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Improved convergence results of an efficient Levenberg–Marquardt method for nonlinear equations

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Abstract

This paper improves convergence results of an efficient Levenberg–Marquardt (LM) method with the LM parameter \(\uplambda _k=\frac{\mu _k\Vert F_k\Vert }{1+\Vert F_k\Vert }\). The global and superlinear convergence are proved under the H\(\ddot{o}\)lderian continuity and the H\(\ddot{o}\)lderian local error bound conditions, which are weaker than the Lipschitz continuity and the local error bound, respectively. Numerical experiments verify the convergence of our algorithm for singular problems, which satisfy the H\(\ddot{o}\)lderian continuity and the H\(\ddot{o}\)lderian local error bound conditions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, 432000, Hubei, China

    Meilan Zeng

  2. School of Mathematical Sciences, Huaibei Normal University, Huaibei, 235000, Anhui, China

    Guanghui Zhou

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  1. Meilan Zeng
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  2. Guanghui Zhou
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Correspondence to Guanghui Zhou.

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This work was supported by National Natural Science Foundation of China (11771210), Foundations of Education Department of Hubei Province (B2020151, 2020628) and University Natural Science Foundation of Anhui Province (KJ2020ZD008).

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Zeng, M., Zhou, G. Improved convergence results of an efficient Levenberg–Marquardt method for nonlinear equations. J. Appl. Math. Comput. 68, 3655–3671 (2022). https://doi.org/10.1007/s12190-021-01599-6

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  • DOI: https://doi.org/10.1007/s12190-021-01599-6

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