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Erschienen in:
2014 | OriginalPaper | Buchkapitel
On the Convergence of Levenberg-Marquardt Method for Solving Nonlinear Systems
verfasst von : Minglei Fang, Feng Xu, Zhibin Zhu, Lihua Jiang, Xianya Geng
Erschienen in: Bio-Inspired Computing - Theories and Applications
Verlag: Springer Berlin Heidelberg
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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
$\lambda_{k}=\min(\|F_{k}\|,\|J_{k}^{T}F_{k}\|)$
of L-M method. We will show that if ∥
F
(
x
k
) ∥ 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.