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.
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© 2004 Springer-Verlag Berlin Heidelberg
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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
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DOI: https://doi.org/10.1007/978-3-540-24669-5_143
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21946-0
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