On the Convergence of Levenberg-Marquardt Method for Solving Nonlinear Systems
Levenberg-Marquardt (L-M forshort) method is one of the most important methods for solving systems of nonlinear equations. In this paper, we consider the convergence under \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{a...
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Published in | Bio-Inspired Computing - Theories and Applications pp. 117 - 122 |
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Main Authors | , , , , |
Format | Book Chapter |
Language | English |
Published |
Berlin, Heidelberg
Springer Berlin Heidelberg
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Series | Communications in Computer and Information Science |
Subjects | |
Online Access | Get full text |
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Summary: | Levenberg-Marquardt (L-M forshort) method is one of the most important methods for solving systems of nonlinear equations. In this paper, we consider the convergence under \documentclass[12pt]{minimal}
\usepackage{amsmath}
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\begin{document}$\lambda_{k}=\min(\|F_{k}\|,\|J_{k}^{T}F_{k}\|)$\end{document} of L-M method. We will show that if ∥ F(xk) ∥ provides a local error bound, which is weaker than the condition of nonsingularity for the system of nonlinear equations, the sequence generated by the L-M method converges to the point of the solution set quadratically. As well, numerical experiments are reported. |
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ISBN: | 3662450488 9783662450482 |
ISSN: | 1865-0929 1865-0937 |
DOI: | 10.1007/978-3-662-45049-9_19 |