Spectral approximation of banded Laurent matrices with localized random perturbations

DOI10.1007/BF01275512zbMath0995.47021OpenAlexW2093841084MaRDI QIDQ5957556

Albrecht Böttcher, Marko Lindner, Mark Embree

Publication date: 21 October 2002

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01275512

zbMATH Keywords

random perturbationsFourier coefficientsbanded Laurent matrixcirculant matricespectral approximation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Eigenvalues, singular values, and eigenvectors (15A18) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Random linear operators (47B80)

Related Items (7)

Infinite Toeplitz and Laurent matrices with localized impurities ⋮ The spectra of large Toeplitz band matrices with a randomly perturbed entry ⋮ Centrality Analysis for Modified Lattices ⋮ Coburn's lemma and the finite section method for random Jacobi operators ⋮ Pseudoergodic operators and periodic boundary conditions ⋮ Quantitative results for banded Toeplitz matrices subject to random and deterministic perturbations ⋮ Exact solution of corner-modified banded block-Toeplitz eigensystems

Cites Work

• Spectral value sets: A graphical tool for robustness analysis
• Eigenvalues and pseudo-eigenvalues of Toeplitz matrices
• On Szegö's eigenvalue distribution theorem and non-Hermitian kernels
• Pseudospectra and singular values of large convolution operators
• Spectra, pseudospectra, and localization for random bidiagonal matrices
• Spectral value sets of closed linear operators
• Spectral properties of random non-self-adjoint matrices and operators
• The Asymptotic Spectra of Banded Toeplitz and Quasi-Toeplitz Matrices
• The Toeplitz Matrices of an Arbitrary Laurent Polynomial.
• The Anderson Model of Localization: A Challenge for Modern Eigenvalue Methods
• Stability Theory for Difference Approximations of Mixed Initial Boundary Value Problems. I
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