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Volume 37, Issue 2
Improved PMHSS Iteration Methods for Complex Symmetric Linear Systems

Kai Liu & Guiding Gu

DOI: 10.4208/jcm.1702-m2017-0007

J. Comp. Math., 37 (2019), pp. 278-296.

Published online: 2018-09

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  • Abstract

Based on the preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration method for the complex symmetric linear system, two improved iterative methods, namely, the modified PMHSS (MPMHSS) method and the double modified PMHSS (DMPMHSS) method, are proposed in this paper. The spectral radii of the iteration matrices of two methods are given. We show that by choosing an appropriate parameter, MPMHSS could speed up the convergence on PMHSS. The DMPMHSS method is a four-step alternating iteration that is developed upon the two-step alternating iteration of MPMHSS. We discuss the choice of the parameters and establish the convergence of DMPMHSS. In particular, we give an analysis of the spectral radius of PMHSS and DMPMHSS at the parameter free situation, and we show that DMPMHSS converges faster than PMHSS in most cases. Our numerical experiments show these points.

  • Keywords

Complex symmetric linear system, PMHSS.

  • AMS Subject Headings

65F10, 65N22.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

752964253@qq.com (Kai Liu)

guiding@mail.shufe.edu.cn (Guiding Gu)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-278, author = {Liu , Kai and Gu , Guiding}, title = {Improved PMHSS Iteration Methods for Complex Symmetric Linear Systems}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {2}, pages = {278--296}, abstract = {

Based on the preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration method for the complex symmetric linear system, two improved iterative methods, namely, the modified PMHSS (MPMHSS) method and the double modified PMHSS (DMPMHSS) method, are proposed in this paper. The spectral radii of the iteration matrices of two methods are given. We show that by choosing an appropriate parameter, MPMHSS could speed up the convergence on PMHSS. The DMPMHSS method is a four-step alternating iteration that is developed upon the two-step alternating iteration of MPMHSS. We discuss the choice of the parameters and establish the convergence of DMPMHSS. In particular, we give an analysis of the spectral radius of PMHSS and DMPMHSS at the parameter free situation, and we show that DMPMHSS converges faster than PMHSS in most cases. Our numerical experiments show these points.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1702-m2017-0007}, url = {http://global-sci.org/intro/article_detail/jcm/12680.html} }
TY - JOUR T1 - Improved PMHSS Iteration Methods for Complex Symmetric Linear Systems AU - Liu , Kai AU - Gu , Guiding JO - Journal of Computational Mathematics VL - 2 SP - 278 EP - 296 PY - 2018 DA - 2018/09 SN - 37 DO - http://doi.org/10.4208/jcm.1702-m2017-0007 UR - https://global-sci.org/intro/article_detail/jcm/12680.html KW - Complex symmetric linear system, PMHSS. AB -

Based on the preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration method for the complex symmetric linear system, two improved iterative methods, namely, the modified PMHSS (MPMHSS) method and the double modified PMHSS (DMPMHSS) method, are proposed in this paper. The spectral radii of the iteration matrices of two methods are given. We show that by choosing an appropriate parameter, MPMHSS could speed up the convergence on PMHSS. The DMPMHSS method is a four-step alternating iteration that is developed upon the two-step alternating iteration of MPMHSS. We discuss the choice of the parameters and establish the convergence of DMPMHSS. In particular, we give an analysis of the spectral radius of PMHSS and DMPMHSS at the parameter free situation, and we show that DMPMHSS converges faster than PMHSS in most cases. Our numerical experiments show these points.

Liu , Kai and Gu , Guiding. (2018). Improved PMHSS Iteration Methods for Complex Symmetric Linear Systems. Journal of Computational Mathematics. 37 (2). 278-296. doi:10.4208/jcm.1702-m2017-0007
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