Applications of Operator Theory to Maximum Entropy Problems
Abstract
This project was concerned with problems in operator theory and matrix theory that underlie the maximum entropy principle in signal processing and systems theory. Two papers have been completed that generalize this principle to a wide class of indefinite hermitian matrices. Three new papers give a thorough study of rank-preserving extensions of band matrices. Factorization theorems are obtained for wide classes of Toeplitz and Hankel matrices, and connections are given to the Kalman partial realization problems in signal processing. Applications are also given to signal processing when the power spectrum consists of a set of pure line spectra. In another paper, new work on orthogonal polynomials and the Gohberg-Semencul formula for the inverse of a Toeplitz matrix has been completed. Three new papers generalize for rational matrix functions a number of well-known interpolation problems for scalar functions. A new approach to tangential interpolation problems is presented, and applications are given to sensitivity minimization in control theory.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 12, 1990
- Accession Number
- ADA230417
Entities
People
- David C. Lay
- Israel Gohberg
- Robert L. Ellis
Organizations
- University of Maryland