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arXiv · 1902.11062

Quadrature rules from finite orthogonality relations for Bernstein-Szego polynomials

J. F. van Diejen·E. Emsiz
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Abstract

We glue two families of Bernstein-Szego 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-Szego 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.

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J. F. van Diejen, E. Emsiz. 2019-02-28. Quadrature rules from finite orthogonality relations for Bernstein-Szego polynomials. https://doi.org/10.1090/proc%2F14186

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