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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arnoldi, W.: The Principle of Minimized Iterations in the Solution of the Matrix Eigenvalue Problem. Quart. Appl. Math. 9, 17–29 (1951)
Saad, Y., Schultz, M.K.: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems. SIAM J. Sci. Stat. Comput. (7), 856–869 (1986)
Schönauer, W.: Scientific Computing on Vector Computers. North Holland, Amsterdam (1987)
Joubert, W.: Lanczos Methods for the Solution of Nonsymmetric Systems of Linear Equations. SIAM J. Matrix. Anal. Appl. 13(3), 928–943 (1992)
Tsuno, N., Nodera, T.: The Speedup of the GMRES(m) Method Using the Early Restarting Procedure. J. of IPSJ 40(4), 1760–1773 (1999) (in Japanese)
Moriya, K., Nodera, T.: The DEFLATED-GMRES (m, k) Method with Switching the Restart Frequency Dynamically. Numer. Linear. Algebra. Appl. 7, 569–584 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Moriya, K., Nodera, T. (2004). New Adaptive GMRES(m) Method with Choosing Suitable Restart Cycle m . In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2003. Lecture Notes in Computer Science, vol 3019. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24669-5_143
Download citation
DOI: https://doi.org/10.1007/978-3-540-24669-5_143
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21946-0
Online ISBN: 978-3-540-24669-5
eBook Packages: Springer Book Archive