### Optimization and Systems Theory Seminar

Friday, March 20, 1998, 11.00-12.00, Room 3721,
Lindstedtsvägen 25

**
Jöran Petersson**

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.
*