A single-step iteration method for non-Hermitian positive definite linear systems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:346

Article

Wang, Xiang^1,2  Xiao, Xiao-Yong¹  Zheng, Qing-Qing³ 

[1] Nanchang Univ, Dept Math, Nanchang 330031, Jiangxi, Peoples R China

[2] Nanchang Univ, Numer Simulat & High Performance Comp Lab, Nanchang 330031, Jiangxi, Peoples R China

[3] Xiamen Univ, Sch Math Sci, Xiamen, Peoples R China

关键词: Non-Hermitian matrix;    Convergence theory;    Matrix splitting;    Preconditioner;    Numerical experiment;   

DOI  :  10.1016/j.cam.2018.07.021

来源: Elsevier

【 摘 要 】

An efficient single-step iteration method is presented for solving the large sparse non-Hermitian positive definite linear systems. We theoretically prove that this method con verges to the unique solution of the system of linear equations under suitable restrictions. Moreover, we derive an upper bound for the spectral radius of the new iteration matrix. Furthermore, we consider acceleration of the new iteration by Krylov subspace methods and some special properties of the new preconditioned matrix are proposed. Numerical experiments on a few model problems are presented to further examine the effectiveness of our new method. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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