A class of iteration methods based on the HSS for Toeplitz systems of weakly nonlinear equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:290

Article

Zhu, Mu-Zheng^1,2  Zhang, Guo-Feng¹ 

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

[2] Hexi Univ, Sch Math & Stat, Zhangye 734000, Peoples R China

关键词: Toeplitz;    Weakly nonlinear systems;    HSS iteration method;    Inner/outer iteration;    Centrosymmetric and skew-centrosymmetric;    Local convergence;   

DOI  :  10.1016/j.cam.2015.05.027

来源: Elsevier

【 摘 要 】

For Toeplitz systems of weakly nonlinear equations, combining the separability and strong dominance between the linear and the nonlinear terms with the Hermitian and skew-Hermitian splitting (HSS) iteration technique, we establish two nonlinear composite iteration schemes, called Picard-cSSS and nonlinear cSSS-like iteration methods, which are based on a special case of the HSS, where the symmetric partH = 1/2 (A + A(T)) is a centrosymmetric matrix and the skew-symmetric part H = 1/2 (A - A(T)) is a skew-centrosymmetric matrix, The advantages of these methods are that they can transfer the linear sub-systems involved in inner iteration to two linear systems of half an order, besides, fast methods are available for computing the two half-steps involved in the inner iteration. Numerical results are provided, to further show that both Picard-cSSS and nonlinear cSSS-like iteration methods are feasible and effective. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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