jacobi
DESCRIPTION
JacobiTRANSCRIPT
A) JACOBI A = -8 1 2 4 0 -7 5 1 1 -3 5 0 1 2 1 7
b = 0 -12 -2 -17
D = -8 0 0 0 0 -7 0 0 0 0 5 0 0 0 0 7
L = 0 0 0 0 0 0 0 0 1 -3 0 0 1 2 1 0
U = 0 1 2 4 0 0 5 1 0 0 0 0 0 0 0 0
BJ = 0 1/8 1/4 1/2 0 0 5/7 1/7 -1/5 3/5 0 0 -1/7 -2/7 -1/7 0
CJ = 0 12/7 -2/5 -17/7
nJ = 7/8
EJERCICIO 1
a) x0=[0 0 0 0]’ x0 =
0 0 0 0
x1 = 0 1.714285714285714 -0.400000000000000 -2.428571428571428
x2 = -1.100000000000000 1.081632653061225 0.628571428571429 -2.861224489795918
x3 = -1.138265306122449 1.754518950437318 0.468979591836735 -2.670262390670554
x4 = -0.998571428571428 1.667805081216160 0.880364431486881 -2.834250312369846
x5 = -0.988558413161183 1.938224549294937 0.800397334443982 -2.888200452192539
x6 = -1.001722823823407 1.873398031432481 0.960646412209199 -2.955469717124667
x7 = -1.003398501580974 1.978251763417332 0.924383383624170 -2.957959950178679
x8 = -1.000602658756130 1.951993852563167 0.987630758366594 -2.982498344125408
x9 = -1.000342250900660 1.993665063958223 0.971316843289126 -2.984430829248114
x10 = -1.000178070806997 1.981736198171074 0.996267488555066 -2.994043531472130
b) x0=[1 2 3 4]'
x0 = 1 2 3 4 x1 =
3.000000000000000 4.428571428571428 0.600000000000000 -3.571428571428571x2 =
-1.082142857142857 1.632653061224490 1.657142857142857 -4.208163265306123x3 =
-1.485714285714286 2.296793002915452 0.796020408163265 -2.977186588921283x4 =
-1.002489067055393 1.857559350270721 1.275218658892128 -2.986270304039983
x5 =
-0.942135568513119 2.198546141488665 0.915033423573511 -2.998264041768310x6 =
-0.995555397304694 1.939557582299892 1.107554798595823 -3.052855734005389x7 =
-1.007094469566252 2.069274036996247 0.962845628840874 -2.998730652270130x8 =
-0.999994664300316 1.973642498847749 1.042983316110999 -3.013471319038159x9 =
-0.999284518135361 2.028777894502405 0.984184432168712 -2.998610521358025x10 =
-0.999661915824034 1.988901662783648 1.017123640328515 -3.006065100434023
B) GAUSS SEIDEL: A = -8 1 2 4 0 -7 5 1 1 -3 5 0 1 2 1 7
b = 0 -12 -2 -17
D = -8 0 0 0 0 -7 0 0 0 0 5 0 0 0 0 7
L = 0 0 0 0 0 0 0 0 1 -3 0 0 1 2 1 0
U = 0 1 2 4 0 0 5 1 0 0 0 0 0 0 0 0
BG = 0 1/8 1/4 1/2 0 0 5/7 1/7 0 -1/40 53/140 -1/70 0 -1/70 -72/245 -27/245
CG = 0 12/7 22/35 -737/245
nG = 7/8
c) x0=[0 0 0 0]'x0 =
0 0 0 0
x1 =
0 1.714285714285714 0.628571428571428 -3.008163265306122
x2 =
-1.132653061224490 1.733527696793003 0.866647230320700 -2.885864223240316
x3 =
-1.009579341940858 1.921053132623312 0.954547747962158 -2.969582095895417
x4 =
-1.006022469379255 1.971879520559339 0.984332206211455 -2.988866968278697
x5 =
-1.001865492516567 1.990399151825511 0.994612589598620 -2.996220771533296
x6 =
-1.000657344388804 1.996691739494258 0.998146512574315 -2.998696092453432
x7 =
-1.000224950646355 1.998862352916878 0.999362401879398 -2.999551736723828
x8 =
-1.000077473777455 1.999608610381880 0.999780660984619 -2.999845772567275
x9 =
-1.000026644739748 1.999865361765117 0.999924546007020 -2.999946946399644
x10 =
-1.000009166477427 1.999953683376494 0.999974043321382 -2.999981749085277
d) b)x0=[1 2 3 4]’
x0 =
1 2 3 4
x1 =
3.000000000000000 4.428571428571428 1.657142857142857 -4.359183673469387
x2 =
-1.211734693877551 2.275218658892128 1.207478134110787 -3.078025822573927
x3 =
-0.952741045397751 2.137052121140001 1.072779481763551 -3.056306096949400
x4 =
-0.992826662891312 2.043941615981193 1.024930302166978 -3.017140981605436
x5 =
-0.996845213263324 2.015358647032779 1.008584230872333 -3.006065187382081
x6 =
-0.998966705093860 2.005265138139940 1.002952423902736 -3.002073713584108
x7 =
-0.999640608548877 2.001812629418510 1.001015699360882 -3.000714335664146
x8 =
-0.999876664314539 2.000623451591466 1.000349403817787 -3.000245663240883
x9 =
-0.999957549217061 2.000214479406865 1.000120197487531 -3.000084515297742
x10 =
-0.999985398351130 2.000073781734273 1.000041348710790 -3.000029073404029
A) JACOBI A = 5 1 3 0 0 7 3 3 1 2 7 1 0 1 5 8
b = -9 10 1 9
D =
5 0 0 0 0 7 0 0 0 0 7 0 0 0 0 8
L = 0 0 0 0 0 0 0 0 1 2 0 0 0 1 5 0
U = 0 1 3 0 0 0 3 3 0 0 0 1 0 0 0 0
BJ = 0 -1/5 -3/5 0 0 0 -3/7 -3/7 -1/7 -2/7 0 -1/7 0 -1/8 -5/8 0
CJ = -9/5 10/7 1/7 9/8
nJ = 6/7
Ejercicio 2
e) x0=[0 0 0 0]’
x0 =
0 0 0 0
x1 =
-1.800000000000000 1.428571428571428 0.142857142857143 1.125000000000000
x2 =
-2.171428571428572 0.885204081632653 -0.168877551020408 0.857142857142857
x3 =
-1.875714285714286 1.133600583090379 0.077696793002916 1.119897959183674
x4 =
-2.073338192419825 0.915316534777176 -0.073054977092878 0.934739431486880
x5 =
-1.939230320699709 1.059278090973999 0.043995098768370 1.056244793835902
x6 =
-2.038252677455822 0.957040046026740 -0.033652950726313 0.965093301898019
x7 =
-1.971216238769560 1.029382706640697 0.022725611929189 1.026403088450603
x8 =
-2.019511908485653 0.978944842694375 -0.016278894708920 0.982123654214170
x9 =
-1.986021631713523 1.014637960212036 0.011356938411819 1.012806203856278
x10 =
-2.009741755089499 0.989644367599387 -0.008008641795261 0.991072168466109
f) x0=[1 2 3 4 ]’x0 =
1 2 3 4
x1 =
-4.000000000000000 -1.571428571428572 -1.142857142857143 -1.000000000000000
x2 =
-0.800000000000000 2.346938775510204 1.306122448979592 2.035714285714286
x3 =
-3.053061224489796 -0.003644314868805 -0.704227405247813 0.015306122448980
x4 =
-1.376734693877551 1.723823406913786 0.577863390254061 1.565597667638484
x5 =
-2.491482715535194 0.509945260903195 -0.376644255369786 0.548357455226989
x6 =
-1.676002498958767 1.354980057204056 0.274747819785974 1.296659501993217
x7 =
-2.235844703312395 0.755111147808918 -0.190088159634652 0.783910105483260
x8 =
-1.836969333780993 1.174076308922025 0.134530328887329 1.149416206295543
x9 =
-2.115533459116802 0.878308627778769 -0.094371355765514 0.894159005830167
x10 =
-1.919038912096445 1.085805292829435 0.066393885389871 1.074193518881100
B) GAUSS SEIDEL
A = 5 1 3 0 0 7 3 3 1 2 7 1 0 1 5 8
b = -9 10 1 9
D = 5 0 0 0 0 7 0 0 0 0 7 0 0 0 0 8
L = 0 0 0 0 0 0 0 0 1 2 0 0 0 1 5 0
U = 0 1 3 0 0 0 3 3 0 0 0 1 0 0 0 0
BG = 0 -1/5 -3/5 0 0 0 -3/7 -3/7 0 1/35 51/245 -1/49 0 -1/56 -15/196 13/196
CG = -9/5 10/7 -2/245 373/392
nG = 6/7
g) x0=[0 0 0 0]’
x0 =
0 0 0 0
x1 =
-1.800000000000000 1.428571428571428 -0.008163265306122 0.951530612244898
x2 =
-2.080816326530612 1.024271137026239 0.011534777176177 0.989756872136610
x3 =
-2.011775093710954 0.999446436008806 0.003303621365247 0.998004432145620
x4 =
-2.001871460020910 0.999439405638200 0.000712602371270 0.999624697813181
x5 =
-2.000315442550402 0.999855442778092 0.000139979883005 0.999930582225860
x6 =
-2.000055076485422 0.999969759096200 0.000026425152451 0.999987264392693
x7 =
-2.000009806910711 0.999994133052081 0.000004896630551 0.999997672974395
x8 =
-2.000001764588747 0.999998898740737 0.000000899161840 0.999999575681258
x9 =
-2.000000319245251 0.999999796495815 0.000000164367480 0.999999922708348
x10 =
-2.000000057919651 0.999999962681788 0.000000029978247 0.999999985928372
h) x0=[1 2 3 4]’x0 = 1 2 3 4
x1 =
-4.000000000000000 -1.571428571428572 0.591836734693878 0.951530612244898
x2 =
-1.840816326530612 0.767128279883382 0.050718450645564 0.997409933361100
x3 =
-1.983856726364015 0.979373549711430 0.003957099082865 1.000105119359281
x4 =
-1.998248969392005 0.998259049239080 0.000232250222081 1.000072462456315
x5 =
-1.999791159981065 0.999869408852116 -0.000002874311355 1.000018120338082
x6 =
-1.999972157183610 0.999993465988545 -0.000004699304509 1.000003753816750
x7 =
-1.999995873615004 1.000000405209039 -0.000001241517118 1.000000725297069
x8 =
-1.999999336131537 1.000000221237164 -0.000000261662837 1.000000135884628
x9 =
-1.999999887249731 1.000000053904947 -0.000000050920684 1.000000025087309
x10 =
-1.999999980228579 1.000000011071446 -0.000000009571660 1.000000004598357
A) JACOBI
A = -4 1 0 2 0 -5 3 1 1 3 6 -2 -1 -2 3 8
Ejercicio 3
b = 2 -3 -17 17
D = -4 0 0 0 0 -5 0 0 0 0 6 0 0 0 0 8
L = 0 0 0 0 0 0 0 0 1 3 0 0 -1 -2 3 0
U = 0 1 0 2 0 0 3 1 0 0 0 -2 0 0 0 0
BJ =
0 1/4 0 1/2 0 0 3/5 1/5 -1/6 -1/2 0 1/3 1/8 1/4 -3/8 0
CJ = -1/2 3/5 -17/6 17/8
nJ = 1
i) a) x0=[0 0 0 0]’x0 =
0 0 0 0
x1 =
-0.500000000000000 0.600000000000000 -2.833333333333333 2.125000000000000
x2 =
0.712500000000000 -0.675000000000000 -2.341666666666666 3.275000000000000
x3 =
0.968750000000000 -0.150000000000000 -1.522916666666667 2.923437500000000
x4 =
0.924218750000000 0.270937500000000 -1.945312500000000 2.779687500000000
x5 =
0.957578125000000 -0.011250000000000 -2.196276041666667 3.037753906250000
x6 =
1.016064453125000 -0.110214843750000 -1.974720052083333 3.065488281250000
x7 =
1.005190429687500 0.028265625000000 -1.925740559895833 2.964974365234375
x8 =
0.989553588867188 0.037550537109375 -2.026673095703125 2.979867919921875
x9 =
0.999321594238281 -0.020030273437500 -2.023744893391927 3.018084243774414
x10 =
1.004034553527832 -0.010630087280273 -1.983843714396159 3.003811965942383
j) b) x0=[1 2 3 4]’
x0 =
1 2 3 4
x1 =
2.000000000000000 3.200000000000001 -2.666666666666667 1.625000000000000
x2 =
1.112500000000000 -0.675000000000000 -4.225000000000000 4.175000000000001
x3 =
1.418750000000000 -1.100000000000000 -1.289583333333333 3.679687500000000x4 =
1.064843750000000 0.562187500000000 -1.293229166666666 2.510937500000000
x5 =
0.896015625000000 0.326250000000000 -2.454921875000000 2.883613281250000
x6 =
1.023369140625000 -0.296230468750000 -2.184589843750000 3.239160156250000
x7 =
1.045522460937500 -0.062921875000000 -1.776059570312500 2.998084716796875
x8 =
0.983311889648437 0.133981201171875 -1.976764567057292 2.905982177734375
x9 =
0.986486389160156 -0.004862304687500 -2.095548522949219 3.022695999145508
x10 =
1.010132423400879 -0.052789913940430 -1.987751246134440 3.032925918579101
B) GAUSS SEIDEL
A = -4 1 0 2 0 -5 3 1 1 3 6 -2 -1 -2 3 8
b = 2 -3 -17 17
D = -4 0 0 0 0 -5 0 0 0 0 6 0 0 0 0 8
L = 0 0 0 0 0 0 0 0 1 3 0 0 -1 -2 3 0
U = 0 1 0 2 0 0 3 1 0 0 0 -2 0 0 0 0
BG = 0 1/4 0 1/2 0 0 3/5 1/5 0 -1/24 -3/10 3/20 0 3/64 21/80 9/160
CG = -1/2 3/5 -61/20 537/160
nG = 4/5
k) X0=[0 0 0 0]’x0 = 0 0 0 0
x1 =
-0.500000000000000 0.600000000000000 -3.050000000000000 3.356250000000000
x2 =
1.328125000000000 -0.558750000000000 -1.656562500000000 2.772539062500000
x3 =
0.746582031250000 0.160570312500000 -2.113869140625000 3.051166259765625
x4 =
1.065725708007813 -0.058088232421875 -1.964854748535156 2.980514186096192
x5 =
0.975735034942627 0.017189988098145 -2.011046104507446 3.005406665582657
x6 =
1.007000829815865 -0.005546329587936 -1.996591418314457 2.998210303197920
x7 =
0.997718569201976 0.001687209650910 -2.001059931959811 3.000534098047904
x8 =
1.000688851436679 -0.000529139566306 -1.999672206106992 2.999830898828131
x9 =
0.999783164522489 0.000162856101431 -2.000101655861753 3.000051730538826
x10 =
1.000066579294771 -0.000050647409287 -1.999968529331543 2.999983859058854
l) X0=[1 2 3 4]’x0 =
1 2 3 4
x1 =
2.000000000000000 3.200000000000001 -3.433333333333334 4.462500000000000
x2 =
2.531250000000000 -0.567500000000000 -1.483958333333333 2.856015625000000
x3 =
0.786132812500000 0.280828125000000 -2.152764322916667 3.100760253906250
x4 =
1.120587158203125 -0.071506542968750 -1.950757836914062 2.978730947875977
x5 =
0.971488838195801 0.025291487426758 -2.014983567454020 3.008377814426423
x6 =
1.010511779069901 -0.007314577587127 -1.995302069575945 2.997723604077936
x7 =
0.997033157642186 0.002363479070020 -2.001446064449396 3.000762288641302
x8 =
1.000972014088156 -0.000715180941377 -1.999550315663570 2.999774074899515
x9 =
0.999708242214413 0.000224625581761 -2.000138994860111 3.000071809744784
x10 =
1.000092061267832 -0.000069034967110 -1.999956889479489 2.999978082471510
A) JACOBI
A = 9 2 0 3 0 3 0 1 2 3 7 1 1 -2 1 6
b = 13 -1 1 15
D = 9 0 0 0 0 3 0 0 0 0 7 0 0 0 0 6
L = 0 0 0 0 0 0 0 0 2 3 0 0 1 -2 1 0
U = 0 2 0 3 0 0 0 1 0 0 0 1 0 0 0 0
BJ =
0 -2/9 0 -1/3 0 0 0 -1/3 -2/7 -3/7 0 -1/7 -1/6 1/3 -1/6 0
CJ = 13/9 -1/3 1/7 5/2
nJ = 6/7
Ejercicio 4
a) x0=[0 0 0 0]’
x0 =
0 0 0 0
x1 =
1.444444444444444 -0.333333333333333 0.142857142857143 2.500000000000000
x2 =
0.685185185185185 -1.166666666666667 -0.484126984126984 2.124338624338624
x3 =
0.995590828924162 -1.041446208112875 0.143613000755858 2.077601410934745
x4 =
0.983343131491280 -1.025867136978248 0.007936507936508 1.962983959015705
x5 =
1.018086932989931 -0.987661319671902 0.021133026990926 1.992831014435953
x6 =
0.999647732892883 -0.997610338145317 -0.009431560200016
1.997576233445890x7 =
1.000276886216996 -0.999192077815297 -0.000577240685100 2.002427191836083
x8 =
0.999011397791372 -1.000809063945361 -0.000772104403455 2.000319366472918
x9 =
1.000073336496885 -1.000106455490973 0.000583575682917 2.000023763120227
x10 =
1.000015735735696 -1.000007921040076 0.000021275765560 1.999855029473042
b)x0=[1 2 3 4]’
x0 =
1 2 3 4 x1 =
-0.333333333333333 -1.666666666666667 -1.571428571428571 2.500000000000000
x2 =
0.981481481481481 -1.166666666666667
0.595238095238095 2.261904761904762
x3 =
0.949735449735450 -1.087301587301587 0.039304610733182 1.848324514991182
x4 =
1.069958847736626 -0.949441504997061 0.073444192491812 1.972726127488032
x5 =
0.997856069725558 -0.990908709162677 -0.037759901138586 1.992952324962907
x6 =
1.000328938159626 -0.997650774987636 -0.002276905275142 2.009681068847946
x7 =
0.996250927047937 -1.003227022949315 -0.002483802886327 2.001107736190041
x8 =
1.000347870814279 -1.000369245396680 0.002295925508862 1.999963138323293
x9 =
1.000094341758165
-0.999987712774431 0.000064122319741 1.999436285480583x10 =
1.000185174345235 -0.999812095160194 0.000048309903769 1.999977685062206
B) GAUSS SEIDEL
A = 9 2 0 3 0 3 0 1 2 3 7 1 1 -2 1 6
b = 13 -1 1 15
D = 9 0 0 0 0 3 0 0 0 0 7 0 0 0 0 6
L = 0 0 0 0 0 0 0 0 2 3 0 0 1 -2 1 0
U = 0 2 0 3 0 0 0 1 0 0 0 1 0 0 0 0
BG = 0 -2/9 0 -1/3 0 0 0 -1/3 0 4/63 0 2/21 0 5/189 0 -1/14
CG = 13/9 -1/3 -8/63 410/189
nG = 5/9
a) x0=[0 0 0 0]’
x0 =
0 0 0 0
x1 =
1.444444444444444 -0.333333333333333 -0.126984126984127 2.169312169312169
x2 =
0.795414462081129 -1.056437389770723 0.058453010833963 2.005542957923910
x3 =
1.010693989529969 -1.001847652641303 -0.003055425579991 1.998111021794569
x4 =
1.001040248877656 -0.999370340598190 -0.000297213965044 2.000086047315168
x5 =
0.999831393250097 -1.000028682438389 0.000048173357115
2.000010511419335
x6 =
1.000002870068753 -1.000003503806445 -0.000000820019644 1.999998490389667
x7 =
1.000001281827099 -0.999999496796556 -0.000000366236314 2.000000015136017
x8 =
0.999999883131673 -1.000000005045339 0.000000033390951 2.000000012231117
x9 =
0.999999997044148 -1.000000004077039 0.000000000844529 1.999999998992874
x10 =
1.000000001241717 -0.999999999664291 -0.000000000354776 1.999999999964079
b) x0=[1 2 3 4]’
x0 = 1 2 3 4
x1 =
-0.333333333333333 -1.666666666666667 0.380952380952381 1.936507936507937x2 =
1.169312169312169 -0.978835978835979 -0.048374905517763 1.986898463088939
x3 =
0.999664063156127 -0.995632821029646 0.000095981955392 2.001495718804865
x4 =
0.998530942849411 -1.000498572934955 0.000419730614454 2.000008696777704
x5 =
1.000107895059644 -1.000002898925901 -0.000030827159898 1.999986189041409
x6 =
1.000005247858620 -0.999995396347136 -0.000001499388177 2.000000909805881
x7 =
0.999998673697403 -1.000000303268627 0.000000378943599 2.000000056803624
x8 =
1.000000048458487 -1.000000018934541 -0.000000013845282 1.999999987919619x9 =
1.000000008234470 -0.999999995973206 -0.000000002352706 2.000000000361971
x10 =
0.999999998984500 -1.000000000120657 0.000000000290143 2.000000000080674