NDLI: On the Elementwise Convergence of Continuous Functions of Hermitian Banded Toeplitz Matrices

Content Provider	IEEE Xplore Digital Library
Author	Crespo, P.M. Gutierrez-Gutierrez, J.
Copyright Year	1963
Abstract	Toeplitz matrices and functions of Toeplitz matrices (such as the inverse of a Toeplitz matrix, powers of a Toeplitz matrix or the exponential of a Toeplitz matrix) arise in many different theoretical and applied fields. They can be found in the mathematical modeling of problems where some kind of shift invariance occurs in terms of space or time. R. M. Gray's excellent tutorial monograph on Toeplitz and circulant matrices has been, and remains, the best elementary introduction to the Szegouml distribution theory on the asymptotic behavior of continuous functions of Toeplitz matrices. His asymptotic results, widely used in engineering due to the simplicity of its mathematical proofs, do not concern individual entries of these matrices but rather, they describe an "average" behavior. However, there are important applications where the asymptotic expressions of interest are directly related to the convergence of a single entry of a continuous function of a Toeplitz matrix. Using similar mathematical tools and to gain insight into the solutions of this sort of problems, the present correspondence derives new theoretical results regarding the convergence of these entries
Sponsorship	IEEE Information Theory Society
Starting Page	1168
Ending Page	1176
Page Count	9
File Size	476989
File Format	PDF
ISSN	00189448
Volume Number	53
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-03-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Convergence Covariance matrix Signal processing H infinity control Books Mathematical model Mean square error methods Stochastic processes Educational programs Eigenvalues and eigenfunctions Toeplitz matrices Circulant matrices covariance matrices elementwise convergence functions of matrices minimum mean square error (MMSE) stationary stochastic time series Szegö's theorem
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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