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 E-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 (c) 2012 John Wiley & Sons, Ltd.
Tridiagonal Toeplitz matrices: Properties and novel applications / Noschese, Silvia; Pasquini, Lionello; Lothar, Reichel. - In: NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS. - ISSN 1070-5325. - STAMPA. - 20:2(2013), pp. 302-326. [10.1002/nla.1811]
Tridiagonal Toeplitz matrices: Properties and novel applications
NOSCHESE, Silvia;PASQUINI, Lionello;
2013
Abstract
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 E-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 (c) 2012 John Wiley & Sons, Ltd.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
