2021/03/17 by Xu Li, Li, Xu, Yin, Xiao-Xia · 1 citation
Computer Science · Mathematics · #65F10 #90C05 #90C30 #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2103.09452
openalex publication_date 2021/03/17 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
A shift splitting modified Newton-type (SSMN) iteration method is introduced for solving large sparse generalized absolute value equations (GAVEs). The SSMN method is established by replacing the regularized splitting of the coefficient matrix of the linear part, which is employed in the modified Newton-type (MN) iteration method, with the shift splitting of the matrix. The conditions for the convergence of the proposed method are discussed in depth for the cases when the coefficient matrix is a general matrix, a symmetric positive definite matrix, and an H+-matrix. Through two numerical examples, we find that the SSMN and MN methods complement each other. The optimal performances of the two methods depend on the definiteness of the coefficient matrix of the linear part. The MN method is more efficient when the coefficient matrix is positive definite, whereas the SSMN method has a better performance when the coefficient matrix is indefinite.