makema :11): E00» A22 = a 022 = Coiumns 1 through 3 12 5000000 0000000 0.777 777777777770 0.687 500000000000 0.7 60000000000000 0.97 22222222222 22 1.367346938775510 2.04687 5000000000 3.197530964197531 Columns 4 through 6 1.2 22222222222222 0.312 500000000000 0.680000000000000 0.694444444644444- 0.836734693077551 1.140625000000000 1.691353024691358 2.650000000000000 131250 0000000000 1.240000000000000 0972222222222222 0.8775510 20603163 0.92 1075000 000000 1.123456790123457 1.550000000000000 2.333312975206612 3.320000000000000 2361111111111111 13163265306122 '15 1.515525000000000 1.395061720395062 1.450000 000000000 1.727272 72727 27 27 234027777 7777778 Columns 7 through 8 6.805 555555555555 14.9133673 169 38776 5.0110816326530612 11.453125000000000 3.921875000000000 3.197 53086} 197531 2.750000000000000 2.537190082644620 2.5763880881388889 2952662721179 3491 9093765432 090766 7.450000000000000 6209256198347108 5.506944444444445 5.07 10059171 59 76"1l 5.025510204081633 34.203125000000000 01.024691358024697 27049382716049383 65.650000000000006 21.949999999999999 54.289256198347104- 10206611570247933 45.673611111111114 15.409722222222221 39.011034319526628 13.319526627213934 33.801020403163268 11.811224489795919 29.728383303888889 10.857777777777779 26.628906250000000 EDD): c = ones[n.1) c: H H H H HIAIA H E00?) 322 = 622*: 322 = l.08+02 “ 1.415561614827412 1.143847129314689 03341-159115 3032803 0.703753740104092 0.67 5867063 045908 0.602461102913702 0.562030139366975 0.5 59915085709348 EDU» b = 322 b = L0e+02 “ 1.445564614027412 1.143047 129 3 14689 0.934159453332303 0.733753740104092 0.67 5367063345903 0.60 2461102913702 0.562030 1 393669 7 5 0.5 59915085709 34-0 EDI»: ehm ans = 0.999999998625742 1.000000021580799 0399999903670 507 1.0 00000 194477352 0.999999 796130623 1.00 0000113966124- 0.99999996 7952 430 100000000 3549383 E00» RFE = [max(abs(x'-c}]}/max{ahs{c}] RFE z 2.038613766686126 3-07 £00» 1132 = maxfabs[022 I (A22‘xj)]]/max[abs[322)j REE 2 F13 5606128 153 8671 B003: EMF = RFEIRBE EMF = 9-16 2.439602642335436e+08 EDUb) type makematrbt n=10; for i= 1:11 for i: 1:31 aUJ}= {[20 + 300050021}: end and EDI!» makemauix E0115: A23 = 21 A23 = 1.03+02 ” Columns 1 through 3 0.012500000000000 0.007777 777777778 0.00687 500 0000000 0.007600000000000 [1.009722222222222 0.013673469387755 0.020468750000000 0.031975303641975 0.051500000000000 0.084876033057851 Columns 4 Ulrougl! 6 0.033200000000000 0.023611111111111 0.018 1632653061 2 2 0.015156250000000 0.013950617283951 0.014500000000000 0.017272727272727 0.023402 777777778 0.0350887 57396450 0.056377551020403 Cotumns 7 Enough 9 0.34203 12 50000000 0.2 704931527 1604-94 02.195000008013000 0.182 066115702479 [1154097222222 222 0.133195266272189 0.118112244897959 0.108577 7777777 78 0.105429687500000 0.111107266435986 Column 1 0 4.880247933884298 4.100902777777778 3.494197041420118 3.013520408163265 2.625822222222222 2309101562500000 2.047 647058823529 1.83 0401234567901 1.649889196675900 1.501825000000000 EDD» c = ones{l1.1] E: AHp—IMWMHMHA £00» 823 = 023*: 823 = 1.02102 “ 629431254871 1709 0.012222222222222 0.008125000000000 0.006800000000000 0.006944444444444 0013836734693 8776 0.011406250000000 0.0 169 135802469 14 0.026500000000000 0.043057851239669 0.071736111111111 006805555 5555556 0.050408163265306 0.039218750000000 0.031975 308641975 0.027500000000000 0.0 25371900826146 0.025763 888808889 0.029526627218935 0.038520608163265 [10563111111 11111 0.310246913580247 0.656500000000000 0.542392561983471 0.4567361 ‘1 1111111 0.3901 183 43 1952 66 0.338010204081633 0.297288888888889 0266289062 500000 0.244740484429066 0.234104930271605 0.018125000000000 0.012400000000000 0.0097 22222222222 0.003775510204082 0.009210750000000 0.011234567901235 0.015500000000000 0.023388429752066 0.037430555555556 0.062189349112426 0.149 183 673469 388 0.114531250000000 0.090987654320988 mnsommunn 0.062892561983471 0.055069444444444 005071005917 1 59 0 0.050255102040816 0.055155555555556 0.060476562500000 1.968500000000000 1.627024793303430 1.3 6743055 5555555 1.165621301775148 1.005867346930776 0.877644444444444 0.773867 107 500000 0689930795847 751 062330246913 5802 0.5 73601108033241 6.871774700430396 5.796087050808477 4962895450042 505 4.307556633006905 3.789207109858147 3.383544385690505 3.080247116125000 28841145765651.2645 282060503 0653740 EDI!» h = 823: E00» elim ans ‘—' 1.000000394916742 0.999987 3 1 3018776 1.000098592566393 0.999665914853790 1.000610051221589 0.999345109598651 1.000424381162313 0999837352 708478 1.000033823462229 0.999997067293670 EDU» REE = [max{abs[x'-c3]]lmaxfabsm) RFE = 6.548904013488066e-04 we» 0015 = {max-{abswfl — (323413)] {maxflabflBZBD RBE: 2.330122273445869e-15 EDU:> EMF = MEIRBE EMF 2 2.8 105409265940842+11 800» type makematrix n=12: fol-1:116 Ear j-11n a{i-i]=i[2"1+ 3‘02'EE'I+J'J"Z)11 end end EDU >> makcmatrix EDU )3 A24 2 a A24 = 1.0e+03 ‘ Coiumns 1 through 3 0.001250000000000 0.000777777777778 0.000687500000000 0.000760000000000 0.000972222222222 0.001357346938776 0.0020468? 5000000 0.003 197 530864 198 0.005150000000000 0008487603 305785 0.0 14243 0555555 56 00 24254437369022 Coiumns 4 through 6 0.003 320000000000 0.002361111111111 0.001816326530612 0.001515625000000 0.001395051728395 000145000 0000000 0.001727272727273 0.002340277777778 0003508875 739645 0.005637755102041 0.009462 222222 222 0.016316406250000 Columns 7 throng 9 0.001222 222222222 0.000812 500000000 0.000680000000000 0.000694444444444 0.00083 6734693878 0.001140625000000 0.001691358024691 0.0026500 00000000 0.004305785123967 0.007173611111111 0.012171597633136 0.020943877551020 0.006805 555555556 0.005040816326531 0.003921875000000 0.003197530864198 000275000 0000000 0.002537190082645 0.002576388333389 0.002952662721893 0.003852040816327 0.005631111111111 0.008949218750000 0.015013840830450 0.001812500000000 0.001240000000000 [10009722222 22222 0.000877551020408 0.008921075000000 0.001123456790123 0.00 '15 50000000000 000233884297 5207 0.003743055555556 0.006218934911243 0.010586734693870 0.0103 24444444444- 0.014918367346939 0.011453 1250 00000 0.009098765432099 0007450000000 000 0.006289256190347 0.005506944444444 0005071005917 160 0.0051025510204032 0.00551555 5555556 00068476562 50000 0.009608996539792 0.014091975308642 0.034203125000000 0.0270493827150119 0.021950000000000 0.018206611570248 0.015409722222222 0.013319526627219 0.011811224489796 0.010057777777778 0.010542968750000 0.011110726643599 0.013070987654321 0.017404432132964 0.08 102469 135302 5 0.065650000000000 0.0 54289256198347 0.045673611111111 0.039011834319527 0.033 801020408163 0.029728888888889 0.026628906250000 0.024474048442907 0.023410493327160 0.0 23847 645429363 0.026642500000000 Columns 10 through 12 0488024793 380-430 0.410090277777778 0.3 49449704142 012 0.3 01 35204081 63 26 0.2 62582222222222 0.2 3 091 0 1 56250000 0.2 047 64705882353 0.183040123456790 0.164988919667590 0.150182500000000 0.138541950113379 0.130464876033038 31311» c 2 an es[n.1}; EDU» 1324 = 7124": 1324- = 1.0 6+ 03 " 5.204265779854735 444636232 0911512 3.345456301452730 3.3 596045623653 62 2.961868052465916 2.63255 5093061085 2.357939805006587 2.128688264244079 1.938801626950614 1.786210673601908 1.673533334203670 1.610543528181826 EDD): 13 = 824; EDI!» elim fi'l'lS ‘—' 0.999 922383 81 63 74 1.003311070265251 [196437009372 1050 1 .172014-1-17566237 0.537861484145601 1.762579185510544- 0.190012533722941 1.562946784195703 0.7 4-62 25841836 665 1.07 129967 62 58688 1198868037 022 20 50 10007742027 49 477 1.230201388888809 10482307692307 69 0.903852040816327 0.787391111111111 0.692105 463750000 0.613186051211073 0.547145061728395 0.491421052631579 0.444147500000000 040401587 3015873 0.370237603305785 0.342614366729679 EDU >> REE : {max[abs[x‘~c}}] [ma 24.313531} RFE = 0.809987466277059 0.196850000000000 0.162702479338843 0.1 3674305555 5 5 56 0.116562130177515 0.100586734693878 0.037754444444444 0.0 773067 187 50000 0.068993079584775 0.062330246913580 0.0 57360110803324 005432750000 0000 005392063492 0635 3.144633136094675 2.711454081632653 2.361995555555556 2.076003906250000 1.839006920415225 1.640447530864197 1.472490304709141 1.329242500000000 1206242630 38 54-87 1.100134297520661 1.130 8485822306238 09297517361 1111 1 E130» RBE = [maxfiahs{824 . [A24‘x‘]]]}/max{abs{824]] REE = 1.411182677342315e-14 EDU‘» EMF = RFEfRBE EMF 2 5.7 39 77755879 5659a:L 13 E00 :9 type makemau-ix for] 1:n a{i.i}= [[Z’W 4' 3"i}f{0+i] "21]: end and EDU>> makematn')‘. EDU>> A25 2 :1 A25 = 1.09+04 ‘ COEumns 1 Lian;th 3 0.000125000000000 0.00007777 7777778 0.000068750000000 0.000 076000000000 0.0 00 097222222 2'22 0.00 0136734693378 0.000204687500000 0.0 003 19753086420 0.00 051 5000000000 000084876033 0579 0.001424305533556 0.002 42 5443786982 0.004181122440980 0.007283111111111 Columns 4- th mugh 6 0.000332000000000 0.000236111111111 0.000181632653061 0.000151562500000 11000139506 172840 0.000145000000000 0.000172727272727 0.000234027777778 0.0003 5088757 3964 0.012105637755102 04- 0.000946222222222 000163164062 5000 0.002862 629757785 (10050817901 23-1-57 Columns 7 thmugh 9 0003420312 500000 1100270493827 1605 0.002 19500000 00 00 0.001020661157025 00015409722 22222 0.001331952662722 0.001181122448980 0.001085777777770 0.0010542? 687.500!) 0.001 1 1 1 072664360 0.001307098765432 0.001740443213296 000259475 0000000 0.004211111111111 0.000122222222222 0.000081250000000 0.000068000000000 0.000069444444444 0.000003673469388 0.000114062500000 0.000169135802469 0.000265000000000 0.000430570512397 0.000717 361111111 0.001217159763314 0.1102094387755102 0.0036443815838839 000640351562 5000 00006805555 555 56 0.000 50408163 2653 0.000392187500000 0.000319753086420 0.0002 75000000000 0.0002 537 190082 64 0.000257633888889 0.000295266272189 0.000385204081633 0.000563111111111 0.000894921875000 0.001501334083045 0.002603 395061728 0004605817 1 745 15 0.0 08102469135002 0.006565000000000 0.005428925619335 0.0045 6736 11 1‘1 ‘1 11 0.003901183431953 0.003380102040816 0.002972888888889 0.002662890625000 0.0 02447404844291 000234104938 2716 0.0023 847 6454-2936 0.002664250000000 0.0 0334-53 5147 3923 0.004740702479339 Coiumns 10 through 12 0.048802479338843 0.041009027777778 00349449704142 01 0.03 01 3 5 20408 1633 0.0262 5322222 22 2.2 0.023 09101 5625000 0.020476470588235 0.018304012345679 0.016498891966759 0.015018250000000 0.013854195011338 0.013046487603306 0.012710964083176 0.0 1 3 [196006944444 0.123020138888889 0.10432 30 76923 077 0.090385204081633 0.078739111111111 0.0692 105 4607 5000 0.0613 18685 12 1107 0.054714506172340 0.049142105263158 0.044414750000000 0.040401587301587 003702376033 0579 003426143667 2968 0.032176909722222 0.0309 6-4-9 50000000 Cnfumns 1381rclugh 14 0.813431122448980 0.7085897? 7777778 0.622785546875000 0.551674394463668 0.492084876543210 0.4416584487 53463 0.393612750000000 0.361 582539682 540 0.329511363636364 0.3 01 577882797 732 0.2771477 43055556 0.255747040000000 0.237058431952663 0.220947462277092 2.125764888888889 136634882812 5000 1.635009342560554 1.4762299382 71605 1.3 2493 102493 0748 1.1957582 50000000 1.084602494331066 0.988269628099174 0.9042 49 7 164-46 125 0.830554340277778 076560272000 0000 0.7 0814-57 10059172 0.657223731138546 0.6121623 72448980 0.000181250000000 0.000124000000000 0.0000972 2222 2222 (100008775510 2041 0000092187 500000 0000112345 679012 0.000155000000000 0.000233 884297521 0.000374305555556 0.000621893491124 0.001058673469388 0.001832444444444 0.00 32 1054-6875000 0.00 5678 546712003 0.001491836734694 0.001145312500000 0.0009 09076543210 0.000745000000000 0.000628925619835 0.000550694444444 0.000507100591716 0.000502551020408 0.00055 1555555 556 000068476562 5000 0.000960899653979 0.001489197530664 000247119113 57 34 0.004278250000000 0.019635000000000 0.016270247933884- 0.013674305555556 0.011656213017751 0.010058673469388 0.008776444444444 0.007738671875000 0.0068993 079 50478 0.006233024691358 0.00 57 36011080 332 0.0 054-32 750000000 0.005392063492063 0.0057 5929752066 1. 0.0063179 58412098 0.314463313609467 0.271145408163265 0.236199555555556 020760039062 5000 0.183908692041522 0.164044753086420 0.147249030470914 0.132924250000000 0.12 062 4263038549 0.11001 34297 52066 0100848582 230624- 009297 5173611111 0.086341280000000 0.081039201103432 5.011;: c = ones{u.,‘l] c: HwHHHMH-mHHHi—IHH EDU>> 825 = AZS‘C 825 : 1.0a +04 ‘ 3.459622539323342 3.02 1 62483 7993929 2.662340519530827 2.3 63 872783971009 2.113202706720549 1.900672208059571 171901422483 1724- 1.562720994206121 1.427641242777550 1.310753290435700 1.210103 796475922 1.124947102877354 1.056184490059307 1.007310803603382 EDIE); b = B25: EDD)»: slim ans = 10e+03 "‘ 0.001134168847627 000141476212 0240 0.003217 009899221 0.091324922404277 41.52 0 2 5422491937 0 1383737486339 344 2.150915104648647 2.122 5281333 29073 1.3535011366741314 055276602233 7271 0.133486332433345 0.017145998522574 0.00082 6610589679 0.0008948? 5696306 EDU>> RFE = [maxLahs(x'-t]]]fmax{abs{c]] RFE= 2.151915104648647e+03 ED lb) RE 2 [maxfahfiBZS - {A25fij}}]}max[abs[825]} RBE = 7.23372027607857lel4 EDU» EMF = RFEJRBL‘ EMF 2.965018723391680e+16 EDU b> type makematrbc 6:6; for 1': 1:n for 52131 a[i.j]= mocifiz "i + 3"}')f[{i+j]"2]. 1‘: end and EM» makematr'tx EDUb-h- A31 = :1 A31 = Columns 1 through 3 0.250000000000000 0.777777777777778 0.687 5000000000 00 0.760000000000000 0372222222222 222 036734693877 5510 Colums 4 through 6 0.3 20000000000000 0.361111111111111 0.816326313612245 0.51562 5000000000 0.395061728395062 0.450000000000000 500» r: = ones[n.1) c: p-lI-‘r-‘I-‘I‘I‘ EDU>§ 831 = A333“: 331 = 3.328645124716554. 2.685330215419500 4.176689184933233 3.495151329050139 4.165149842341942 2.125563255988040 EDD» 13 = I331 13: 3.328645124716554 2.685330215419500 4.176689184033233 3.495 151329 050139 4.165149842841942 2.125563255988040 EDU» elim ans = 1.000000000090016 0.999999999999992 1.000000000000000 0.999999999999988 1.000000000000006 0.999999999999996 0.2 2222222222 2222 0.312500000000000 0.680000000000000 0.694444444444444 0.83 6734693877551 0.14062 5000000000 0.805555555555555 0.040816326530612 0.921875000000000 0.197530364197531 0.7 50000000000000 0.537190082644628 E130» RFE = {max[abs{x'-cjj]{maflabslcjj RFE = 1.5 543 1223 447 52 19e- 14 0.812500000000000 0.240000000000000 0.972222 22 2222222 0.877551020408163 0.921875000000000 0.123456790123457 0.918367346938776 0.453125000000000 0.098765432098766 0.450000000000000 0.289256198347108 0.5 06944444444445 EDU3> RBE = [max[abs(831 - [A31'x']]j]fmax[ahs(83l}] REE = 1.9138617750482463-15 mu» EMF = magma EMF = 8.121340081814619 8.121340081314619 Ems» type makemau'ix a[i,j]='mod[{2n1 + 3 "fif{[1+”“2]. 1}: and and £009: makematrix 0002:: A32 = 3 A32 = Columns 1 through 3 0.250000000000000 0.777777777777778 0.637 500000000000 0.760000000000000 0.972222222222222 0.3 67 34693 3775510 0.046217515000011 000 0.19 7 530864 1.97 53 1 Columns 4 through 6 0.3 20000000000000 0.3 61111111111111 0.816326530612245 0.515625000000000 0.3 95061728395062 0.450000000000000 0.727272727272727 0.340277777777778 Columns 7 through 3 0.203125000000000 0.049382716049383 0.949999999999999 0206611370 247933 0.409722222222221 0.319526627218934 0.81122 4-189 79 59 19 0.857777777777779 E00» :2 2‘ ones[n.1) c: wr-u—u—u—u-awo-t EDU>> 332 = AEZ‘C 1332 = 3.556461482741251. 3.384712931468889 3.415945303280336 4.375374010409105 4.506706304590792 3.246110291370242 4.203013936697546 199150857 0934023 EDD» b = 932: EDIE» slim 6113: 0.999999999999874 1.000000000000111 0.999999999999995 1.000000000000188 1.000000000000155 0.999999999999373 0.999999999999717 1.000000000000009 0.222222222222222 0.812500000000000 0.680000000000000 0.694444444444444 0.836734693877531 0.140625000000000 0.6913 5302469 13 58 0.650 000000000000 0.805555555555555 0.040816326530612 0.921875000000000 0.197530064197531 0.750000 000000000 0.537190082644628 0.57 6389080808889 0.952662721393491 0.024691358024697 0.6 50000000000006 0.289256198347104 0.673611111111114 0.0118343 1952 6628 0.30 1020408 1 63263 0.7 28038888880339 0.628906250000000 mu» RFE‘ = {maxfahsfx'-c}]]7max[abs[c}] RFE = 2.8321789359187749-13 0.912500000000000 0.240000000000000 037222222 2222222 0.877551 020403163 0.921875000000000 0.123456790123457 0.550000000000000 0.338812 975206612 0.910367346938776 0.453125000000000 0098765432 098766 0.450000000000000 0.289256 19334-7 .108 0.506944444444445 0.071005917159764- 0132 5510204081633 EDU >> RBE .—— [muf'absi'832 -[A32‘x‘]]])/max{ahs[1332]) REE = 1.14795266530830691-1 EDUb> = RFE ,rRBE E111: = 24.671565497050245 EBB >> type makematrix afij]: modflZ“! + 3‘;];‘[[t+}]" 2}. 1}; end and E00» makemanix E00» A33 = a A33 = Columns 1. through 3 025000000 0000000 0.7 7777777777 7773 0.687500000000000 076000000 0000000 0.972222 222222222 0.367346938775510 0.04687 5000000000 0.197530864197531 0.150000000000000 0.487503305785123 Comm ns 4 mmugh 6 032990000 0000000 0.361111111111111 0.816326530612245 0.515625000000000 0.395061728395062 0.450000000000000 [1727272727 272 727 0.340 277777 777778 0.503875 739644970 0.63 7755102040816 Columns 7 through 9 0.203123000000000 0.049382716049383 0.949999999999999 0.2066115? 0247933 0.409722222222221 0.319526627218934 0.811224439795919 0.857777777777779 0.542968750000000 0.110726643598616 Caium n ‘I 0 0.0247933813429771 0.1190 277777777771 0.449704142011853 0.352040816326307 0.582 222222222242 0.910156250000000 0.764705082332928 0.040123456790127 [1988919667 590039 0.132500000000005 EDU» I: = ones-[11.1) L': HHHHHHHHMH EDD): 1333 = 21331:: B33 2 4x431254071171015 0.222222 22222 2222 0.8125000 00000000 0.600000000000000 0.694444444444444 0.836734693077551 0.140625000000000 0.691358024691358 0.650000000000000 0.3 0.57851 2 39 56942 0.173611111111111 0.805 555555555555 0.040016326330612 0.921075000000000 0.197530864197531 0.750000000000000 0.537190082644628 0.576300388888889 0.952662721893491 0.852060016326531 0.631111111111111 0.024691359024697 0.650000000000006 0.289256193347104 0.673611111111114- 0.01 18343 1952 66 23 0.30 1 0204081 53263 0.? 23888888883809 0.620906250000000 0.474048442906575 0.410493827160494 0.312500000000000 0.240000000000000 0.972222222222222 0.87755 10204103163 0.92187 5000000000 0.1.2 3456790 123 457 0.550000000000000 0.338012975206612 0.7 43055555 555535 0.218934911242603 0.9183673 46938776 0.453125000000000 0.0907654?! 2098766 0.450000 000000000 0.209256190347103 0.506944444444445 0.071005917159764 0.025510204001633 0.5 1555555555 5555 0.847656250000000 0.049999999999994 0.70 2479338842977 0.743055555535543 0.562130177514780 0.586734693877516 0.7 64444444444450 0.3 867 10750000000 0.993079 584775009 0330245913 580247 0.360110003324098 4.177470048009638 6.60 8705080847733 5289 545004250401 5.755663 30 0690579 4.920710905014693 53544385690 50-1-73 5024711612 5000 38 5.411496515512641 5 4.0 50503065373976 EDU>§ E} = 033: E00): efim 311.9: 0.999999999999997 1.000000000000041 0.999999999999900 0.999999999999902 0.999999999999981 1.00000000 0000085 1.000000000000130 1.000000000000012 0.9999999999999411I 0.999999999999997 E00» RFE = [max{abs{x":]J)lmax(ai:ls[c]] RFE: 1.30 11813848606832-13 E00» 000 = [max[abs{833 - {7133‘}:']]]}7max(abs(833]j RBE = 4.703 83294597 20 41 E- 1 5 500:: EMF —- RFEIRBE EMF = 27.662151266976938 E00 >5 type makema trix aihjiémuuazni + 30730272). 11: end and E00» makemaLrix 500» A34 = 21 A34 = Columns 1 through 3 0.250000000000000 0.777 777777777778 0.607 500000 000000 0.760 00000 0000000 0.972222222222222 036734693877 5 5 10 0.046075000000000 0.197530864197531 015000000 0000000 0.407603305705123 0.243 055555555555 0.2 5443786982 2 435 Columns 4 through 6 032000000000 0000 0.361111111111111 0.916326 530612 245 0.51562 5000000000 0.395061723395062 0.450000000000000 0.727272 727272727 0.340277777772778 050887 5739644970 0.637755102040816 0.462 22222 2222222 0.316406250000000 Coimrms 7 through 9 0.203125000000000 0.049302716049383 0.222222222222222 0.012500000000000 0.600000000000000 0.694444444444444 0.835734693877551 {1.140625000000000 0.691358024691358 0.650000000000000 0.3 05785 1239669 42 0.173611111111111 0.171597633136095 0.943877551020407 011035555555 55555 0.0408 163 2 6530612 0921 B75 0 00000000 0. 1 9753 036419753 1 0.750000000000000 0537190002 644628 0.576388888088089 0.952662721093491 0.8 52040816326531 0.631111111111111 0.949218750000000 0.013840830449026 0 .0 24459 1 35802469 7 0.6500 00000000006 0.812500000000000 0.2 400 00000000000 0.97 2222222222222 0.8775510 20408163 0.921375000000000 0.1 23456790123 457 0.550000000000000 0.3380429 75206612 0743055555 555555 0.218934911242603 0.5867 3469 3077551 0.324444444444445 0.910367346938776 0.453125000000000 0.09876 5432 090766 0.450000000000000 0.289256198347108 0.50 6944444444445 0071005917 159 764 0.025510204081633 0.515555555555555 0.84765 6250000000 0.608996539792388 0.891975308641975 0.8499999999999941- 0.702479330042977 0.949999999999999 0.206611570247933 0.409722222222221 0.319526627218934 0.811224489795919 0.857777777777779 0.542963750000000 0.1107 2664-3598616 0.07 0987654320907 0.404432132963990 0.289256198347104 {16736111111111 14 0.011834319526628 0.801 020403 1 63268 0.728888888888889 0.6289062 50000000 0.474048442906575 0.410493027160494 0.847645429362081 0.642499999999998 Columns 10 u'mjugh 12 0024793388429 771 0.090 277777777771. 0.449704142011853 0.352040816326507 058222222222 2242 0.910156250000000 0.764705882352928 0.040123456790127 0.988919667590039 0.182500000000005 0.541950113370675 0464876033 057863 EDU» c = unes[n.l] c: HHHHHwMHHpr—o ED 03-: E34- = .3134“: 83-4: 5.265779854734612 436232091 151 19 36 0.45630 14527 2995 l 5.684562365361510 5.860052465915420 5.555093061084775 5.989805006586064 5.6813126424407911 6]. 5.801626950613367 4.210673601903209 5533334203 669689 6.543528181025629 EDU‘J: h = 034; EDD» ellm ans 3 '1 .0 0000000000 00 54 0.999999999999904 1.000000000000004 0.999999999999914 0.999999999999991 1.00000 0000000054 1.000013000001101 0? 1.000000000000029 0.999999999999937 0.999 999999999991 0.999999999999957 1.000000000000020 0.20.13 088888889 14 0.2307 692307 692 83 0.852 040816326507 0.391111111111059 0.105 4687 50000000 0.186851211072621 0.145061728395035 0.421052631578959 0.147499999999930 0.015873015873012 0.237603305785115 0.614366729678636 EDU>> RFE u (max(ab5(x'—c]]) {maxfab 302]] RFE: 1.07 24754-41 787901245 0.743055555555543 0.562130177514788 0586734693 877 546 0.764444444444450 038671875 0000000 039507958477 5089 0.330246913500247 0.360110803324098 032750000000 0001 032063492 0634917 0.63313 6094674683 0.4 54081632 653015 0.995555555555711 0.0039 06250000000 0.006920415224840 0.44753 0864197461 0.490304709141355 0.242500000000064 0.24263 0335407473 0.134213732066122 1 0.485822306238219 0.751736111111006 E00» REF, = (n‘lax(abs{834 - {A34’x'})]jfmax{abs[034)] REE — 2.7308202103826679-15 500-» EMF = RFEIRBF. EMF = 39.273015400659290 EDU >> type mahemarrix 500 >> makcmatrinc E00» A35 = a A35: Coiumns 1 chmugh 3 0.250000000000000 0.777777 777 777778 0.687 500000000000 0.760000000000000 0.972222222222222 0.367 3469387755 10 00468750000000 00 0197530864197 531 0.15 000000000 0000 0.487603303705123 0.243 055555555555 0.2 54437869022485 0.811224489795919 0.331111111111113 Columns 4 th m ugh 6 032000000000 0000 0.361111111111111 0.81 632653061 2 245 0.515625000000000 0.395061728395062 0.450 00000000 0000 0.727272727272727 0.3 4027777777 77 70 0.50887 5739644970 0.637755102040816 0.462222222222222 0.3 1.640 6250000000 0.626297 577854672 0.817901234567898 Columns 7 through 9 0.203125000000000 0.049382716049383 0.949999999999999 0206611570 247933 0.409722 222222221 0.3 1 952662 7.2 I 8934 0.811224409795919 0.8 57777777777779 0.5429687 50000000 0.110 726643 5986 16 0.070987 654320907 0.404432132963990 0.947 50000 0000002 0.111 111111111114 'mndztzni +3-1- }{'{{5+J}"21 1]: 0.2 22 2222222 222 22 0.012 500000000000 0.600000000000000 0.594444444144444 0.036734693877551 0.140625000000000 0.691358024691358 0.650000000000000 0.305785123966942 0.173611111111111 0.171597633136095 0.943077551020407 0.448808808888883 0.0351562 50000000 0.805555555555555 0.040816326530612 0.92 1117 5000000000 0.197531136419753 1 0.7500000 00000000 0.537190082644628 0.5763 80388888889 0.952 662 72 1.093491 0.852 040016326531 063111111 1111111 0.9492137 50000000 0.013840330449826 0.033950 61 7233949 0058171745} 523 S7 0.024691350024697 0.6 50000000000006 0.269256198347104 0.673611 1111 11114 0.0118343 19526628 0.001020408163260 0.7238888888m 0.628906250000000 0.474048442906575 0.410493027160494 0.047645429362861 0.642499999999993 0.453514739229020 0.407024793388430 Columns 10 through 12 00247933884297 71 0.090277777777771 0.44970 41420 1 1853 0.352040316326507 0.58222 22 Z 2 222242 0.91 D 15 62 50000000 0764705882 352928 0.040 123 45 6790 127 0388919667 590039 0102500000 000005 0.541950113378675 0.464076033057063 0.109640831758028 0.960 069444444457 0.2013 83363808914 02307692307 69283 0.852040316325507 0.3911111 1.1111059 0.1054687 50000000 0.166851211072621 014506172839 5035 0.421052631578959 0.147499999999980 0.015073015873012 0.2 37603305785115 0.614366729670636 0.7 690972222222 29 0.649600000000021 Columns 13 through 14 0.3 1 1 224489795677 0.89 777777777 3174- 0.855468750000000 0.7 4394463667 7952 0.640880800088905 0.4382 81250000000 0.093425605537050 0.299382716049877 0.812500000000000 0.240000000000000 0.972222222222222 0.87 7551020408163 0.921075000000000 0.123456790123457 0.550000000000000 0.3 30842975206612 0.743055555555555 0.218934911242603 0.5067 34693877551 0.324444444444445 0.105468750000000 0.785467128027633 0.918367346938776 0.453125000000000 0.0987 65432098766 0.450000000000000 0.289256198347108 0.506944444444445 0.071005917159764 0.025510204001633 0515555555 555555 0.847656250000000 0.608996539792388 0.891975303641975 0.711911357340721 0.7 82499999 999999 0.649999999999994 8.70 2479338842977 0.7430 55 555555 54-3 0.562130177514788 0.506734693077546 0.791446014444150 0.386710750000000 0.99 3079 58477 5039 0.33 02 469 13 58024-7 0.360110003324098 0.327500 000000001 0.92063 4920634917 0.59297 5 20661157 0 0.179584120902900 0.633136094674683 0.454081632653015 0.995 55555 5555711 0.003906250000000 0.006920415224840 0.447 530864197461 0.490304709141355 0.242500000000064. 0.24263 0383487473 0.134297520661221 048532230623 B219 0.751736111111086 0.412799999999947 0.392011834319533 11848765432 098844 0.310249307478443 058448753462 5623 6.5825000 0 000041-37 0.127500000000055 0.02 539682539 6638 0.1 1363 636363 6483 0.778827977315814 0.477430555555657 0.470400000000154 0.584319526627041 0.474622770919258 500» c = unes[n,1); 500» 835 = 1135‘: 835: 6.225393233419194 624837995 9290110 940519580826 7001 6.727889718089369 7.0 2 706720549 2707 5.722080595710834 6.142248317245191 7.209942061210665 6.412427775497294 5.532904357001397 6.03 7964-75922 5794 7.471028773541754 6.844900593071173 7.108056033820532 50033 E: = 835; E00» eiim 8115 = 1.000000000000208 1.000 000000000272 0999999999999 623 1.000000000000440 10000000000003 23 0.999999999999333 0.999999999999515 039999999999 9882 1.000000000000240 1.000000000000020 1.000000 000000492 0.999999999999759 0.999999999999435 1.000000000000040 0.024943310658273 0.696200991734966 0.497160161246939 0.5 43402777777374 0.027200000000440 031571005917 15971 0.2 37311385459179 0.623724489795677 EDU» RFE = (m(abs(x'—c]jjfmaxtabsicfl RFE = 5.65436 586441592 2?- 13 500)) REE = [max[abs{835 A [A35'x'}]]jfmax{ahs{335]] REE = 1.227653277133541e-14 EDU>> EMF = RFEIRBE EMF : 46.058329087984454 diary and ...
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This note was uploaded on 10/27/2010 for the course MATH 446 taught by Professor Staff during the Spring '08 term at George Mason.

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p4 - I C David Mahen MATH Mes/OR 4816001 3-18-2010 Project...

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