A New Modified Newton-Type Iteration Method for Solving Generalized Absolute Value Equations

03/17/2021

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by   Xu Li, et al.

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For the large sparse generalized absolute value equations (GAVEs) , the shift splitting for the linear part's coefficient matrix is utilized to establish a new modified Newton-type (NMN) iteration method. The conditions for the convergence of the NMN iteration method are discussed in depth. Furthermore, certain sufficient convergence conditions are obtained when the coefficient matrix is a symmetric positive definite matrix or an H_+-matrix. According to both two numerical examples, the NMN iteration method is an effective approach to solve the GAVEs, especially when the coefficient matrix is indefinite.