Title: Positive rational interpolatory quadrature formulas on the unit circle and the interval
Authors: Deckers, Karl ×
Bultheel, Adhemar
Cruz Barroso, Ruyman
Perdomo-Pío, Francisco #
Issue Date: Dec-2010
Publisher: North-Holland
Series Title: Applied Numerical Mathematics vol:60 issue:12 pages:1286-1299
Abstract: We present a relation between rational Gauss-type quadrature formulas that approximate integrals of the form Jμ(F)=∫(F(x)dμ(x), x=−1..1), and rational Szegő quadrature formulas that approximate integrals of the form Iμº(F)=∫(F(eiθ)dμº(θ),x=−π..π). The measures μ and μº are assumed to be positive bounded Borel measures on the interval [−1,1] and the complex unit circle respectively and are related by (μº)'(θ) = μ'(cos θ)|sin θ|. Next, making use of the so-called para-orthogonal rational functions, we obtain a one-parameter family of rational interpolatory quadrature formulas with positive weights for Jμ(F). Finally we include some error estimates and some numerical examples.
ISSN: 0168-9274
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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