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Tridiagonal Toeplitz matrices: properties and novel applications
Author(s) -
Noschese Silvia,
Pasquini Lionello,
Reichel Lothar
Publication year - 2013
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1811
Subject(s) - tridiagonal matrix , toeplitz matrix , mathematics , krylov subspace , eigenvalues and eigenvectors , chebyshev polynomials , levinson recursion , tikhonov regularization , subspace topology , algebra over a field , pure mathematics , mathematical analysis , linear system , inverse problem , physics , quantum mechanics
SUMMARY The eigenvalues and eigenvectors of tridiagonal Toeplitz matrices are known in closed form. This property is in the first part of the paper used to investigate the sensitivity of the spectrum. Explicit expressions for the structured distance to the closest normal matrix, the departure from normality, and the ϵ ‐pseudospectrum are derived. The second part of the paper discusses applications of the theory to inverse eigenvalue problems, the construction of Chebyshev polynomial‐based Krylov subspace bases, and Tikhonov regularization. Copyright © 2012 John Wiley & Sons, Ltd.