The inverse problem of analytic interpolation with degree constraint

Johan Karlsson, Tryphon Georgiou, Anders Lindquist

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

In [7], [6] a theory for degree-constrained analytic interpolation was developed in terms of the minimizers of certain convex entropy functionals. In the present paper, we introduce and study relevant inverse problems. More specifically, we answer the following two questions. First, given a function f which satisfies specified interpolation conditions, when is it that f can be obtained as the minimizer of a suitably chosen entropy functional? Second, given a function g, when does there exist a suitably entropy functional so that the unique minimizer f which is subject to interpolation constraints also satisfies |f| = |g| on the unit circle. The theory and answers to these questions suggest an approach to identifying interpolants of a given degree and of a given approximate shape.

Original languageEnglish (US)
Title of host publicationProceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages559-564
Number of pages6
ISBN (Print)1424401712, 9781424401710
DOIs
StatePublished - 2006
Event45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States
Duration: Dec 13 2006Dec 15 2006

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other45th IEEE Conference on Decision and Control 2006, CDC
Country/TerritoryUnited States
CitySan Diego, CA
Period12/13/0612/15/06

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