Length Scales in Bayesian Automatic Adaptive 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
Published online: 9 February 2016
Two conceptual developments in the Bayesian automatic adaptive quadrature approach to the numerical solution of one-dimensional Riemann integrals [Gh. Adam, S. Adam, Springer LNCS 7125, 1–16 (2012)] are reported. First, it is shown that the numerical quadrature which avoids the overcomputing and minimizes the hidden floating point loss of precision asks for the consideration of three classes of integration domain lengths endowed with specific quadrature sums: microscopic (trapezoidal rule), mesoscopic (Simpson rule), and macroscopic (quadrature sums of high algebraic degrees of precision). Second, sensitive diagnostic tools for the Bayesian inference on macroscopic ranges, coming from the use of Clenshaw-Curtis quadrature, are derived.
© Owned by the authors, published by EDP Sciences, 2016
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