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

Kentaro Moriya; Takashi Nodera

doi:10.1007/978-3-540-24669-5_143

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

Kentaro Moriya, Takashi Nodera

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Roman Wyrzykowski, Jack Dongarra, Marcin Paprzycki, Jerzy Wasniewski
Publisher	Springer Verlag
Pages	1105-1113
Number of pages	9
ISBN (Print)	3540219463, 9783540219460
DOIs	https://doi.org/10.1007/978-3-540-24669-5_143
Publication status	Published - 2004 Jan 1
Event	5th International Conference on Parallel Processing and Applied Mathematics, PPAM 2003 - Czestochowa, Poland Duration: 2003 Sept 7 → 2003 Sept 10

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3019
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	5th International Conference on Parallel Processing and Applied Mathematics, PPAM 2003
Country/Territory	Poland
City	Czestochowa
Period	03/9/7 → 03/9/10

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-540-24669-5_143

Cite this

Moriya, K., & Nodera, T. (2004). New adaptive GMRES(m) method with choosing suitable restart cycle m. In R. Wyrzykowski, J. Dongarra, M. Paprzycki, & J. Wasniewski (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 1105-1113). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3019). Springer Verlag. https://doi.org/10.1007/978-3-540-24669-5_143

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). ed. / Roman Wyrzykowski; Jack Dongarra; Marcin Paprzycki; Jerzy Wasniewski. 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 proceeding › Conference contribution

Moriya, K & Nodera, T 2004, New adaptive GMRES(m) method with choosing suitable restart cycle m. in R Wyrzykowski, J Dongarra, M Paprzycki & J Wasniewski (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 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. https://doi.org/10.1007/978-3-540-24669-5_143

Moriya K, Nodera T. New adaptive GMRES(m) method with choosing suitable restart cycle m. In Wyrzykowski R, Dongarra J, Paprzycki M, Wasniewski J, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2004. p. 1105-1113. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-24669-5_143

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). editor / Roman Wyrzykowski ; Jack Dongarra ; Marcin Paprzycki ; Jerzy Wasniewski. Springer Verlag, 2004. pp. 1105-1113 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{3d64b9a7b7124a5ab7d4649add159098,

title = "New adaptive GMRES(m) method with choosing suitable restart cycle m",

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.",

author = "Kentaro Moriya and Takashi Nodera",

year = "2004",

month = jan,

day = "1",

doi = "10.1007/978-3-540-24669-5_143",

language = "English",

isbn = "3540219463",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "1105--1113",

editor = "Roman Wyrzykowski and Jack Dongarra and Marcin Paprzycki and Jerzy Wasniewski",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

note = "5th International Conference on Parallel Processing and Applied Mathematics, PPAM 2003 ; Conference date: 07-09-2003 Through 10-09-2003",

}

TY - GEN

T1 - New adaptive GMRES(m) method with choosing suitable restart cycle m

AU - Moriya, Kentaro

AU - Nodera, Takashi

PY - 2004/1/1

Y1 - 2004/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84952324430&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952324430&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-24669-5_143

DO - 10.1007/978-3-540-24669-5_143

M3 - Conference contribution

AN - SCOPUS:84952324430

SN - 3540219463

SN - 9783540219460

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 1105

EP - 1113

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Wyrzykowski, Roman

A2 - Dongarra, Jack

A2 - Paprzycki, Marcin

A2 - Wasniewski, Jerzy

PB - Springer Verlag

T2 - 5th International Conference on Parallel Processing and Applied Mathematics, PPAM 2003

Y2 - 7 September 2003 through 10 September 2003

ER -

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

Abstract

Publication series

Other

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this