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 -