A Class of Relaxed TTSCSP Iteration Methods for Weakly Nonlinear Systems

Abstract

A relaxed TTSCSP (RTTSCSP) iteration method for complex linear systems is constructed. Based on the strong dominance and separability of linear and nonlinear terms, Picard-RTTSCSP and nonlinear RTTSCSP-like iterative methods are developed and applied to complex systems of weakly nonlinear equations. The convergence of the method is investigated. Besides, optimal iterative parameters minimizing the upper bound of the spectral radius are derived. Numerical examples show the effectiveness and applicability of the methods to complex systems of weakly nonlinear equations.