Open Access
2014 A Generalized HSS Iteration Method for Continuous Sylvester Equations
Xu Li, Yu-Jiang Wu, Ai-Li Yang, Jin-Yun Yuan
J. Appl. Math. 2014: 1-9 (2014). DOI: 10.1155/2014/578102


Based on the Hermitian and skew-Hermitian splitting (HSS) iteration technique, we establish a generalized HSS (GHSS) iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semidefinite matrices. The GHSS method is essentially a four-parameter iteration which not only covers the standard HSS iteration but also enables us to optimize the iterative process. An exact parameter region of convergence for the method is strictly proved and a minimum value for the upper bound of the iterative spectrum is derived. Moreover, to reduce the computational cost, we establish an inexact variant of the GHSS (IGHSS) iteration method whose convergence property is discussed. Numerical experiments illustrate the efficiency and robustness of the GHSS iteration method and its inexact variant.


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Xu Li. Yu-Jiang Wu. Ai-Li Yang. Jin-Yun Yuan. "A Generalized HSS Iteration Method for Continuous Sylvester Equations." J. Appl. Math. 2014 1 - 9, 2014.


Published: 2014
First available in Project Euclid: 26 March 2014

zbMATH: 07010683
MathSciNet: MR3166774
Digital Object Identifier: 10.1155/2014/578102

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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