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ANZIAM J. 46(E) ppC409--C425, 2005.

A new adaptive restart for GMRES($m$) method

Linjie Zhang

Takashi Nodera

(Received 27 October 2004, revised 13 April 2005)

Abstract

GMRES($m$) is a Krylov subspace method for solving nonsymmetric linear systems of equations. The difficulty of this method lies in choosing the appropriate restart cycle $m$. We propose a new strategy for the adaptive restart for GMRES($m$) which is based on using the difference of the Ritz and harmonic Ritz values. We also report on numerical experiments which show that this new approach is both effective and robust.

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Authors

Linjie Zhang

School of Fundamental Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku, Yokohama, 223-8522, Japan. mailto:zhang@math.keio.ac.jp

Takashi Nodera

Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku, Yokohama, 223-8522, Japan. mailto:nodera@math.keio.ac.jp

Published May 24, 2005. ISSN 1446-8735

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