Zeros of quasi-paraorthogonal polynomials and positive quadrature

@article{Bultheel2022ZerosOQ,
  title={Zeros of quasi-paraorthogonal polynomials and positive quadrature},
  author={Adhemar Bultheel and Ruym{\'a}n Cruz-Barroso and Carlos D{\'i}az-Mendoza},
  journal={J. Comput. Appl. Math.},
  year={2022},
  volume={407},
  pages={114039}
}

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Quadrature formula and zeros of para-orthogonal polynomials on the unit circle
Given a probability measure μ on the unit circle T, we study para-orthogonal polynomials Bn(.,w) (with fixed w ∈ T) and their zeros which are known to lie on the unit circle. We focus on the
Zeros of para–orthogonal polynomials and linear spectral transformations on the unit circle
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The interlacing properties of zeros of para–orthogonal polynomials associated with a nontrivial probability measure supported on the unit circle dµ are studied and some results related with the Christoffel transformation are presented.
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It is shown that the nodes polynomial can be generated by a simple recurrence relation and as a byproduct interlacing properties of zeros of para-orthogonal polynomials are obtained.
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