### Optimization and Systems Theory Seminar

Friday, March 30, 2001, 11.00-12.00, Room 3721, Lindstedtsv. 25

**Per Enqvist**

Division of Optimization and Systems Theory

Department of Mathematics

KTH

E-mail: pere@math.kth.se

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Spectral estimation by geometric, topological and optimization methods

The purpose of this presentation is to give a survey of my thesis that
will be defended on April 6. The
thesis consists of four papers dealing with various aspects of
spectral estimation and the stochastic realization problem.
Since cepstrum parameters characterize a spectrum in a similar way as
covariances, and can be estimated from data, it makes sense to
consider realization based on the cepstrum. By considering a cepstrum
interpolation problem, the approaches used in the thesis are
described. In particular, an optimization problem is formulated for
determining a minimum variance interpolant. Duality theory is then
used to obtain a convex optimization problem that can be solved using
homotopy methods. Differential geometry is used to study the set of
solutions corresponding to different choices of parameter values. The
parameters are shown to form local coordinates for the set of
interpolants. Since this particular interpolation problem lacks
solutions for some parameter combinations, an approximative
interpolation problem is introduced and the entropy of the
approximative interpolant is studied.

Other interpolation problems studied in the thesis, such as the
covariance extension problem with a degree constraint, are described
and the main theorems are presented.

Calendar of seminars

*Last update: March 22, 2001 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*