Quadrature rules from finite orthogonality relations for Bernstein-Szego polynomials
Numerical Analysis
2019-03-01 v1 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.1902.11062,
title = {Quadrature rules from finite orthogonality relations for Bernstein-Szego polynomials},
author = {J. F. van Diejen and E. Emsiz},
journal= {arXiv preprint arXiv:1902.11062},
year = {2019}
}
Comments
15 pages, LaTeX