A Variable Preconditioned GMRES Using the SOR Method for Linear Systems with Zero Diagonal Entries

The Generalized Minimal RESidual (GMRES) method with variable preconditioning is an efficient method for solving a large sparse linear system Ax = b. It has been clarified by some numerical experiments that the Successive Over-Relaxation (SOR) method is more effective than Krylov subspace methods su...

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Published inTransactions of the Japan Society for Computational Engineering and Science Vol. 2008; p. 20080010
Main Authors Nagahara, Rika, Abe, Kuniyoshi, Ishiwata, Emiko, Fujino, Seiji
Format Journal Article
LanguageJapanese
Published JAPAN SOCIETY FOR COMPUTATIONAL ENGINEERING AND SCIENCE 17.04.2008
Subjects
diagonal entries of zero
GMRES method
Krylov subspace method
linear system
variable preconditioning
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Abstract The Generalized Minimal RESidual (GMRES) method with variable preconditioning is an efficient method for solving a large sparse linear system Ax = b. It has been clarified by some numerical experiments that the Successive Over-Relaxation (SOR) method is more effective than Krylov subspace methods such as GMRES and ILU(0) preconditioned GMRES for performing variable preconditioning. However, SOR cannot be applied for performing variable preconditioning, when solving the linear system with zero diagonal entries. Therefore, we propose to make good use of a strategy proposed by Duff and Koster, namely, an algorithm for permuting large nonzero entries onto the diagonal in order to enable SOR to be used for performing variable preconditioning. By numerical experiments, we show the efficiency of the variable preconditioned GMRES using SOR when applying the algorithm for permuting large nonzero entries onto the diagonal.
AbstractList The Generalized Minimal RESidual (GMRES) method with variable preconditioning is an efficient method for solving a large sparse linear system Ax = b. It has been clarified by some numerical experiments that the Successive Over-Relaxation (SOR) method is more effective than Krylov subspace methods such as GMRES and ILU(0) preconditioned GMRES for performing variable preconditioning. However, SOR cannot be applied for performing variable preconditioning, when solving the linear system with zero diagonal entries. Therefore, we propose to make good use of a strategy proposed by Duff and Koster, namely, an algorithm for permuting large nonzero entries onto the diagonal in order to enable SOR to be used for performing variable preconditioning. By numerical experiments, we show the efficiency of the variable preconditioned GMRES using SOR when applying the algorithm for permuting large nonzero entries onto the diagonal.
Author Abe, Kuniyoshi
Ishiwata, Emiko
Nagahara, Rika
Fujino, Seiji
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  fullname: Abe, Kuniyoshi
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  fullname: Ishiwata, Emiko
  organization: Department of Mathematical Infomation Science, Tokyo University of Science
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  fullname: Fujino, Seiji
  organization: Research Institute for Information Technology, Kyushu University
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Snippet The Generalized Minimal RESidual (GMRES) method with variable preconditioning is an efficient method for solving a large sparse linear system Ax = b. It has...
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StartPage 20080010
SubjectTerms diagonal entries of zero
GMRES method
Krylov subspace method
linear system
variable preconditioning
Title A Variable Preconditioned GMRES Using the SOR Method for Linear Systems with Zero Diagonal Entries
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