### 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.
*