Computational Behavior of Gauss-Newton Methods

Abstract: "This paper is concerned with the behavior of Gauss-Newton methods for nonlinear least-squares problems. Here we assume that the defining feature of a Gauss-Newton method is that the direction from one iterate to the next is the numerical solution of a particular linear least-squares problem, with a steplength subsequently determined by a linesearch procedure. It is well known that Gauss-Newton methods cannot be successfully applied to nonlinear least-squares problems as a class without modification. Our purpose is to give specific examples illustrating some of the difficulties that arise in practice which we believe have not been fully described in the literature."