A Global Property of Restarted FOM Algorithm
Year: 2006
Journal of Information and Computing Science, Vol. 1 (2006), Iss. 1 : pp. 11–20
Abstract
In this paper an interesting property of the restarted FOM algorithm for solving large nonsymmetric linear systems is presented and studied. By establishing a relationship between the convergence of its residual vectors and the convergence of Ritz values in the Arnoldi procedure, it is shown that some important information of previous FOM(m) cycles may be saved by the iteration approximates at the time of restarting, with which the FOM(m) cycles can complement one another harmoniously in reducing the iteration residual. Based on the study of FOM(m), two polynomial preconditioning techniques are proposed; one is for solving nonsymmetric linear systems and another is for forming an effective starting vector in the restarted Arnoldi method for solving nonsymmetric eigenvalue problems.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2024-JICS-22855
Journal of Information and Computing Science, Vol. 1 (2006), Iss. 1 : pp. 11–20
Published online: 2006-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10