Question: (a) Explain what happens to the GMRES algorithm if the right-hand side b of the linear system Ax = b is an eigenvector of A.

(a) Explain what happens to the GMRES algorithm if the right-hand side b of the linear system Ax = b is an eigenvector of A.

(b) More generally, prove that if the Krylov subspaces generated by b stabilize at order m, then the solution to the linear system lies in V^(m)and so the GMRES algorithm converges to the solution at order m.

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a If the righthand side b of the linear system Ax b is an eigenvector of A then the GMRES algorithm will converge to the exact solution x b where is t... View full answer

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