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Modified Newton-PBS method for solving a class of complex symmetric nonlinear systems

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Abstract

The parameterized block splitting (PBS) is a convergent and efficient iterative method to solve the large complex symmetric linear systems. In this paper, by using PBS iterative technique, the Newton equation is approximately solved, then we establish the modified Newton-PBS iterative method to solve the complex nonlinear systems whose Jacobian matrices are large, sparse, and complex symmetric. Subsequently, the local convergence analysis are explored under appropriate conditions. Ultimately, we apply the new method and several known methods to experimental numerical examples, and experimental results verify the superiority and efficiency of our new method. Especially, in terms of CPU time and iteration steps, our method is obviously better.

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The data used to support the findings of this study are available from the corresponding author upon request.

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Funding

This work is supported by the National Natural Science Foundation of China (Grant no. 12271479).

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Authors and Affiliations

  1. School of Mathematics, China University of Mining and Technology, 221116, Jiangsu, Xuzhou, People’s Republic of China

    Yuanyuan Zhang

  2. School of Mathematical Science, Zhejiang University, 310027, Zhejiang, Hangzhou, People’s Republic of China

    Yuanyuan Zhang, Qingbiao Wu, Yao **ao & Zhewei **e

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  1. Yuanyuan Zhang
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  2. Qingbiao Wu
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  3. Yao **ao
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  4. Zhewei **e
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Correspondence to Qingbiao Wu.

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Zhang, Y., Wu, Q., **ao, Y. et al. Modified Newton-PBS method for solving a class of complex symmetric nonlinear systems. Numer Algor 96, 333–368 (2024). https://doi.org/10.1007/s11075-023-01649-z

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