# Gauss-jacobi Iteration Method

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

x_{1} = 1.0, x_{2} = – 1, x_{3} = – 1.0.

**Note :
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What is the disadvantage of the Gauss-Jacobi method?

At any iteration step, the value of the first variable x_{1} is obtained using the values of the previous iteration. The value of the second variable x_{2} is also obtained using the values of the previous iteration, even though the updated value of x_{1} 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 x_{1}, x_{2},..., x_{i-1} in computing the value of the variable x_{i}, then we obtain a new method called Gauss-Seidel iteration method.