A New Modified Efficient Levenberg–Marquardt Method for Solving Systems of Nonlinear Equations

For systems of nonlinear equations, a modified efficient Levenberg–Marquardt method with new LM parameters was developed by Amini et al. (2018). The convergence of the method was proved under the local error bound condition. In order to enhance this method, using nonmonotone technique, we propose a...

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Bibliographic Details
Published in:Mathematical problems in engineering 2021-08, Vol.2021, p.1-11
Main Authors: Wu, Zhenxiang, Zhou, Tong, Li, Lei, Chen, Liang, Ma, Yanfang
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Nonlinear equations
Nonlinear systems
Parameter modification
System effectiveness
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Summary:For systems of nonlinear equations, a modified efficient Levenberg–Marquardt method with new LM parameters was developed by Amini et al. (2018). The convergence of the method was proved under the local error bound condition. In order to enhance this method, using nonmonotone technique, we propose a new Levenberg–Marquardt parameter in this paper. The convergence of the new Levenberg–Marquardt method is shown to be at least superlinear, and numerical experiments show that the new Levenberg–Marquardt algorithm can solve systems of nonlinear equations effectively.
ISSN:1024-123X
1563-5147
DOI:10.1155/2021/5608195