Tools for determining the asymptotic spectral distribution of non-Hermitian perturbations of Hermitian matrix-sequences and applications

DOI10.1007/s00020-014-2157-6zbMath1337.47045OpenAlexW2060156709MaRDI QIDQ2253783

Carlo Garoni, Debora Sesana, Stefano Serra Capizzano

Publication date: 12 February 2015

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

Full work available at URL: https://doi.org/10.1007/s00020-014-2157-6

zbMATH Keywords

perturbationsstiffness matrixblock Toeplitz matrixJacobi matrixtrace normasymptotic eigenvalue distribution

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

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Cites Work

• On the spectrum of stiffness matrices arising from isogeometric analysis
• The asymptotic properties of the spectrum of nonsymmetrically perturbed Jacobi matrix sequences
• Tools for the eigenvalue distribution in a non-Hermitian setting
• Introduction to large truncated Toeplitz matrices
• Influence of matrix operations on the distribution of eigenvalues and singular values of Toeplitz matrices
• A unifying approach to some old and new theorems on distribution and clustering
• Mass concentration in quasicommutators of Toeplitz matrices
• A note on the spectral distribution of toeplitz matrices
• Asymptotic Spectra of Hermitian Block Toeplitz Matrices and Preconditioning Results
• Spectral Properties of Banded Toeplitz Matrices
• Distribution results on the algebra generated by Toeplitz sequences: A finite-dimensional approach
• Spectral behavior of matrix sequences and discretized boundary value problems
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