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Volume 32, Issue 3
The Generalized Local Hermitian and Skew-Hermitian Splitting Iteration Methods for the Non-Hermitian Generalized Saddle Point Problems

Hongtao Fan & Bing Zheng

DOI: 10.4208/jcm.1401-CR6

J. Comp. Math., 32 (2014), pp. 312-331.

Published online: 2014-06

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  • Abstract

For large and sparse saddle point problems, Zhu studied a class of generalized local Hermitian and skew-Hermitian splitting iteration methods for non-Hermitian saddle point problem [M.-Z. Zhu, Appl. Math. Comput. 218 (2012) 8816-8824 ]. In this paper, we further investigate the generalized local Hermitian and skew-Hermitian splitting (GLHSS) iteration methods for solving non-Hermitian generalized saddle point problems. With different choices of the parameter matrices, we derive conditions for guaranteeing the convergence of these iterative methods. Numerical experiments are presented to illustrate the effectiveness of our GLHSS iteration methods as well as the preconditioners.

  • Keywords

Generalized saddle point problems, Hermitian and skew-Hermitian matrix splitting, Iteration method, Convergence.

  • AMS Subject Headings

65F10, 65F50.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-32-312, author = {Hongtao Fan and Bing Zheng}, title = {The Generalized Local Hermitian and Skew-Hermitian Splitting Iteration Methods for the Non-Hermitian Generalized Saddle Point Problems}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {3}, pages = {312--331}, abstract = {

For large and sparse saddle point problems, Zhu studied a class of generalized local Hermitian and skew-Hermitian splitting iteration methods for non-Hermitian saddle point problem [M.-Z. Zhu, Appl. Math. Comput. 218 (2012) 8816-8824 ]. In this paper, we further investigate the generalized local Hermitian and skew-Hermitian splitting (GLHSS) iteration methods for solving non-Hermitian generalized saddle point problems. With different choices of the parameter matrices, we derive conditions for guaranteeing the convergence of these iterative methods. Numerical experiments are presented to illustrate the effectiveness of our GLHSS iteration methods as well as the preconditioners.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1401-CR6}, url = {http://global-sci.org/intro/article_detail/jcm/9889.html} }
TY - JOUR T1 - The Generalized Local Hermitian and Skew-Hermitian Splitting Iteration Methods for the Non-Hermitian Generalized Saddle Point Problems AU - Hongtao Fan & Bing Zheng JO - Journal of Computational Mathematics VL - 3 SP - 312 EP - 331 PY - 2014 DA - 2014/06 SN - 32 DO - http://doi.org/10.4208/jcm.1401-CR6 UR - https://global-sci.org/intro/article_detail/jcm/9889.html KW - Generalized saddle point problems, Hermitian and skew-Hermitian matrix splitting, Iteration method, Convergence. AB -

For large and sparse saddle point problems, Zhu studied a class of generalized local Hermitian and skew-Hermitian splitting iteration methods for non-Hermitian saddle point problem [M.-Z. Zhu, Appl. Math. Comput. 218 (2012) 8816-8824 ]. In this paper, we further investigate the generalized local Hermitian and skew-Hermitian splitting (GLHSS) iteration methods for solving non-Hermitian generalized saddle point problems. With different choices of the parameter matrices, we derive conditions for guaranteeing the convergence of these iterative methods. Numerical experiments are presented to illustrate the effectiveness of our GLHSS iteration methods as well as the preconditioners.

Hongtao Fan and Bing Zheng. (2014). The Generalized Local Hermitian and Skew-Hermitian Splitting Iteration Methods for the Non-Hermitian Generalized Saddle Point Problems. Journal of Computational Mathematics. 32 (3). 312-331. doi:10.4208/jcm.1401-CR6
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