Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

DOI10.1088/1742-5468/2009/05/P05012zbMath1456.15005arXiv0901.3436OpenAlexW3098636058MaRDI QIDQ3301058

Hui Dai, Zachary Geary, Leo P. Kadanoff

Publication date: 11 August 2020

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.3436

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Applications of operator theory in the physical sciences (47N50) Eigenvalues, singular values, and eigenvectors (15A18) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (13)

The part of my path I walked together with Sergei Grudsky ⋮ Eigenpairs of Toeplitz and disordered Toeplitz matrices with a Fisher-Hartwig symbol ⋮ Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices ⋮ A Fast Contour-Integral Eigensolver for Non-Hermitian Matrices ⋮ Asymptotics of eigenvectors of large symmetric banded Toeplitz matrices ⋮ Eigenvectors of Hessenberg Toeplitz matrices and a problem by Dai, Geary, and Kadanoff ⋮ Asymptotic eigenvalue expansions for Toeplitz matrices with certain Fisher-Hartwig symbols ⋮ Fast Non-Hermitian Toeplitz Eigenvalue Computations, Joining Matrixless Algorithms and FDE Approximation Matrices ⋮ Eigenvalues of Hermitian Toeplitz matrices with smooth simple-loop symbols ⋮ Band Toeplitz preconditioners for non-symmetric real Toeplitz systems by preconditioned GMRES method ⋮ Asymptotics of eigenvalues of large symmetric Toeplitz matrices with smooth simple-loop symbols ⋮ Iterative deconvolution for kernels with strictly positive Fourier transforms ⋮ Circulant L-ensembles in the thermodynamic limit

Cites Work

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• Introduction to large truncated Toeplitz matrices
• The Fisher-Hartwig conjecture and Toeplitz eigenvalues
• Asymptotic behavior of Toeplitz matrices and determinants
• Applications and generalizations of Fisher–Hartwig asymptotics
• Toeplitz Determinants with Singular Generating Functions

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