Handling accuracy in Bayesian automatic adaptive quadrature. (June 2015) - Adam, Gh; Adam, S
Abstract: 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.