Question

Is convergence guaranteed always with Jacobi and Gauss-Siedel methods,as applied to iterative solutions of linear algebraic equations?

(a) Yes

(b) No

Short answer

Therefore, the correct answer is (b) No.

Step-by-step solution

Determine the iterative methods.

There are two iterative methods, Gauss Siedel and Jacobi method.

The convergence rate is faster with Gauss Siedel for somematrix and faster withJacobi method for anothermatrix.

In some cases, both methods can diverge, or one method can diverge and other can converge.

Determine the answer.

From the description in step 1, the convergence may not be possible for allmatrices.

Therefore, the correct answer is (b) No.