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Volume 7, Issue 1
Preconditioned Positive-Definite and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations AX + XB = C

Rong Zhou, Xiang Wang & Xiao-Bin Tang

DOI: 10.4208/eajam.190716.051116a

East Asian J. Appl. Math., 7 (2017), pp. 55-69.

Published online: 2018-02

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  • Abstract

In this paper, we present a preconditioned positive-definite and skew-Hermitian splitting (PPSS) iteration method for continuous Sylvester equations $AX+XB=C$ with positive definite/semi-definite matrices. The analysis shows that the PPSS iteration method will converge under certain assumptions. An inexact variant of the PPSS iteration method (IPPSS) has been presented and the analysis of its convergence property in detail has been discussed. Numerical results show that this new method is more efficient and robust than the existing ones.

  • Keywords

PPSS iteration method, IPPSS iteration method, Sylvester equations, convergence.

  • AMS Subject Headings

65F10, 65F50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-55, author = {Rong Zhou, Xiang Wang and Xiao-Bin Tang}, title = {Preconditioned Positive-Definite and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations AX + XB = C}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {1}, pages = {55--69}, abstract = {

In this paper, we present a preconditioned positive-definite and skew-Hermitian splitting (PPSS) iteration method for continuous Sylvester equations $AX+XB=C$ with positive definite/semi-definite matrices. The analysis shows that the PPSS iteration method will converge under certain assumptions. An inexact variant of the PPSS iteration method (IPPSS) has been presented and the analysis of its convergence property in detail has been discussed. Numerical results show that this new method is more efficient and robust than the existing ones.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.190716.051116a}, url = {http://global-sci.org/intro/article_detail/eajam/10734.html} }
TY - JOUR T1 - Preconditioned Positive-Definite and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations AX + XB = C AU - Rong Zhou, Xiang Wang & Xiao-Bin Tang JO - East Asian Journal on Applied Mathematics VL - 1 SP - 55 EP - 69 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.190716.051116a UR - https://global-sci.org/intro/article_detail/eajam/10734.html KW - PPSS iteration method, IPPSS iteration method, Sylvester equations, convergence. AB -

In this paper, we present a preconditioned positive-definite and skew-Hermitian splitting (PPSS) iteration method for continuous Sylvester equations $AX+XB=C$ with positive definite/semi-definite matrices. The analysis shows that the PPSS iteration method will converge under certain assumptions. An inexact variant of the PPSS iteration method (IPPSS) has been presented and the analysis of its convergence property in detail has been discussed. Numerical results show that this new method is more efficient and robust than the existing ones.

Rong Zhou, Xiang Wang and Xiao-Bin Tang. (2018). Preconditioned Positive-Definite and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations AX + XB = C. East Asian Journal on Applied Mathematics. 7 (1). 55-69. doi:10.4208/eajam.190716.051116a
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