Example 1.  Use successive over relaxation - SOR iteration to solve the linear system  .   
1 (b).  Use 20 iterations.  Compare the speed of convergence with Jacobi and Gauss-Seidel iteration.

Solution 1 (b).

The matrix A can be constructed with the command.

The column vector B can be constructed with the command.

Use 20 iterations of Jacobi iteration.

Use 20 iterations of Gauss-Seidel iteration.

Use 20 iterations of the SOR method with the parameter  .  

We can compare the approximations with the "true solution."

(c) John H. Mathews 2004