Positive trigonometric quadrature formulas and quadrature on the unit circle

@article{Peherstorfer2011PositiveTQ,
  title={Positive trigonometric quadrature formulas and quadrature on the unit circle},
  author={Franz Peherstorfer},
  journal={Math. Comput.},
  year={2011},
  volume={80},
  pages={1685-1701}
}
We give several descriptions of positive quadrature formulas which are exact for trigonometric -, respectively, Laurent polynomials of degree less or equal $n-1-m$, $0\leq m\leq n-1$. A complete and simple description is obtained with the help of orthogonal polynomials on the unit circle. In particular it is shown that the nodes polynomial can be generated by a simple recurrence relation. As a byproduct interlacing properties of zeros of para-orthogonal polynomials are obtained. Finally… 
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TRIGONOMETRIC MULTIPLE ORTHOGONAL POLYNOMIALS OF SEMI-INTEGER DEGREE AND THE CORRESPONDING QUADRATURE FORMULAS
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A connection between Szegő-Lobatto and quasi Gauss-type quadrature formulas
Orthogonal polynomials on the unit circle and chain sequences
Zeros of para–orthogonal polynomials and linear spectral transformations on the unit circle
TLDR
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.
Orthogonal polynomials and quadrature rules on the unit circle associated with perturbations of symmetric measures
Para-orthogonal polynomials on the unit circle satisfying three term recurrence formulas
Sieved para-orthogonal polynomials on the unit circle
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