A Class of Preconditioned TGHSS-Based Iteration Methods for Weakly Nonlinear Systems. Issue 4 (19th October 2016)

• Record Type: Journal Article
• Authors: Zeng, Min-Li; Zhang, Guo-Feng
• Is Part Of: East Asian journal on applied mathematics. Volume 6:Issue 4(2016)
• Page Start: 367
• Page End: 383
• Publication Date: 2016-10-19
• Subjects: 65F10, -- 65F50; System of weakly nonlinear equations, -- GHSS iteration method, -- local convergence, -- inner iteration, -- outer iteration; Applied mathematics -- Periodicals; 519.05
• DOI: 10.4208/eajam.150116.240516a
• Languages: English
• ISSNs: 2079-7362

Abstract

Abstract: In this paper, we first construct a preconditioned two-parameter generalized Hermitian and skew-Hermitian splitting (PTGHSS) iteration method based on the two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration method for non-Hermitian positive definite linear systems. Then a class of PTGHSS-based iteration methods are proposed for solving weakly nonlinear systems based on separable property of the linear and nonlinear terms. The conditions for guaranteeing the local convergence are studied and the quasi-optimal iterative parameters are derived. Numerical experiments are implemented to show that the new methods are feasible and effective for large scale systems of weakly nonlinear systems.