#563 Use the Gauss-Seidel method to solve the

Use the Gauss Seidel method to solve the - Math

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Free Chegg Question

Use the Gauss Seidel method to solve the following system until the percent relative error falls below ε_s = 5%

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Free Chegg Answer

The first iteration can be implemented as

Second iteration:

The error estimates can be computed as

Note that because  is greater than the stopping criterion, the computation of  is unnecessary for this iteration. The remainder of the calculation proceeds until all the errors fall below the stopping criterion of 5%. The entire computation can be summarized as

Thus, after 5 iterations, the maximum error is 0.59% and we arrive at the result: x1 = 0.500253, x2 = 8.000112 and x3 = -6.00007