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On the convergence behavior of the restarted GMRES algorithm for solving nonsymmetric linear systems
Author(s) -
Joubert Wayne
Publication year - 1994
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1680010502
Subject(s) - generalized minimal residual method , convergence (economics) , mathematics , linear system , algorithm , mathematical optimization , integer (computer science) , iterative method , computer science , mathematical analysis , economics , programming language , economic growth
The solution of nonsymmetric systems of linear equations continues to be a difficult problem. A main algorithm for solving nonsymmetric problems is restarted GMRES. The algorithm is based on restarting full GMRES every s iterations, for some integer s >0. This paper considers the impact of the restart frequency s on the convergence and work requirements of the method. It is shown that a good choice of this parameter can lead to reduced solution time, while an improper choice may hinder or preclude convergence. An adaptive procedure is also presented for determining automatically when to restart. The results of numerical experiments are presented.