Journal
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Volume 20, Issue 2, Pages 302-326Publisher
WILEY
DOI: 10.1002/nla.1811
Keywords
eigenvalues; conditioning; Toeplitz matrix; matrix nearness problem; distance to normality; inverse eigenvalue problem; Krylov subspace bases; Tikhonov regularization
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Funding
- SAPIENZA Universita di Roma
- NSF [DMS-1115385]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1115385] Funding Source: National Science Foundation
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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.
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