Optimization and Systems Theory Seminar
Friday, December 4, 1998, 10.00-12.00, Room 3721, Lindstedtsvägen 25

Jöran Petersson
Mälardalen University

Algorithms for fitting two classes of exponential sums to empirical data

When fitting an exponential sum model to data and estimating the parameters determining its shape, often a least squares criterion is used. Least squares algorithms are iterative methods, which demand an initial point to start from. A least squares criterion may have several points that render a local minimum. Well founded initial value algorithms is no guarantee of reaching a global minimum, but for stiff problems they not seldom give solutions with a smaller residual than more crude initial values. One natural strategy is to interpolate in a set of points and solve the interpolation equations. The draw-back of this is that usually only a few data points are involved in the interpolation equations. A remedy is to cluster the data in subgroups and interpolate in the mean value of each subgroup -- generalized interpolation. For exponential sums this is simple to apply as the sum of a set of equidistant data points is a geometrical sum. The interpolation in single points of a classical exponential sum is equivalent to the classical Prony method and thus generalized interpolation can be viewed as a generalization of the Prony method. It is possible to find explicit solutions to the generalized interpolation equations for exponential sums of order two. For exponential sums of order three and four useful, but large, expressions in one variable can be derived. Higher order models are not common in practice as they are hard to identify. For such models there is a need to rely on numerical algorithms.

The contribution of this work is to use generalized interpolation and to find explicit formulas or useful expressions for the initial value algorithms by using computer algebra.

Calendar of seminars
Last update: December 1, 1998 by Anders Forsgren, andersf@math.kth.se.