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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Min-Li Zeng & Guo-Feng Zhang, 2020. "On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations," Mathematics, MDPI, vol. 8(2), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:208-:d:317481
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    References listed on IDEAS

    as
    1. Abdolreza Amiri & Mohammad Taghi Darvishi & Alicia Cordero & Juan Ramón Torregrosa, 2019. "An Efficient Iterative Method Based on Two-Stage Splitting Methods to Solve Weakly Nonlinear Systems," Mathematics, MDPI, vol. 7(9), pages 1-17, September.
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