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Fast, Globally Converging Algorithms for Spectral Moments Problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper, we consider the matricial version of generalized moment problem with degree constraint. Specifically we focus on computing the solution that minimize the Kullback-Leibler criterion. Several strategies to find such optimum via descent methods are considered and their convergence studied. In particular a parameterization with better numerical properties is derived from a spectral factorization problem. Such parameterization, in addition to guaranteeing descent methods to be globally convergent, it appears to be very reliable in practice.

National Category
URN: urn:nbn:se:kth:diva-39040OAI: diva2:439280
QC 20110907Available from: 2011-09-08 Created: 2011-09-07 Last updated: 2011-09-08Bibliographically approved
In thesis
1. Spectral Moment Problems: Generalizations, Implementation and Tuning
Open this publication in new window or tab >>Spectral Moment Problems: Generalizations, Implementation and Tuning
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Spectral moment interpolation find application in a wide array of use cases: robust control, system identification, model reduction to name the most notable ones. This thesis aims to expand the theory of such methods in three different directions. The first main contribution concerns the practical applicability. From this point of view various solving algorithm and their properties are considered. This study lead to identify a globally convergent method with excellent numerical properties. The second main contribution is the introduction of an extended interpolation problem that allows to model ARMA spectra without any explicit information of zero’s positions. To this end it was necessary for practical reasons to consider an approximated interpolation insted. Finally, the third main contribution is the application to some problems such as graphical model identification and ARMA spectral approximation.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. xii, 10 p.
Trita-MAT. OS, ISSN 1401-2294 ; 11:06
National Category
Computational Mathematics
urn:nbn:se:kth:diva-39026 (URN)978-91-7501-087-8 (ISBN)
Public defence
2011-09-16, Sal F2, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
QC 20110906Available from: 2011-09-06 Created: 2011-09-06 Last updated: 2011-09-08Bibliographically approved

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Avventi, Enrico
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