Eigenvectors of Hermitian Toeplitz matrices with smooth simple-loop symbols

DOI10.1016/j.laa.2015.12.017zbMath1331.47046OpenAlexW2236529324MaRDI QIDQ905747

J. M. Bogoya, Sergei M. Grudsky, Egor A. Maksimenko, Albrecht Böttcher

Publication date: 28 January 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2015.12.017

zbMATH Keywords

asymptotic expansionToeplitz matrixspectral asymptoticseigenfunction

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (12)

Spectral properties of Kac-Murdock-Szegö matrices with a complex parameter ⋮ Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices ⋮ Distribution of eigenvalues of Toeplitz matrices with smooth entries ⋮ Computation of asymptotic spectral distributions for sequences of grid operators ⋮ Eigenvalue bifurcations in Kac-Murdock-Szegő matrices with a complex parameter ⋮ On the inversion of the block double-structured and of the triple-structured Toeplitz matrices and on the corresponding reflection coefficients ⋮ Eigenvalue contour lines of Kac-Murdock-Szegő matrices with a complex parameter ⋮ On the \(\ell^\infty\)-norms of the singular vectors of arbitrary powers of a difference matrix with applications to sigma-delta quantization ⋮ On the structure of the inverse to Toeplitz-block Toeplitz matrices and of the corresponding polynomial reflection coefficients ⋮ Fast Toeplitz eigenvalue computations, joining interpolation-extrapolation matrix-less algorithms and simple-loop theory ⋮ Fine spectral estimates with applications to the optimally fast solution of large FDE linear systems ⋮ Asymptotics of eigenvalues for Toeplitz matrices with rational symbols that have a minimum of the 4th order

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