On CSCS-based iteration methods for Toeplitz system of weakly nonlinear equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Zhu, Mu-Zheng^1,2  Zhang, Guo-Feng¹ 

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

[2] Hexi Univ, Dept Math, Zhangye 734000, Peoples R China

关键词: Weakly nonlinear equations;    Nonlinear iteration scheme;    CSCS iteration method;    Inner/outer iteration scheme;    Toeplitz system;   

DOI  :  10.1016/j.cam.2011.04.038

来源: Elsevier

【 摘 要 】

For Toeplitz system of weakly nonlinear equations, by using the separability and strong dominance between the linear and the nonlinear terms and using the circulant and skew-circulant splitting (CSCS) iteration technique, we establish two nonlinear composite iteration schemes, called Picard-CSCS and nonlinear CSCS-like iteration methods, respectively. The advantage of these methods is that they do not require accurate computation and storage of Jacobian matrix, and only need to solve linear sub-systems of constant coefficient matrices. Therefore, computational workloads and computer storage may be saved in actual implementations. Theoretical analysis shows that these new iteration methods are local convergent under suitable conditions. Numerical results show that both Picard-CSCS and nonlinear CSCS-like iteration methods are feasible and effective for some cases. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free