Zeros of quasiparaorthogonal polynomials and positive quadrature
Abstract
In this paper we illustrate that paraorthogonality on the unit circle $\mathbb{T}$ is the counterpart to orthogonality on $\mathbb{R}$ when we are interested in the spectral properties. We characterize quasiparaorthogonal polynomials on the unit circle as the analogues of the quasiorthogonal polynomials on $\mathbb{R}$. We analyze the possibilities of preselecting some of its zeros, in order to build positive quadrature formulas with prefixed nodes and maximal domain of validity. These quadrature formulas on the unit circle are illustrated numerically.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.10460
 Bibcode:
 2021arXiv211010460B
 Keywords:

 Mathematics  Numerical Analysis;
 65D32;
 30C10;
 33C47