## ABSTRACT

This chapter focuses on locating a solution of a nonlinear least squares problem by using inexact Gauss-Newton method. In computational sciences the practice of numerical analysis is essentially connected to variants of Newton’s method. The chapter considers the local convergence of inexact Gauss-Newton method for solving the nonlinear least squares problem. It present some auxiliary results on Moore-Penrose inverses, as well as the local convergence of inexact Gauss-Newton method and inexact Gauss-Newton-like method. The chapter also provides numerical examples of the nonlinear least squares problem.