Perturbations in Toeplitz matrices. II. Asymptotic properties
نویسندگان
چکیده
منابع مشابه
The Asymptotic Spectra of Banded Toeplitz and Quasi-Toeplitz Matrices
Toeplitz matrices occur in many mathematical as well as scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations ...
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We study the asymptotic eigenvalue distribution of Toeplitz matrices generated by a singular symbol. It has been conjectured by Widom that, for a generic symbol, the eigenvalues converge to the image of the symbol. In this paper we ask how the eigenvalues converge to the image. For a given Toeplitz matrix Tn(a) of size n, we take the standard approach of looking at det(ζ − Tn(a)), of which the ...
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1 Dipartimento di Matematica “Guido Castelnuovo”, SAPIENZA Università di Roma, P.le A. Moro, 2, I-00185 Roma, Italy. E-mail: [email protected]. Research supported by a grant from SAPIENZA Università di Roma. 2 Dipartimento di Matematica “Guido Castelnuovo”, SAPIENZA Università di Roma, P.le A. Moro, 2, I-00185 Roma, Italy. E-mail: [email protected]. 3 Department of Mathematic...
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We consider the Givens QR factorization of banded Hessenberg-Toeplitz matrices of large order and relatively small bandwidth. We investigate the asymptotic behavior of the R factor and the Givens rotation when the order of the matrix goes to infinity, and present some interesting convergence properties. These properties can lead to savings in the computation of the exact QR factorization and gi...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1991
ISSN: 0022-247X
DOI: 10.1016/0022-247x(91)90381-9