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Asymptotic eigenvalue expansions for Toeplitz matrices with certain Fisher-Hartwig symbols. (English) Zbl 07798264

Summary: The present paper is a survey of some of the authors’ results on the asymptotic behavior of individual eigenvalues and eigenvectors of sequences of Toeplitz matrices when their size tends to infinity. The symbols of the matrices are supposed to have power singularities and are special cases of so-called Fisher-Hartwig symbols.

MSC:

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

Software:

Eigtool
Full Text: DOI

References:

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