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Volume 6, Issue 2
On Preconditioned MHSS Real-Valued Iteration Methods for a Class of Complex Symmetric Indefinite Linear Systems

Zhi-Ru Ren, Yang Cao & Li-Li Zhang

DOI: 10.4208/eajam.141015.260216a

East Asian J. Appl. Math., 6 (2016), pp. 192-210.

Published online: 2018-02

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  • Abstract

A generalized preconditioned modified Hermitian and skew-Hermitian splitting (GPMHSS) real-valued iteration method is proposed for a class of complex symmetric indefinite linear systems. Convergence theory is established and the spectral properties of an associated preconditioned matrix are analyzed. We also give several variants of the GPMHSS preconditioner and consider the spectral properties of the preconditioned matrices. Numerical examples illustrate the effectiveness of our proposed method.

  • Keywords

Complex linear systems, PMHSS iteration, real-valued form, convergence, preconditioning.

  • AMS Subject Headings

65F10, 65F50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-6-192, author = {Zhi-Ru Ren, Yang Cao and Li-Li Zhang}, title = {On Preconditioned MHSS Real-Valued Iteration Methods for a Class of Complex Symmetric Indefinite Linear Systems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {2}, pages = {192--210}, abstract = {

A generalized preconditioned modified Hermitian and skew-Hermitian splitting (GPMHSS) real-valued iteration method is proposed for a class of complex symmetric indefinite linear systems. Convergence theory is established and the spectral properties of an associated preconditioned matrix are analyzed. We also give several variants of the GPMHSS preconditioner and consider the spectral properties of the preconditioned matrices. Numerical examples illustrate the effectiveness of our proposed method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.141015.260216a}, url = {http://global-sci.org/intro/article_detail/eajam/10789.html} }
TY - JOUR T1 - On Preconditioned MHSS Real-Valued Iteration Methods for a Class of Complex Symmetric Indefinite Linear Systems AU - Zhi-Ru Ren, Yang Cao & Li-Li Zhang JO - East Asian Journal on Applied Mathematics VL - 2 SP - 192 EP - 210 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.141015.260216a UR - https://global-sci.org/intro/article_detail/eajam/10789.html KW - Complex linear systems, PMHSS iteration, real-valued form, convergence, preconditioning. AB -

A generalized preconditioned modified Hermitian and skew-Hermitian splitting (GPMHSS) real-valued iteration method is proposed for a class of complex symmetric indefinite linear systems. Convergence theory is established and the spectral properties of an associated preconditioned matrix are analyzed. We also give several variants of the GPMHSS preconditioner and consider the spectral properties of the preconditioned matrices. Numerical examples illustrate the effectiveness of our proposed method.

Zhi-Ru Ren, Yang Cao and Li-Li Zhang. (2018). On Preconditioned MHSS Real-Valued Iteration Methods for a Class of Complex Symmetric Indefinite Linear Systems. East Asian Journal on Applied Mathematics. 6 (2). 192-210. doi:10.4208/eajam.141015.260216a
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