The inverse problem of analytic interpolation with degree constraint

Johan Karlsson; Tryphon Georgiou; Anders Lindquist

doi:10.1109/cdc.2006.376827

The inverse problem of analytic interpolation with degree constraint

Johan Karlsson, Tryphon Georgiou, Anders Lindquist

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

5 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 language	English (US)
Title of host publication	Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	559-564
Number of pages	6
ISBN (Print)	1424401712, 9781424401710
DOIs	https://doi.org/10.1109/cdc.2006.376827
State	Published - 2006
Event	45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: Dec 13 2006 → Dec 15 2006

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	45th IEEE Conference on Decision and Control 2006, CDC
Country/Territory	United States
City	San Diego, CA
Period	12/13/06 → 12/15/06

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10.1109/cdc.2006.376827

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Karlsson, J., Georgiou, T., & Lindquist, A. (2006). The inverse problem of analytic interpolation with degree constraint. In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC (pp. 559-564). Article 4177625 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/cdc.2006.376827

The inverse problem of analytic interpolation with degree constraint. / Karlsson, Johan; Georgiou, Tryphon; Lindquist, Anders.
Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. Institute of Electrical and Electronics Engineers Inc., 2006. p. 559-564 4177625 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Karlsson, J, Georgiou, T & Lindquist, A 2006, The inverse problem of analytic interpolation with degree constraint. in Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC., 4177625, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 559-564, 45th IEEE Conference on Decision and Control 2006, CDC, San Diego, CA, United States, 12/13/06. https://doi.org/10.1109/cdc.2006.376827

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AB - 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.

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The inverse problem of analytic interpolation with degree constraint

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