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Volume 35, Issue 5
On PMHSS Iteration Methods for Continuous Sylvester Equations

Yongxin Dong & Chuanqing Gu

DOI: 10.4208/jcm.1607-m2016-0613

J. Comp. Math., 35 (2017), pp. 600-619.

Published online: 2017-10

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  • Abstract

The modified Hermitian and skew-Hermitian splitting (MHSS) iteration method and preconditioned MHSS (PMHSS) iteration method were introduced respectively. In the paper, on the basis of the MHSS iteration method, we present a PMHSS iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and complex symmetric positive definite ⁄ semi-definite matrices. Under suitable conditions, we prove the convergence of the PMHSS iteration method and discuss the spectral properties of the preconditioned matrix. Moreover, to reduce the computing cost, we establish an inexact variant of the PMHSS iteration method and analyze its convergence property in detail. Numerical results show that the PMHSS iteration method and its inexact variant are efficient and robust solvers for this class of continuous Sylvester equations.

  • Keywords

Continuous Sylvester equation, PMHSS iteration, Inexact PMHSS iteration, Preconditioning, Convergence.

  • AMS Subject Headings

65F10, 65F50.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-35-600, author = {Dong , Yongxin and Gu , Chuanqing}, title = {On PMHSS Iteration Methods for Continuous Sylvester Equations}, journal = {Journal of Computational Mathematics}, year = {2017}, volume = {35}, number = {5}, pages = {600--619}, abstract = {

The modified Hermitian and skew-Hermitian splitting (MHSS) iteration method and preconditioned MHSS (PMHSS) iteration method were introduced respectively. In the paper, on the basis of the MHSS iteration method, we present a PMHSS iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and complex symmetric positive definite ⁄ semi-definite matrices. Under suitable conditions, we prove the convergence of the PMHSS iteration method and discuss the spectral properties of the preconditioned matrix. Moreover, to reduce the computing cost, we establish an inexact variant of the PMHSS iteration method and analyze its convergence property in detail. Numerical results show that the PMHSS 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.1607-m2016-0613}, url = {http://global-sci.org/intro/article_detail/jcm/10034.html} }
TY - JOUR T1 - On PMHSS Iteration Methods for Continuous Sylvester Equations AU - Dong , Yongxin AU - Gu , Chuanqing JO - Journal of Computational Mathematics VL - 5 SP - 600 EP - 619 PY - 2017 DA - 2017/10 SN - 35 DO - http://doi.org/10.4208/jcm.1607-m2016-0613 UR - https://global-sci.org/intro/article_detail/jcm/10034.html KW - Continuous Sylvester equation, PMHSS iteration, Inexact PMHSS iteration, Preconditioning, Convergence. AB -

The modified Hermitian and skew-Hermitian splitting (MHSS) iteration method and preconditioned MHSS (PMHSS) iteration method were introduced respectively. In the paper, on the basis of the MHSS iteration method, we present a PMHSS iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and complex symmetric positive definite ⁄ semi-definite matrices. Under suitable conditions, we prove the convergence of the PMHSS iteration method and discuss the spectral properties of the preconditioned matrix. Moreover, to reduce the computing cost, we establish an inexact variant of the PMHSS iteration method and analyze its convergence property in detail. Numerical results show that the PMHSS iteration method and its inexact variant are efficient and robust solvers for this class of continuous Sylvester equations.

Dong , Yongxin and Gu , Chuanqing. (2017). On PMHSS Iteration Methods for Continuous Sylvester Equations. Journal of Computational Mathematics. 35 (5). 600-619. doi:10.4208/jcm.1607-m2016-0613
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