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Write down the iterative schemes for the Jacobi, Gauss-Seidel and SOR methods. Explain how SOR is obtained from the Gauss-Seidel method. Explore convergence property of the Jacobi and SOR method for the system A„I = b 2 -1 ... -1 2 -1 An b= (1.. 1]" n= 30 -1 2 -1 0 -1 ... Use z) = [000... 0f*, wiapt = I+ sin – Iterate until ||z – 24|< 0.0005 The exact solution r can be found as r= A\b Implement the SOR method (.m file should be submitted). Jacobi and Gauss-Seidel can be found on the webpage code Create a table k |Error Jacobi Error SOR Ratio Jacobi (c) Ratio SOR (c) E ESOR 1 10 K where Eohi - error estimate for Jacobi, EOR - error estimate for SOR, K number of iterations which SOR method needed to reach the prescribed accuracy.

Write down the iterative schemes for the Jacobi, Gauss-Seidel and SOR methods. Explain how SOR is obtained from the Gauss-Seidel method. Explore convergence property of the Jacobi and SOR method for the system A„I = b 2 -1 ... -1 2 -1 An b= (1.. 1]" n= 30 -1 2 -1 0 -1 ... Use z) = [000... 0f*, wiapt = I+ sin – Iterate until ||z – 24|< 0.0005 The exact solution r can be found as r= A\b Implement the SOR method (.m file should be submitted). Jacobi and Gauss-Seidel can be found on the webpage code Create a table k |Error Jacobi Error SOR Ratio Jacobi (c) Ratio SOR (c) E ESOR 1 10 K where Eohi - error estimate for Jacobi, EOR - error estimate for SOR, K number of iterations which SOR method needed to reach the prescribed accuracy.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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Write down the iterative schemes for the Jacobi, Gauss-Seidel and SOR methods. Explain how SOR is obtained from the Gauss-Seidel method. Explore convergence property of the Jacobi and SOR method for the system A,r = b 2 -1 0 ... -1 2 -1 An = b = [1... 1]" n = 30 -1 2 -1 0 -1 2 Use r0) = [000... o]", wopt 1+sin Iterate until ||r – 1®| < 0.00005 The exact solution z can be found as r = A\b Implement the SOR method (.m file should be submitted). Jacobi and Gauss-Seidel can be found on the webpage code Create a table k | Error Jacobi Error SOR Ratio Jacobi (c) Ratio SOR (c) E Jacobi SOR 1 2 10 K where Ebi - error estimate for Jacobi, EOR - error estimate for SOR, K number of iterations which SOR method needed to reach the prescribed accuracy.
Transcribed Image Text:Write down the iterative schemes for the Jacobi, Gauss-Seidel and SOR methods. Explain how SOR is obtained from the Gauss-Seidel method. Explore convergence property of the Jacobi and SOR method for the system A,r = b 2 -1 0 ... -1 2 -1 An = b = [1... 1]" n = 30 -1 2 -1 0 -1 2 Use r0) = [000... o]", wopt 1+sin Iterate until ||r – 1®| < 0.00005 The exact solution z can be found as r = A\b Implement the SOR method (.m file should be submitted). Jacobi and Gauss-Seidel can be found on the webpage code Create a table k | Error Jacobi Error SOR Ratio Jacobi (c) Ratio SOR (c) E Jacobi SOR 1 2 10 K where Ebi - error estimate for Jacobi, EOR - error estimate for SOR, K number of iterations which SOR method needed to reach the prescribed accuracy.
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