TY - GEN

T1 - The inverse problem of analytic interpolation with degree constraint

AU - Karlsson, Johan

AU - Georgiou, Tryphon

AU - Lindquist, Anders

PY - 2006/12/1

Y1 - 2006/12/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=39649118367&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39649118367&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:39649118367

SN - 1424401712

SN - 9781424401710

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 559

EP - 564

BT - Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC

T2 - 45th IEEE Conference on Decision and Control 2006, CDC

Y2 - 13 December 2006 through 15 December 2006

ER -