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Volume 40, Issue 5
Heavy Ball Flexible GMRES Method for Nonsymmetric Linear Systems

Mei Yang & Ren-Cang Li

J. Comp. Math., 40 (2022), pp. 715-731.

Published online: 2022-05

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  • Abstract

Flexible GMRES (FGMRES) is a variant of preconditioned GMRES, which changes preconditioners at every Arnoldi step. GMRES often has to be restarted in order to save storage and reduce orthogonalization cost in the Arnoldi process. Like restarted GMRES, FGMRES may also have to be restarted for the same reason. A major disadvantage of restarting is the loss of convergence speed. In this paper, we present a heavy ball flexible GMRES method, aiming to recoup some of the loss in convergence speed in the restarted flexible GMRES while keep the benefit of limiting memory usage and controlling orthogonalization cost. Numerical tests often demonstrate superior performance of the proposed heavy ball FGMRES to the restarted FGMRES.

  • Keywords

GMRES, Flexible GMRES, Heavy ball GMRES, Preconditioner, Linear system.

  • AMS Subject Headings

65F10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ymsjtu@sjtu.edu.cn (Mei Yang)

rcli@uta.edu (Ren-Cang Li)

  • BibTex
  • RIS
  • TXT
@Article{JCM-40-715, author = {Mei and Yang and ymsjtu@sjtu.edu.cn and 23354 and School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China and Mei Yang and Ren-Cang and Li and rcli@uta.edu and 13355 and Department of Mathematics, University of Texas at Arlington, P.O. Box 19408, Arlington, TX 76019, USA and Ren-Cang Li}, title = {Heavy Ball Flexible GMRES Method for Nonsymmetric Linear Systems}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {40}, number = {5}, pages = {715--731}, abstract = {

Flexible GMRES (FGMRES) is a variant of preconditioned GMRES, which changes preconditioners at every Arnoldi step. GMRES often has to be restarted in order to save storage and reduce orthogonalization cost in the Arnoldi process. Like restarted GMRES, FGMRES may also have to be restarted for the same reason. A major disadvantage of restarting is the loss of convergence speed. In this paper, we present a heavy ball flexible GMRES method, aiming to recoup some of the loss in convergence speed in the restarted flexible GMRES while keep the benefit of limiting memory usage and controlling orthogonalization cost. Numerical tests often demonstrate superior performance of the proposed heavy ball FGMRES to the restarted FGMRES.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2101-m2019-0243}, url = {http://global-sci.org/intro/article_detail/jcm/20544.html} }
TY - JOUR T1 - Heavy Ball Flexible GMRES Method for Nonsymmetric Linear Systems AU - Yang , Mei AU - Li , Ren-Cang JO - Journal of Computational Mathematics VL - 5 SP - 715 EP - 731 PY - 2022 DA - 2022/05 SN - 40 DO - http://doi.org/10.4208/jcm.2101-m2019-0243 UR - https://global-sci.org/intro/article_detail/jcm/20544.html KW - GMRES, Flexible GMRES, Heavy ball GMRES, Preconditioner, Linear system. AB -

Flexible GMRES (FGMRES) is a variant of preconditioned GMRES, which changes preconditioners at every Arnoldi step. GMRES often has to be restarted in order to save storage and reduce orthogonalization cost in the Arnoldi process. Like restarted GMRES, FGMRES may also have to be restarted for the same reason. A major disadvantage of restarting is the loss of convergence speed. In this paper, we present a heavy ball flexible GMRES method, aiming to recoup some of the loss in convergence speed in the restarted flexible GMRES while keep the benefit of limiting memory usage and controlling orthogonalization cost. Numerical tests often demonstrate superior performance of the proposed heavy ball FGMRES to the restarted FGMRES.

Mei Yang & Ren-Cang Li. (2022). Heavy Ball Flexible GMRES Method for Nonsymmetric Linear Systems. Journal of Computational Mathematics. 40 (5). 715-731. doi:10.4208/jcm.2101-m2019-0243
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