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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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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