Tridiagonal Toeplitz matrices: properties and novel applications‡. Issue 2 (13th March 2012)

• Record Type: Journal Article
• Authors: Noschese, Silvia; Pasquini, Lionello; Reichel, Lothar
• Other Names: Chu Eric guestEditor.; Lin Wen‐wei guestEditor.; Reichel Lothar guestEditor.
• Is Part Of: Numerical linear algebra with applications. Volume 20:Issue 2(2013:Mar.)
• Page Start: 302
• Page End: 326
• Publication Date: 2012-03-13
• Subjects: eigenvalues -- conditioning -- Toeplitz matrix -- matrix nearness problem -- distance to normality -- inverse eigenvalue problem -- Krylov subspace bases -- Tikhonov regularization; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.1811
• Languages: English
• ISSNs: 1070-5325

Abstract

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.