Quadrature rules from finite orthogonality relations for Bernstein-Szegö polynomials

Quadrature rules from finite orthogonality relations for Bernstein-Szegö polynomials

We glue two families of Bernstein-Szegö polynomials to construct the eigenbasis of an associated finite-dimensional Jacobi matrix. This gives rise to finite orthogonality relations for this composite eigenbasis of Bernstein-Szegö polynomials. As an application, a number of Gauss-like quadrature rule...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2018-12, Vol.146 (12), p.5333-5347
Hauptverfasser: van Diejen, J. F., Emsiz, E.
Format: Artikel
Sprache:eng
Schlagworte:
C. APPLIED MATHEMATICS
Research article
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Zusammenfassung:We glue two families of Bernstein-Szegö polynomials to construct the eigenbasis of an associated finite-dimensional Jacobi matrix. This gives rise to finite orthogonality relations for this composite eigenbasis of Bernstein-Szegö polynomials. As an application, a number of Gauss-like quadrature rules are derived for the exact integration of rational functions with prescribed poles against the Chebyshev weight functions.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/14186