Original Article: Simpler GMRES with deflated restarting

Authors:
Yiqin Lin;Liang Bao;Qinghua Wu
Affiliations:
Institute of Computational Mathematics, Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou 425100, PR China;Department of Mathematics, East China University of Science and Technology, Shanghai 200237, PR China;Institute of Computational Mathematics, Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou 425100, PR China
Venue:
Mathematics and Computers in Simulation
Year:
2012

Citing 10
Cited 0

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Abstract

In this paper we consider the simpler GMRES method augmented by approximate eigenvectors for solving nonsymmetric linear systems. We modify the augmented restarted simpler GMRES proposed by Boojhawon and Bhuruth to obtain a simpler GMRES with deflated restarting. Moreover, we also propose a residual-based simpler GMRES with deflated restarting, which is numerically more stable. The main advantage over the augmented version is that the simpler GMRES with deflated restarting requires less matrix-vector products per restart cycle. Some details of implementation are also considered. Numerical experiments show that the residual-based simpler GMRES with deflated restarting is effective.