New adaptive GMRES(m) method with choosing suitable restart cycle m

Kentaro Moriya, Takashi Nodera

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

GMRES method is one of the major iterative algorithms for solving large and sparse linear systems of equations. However, it is difficult to implement GMRES algorithm because its storatege and computation cost are so exceeded. Therefore, GMRES(m) algorithm is often used. In this paper, we propose a new variant of GMRES(m) algorithm. Our algorithm chooses the restart cycle m based both on the convergence test of residual norm and on the distribution of zeros of residual polynomial of GMRES(m) algorithm. From the numerical examples on Compaq Beowulf, we also show the effectiveness of our proposed algorithm.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages1105-1113
Number of pages9
Volume3019
ISBN (Print)3540219463, 9783540219460
Publication statusPublished - 2004
Event5th International Conference on Parallel Processing and Applied Mathematics, PPAM 2003 - Czestochowa, Poland
Duration: 2003 Sep 72003 Sep 10

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3019
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other5th International Conference on Parallel Processing and Applied Mathematics, PPAM 2003
CountryPoland
CityCzestochowa
Period03/9/703/9/10

Fingerprint

GMRES
Restart
Cycle
GMRES Method
Distribution of Zeros
Sparse Linear Systems
Linear system of equations
Iterative Algorithm
Choose
Linear systems
Norm
Numerical Examples
Polynomials
Polynomial
Costs

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Moriya, K., & Nodera, T. (2004). New adaptive GMRES(m) method with choosing suitable restart cycle m. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3019, pp. 1105-1113). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3019). Springer Verlag.

New adaptive GMRES(m) method with choosing suitable restart cycle m. / Moriya, Kentaro; Nodera, Takashi.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3019 Springer Verlag, 2004. p. 1105-1113 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3019).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Moriya, K & Nodera, T 2004, New adaptive GMRES(m) method with choosing suitable restart cycle m. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 3019, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3019, Springer Verlag, pp. 1105-1113, 5th International Conference on Parallel Processing and Applied Mathematics, PPAM 2003, Czestochowa, Poland, 03/9/7.
Moriya K, Nodera T. New adaptive GMRES(m) method with choosing suitable restart cycle m. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3019. Springer Verlag. 2004. p. 1105-1113. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Moriya, Kentaro ; Nodera, Takashi. / New adaptive GMRES(m) method with choosing suitable restart cycle m. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 3019 Springer Verlag, 2004. pp. 1105-1113 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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