The Asymptotic Spectra of Banded Toeplitz and Quasi-Toeplitz Matrices

DOI10.1137/0914059zbMath0788.65049OpenAlexW2048683800MaRDI QIDQ3140149

Robert F. Warming, Richard M. Beam

Publication date: 30 May 1994

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/338c4e56e76984c9c76ccafbf84c18cc1f29f95d

zbMATH Keywords

eigenvectorsasymptotic spectrafinite differenceQR algorithmdiagonal scalingquasi-Toeplitz matriceseigenvalue algorithms

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (24)

On large Toeplitz band matrices with an uncertain block ⋮ Eigenvalue clusters of large tetradiagonal Toeplitz matrices ⋮ A fast algorithm for solving diagonally dominant symmetric quasi-pentadiagonal Toeplitz linear systems ⋮ Infinite Toeplitz and Laurent matrices with localized impurities ⋮ The spectra of large Toeplitz band matrices with a randomly perturbed entry ⋮ Unnamed Item ⋮ High-order transverse schemes for the numerical solution of PDEs ⋮ The conditioning of Toeplitz band matrices ⋮ A fast method for solving quasi-pentadiagonal Toeplitz linear systems and its application to the Lax-Wendroff scheme ⋮ Generalized second derivative linear multistep methods based on the methods of Enright ⋮ Continuous spectra and numerical eigenvalues ⋮ Stability analysis of the numerical method of characteristics applied to a class of energy-preserving hyperbolic systems. II: Nonreflecting boundary conditions ⋮ Integer powers of anti-tridiagonal matrices of the form antitridiag_n(a,c,−a),a,c∈ ℂ ⋮ Unnamed Item ⋮ A fast method for solving a block tridiagonal quasi-Toeplitz linear system ⋮ Non-self-adjoint Toeplitz matrices whose principal submatrices have real spectrum ⋮ Eigenvalues and pseudo-eigenvalues of Toeplitz matrices ⋮ Free fermions behind the disguise ⋮ Spectral approximation of banded Laurent matrices with localized random perturbations ⋮ Upper Hessenberg and Toeplitz Bohemian matrix sequences: a note on their asymptotical eigenvalues and singular values ⋮ A matrix-less method to approximate the spectrum and the spectral function of Toeplitz matrices with real eigenvalues ⋮ The structured distance to normality of banded Toeplitz matrices ⋮ Exact solution of corner-modified banded block-Toeplitz eigensystems ⋮ Can spectral value sets of Toeplitz band matrices jump?

This page was built for publication: The Asymptotic Spectra of Banded Toeplitz and Quasi-Toeplitz Matrices