In this paper, a single direction with double step length method for solving systems of nonlinear equations is presented. Main idea used in the algorithm is to approximate the Jacobian via acceleration parameter. Furthermore, the two step lengths are calculated using inexact line search procedure. This method is matrix-free, and so is advantageous when solving large-scale problems. The proposed method is proven to be globally convergent under appropriate conditions. The preliminary numerical results reported in this paper using a large-scale benchmark test problems show that the proposed method is practically quite effective.

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.

This paper presents a Globally Convergent Hyper plane system of equations. The attractive attributes of our method are due to singularity free requirements and global convergence properties. Numerical performance on some b problems that demonstrates there liability shown that the proposed method is very rigorous and efficiently competitive.

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