Title: Rational quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: Oct-2010
Publisher: Academic Press
Series Title: IMA Journal of Numerical Analysis vol:30 issue:4 pages:940-963
Abstract: This paper is concerned with rational Szegő quadrature formulas to approximate integrals of the form
I_μ(f)=∫_{-π..π} f(exp(iθ)) dμ(θ)
by a formula like
I_n(f)= ∑_{k=1..n} λ_k f(z_k)
where the weights λ_k are positive and the nodes z_k are carefully chosen on the complex unit circle. It will be shown that for a given set of poles, the quadrature formulas can be chosen to be exact in certain subspaces of rational functions of dimension 2n. Also the problem where one node (Radau) or two nodes (Lobatto) are prefixed will be analyzed and the corresponding rational rational Szegő-Radau and rational Szegő-Lobatto quadrature formulas shall be characterized.
Description: Published online 21 August 2009
ISSN: 0272-4979
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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