Tridiagonal Toeplitz matrices: properties and novel applications

作者：Silvia Noschese, Lionello Pasquini, Lothar Reichel · 发表于：Numerical Linear Algebra with Applications · 年份：2012 · DOI：10.1002/nla.1811 · 被引用次数：228 · 研究领域：Matrix Theory and Algorithms、Numerical methods in inverse problems、Electromagnetic Scattering and Analysis

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.