https://doi.org/10.1051/epjconf/201610802003
Summation Paths in Clenshaw-Curtis Quadrature
1 Laboratory of Information Technologies, Joint Institute for Nuclear Research, 6, Joliot Curie St., 141980, Dubna, Moscow Region, Russia
2 Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 30, Reactorului St., Mǎgurele - Bucharest, 077125, Romania
a e-mail: adams@jinr.ru, adams@theory.nipne.ro
b e-mail: adamg@jinr.ru, adamg@theory.nipne.ro
Published online: 9 February 2016
Two topics concerning the use of Clenshaw-Curtis quadrature within the Bayesian automatic adaptive quadrature approach to the numerical solution of Riemann integrals are considered. First, it is found that the efficient floating point computation of the coefficients of the Chebyshev series expansion of the integrand is to be done within a mathematical structure consisting of the union of coefficient families ordered into complete binary trees. Second, the scrutiny of the decay rates of the involved even and odd rank Chebyshev expansion coefficients with the increase of their rank labels enables the definition of Bayesian decision paths for the advancement to the numerical output.
© Owned by the authors, published by EDP Sciences, 2016
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