Accelerated normal and skew-Hermitian splitting methods for positive definite linear systems

Document Type : Research Article

Authors

• F. Toutounian
• D. Hezari

Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

10.22067/ijnao.v3i1.18830

Abstract

For solving large sparse non-Hermitian positive definite linear equations, Bai et al. proposed the Hermitian and skew-Hermitian splitting methods (HSS). They recently generalized this technique to the normal and skew-Hermitian splitting methods (NSS). In this paper, we present an accelerated normal and skew-Hermitian splitting methods (ANSS) which involve two parameters for the NSS iteration. We theoretically study the convergence properties of the ANSS method. Moreover, the contraction factor of the ANSS iteration is derived. Numerical examples illustrating the effectiveness of ANSS iteration are presented.

Keywords

• Non-Hermitian matrix
• Normal matrix
• Hermitian matrix
• Skew- Hermitian matrix
• Splitting iteration method

20.1001.1.24236977.2013.3.1.4.5

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References

1. Bai, Z-Z. and Golub, G.H. and Ng, M.K., On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations, Numer. Linear. Algebra. Appl., 14 (2007) 319-335.
2. Bai, Z-Z., Golub, G.H. and Ng, M.K., Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems , SIAM J. Matrix. Anal. Appl., 24 (2003) 603-626.
3. Huhtanen, M., Aspects of nonnormality for iterative methods, Linear Algebra Appl., 394 (2005) 119-144.
4. Huhtanen, M.,A Hermitain Lanczos method for normal matrices., SIAM J. Matrix. Anal. Appl., 23 (2002) 1092-1108.
5. Li, L., Huang, T-Z. and Liu, X. P., Asymmetric Hermitian and skew-Hermitian spliting methods for positive definite linear systems, Comput. Math. Appl., 54 (2007) 147-159