On HSS and AHSS iteration methods for nonsymmetric positive definite Toeplitz systems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article

Chen, Fang^1,2  Jiang, Yao-Lin² 

[1] Xian Univ Post & Telecommun, Dept Math Sci, Xian 710121, Peoples R China

[2] Xi An Jiao Tong Univ, Dept Math Sci, Xian 710049, Peoples R China

关键词: Toeplitz matrix;    Centrosymmetric matrix;    Skew-centrosymmetric matrix;    HSS iteration method;    AHSS iteration method;   

DOI  :  10.1016/j.cam.2010.03.005

来源: Elsevier

【 摘 要 】

Two iteration methods are proposed to solve real nonsymmetric positive definite Toeplitz systems of linear equations. These methods are based on Hermitian and skew-Hermitian splitting (HSS) and accelerated Hermitian and skew-Hermitian splitting (AHSS). By constructing an orthogonal matrix and using a similarity transformation, the real Toeplitz linear system is transformed into a generalized saddle point problem. Then the structured HSS and the structured AHSS iteration methods are established by applying the HSS and the AHSS iteration methods to the generalized saddle point problem. We discuss efficient implementations and demonstrate that the structured HSS and the structured AHSS iteration methods have better behavior than the HSS iteration method in terms of both computational complexity and convergence speed. Moreover, the structured AHSS iteration method outperforms the HSS and the structured HSS iteration methods. The structured AHSS iteration method also converges unconditionally to the unique solution of the Toeplitz linear system. In addition, an upper bound for the contraction factor of the structured AHSS iteration method is derived. Numerical experiments are used to illustrate the effectiveness of the structured AHSS iteration method. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free