Matrix splitting iteration method for new generalized absolute value equations

Abstract

In this dissertation, using the matrix splitting technique, a Newton-based matrix splitting iterative method and a relaxed Newton-based matrix splitting iterative method are established to solve new generalized absolute value equations, which include Picard’s method and the modified Newton-type iteration method. We analyze the sufficient convergence conditions of the proposed methods, with some special coefficient matrices presented. The effectiveness and feasibility of the proposed method are confirmed by some numerical experiments involving both symmetric and non-symmetric matrices.