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Journal of Applied Mathematics
Volume 2014, Article ID 578102, 9 pages
Research Article

A Generalized HSS Iteration Method for Continuous Sylvester Equations

1School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu, China
2Department of Mathematics, Federal University of Paraná, Centro Politécnico, CP 19.081, 81531-980 Curitiba, PR, Brazil

Received 20 August 2013; Accepted 13 December 2013; Published 12 January 2014

Academic Editor: Qing-Wen Wang

Copyright © 2014 Xu Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.