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Quadrature rules from finite orthogonality relations for Bernstein-Szegö polynomials


Authors: J. F. van Diejen and E. Emsiz
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 65D32; Secondary 33C47, 33D45, 47B36
DOI: https://doi.org/10.1090/proc/14186
Published electronically: August 14, 2018
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Abstract: 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.


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Additional Information

J. F. van Diejen
Affiliation: Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile
Email: diejen@inst-mat.utalca.cl

E. Emsiz
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile
Email: eemsiz@mat.uc.cl

DOI: https://doi.org/10.1090/proc/14186
Keywords: Quadrature rules, Bernstein-Szeg\"o polynomials, orthogonality relations, Jacobi matrices
Received by editor(s): January 3, 2018
Received by editor(s) in revised form: April 5, 2018
Published electronically: August 14, 2018
Additional Notes: This work was supported in part by the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) Grants # 1170179 and # 1181046
Communicated by: Mourad Ismail
Article copyright: © Copyright 2018 American Mathematical Society

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