On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations

Min-Li Zeng and Guo-Feng Zhang
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Min-Li Zeng: School of Mathematics and Finance, Putian University, Putian 351100, China
Guo-Feng Zhang: School of Mathematics and Statistic, Lanzhou University, Lanzhou 730000, China

Mathematics, 2020, vol. 8, issue 2, 1-17

Abstract: To avoid solving the complex systems, we first rewrite the complex-valued nonlinear system to real-valued form (C-to-R) equivalently. Then, based on separable property of the linear and the nonlinear terms, we present a C-to-R-based Picard iteration method and a nonlinear C-to-R-based splitting (NC-to-R) iteration method for solving a class of large sparse and complex symmetric weakly nonlinear equations. At each inner process iterative step of the new methods, one only needs to solve the real subsystems with the same symmetric positive and definite coefficient matrix. Therefore, the computational workloads and computational storage will be saved in actual implements. The conditions for guaranteeing the local convergence are studied in detail. The quasi-optimal parameters are also proposed for both the C-to-R-based Picard iteration method and the NC-to-R iteration method. Numerical experiments are performed to show the efficiency of the new methods.

Keywords: weakly nonlinear equations; C-to-R preconditioner; local convergence; Picard iteration; complex symmetric matrix. (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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