A modified Newton-based matrix splitting iteration method for generalized absolute value equations

Abstract

Many problems in scientific computing and engineering fields lead to the solution of generalized absolute value equations (GAVE). In this paper, by simultaneously splitting both coefficient matrices in the differential and non-differential parts of the GAVE, a modified Newton-based matrix splitting (MNMS) iteration method is proposed. The MNMS iteration method not only covers the well-known generalized Newton iteration method as well as the recent proposed modified Newton-based iteration method and the Newton-based matrix splitting iteration method for solving the GAVE, but also results in a series of relaxation versions that are very flexible in real applications. Convergence properties of the MNMS iteration method are studied in detail when the coefficient matrices are positive definite matrices and H+-matrices. Finally, three numerical examples are presented to show the feasibility and effectiveness of the proposed MNMS iteration method.