Title: A connection between quadrature formulas on the unit circle and the interval [-1,1]
Authors: Bultheel, Adhemar ×
Daruis, Leila
González-Vera, Pablo #
Issue Date: Jul-2001
Publisher: Elsevier
Series Title: Journal of computational and applied mathematics vol:132 issue:1 pages:1-14
Abstract: We establish a relation between Gauss quadrature formulas on the interval [-1,1] that approximate integrals of the form
I_s(F) = ∫_{x=-1..+1}F(x)s(x) dx
and Szegö quadrature formulas on the unit circle of the complex plane that approximate integrals of the form
I_w(f) = ∫_{t=-π..π} f(e^{it})w(t)dt.
The weight s(x) is positive on [-1,1] while the weight w(t) is positive on [-π,π]. It is shown that if w(t)=s(cos t)|sin t|, then there is an intimate relation between the Gauss and Szegö quadrature formulas. Moreover, as a side result we also obtain an easy derivation for relations between orthogonal polynomials with respect to s(x) and orthogonal Szegö polynomials with respect to w(t). Inclusion of Gauss-Lobatto and Gauss-Radau formulas is natural.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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