Title: Rational interpolation: II. Quadrature and convergence
Authors: Deckers, Karl ×
Bultheel, Adhemar #
Issue Date: Jan-2013
Publisher: Elsevier
Series Title: Journal of Mathematical Analysis and Applications vol:397 issue:1 pages:124-141
Abstract: Consider an nth rational interpolatory quadrature rule J_n(f;σ) = Σ {L_j f(x_j); j=1..n} to approximate integrals of the form J(f;σ) = ∫{f(x)dσ(x); x=-1..1}, where σ is a (possibly complex) bounded measure with infinite support on the interval [−1,1]. First, we discuss the connection of J_n(f;σ) with certain rational interpolatory quadratures on the complex unit circle to approximate integrals of the form ∫{fₒ(exp(iθ))dσₒ(θ):θ=-π..π} where σₒ is a (possibly complex) bounded measure with infinite support on [−π,π]. Next, we provide conditions to ensure the convergence of J_n(f;σ) to J(f;σ) for n tending to infinity. Finally, an upper bound for the error on the nth approximation and an estimate for the rate of convergence is provided.
ISSN: 0022-247X
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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