Abstract
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.
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Fang, M., Xu, F., Zhu, Z., Jiang, L., Geng, X. (2014). On the Convergence of Levenberg-Marquardt Method for Solving Nonlinear Systems. In: Pan, L., Păun, G., Pérez-Jiménez, M.J., Song, T. (eds) Bio-Inspired Computing - Theories and Applications. Communications in Computer and Information Science, vol 472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45049-9_19
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DOI: https://doi.org/10.1007/978-3-662-45049-9_19
Publisher Name: Springer, Berlin, Heidelberg
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