# The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence

```@article{Fan2012TheML,
title={The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence},
author={Jinyan Fan},
journal={Math. Comput.},
year={2012},
volume={81},
pages={447-466}
}```
• Jinyan Fan
• Published 2012
• Computer Science, Mathematics
• Math. Comput.
We propose a modified Levenberg-Marquardt method for nonlinear equations, in which not only a LM step but also an approximate LM step are computed at every iteration. To ensure the global convergence of the new method, a new kind of predicted reduction is introduced for the merit function when using the trust region technique. The cubic convergence of the modified LM method is proved under the local error bound condition which is weaker than nonsingularity. Numerical results show that the new… Expand
60 Citations
A higher-order Levenberg-Marquardt method for nonlinear equations
• X. Yang
• Mathematics, Computer Science
• Appl. Math. Comput.
• 2013
• 23
On a New Updating Rule of the Levenberg–Marquardt Parameter
• Mathematics, Computer Science
• J. Sci. Comput.
• 2018
• 1
A modified two steps Levenberg-Marquardt method for nonlinear equations
• Computer Science, Mathematics
• J. Comput. Appl. Math.
• 2015
• 29
An Adaptive Multi-step Levenberg–Marquardt Method
• Mathematics, Computer Science
• J. Sci. Comput.
• 2019
• 2
A Shamanskii-like Levenberg-Marquardt method for nonlinear equations
• Jinyan Fan
• Mathematics, Computer Science
• Comput. Optim. Appl.
• 2013
• 7
Three-steps modified Levenberg-Marquardt method with a new line search for systems of nonlinear equations
• Computer Science, Mathematics
• J. Comput. Appl. Math.
• 2016
• 14
• Highly Influenced
{"ft_lang_label":"__label__en","ft_lang_prob":0.63917243,"math_prob":0.7536045,"size":3308,"snap":"2021-04-2021-17","text_gpt3_token_len":887,"char_repetition_ratio":0.19309928,"word_repetition_ratio":0.15927419,"special_character_ratio":0.2493954,"punctuation_ratio":0.1184466,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9906429,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-18T21:47:49Z\",\"WARC-Record-ID\":\"<urn:uuid:e7a321f8-3289-4b0e-b3e6-4050027a56d7>\",\"Content-Length\":\"304302\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1df803a7-e6e6-4c45-be28-1377a76430f7>\",\"WARC-Concurrent-To\":\"<urn:uuid:cf7032a6-8172-4294-88ca-48bd69bab871>\",\"WARC-IP-Address\":\"99.86.186.29\",\"WARC-Target-URI\":\"https://www.semanticscholar.org/paper/The-modified-Levenberg-Marquardt-method-for-with-Fan/bb31e352207e2f79c32e941487595eb5f4c4d255?p2df\",\"WARC-Payload-Digest\":\"sha1:NA5RDLISMCOLBZJPZDVQDLBML3MGQAEO\",\"WARC-Block-Digest\":\"sha1:BYBIUOYGYU6QLJ22BC6T37JWWB4GD5SF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038860318.63_warc_CC-MAIN-20210418194009-20210418224009-00307.warc.gz\"}"}