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Keywords = C-to-R preconditioner

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17 pages, 800 KB  
Article
On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations
by Min-Li Zeng and Guo-Feng Zhang
Mathematics 2020, 8(2), 208; https://doi.org/10.3390/math8020208 - 6 Feb 2020
Viewed by 2244
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) [...] Read more.
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. Full article
(This article belongs to the Special Issue Computational Methods in Applied Analysis and Mathematical Modeling)
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