On the Superlinear Convergence of MINRES
نویسندگان
چکیده
Quantitative bounds are presented for the superlinear convergence of the MINRES method of Paige and Saunders [SIAM J. Numer. Anal., 1975] for the solution of sparse linear systems Ax = b, with A symmetric and indefinite. It is shown that the superlinear convergence is observed as soon as the harmonic Ritz values approximate well the eigenvalues of A that are either closest to zero or farthest from zero. This generalizes a well-known corresponding result obtained by van der Sluis and van der Vorst with respect to the Conjugate Gradients method, for A symmetric and positive definite.
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