On convergence of splitting iteration methods for non-Hermitian positive-definite linear systems

Abstract

A new splitting iteration method is presented for the system of linear equations when the coefficient matrix is a non-Hermitian positive-definite matrix. The spectral radius, the optimal parameter, and some norm properties of the iteration matrix for the new method are discussed in detail. Based on these results, the new method is convergent under reasonable conditions for any non-Hermitian positive-definite linear system. Finally, the numerical examples show that the new method is more effective than the Hermitian and skew-Hermitian splitting iterative (or positive-definite and skew-Hermitian splitting iterative) method in central processing unit time.

2010 AMS Subject Classifications:

• 65F10
• 15A06

Keywords:

• non-Hermitian
• positive-definite matrix
• splitting
• iteration method
• convergence

Acknowledgements

We thank the anonymous referees for their comments on an earlier version of the manuscript. This work is supported by NSF of China (11071184) and NSF of Shanxi Province (2010011006, 2012011015-6).