Numerical Methods

Gauss-seidel Iteration Method

Second iteration

Third iteration

Fourth iteration

 

We find

Since, all the errors in magnitude are less than 0.0005, the required solution is

x1 = 1.0, x2 = 1.99999, x3 = 3.0.
Rounding to three decimal places, we get x1 = 1.0, x2 = 2.0, x3 = 3.0.