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Modified Newton-SSTS method for solving a class of nonlinear systems with complex symmetric Jacobian matrices

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Abstract

This paper is intended to establish an effective iteration method for solving nonlinear systems with complex symmetric Jacobian matrices. Single-step triangular splitting (SSTS) iteration method is proved to be efficient and robust for solving a class of two-by-two block linear systems. By making use of the SSTS iteration scheme as the inner solver and the modified Newton method as the outer solver, we establish a new modified Newton-SSTS method to solve the class of nonlinear systems. Whereafter, we discuss the local and semilocal convergence properties of our method under the H\(\ddot{\text {o}}\)lder hypothesis. Finally, the numerical results of some nonlinear equations show that the Newton-SSTS method is vastly superior over some previous methods.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant no. 11771393, 11632015).

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, HangZhou, 310027, Zhejiang, People’s Republic of China

    Xiaohui Yu & Qingbiao Wu

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  1. Xiaohui Yu
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  2. Qingbiao Wu
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Correspondence to Qingbiao Wu.

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Communicated by yimin wei.

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Yu, X., Wu, Q. Modified Newton-SSTS method for solving a class of nonlinear systems with complex symmetric Jacobian matrices. Comp. Appl. Math. 41, 258 (2022). https://doi.org/10.1007/s40314-022-01961-9

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  • DOI: https://doi.org/10.1007/s40314-022-01961-9

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