### Optimization and Systems Theory Seminar Friday, March 20, 1998, 11.00-12.00, Room 3721, Lindstedtsvägen 25

Mälardalen University

#### How to find initial values for the least squares problem when estimating parameters in exponential sums?

The answer turns out to require simple mathematics:
-Change of variables
-Interpolation
-Interpretation as a geometrical sum
-Solution of a system of polynomial equations of high degree
But good advice is to use computer algebra.

Exponential sum models are used frequently: In heat diffusion, diffusion of chemical compounds, time series in medicine, economics and the physical sciences and technology.

Thus it is important to have good methods for estimation of parameters in exponential sums. The fitting of an exponential sum by e.g. a least squares criterion is difficult and good initial values are needed to help convergence.

The method of "Generalised Interpolation" (GI) will be presented as a tool for finding initial values. For one and two terms it gives a direct formula. For three and four terms it can be rewritten as an equation in one variable. For more than four terms (and also for three and four terms) it can be used to find a heuristic approach.

Calendar of seminars
Last update: February 4, 1998 by Anders Forsgren, andersf@math.kth.se.