An Improved Inexact Newton Method for Nonlinear Equations 

Meihong Zhou 

College of Mathematics and Information Science, Hebei University, Baoding, 071002, China 

Abstract: In this paper, we describe a variant of the Inexact Newton method for solving the nonlinear equa-tions. We make a study of a new nonmonotone inexact Newton method with a nonmonotone backtracking strategy. To decrease the computational complexity, the BFGS ｕｐｄａｔｅ formula is used to generate an approx-imated matrix rather than a normal Jacobian matrix. Theoretical analysis indicates that the new method pre-serves the global convergence under mild conditions.

Keywords: Nonlinear equations; Inexact Newton method; Nonmonotone strategy; Global convergence