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Asymptotic Spectra of Dense Toeplitz Matrices Are Unstable

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Abstract

The paper is concerned with the limiting set of the eigenvalues of the truncations of an infinite Toeplitz matrix whose symbol is continuous but not rational. This limiting set is shown to be unstable with respect to small perturbations of the symbol in the uniform norm, which reveals that the numerical computation of the asymptotic spectra of dense Toeplitz matrices is a genuine mathematical challenge.

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Authors and Affiliations

  1. Fakultät für Mathematik, TU Chemnitz, 09107, Chemnitz, Germany

    A. Böttcher

  2. Faculty of Mechanics and Mathematics, Rostov-on-Don State University, B. Sadovaya, 105, 344711, Rostov-on-Don, Russia

    S.M. Grudsky

Authors
  1. A. Böttcher
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  2. S.M. Grudsky
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Böttcher, A., Grudsky, S. Asymptotic Spectra of Dense Toeplitz Matrices Are Unstable. Numerical Algorithms 33, 105–112 (2003). https://doi.org/10.1023/A:1025547501771

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  • DOI: https://doi.org/10.1023/A:1025547501771

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