Computation of Parameters in Separable Nonlinear Dynamic Models by Use of Short-Cut Methods

Abstract

In computational science it is common to describe dynamic systems by mathematical models in forms of di#erential or integral equations. These models may contain parameters that must be computed. For the special type of ordinary di#erential equations studied in this paper, the resulting parameter estimation problem is a separable nonlinear least squares problem with equality constraints. This problem is solved by iteration and initial values can be found by use of short-cut methods. An algorithm, called the modified Kaufman algorithm, is proposed and it takes the separability into account. Moreover, di#erent kinds of discretizations and formulations of the optimization problem are discussed as well as the e#ect of ill-conditioning