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Use the Gauss-Seidel method with relaxation to solve the following system to a specified tolerance

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Gauss-Seidel Method with Relaxation

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Problem Description: Use the Gauss-Seidel method with relaxation to solve the following system to a specified tolerance (approximate absolute percent relative error). If necessary, rearrange the equations to achieve convergence.

10x12x2327

=

X1+2+5x3 = -21.5

3x16x2+2x=-61.5

The relaxation parameter() should be an input parameter of your function.

Function >

1 function x=GaussSeidel_Relax_Example(lambda, es)

2 % Gauss-Seidel for a 3-by-3 linear system of equations

3 %

4 %--Input

5% lambda: relaxation parameter

6 % es: error tolerance (approximate absolute percent relative error in solution)

7 %

8 %--Output

9 % X: Gauss-Seidel linear solution (3-by-1 vector)

10

11 % Note: 1. Use the Euclidian norm (i.e. 2-norm) to compute relative error.

12 %

13

2. You may need to rearrange the linear equations to achieve diagonal dominance.

14 % Write your code here.

15 A [10 2 -1; 1 1 5; -3 -6 2];

16 b = [27; 21.5; -61.5];

17 N = 3;

 

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