Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Inexact Levenberg-Marquardt method for nonlinear equations

Pages: 1223 - 1232, Volume 4, Issue 4, November 2004      doi:10.3934/dcdsb.2004.4.1223

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Jinyan Fan - Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China (email)
Jianyu Pan - Department of Mathematics, East China Normal University, Shanghai 200062, China (email)

Abstract: 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:  Nonlinear equations, Levenberg-Marquardt method, local error bound condition, quadratic convergence.
Mathematics Subject Classification:  90C30, 65K05, 34A34.

Received: March 2004;      Available Online: August 2004.