HW6 - Seidel iteration without and with overrelaxation...

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HOMEWORK ASSIGNMENT 6 EGM 3344 Problems from Chapra book chapters 10-12 Due: Monday, 11/1/2010 Problem Approach Comments 10.3 Hand Factor means convert the A matrix into L and U . Check that A = LU using Matlab. 10.5 Hand Use partial pivoting and Gauss elimination to find the L & U. Carry out all the necessary steps. 10.8 Hand 10.10 Matlab 11.1 Matlab Calculate 1 A - using the LU decomposition of A. Use the Matlab lu command to perform the LU decomposition. Use the Matlab backslash \ operator to perform intermediate linear system solutions. Use Matlab matrix multiplication to verify that 1 A - was correctly calculated. 11.3 Matlab Hint: Review section 11.1.2 on Stimulus-Response Computations. 11.6 Hand Make sure you scale each row first. 11.13 Matlab Use the Matlab inv command to calculate the matrix inverse. Check the help file on the cond command. 12.1 Matlab Write a simple Matlab program to perform each Gauss-

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Unformatted text preview: Seidel iteration without and with overrelaxation. Answer 10.3 10.5 1 4 x = , 2 8 x = , 3 2 x = -10.8 (a) (c) x = -2.7344 4.8828 -1.7187 10.10 x = 1.0000 5.0000 -3.0000 11.1 11.3 (a) AI = 0.07253886010363 0.01278065630397 0.01243523316062 0.02072538860104 0.06079447322971 0.03212435233161 0.02590673575130 0.00932642487047 0.09015544041451 (b) c = 320.2073 227.2021 321.5026 (c) 3 g 804.1667 d b ∆ = (d) 3 3 g 15.285 m c ∆ = 11.6 These norms are: 1.9920, 2.8000, 2 11.13 (a) Condition number = 3.8131e+016 (b) Condition number = 994.8787 12.1 (a) After 6 iterations, 1 167.8711 x = , 2 239.1211 x = , 3 250.8105 x = , maximum error = 3.5% (b) After 6 iterations, 1 171.423 x = , 2 244.389 x = , 3 253.622 x = , maximum error = 4.997%...
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