@article{Zhu2024, 
author = {Dingyu Zhu and Yueting Yang and Mingyuan Cao},
title = {An accelerated adaptive two-step Levenberg–Marquardt method with the modified Metropolis criterion},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {24610-24635},
keywords = {nonlinear equations, Levenberg–Marquardt method, Metropolis criterion, Hölderian local error bound, Hölderian continuity},
url = {https://www.sciopen.com/article/10.3934/math.20241199},
doi = {10.3934/math.20241199},
abstract = {In this paper, aiming at the nonlinear equations, a new two-step Levenberg–Marquardt method was proposed. We presented a new Levenberg–Marquardt parameter to obtain the trial step. A new modified Metropolis criterion was used to adjust the upper bound of the approximate step. The convergence of the method was analyzed under the H o¨lderian local error bound condition and the H ¨olderian continuity of the Jacobian. Numerical experiments showed that the new algorithm is effective and competitive in the numbers of functions, Jacobian evaluations and iterations.}
}