Local convergence of inexact Gauss-Newton-like method for least square problems under weak Lipschitz condition

Abstract

We present a local convergence analysis of inexact Gauss-Newton-like method for solving nonlinear least-squares problems in a Euclidian space setting. The convergence analysis is based on a combination of a weak Lipschitz and a center-weak Lipschitz condition. Our approach has the following advantages and under the same computational cost as earlier studies such as [5, 6, 7, 15]: A large radius of convergence; more precise estimates on the distances involved to obtain a desired error tolerance. Numerical examples are also presented to show these advantages.