Modified Newton-Type Iteration Methods for Generalized Absolute Value Equations

Abstract

In this paper, by separating the differential and the non-differential parts of the generalized absolute value equations, a class of modified Newton-type iteration methods are proposed. The modified Newton-type iteration method involves the well-known Picard iteration method as the special case. Convergence properties of the new iteration schemes are analyzed in detail. In particular, some specific sufficient conditions are presented for two special coefficient matrices. Finally, two numerical examples are given to illustrate the effectiveness of the proposed modified Newton-type iteration methods.