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An efficient m-step Levenberg-Marquardt method for nonlinear equations

Submit Time: 2016-07-11
Author: Chen, Liang 1 ; Ma, Yanfang ; Su, Chencheng ;
Institute: 1.Huaibei Normal University;

Abstracts

In this paper, we construct and analyze an efficient m-step Levenberg-Marquardt method for nonlinear equations. The main advantage of this method is that the m-step LM method could save more Jacobian calculations with frozen $(J_k^TJ_k+\lambda_kI)^{-1}J_k^T$ at every iteration. Under the local error bound condition which is weaker than nonsingularity, the m-step LM method has been proved to have $(m+1)$th convergence order. The global convergence has also been given by trust region technique. Numerical results show that the m-step LM method is efficient and could save many calculations of the Jacobian especially for large scale problems.
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From: 陈亮
DOI:doi:10.1137/0721054.
Recommended references: Chen, Liang,Ma, Yanfang,Su, Chencheng.(2016).An efficient m-step Levenberg-Marquardt method for nonlinear equations.doi:doi:10.1137/0721054. (Click&Copy)
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[V1] 2016-07-11 11:17:24 chinaXiv:201607.00035V1 Download
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