Prove that Gauss-Jacobi method converges for solving a linear system with coefficient matrix A but it does not converge for the coefficient matrix B, where A = [{1, 1/2, 0}, {1/2, 1, 1/2}, {0, 1/2, 1}] and B = [{1, 1/2, 1/2}, {1/2, 1, 1/2}, {1/2, 1/2, 1}]. Hint: To prove the convergence consider using the Gerschgorin Theorem with a similar transformation through a suitable diagonal matrix.

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Prove that Gauss-Jacobi method converges for solving a linear system with coefficient matrix

A

but it does not converge for the coefficient matrix

B

, where

A = ? ? 1 1/2 0 1/2 1 1/2 0 1/2 1 ? ? B = ? ? 1 1/2 1/2 1/2 1 1/2 1/2 1/2 1 ? ?

Hint: To prove the convergence consider using the Gerschgorin Theorem with a similar transformation through a suitable diagonal matrix.

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