SKEDSOFT

We have the following results.

First iteration

Second iteration

Third iteration

Fourth iteration

Fifth iteration

It is interesting to note that the iterations oscillate and converge to the exact solution

x₁ = 1.0, x₂ = – 1, x₃ = – 1.0.

Note :

What is the disadvantage of the Gauss-Jacobi method?

At any iteration step, the value of the first variable x₁ is obtained using the values of the previous iteration. The value of the second variable x₂ is also obtained using the values of the previous iteration, even though the updated value of x₁ is available. In general, at every stage in the iteration, values of the previous iteration are used even though the updated values of the previous variables are available. If we use the updated values of x₁, x₂,..., x_i-1 in computing the value of the variable x_i, then we obtain a new method called Gauss-Seidel iteration method.