Handling accuracy in Bayesian automatic adaptive quadrature

IWTCP-2; NCTP-39

Adam, Gh^1,2 ; Adam, S.^1,2

Laboratory of Information Technologies, Joint Institute for Nuclear Research, 6 Joliot Curie St., Moscow Region, Dubna

141980, Russia^1

Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 30 Reactorului St., Magurele - Bucharest

077125, Romania^2

关键词: Analysis tools;    Automatic adaptive;    Bayesian;    Bayesian inference;    Floating points;    Mesoscopics;    Reversible addition;    Riemann integral;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/627/1/012010/pdf
DOI  :  10.1088/1742-6596/627/1/012010

来源: IOP

【 摘 要 】

New Bayesian inferences which significantly extend the coverage of the Bayesian automatic adaptive quadrature (BAAQ) approach to the solution of Riemann integrals are reported. The scrutiny of the possible floating-point machine number approximations of abscissa values inside an integration domain unveiled the occurrence of five classes of integration domains entering the quadrature problems: zero-length, open void, microscopic, mesoscopic, macroscopic. Correct approach to the class identifications and class adapted advancement to the solution are described. In the most complex, macroscopic case, the reversible addition of a new decision branch extends the BAAQ approach coverage to both difficult and easy integrals. The reliability of the code used for solving easy integrals was enhanced with four new analysis tools as compared to the standard automatic adaptive quadrature solution.