Relative entropy and moment problems

Tryphon T Georgiou

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

Abstract

We consider the von Neumann entropy (ρ) := -trace(ρlogρ) and the Kullback-Leibler-Umegaki distance double-struk S sign (ρ∥σ) := trace(ρlogρ- ρlogρ) as regularizing functional in seeking solutions to multi-variable and multi-dimensional moment problems. We show how to obtain extrema for such functional via a suitable homotopy and how to characterize all the solutions to moment problems. The range of possible applications includes the inverse problem of describing power spectra which are consistent with second-order statistics, measurement in classical thermodynamics as well as a quantum mechanics, as well as analytic interpolation encountered in modern robust control (cf. [6], [14], [15], [16], [17]).

Original languageEnglish (US)
Title of host publicationProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages4397-4403
Number of pages7
DOIs
StatePublished - Dec 1 2005
Event44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain
Duration: Dec 12 2005Dec 15 2005

Publication series

NameProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume2005

Other

Other44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Country/TerritorySpain
CitySeville
Period12/12/0512/15/05

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