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A high-order modified Levenberg–Marquardt method for systems of nonlinear equations with fourth-order convergence

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  • Chen, Liang

Abstract

Fan (2014) presented an accelerated modified Levenberg–Marquardt method for nonlinear equations. At every iteration, the accelerated modified LM method computed not only a LM trial step, but also an additional approximate LM step which employed a line search. In this paper, based on the accelerated modified LM method, we compute the approximate LM step one more time at every iteration, and obtain a high-order accelerating modified Levenberg–Marquardt method. Under the local error bound condition which is weaker than nonsingularity, the convergence order of this new method is shown to be fourth. A globally convergence is also given by the trust region technique. Numerical results show that the new method is efficient and could save many calculations of the Jacobian.

Suggested Citation

  • Chen, Liang, 2016. "A high-order modified Levenberg–Marquardt method for systems of nonlinear equations with fourth-order convergence," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 79-93.
    • Handle: RePEc:eee:apmaco:v:285:y:2016:i:c:p:79-93
    DOI: 10.1016/j.amc.2016.03.031
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    References listed on IDEAS

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    1. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, December.
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    Cited by:

    1. Zhiqi Yan & Shisheng Zhong & Lin Lin & Zhiquan Cui, 2021. "Adaptive Levenberg–Marquardt Algorithm: A New Optimization Strategy for Levenberg–Marquardt Neural Networks," Mathematics, MDPI, vol. 9(17), pages 1-17, September.
    2. Alexey V. Shkirin & Sergey N. Chirikov & Nikolai V. Suyazov & Veronika E. Reut & Daria V. Grigorieva & Irina V. Gorudko & Vadim I. Bruskov & Sergey V. Gudkov, 2022. "Modeling the Kinetics of the Singlet Oxygen Effect in Aqueous Solutions of Proteins Exposed to Thermal and Laser Radiation," Mathematics, MDPI, vol. 10(22), pages 1-12, November.

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