The Gauss-Seidel method as an iterative technique often refers to an improved version of the Jacobi method, since the Gauss-Seidel method generally achieves a faster convergence. Describe the difference between the Gauss-Seidel and Jacobi methods.

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Computers & Technology

Lindsay Hill

3 March, 01:40

The Gauss-Seidel method as an iterative technique often refers to an improved version of the Jacobi method, since the Gauss-Seidel method generally achieves a faster convergence. Describe the difference between the Gauss-Seidel and Jacobi methods.

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Julia Fisher · Answer 1

The Gauss Siedel Method as an iterative technique often refers to an improved version of the Jacob method, however we can describe some differences.

Explanation:

In Jacobi method each iteration is done using a set of previous values, even if new values become available in the middle of an iteration. Gauss-Siedel, in the other hand, as soon as we have a new iterate for a particular component, we use it for all subsequent computation.

If you apply the computional form from Gauss-Seidel methods, in the end, we come to the conclusion that it becomes identical to Jacobi method, if we take the kth generation iterates, for the summation that handles values to the left of the main diagonal of our matrix.