Generalized successive overrelaxation iterative method for a class of complex symmetric linear system of equations

Abstract

In this paper, to solve a broad class of complex symmetric linear systems, we recast the complex system in a real formulation and apply the generalized successive overrelaxation (GSOR) iterative method to the equivalent real system. We then investigate its convergence properties and determine its optimal iteration parameter as well as its corresponding optimal convergence factor. In addition, the resulting GSOR preconditioner is used to precondition Krylov subspace methods such as the generalized minimal residual method for solving the real equivalent formulation of the system. Finally, we give some numerical experiments to validate the theoretical results and compare the performance of the GSOR method with the modified Hermitian and skew-Hermitian splitting iteration.

Keywords:

• complex linear systems
• symmetric positive definite
• SOR
• HSS
• MHSS

2000 AMS Subject Classifications::

• 65F10
• 65F50

Acknowledgements

The authors are grateful to the anonymous referees and the editor of the journal for their valuable comments and suggestions.