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} }
14 Citations
On Gauss-type quadrature formulas with prescribed nodes anywhere on the real line
- Mathematics, Computer Science
- 2008
In this paper, quadrature formulas on the real line with the highest degree of accuracy, with positive weights, and with one or two prescribed nodes anywhere on the interval of integration are…
Computation of Gauss-type quadrature formulas with some preassigned nodes
- Computer Science, Mathematics
- 2010
This work will add to the above quadratures an extra fixed node in (a, b) and take advantage of the so-called Szeg˝o-Lobatto quadrature rules recently introduced in [27] and [6].
A connection between Szegő-Lobatto and quasi Gauss-type quadrature formulas
- MathematicsJ. Comput. Appl. Math.
- 2015
On Gausstype Gausstype Gausstype quadrature formulas with prescribed nodes anywhere on the real line
- Computer Science, Mathematics
- 2008
In this paper, quadrature formulas on the real line with the highest degree of accuracy, with positive weights, and with one or two prescribed nodes anywhere on the interval of integration are…
Zeros of quasi-paraorthogonal polynomials and positive quadrature
- MathematicsJ. Comput. Appl. Math.
- 2022
Orthogonality, interpolation and quadratures on the unit circle and the interval [-1, 1]
- MathematicsJ. Comput. Appl. Math.
- 2010
On the computation of symmetric Szeg˝o-type quadrature formulas
- Mathematics
- 2010
By z = ei and x = cos , one may relate x ∈ I = (−1, 1], with ∈ (−, ]
and a point z on the complex unit circle T. Hence there is a connection between
the integrals of 2-periodic functions,…
On the computation of the Fourier transform under the presence of nearby polar singularities
- Mathematics
- 2011
In this paper we present a procedure for the computation of integrals on the whole real line with nearby singularities. The method is based in collecting the possible singularities of the integrand…
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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…
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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…
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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
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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.
Rational quadrature formulae on the unit circle with arbitrary poles
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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
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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
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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.