Interval enclosures for a certain class of multiple integrals

摘要

An interval algorithm for bounding multiple integrals of integrands f: Rn × Rm → R1 over compact rectangular regions in Rm is described. It is supposed that the limits of integration in Rm are constant, that x varies over a rectangular compact subset of Rn and that f(x, y) is continuously differentiable with respect to x and is either once, twice, or four times continuously differentiable with respect to y. A pseudocode Fortran 90 implementation of the algorithm is described and numerical results from Fortran 90 implementations of the algorithm are presented.