SOME COMPUTATIONAL TECHNIQUES FOR THE NONLINEAR LEAST SQUARES PROBLEM

Abstract

This chapter discusses some computational techniques for the nonlinear least squares problem. It presents one way of looking at some of the more useful computational techniques for solving the over-determined nonlinear least squares problem. In particular, it shows that these methods can profitably be viewed as Newton-like methods. The chapter also discusses the advantages and disadvantages of the Gauss–Newton method. The large residual problems are of prime importance. These are usually the problems that have the added complication of a large number of equations. In the linear case, such problems have become fairly routine through the use of the so-called Kalman filter. Little is known about the adaptability of Kalman filtering to large nonlinear problems. Recently there has been a flurry of activity concerning the exploitation of any linearity in the problem.