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November  2004, 4(4): 1223-1232. doi: 10.3934/dcdsb.2004.4.1223

Inexact Levenberg-Marquardt method for nonlinear equations

Jinyan Fan 1, and  Jianyu Pan 2,

1. 

Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
2. 

Department of Mathematics, East China Normal University, Shanghai 200062, China

Received  March 2004 Published  August 2004

In this paper, we present an inexact Levenberg-Marquardt (LM) method for singular system of nonlinear equations, where the LM parameter is chosen as the norm of the function and the trial step is computed approximately. Under the local error bound condition which is weaker than the non- singularity, we show that the new inexact LM method preserves the quadratic convergence of the traditional LM method where the parameter is chosen to be larger than a positive constant and the Jacobi at the solution is nonsingular.
Keywords: local error bound condition, Levenberg-Marquardt method, quadratic convergence., Nonlinear equations.
Mathematics Subject Classification: 90C30, 65K05, 34A3.
Citation: Jinyan Fan, Jianyu Pan. Inexact Levenberg-Marquardt method for nonlinear equations. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 1223-1232. doi: 10.3934/dcdsb.2004.4.1223
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