Modified Newton-PAGSOR Method for Solving Nonlinear Systems with Complex Symmetric Jacobian Matrices

doi:10.1007/s42967-024-00410-0

Abstract

Abstract: We propose, in this paper, the preconditioned accelerated generalized successive overrelaxation (PAGSOR) iteration method for efficiently solving the large complex symmetric linear systems. To solve the nonlinear systems whose Jacobian matrices are complex and symmetric, treating the PAGSOR method as internal iteration, we construct a modified Newton-PAGSOR (MN-PAGSOR) method to provide an effective approach for solving a wide range of problems in various scientific and engineering fields. Based on the Hölder continuous condition we present the theoretical framework of the modified method, demonstrate its local convergence properties, and provide numerical experiments to validate its effectiveness in solving a class of nonlinear systems.

Key words: Preconditioned accelerated generalized successive overrelaxation (PAGSOR), Complex symmetric Jacobian matrix, Large sparse nonlinear systems, Modified Newton-PAGSOR (MN-PAGSOR) method, Local convergence

Rong Ma, Yu-Jiang Wu, Lun-Ji Song. Modified Newton-PAGSOR Method for Solving Nonlinear Systems with Complex Symmetric Jacobian Matrices[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 1880-1906.

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