Abstract
In this paper we consider the spectrum and quasi-eigenvalues of a family of banded Toeplitz matrices and define their extensions to the generalized eigenvalue problem. A diagonal similarity transformation on such matrices that allows a suitable modification of the region containing the quasi-eigenvalues is reported. Two kind of applications have been analyzed: the computation of the eigenvalues and the asymptotic spectra of Toeplitz matrices and the solution of block banded quasi-Toeplitz linear systems that arise after the discretization of an ODE using a boundary value method.
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Iavernaro, F., Mazzia, F. & Trigiante, D. Eigenvalues and Quasi-Eigenvalues of Banded Toeplitz Matrices: Some Properties and Applications. Numerical Algorithms 31, 157–170 (2002). https://doi.org/10.1023/A:1021197900145
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DOI: https://doi.org/10.1023/A:1021197900145