Quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity

@article{Bultheel2009QuadratureFO,
  title={Quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity},
  author={Adhemar Bultheel and Leyla Daruis and Pablo Gonz{\'a}lez-Vera},
  journal={J. Comput. Appl. Math.},
  year={2009},
  volume={231},
  pages={948-963}
}

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References

SHOWING 1-10 OF 37 REFERENCES
Rational quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity
This paper is concerned with rational Szegő quadrature formulas to approximate integrals of the form I μ (f) = ∫ π ―π f(e iθ )dμ(θ) by a formula such as I n (f) = Σ n k=1 λ k f(z k ), where the
Szegö quadrature formulas for certain Jacobi-type weight functions
In this paper we are concerned with the estimation of integrals on the unit circle of the form ∫02π f(eiθ)ω(θ)dθ by means of the so-called Szego quadrature formulas, i.e., formulas of the type Σj=1n
Bounds for remainder terms in Szego¨ quadrature on the unit circle
This paper deals with Szego quadrature for integration around the unit circle in the complex plane. Nodes for the quadrature formulas are the zeros ζ j (n) ( w n), j = 1,2,…, n, of para-orthogonal
Orthogonal rational functions and quadrature on the unit circle
TLDR
In order to get nodes {xj(n)} of modulus 1 and positive weightsAj( n), it will be fundamental to use rational functions orthogonal on the unit circle analogous to Szegő polynomials.
Domain of validity of Szegö quadrature formulas
Rational quadrature formulae on the unit circle with arbitrary poles
TLDR
Interpolatory quadrature rules exactly integrating rational functions on the unit circle are considered and a computable upper bound of the error is obtained which is valid for any choice of poles, arbitrary weight functions and any degree of exactness.
Orthogonality and quadrature on the unit circle
In a recent paper, Jones et a1. (see [1)) deal with a classical topic, namely "Quadratures on the unit circle" from a new point of view. They introduce the concept of "a sequence of para-orthogonal
On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle
TLDR
The convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [−π, π] results in quadrature formulas which integrate exactly certain rational functions.
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