Orthogonal polynomials on the unit circle: distribution of zeros (Q1184791)
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scientific article; zbMATH DE number 35019
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Orthogonal polynomials on the unit circle: distribution of zeros |
scientific article; zbMATH DE number 35019 |
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Orthogonal polynomials on the unit circle: distribution of zeros (English)
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28 June 1992
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The paper deals with some results concerning the location of the zeros of orthogonal polynomials with respect to a real measure supported on the unit circle. A characterization of these zeros as eigenvalues of a Hessenberg matrix is given. Also, an analog of the quadrature formula is stated. Its connection with the Gohberg-Semencul formula is deduced. Finally, some numerical examples concerning the distribution of zeros in terms of the reflection parameters (the values at \(z=0\) of the monic orthogonal polynomials) are presented.
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Toeplitz matrices
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zeros of orthogonal polynomials
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Hessenberg matrix
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quadrature formula
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Gohberg-Semencul formula
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