A new Gauss–Newton-like method for nonlinear equations

Abstract

In this paper, a new Gauss–Newton-like method that is based on a rational approximation model with linear numerator is proposed for solving nonlinear equations. The new method revises the J T k Jk matrix by a rank-one matrix at each iteration. Furthermore, we design a new iterative algorithm for nonlinear equations and prove that it is locally q-quadratically convergent. The numerical results show that the new proposed method has better performance than the classical Gauss–Newton method.