Determine the jacobi and gauss-seidel iteration

Question

Jacobi and Gauss-Seidel iteration

Response to the following problems:

(a)    Start with P_o = 0 and use Jacobi iteration to find P_k for k = I, 2, 3. Will Jacobi iteration converge to the solution?

(b)    Start with P_o = 0 and use Gauss-Seidel iteration to find P_k for k = 1, 2, 3. Will Gauss-Seidel iteration converge to the solution?

1.    4x— y= 15            2.    8x — 3y = 10
        x + 5y = 9                  — x + 4y = 6

3.     - x + 3y = 1         4.      2x + 3y = 1
        6x — 2y = 2                 7x — 2y = 1

5.    5x— y+ z= 10        6.     2x + 8y — z= 11
       2x + 8y — z= 11            5x— y+ z= 10
      — x + y + 4z = 3           — x + y + 4z = 3

7.    x — 5y — z = —8     8.    4x+ y— z= 13
      4x+ y— z= 13                 x— 5y — z = —8
      2x— y — 6z = —2            2x— y — 6z = —2

(Please solve for only #5 part (a) and (b).)

(The problem is from Iterative Methods for Linear Systems.)