Computational Behavior of Gauss–Newton Methods

Abstract

This paper is concerned with the numerical behavior of Gauss–Newton methods for nonlinear least-squares problems. It is well known that Gauss–Newton methods often cannot be applied successfully without modification. However, no a priori characterization has been given of those problems on which a particular Gauss–Newton method or class of Gauss–Newton methods will or will not work well. The present paper gives some insight into why it is difficult to do so.