Extreme eigenvalues of real symmetric Toeplitz matrices (Q2701556)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extreme eigenvalues of real symmetric Toeplitz matrices |
scientific article |
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19 February 2001
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Toeplitz matrix
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extreme eigenvalues
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odd and even spectra
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spectral equation
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secular equation
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rational approximation
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numerical results
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error analysis
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Extreme eigenvalues of real symmetric Toeplitz matrices (English)
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Spectral equations (with possibly unknown singularities) are used for computing the smallest and largest eigenvalues of real symmetric Toeplitz matrices (other papers on this problem are quoted) from two equations, one for the even and one for the odd eigenvalues, that have already been used by others. The present paper presents a shorter analysis of the rootfinder used in two other works. This also leads to a better stopping rule, based on rational rather than on polynomial approximation. The paper also presents an error analysis not contained in those other works. Numerical results given concern positive semidefinite Toeplitz matrices earlier considered by G. Szegő, Cybenko, and others.
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