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Divergence-based spectral approximation with degree constraint as a concave optimization problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The Kullback-Leibler pseudo-distance, or divergence, can be used as a criterion for spectral approximation. Unfortunately this criterion is not convex over the most general classes of rational spectra. In this work it will be shown that divergence minimization is equivalent to a costrained entropy minimization problem, whose concave structure can be exploited in order to guarantee global convergence in the most general case.

National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-39066OAI: oai:DiVA.org:kth-39066DiVA: diva2:439408
Note
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.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 11:06
National Category
Computational Mathematics
Identifiers
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)
Opponent
Supervisors
Note
QC 20110906Available from: 2011-09-06 Created: 2011-09-06 Last updated: 2011-09-08Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf