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Volume 29, Issue 2
On Hermitian and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations

Zhongzhi Bai

DOI: 10.4208/jcm.1009-m3152

J. Comp. Math., 29 (2011), pp. 185-198.

Published online: 2011-04

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  • Abstract

We present a Hermitian and skew-Hermitian splitting (HSS) iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semi-definite matrices. The unconditional convergence of the HSS iteration method is proved and an upper bound on the convergence rate is derived. Moreover, to reduce the computing cost, we establish an inexact variant of the HSS iteration method and analyze its convergence property in detail. Numerical results show that the HSS iteration method and its inexact variant are efficient and robust solvers for this class of continuous Sylvester equations.

  • Keywords

Continuous Sylvester equation, HSS iteration method, Inexact iteration, Convergence.

  • AMS Subject Headings

15A24, 15A30, 15A69, 65F10, 65F30, 65F50, 65H10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-29-185, author = {Zhongzhi Bai}, title = {On Hermitian and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {2}, pages = {185--198}, abstract = {

We present a Hermitian and skew-Hermitian splitting (HSS) iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semi-definite matrices. The unconditional convergence of the HSS iteration method is proved and an upper bound on the convergence rate is derived. Moreover, to reduce the computing cost, we establish an inexact variant of the HSS iteration method and analyze its convergence property in detail. Numerical results show that the HSS iteration method and its inexact variant are efficient and robust solvers for this class of continuous Sylvester equations.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1009-m3152}, url = {http://global-sci.org/intro/article_detail/jcm/8472.html} }
TY - JOUR T1 - On Hermitian and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations AU - Zhongzhi Bai JO - Journal of Computational Mathematics VL - 2 SP - 185 EP - 198 PY - 2011 DA - 2011/04 SN - 29 DO - http://doi.org/10.4208/jcm.1009-m3152 UR - https://global-sci.org/intro/article_detail/jcm/8472.html KW - Continuous Sylvester equation, HSS iteration method, Inexact iteration, Convergence. AB -

We present a Hermitian and skew-Hermitian splitting (HSS) iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semi-definite matrices. The unconditional convergence of the HSS iteration method is proved and an upper bound on the convergence rate is derived. Moreover, to reduce the computing cost, we establish an inexact variant of the HSS iteration method and analyze its convergence property in detail. Numerical results show that the HSS iteration method and its inexact variant are efficient and robust solvers for this class of continuous Sylvester equations.

Zhongzhi Bai. (2011). On Hermitian and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations. Journal of Computational Mathematics. 29 (2). 185-198. doi:10.4208/jcm.1009-m3152
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