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King-NSS iteration method for solving a class of large sparse nonlinear systems

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Abstract

In order to seek the numerical solution of large sparse nonlinear systems with positive definite Jacobian matrix, treating the normal and skew-Hermitian splitting(NSS) method (Bai et al., Numer Linear Algebra Appl 14:319–335, 2007) as internal iteration, we establish a new iteration method named the King-NSS method in this paper. The convergence of our new presented method is analyzed theoretically under suitable conditions. Furthermore, we compare the King-NSS method with other Newton-like methods, which take the Newton or modified Newton methods as the external iteration. Numerical experimental results corroborate the feasibility and superiority of our new method when the nonlinear systems with positive definite Jacobian matrix are large sparse.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant Nos. 11771393, 11632015).

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Authors and Affiliations

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

    Yuanyuan Zhang, Qingbiao Wu & Yao Xiao

  2. School of Mathematics, Hangzhou Normal University, Hangzhou, 310036, Zhejiang, People’s Republic of China

    Pingfei Dai

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  1. Yuanyuan Zhang
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  2. Qingbiao Wu
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  3. Pingfei Dai
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  4. Yao Xiao
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Correspondence to Qingbiao Wu.

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Zhang, Y., Wu, Q., Dai, P. et al. King-NSS iteration method for solving a class of large sparse nonlinear systems. J. Appl. Math. Comput. 68, 2913–2935 (2022). https://doi.org/10.1007/s12190-021-01649-z

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  • DOI: https://doi.org/10.1007/s12190-021-01649-z

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