Example

Solve the following system of equations using (a) the Jacobi methos, (b) the Gauss Seidel iteration method.

(a) Jacobi method: use initial guess X0=Y0=Z0=1,

stop when max?Xk-Xk-1,Yk-Yk-1,Zk-Zk-1? ? 0.1

First iteration:

X1= (11/4) - (1/2)Y0 - (1/4)Z0 = 2

Y1= (3/2) + (1/2)X0 = 2

Z1= 4 - (1/2) X0 - (1/4)Y0 = 13/4