Two-parameter generalized Hermitian and skew-Hermitian splitting iteration method

Abstract

It is known that the Hermitian and skew-Hermitian splitting (HSS) iteration method is an efficient solver for non-Hermitian positive-definite linear system of equations. Benzi [A generalization of the Hermitian and skew-Hermitian splitting iteration, SIAM J. Matrix Anal. Appl. 31 (2009), pp. 360–374] proposed a generalized HSS (GHSS) iteration method. In this paper, we present a two-parameter version of the GHSS (TGHSS) method and investigate its convergence properties. To show the effectiveness of the proposed method the TGHSS iteration method is applied to image restoration and convection–diffusion problems and the results are compared with those of the HSS and GHSS methods.

Keywords:

• two-parameter
• HSS
• GHSS
• image restoration
• convection–diffusion problem

2010 AMS Subject Classifications:

• 65F10
• 65D18

Acknowledgments

The authors are grateful to seven anonymous referees and editor of the journal for their valuable comments and suggestions which greatly improved the original version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.