Convergence Behavior of Deflated GMRES(m) Algorithms on AP3000
by
Takashi Nodera
Department of Mathematics, Keio University
Coauthors: Kentaro Moriya (Keio University)

GMRES(m) method, the restarted version of the GMRES (generalized minimal residual) method, is one of the major iterative methods for numerically solving large and sparse non- symmetric problems of the form Ax=b. However, the information of some eigenvectors that compose the approximation disappears and then the good approximate solution cannot be obtained, because of this restart. Recently, in order to improve such a weak point, some algorithms which named MORGAN, DEFLATION and DEFLATED-GMRES algorithm, have been proposed. Those algorithms add the information of eigenvectors that can be obtained in the previous restart frequency. In this paper, we study those algorithms and also compare their performances. We will also propose the new restarting procedure that accelerates the convergence of their algorithms. From the numerical experiments on the distributed memory machine Fujitsu AP3000, we show that DEFLATED-GMRES(m, k) method performs the best reduction of residual norms in these algorithms.

Date received: August 19, 1999