Probabilistic analysis of numerical integration algorithms

Feng Gao
1991 Journal of Complexity  
We study the conditional expected error of approximation for a class of adaptive numerical integration algorithms. We analyze a type of divided difference test-an error estimate obtained by replacing the higher derivative of the integrand in the local error remainder term of a quadrature formula by the higher divided differences of the nearby computed integrand values. We show that this type of heuristic error criterion which is consistent with ones used in practical quadrature algorithms, when
more » ... modified, can be used to choose the initial approximation and to serve as the termination and adaptation criterion, with a rigorous mathematical (probabilistic) basis. 6 1991 Academic PESS, IW.
doi:10.1016/0885-064x(91)90044-x fatcat:sqetuwxrk5dzlgoso2jygbrgim