Tridiagonal Toeplitz matrices: properties and novel applications
Copyright policy )Tridiagonal Toeplitz matrices: properties and novel applications
SUMMARYThe 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 theϵ‐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.
- Sapienza University of Rome Italy
- Roma Tre University Italy
- University System of Ohio United States
- Kent State University United States
Numerical computation of eigenvalues and eigenvectors of matrices, Toeplitz, Cauchy, and related matrices, eigenvalue sensitivities, distance to normality, Tikhonov regularization, Numerical computation of matrix norms, conditioning, scaling, eigenvalues, condition numbers, eigenvectors, Numerical solutions to inverse eigenvalue problems, inverse eigenvalue problem, Krylov subspace bases, matrix nearness problem; toeplitz matrix; krylov subspace bases; conditioning; eigenvalues; inverse eigenvalue problem; tikhonov regularization; distance to normality, tridiagonal Toeplitz matrix, pseudospectra, Computational methods for sparse matrices, Ill-posedness and regularization problems in numerical linear algebra, matrix nearness problem
Numerical computation of eigenvalues and eigenvectors of matrices, Toeplitz, Cauchy, and related matrices, eigenvalue sensitivities, distance to normality, Tikhonov regularization, Numerical computation of matrix norms, conditioning, scaling, eigenvalues, condition numbers, eigenvectors, Numerical solutions to inverse eigenvalue problems, inverse eigenvalue problem, Krylov subspace bases, matrix nearness problem; toeplitz matrix; krylov subspace bases; conditioning; eigenvalues; inverse eigenvalue problem; tikhonov regularization; distance to normality, tridiagonal Toeplitz matrix, pseudospectra, Computational methods for sparse matrices, Ill-posedness and regularization problems in numerical linear algebra, matrix nearness problem
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