Applications of Operator Theory to Maximum Entropy Problems
Abstract
This project is focusing on problems in operator theory and matrix theory that underlie the maximum entropy principle in signal processing and system theory. We have found generalizations of this principle for finite-dimensional problems to certain broad classes of hermitian band matrices, including Toeplitz matrices, and we have shown why a similar principle cannot exist for all hermitian band matrices. Zeros of orthogonal polynomials are studied in a setting that generalizes the usual minimum phase theorem for the errror prediction filters related to stationary time series. In another paper, we analyze the number of negative eigenvalues of an extension of a hermitian band matrix in terms of the entries in the band matrix. From this we obtain results on maximum entropy and on singular values of extensions of triangular matrices. The latter results are related to the finite-dimensional model reduction problem for linear systems. Keywords: Operator theory, Matrix theory, Maximum entropy principle, Band matrices, Toeplitz matrix, Orgothogonal polynomials, Negative eigenvalues, Signal processing, Model reduction, Linear systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 08, 1988
- Accession Number
- ADA200566
Entities
People
- David C. Lay
- Israel Gohberg
- Robert L. Ellis
Organizations
- University of Maryland