Matrix-Norm Approach of Computing Levenberg-Marquardt Reg- ularization Parameter for Nonlinear Equations

Abstract

In this paper, we present Levenberg-Marquardt method for solving nonlinear systems of  equations. Here, both the objective function and the symmetric Jacobian matrix are assumed to be Lipchitz continuous. The regularization parameter is derived using Matrix-Norm approach. Numerical performance on some benchmark problems that demonstrates the effectiveness and efficiency of our approach are reported and have shown that the proposed algorithm is very promising.

Mathematics Subject Classification: 65H10, 65K05, 65F22, 65F35.

keywords: Nonlinear system of equations. Levenberg-Marquardt method. Regularization. Matrix-norm. Global convergence.