Practical error estimation in adaptive multidimensional quadrature routines
Journal of Computational and Applied Mathematics
An adaptive algorithm for the approximate calculation of multiple integrals
ACM Transactions on Mathematical Software (TOMS)
Comments on the Nature of Automatic Quadrature Routines
ACM Transactions on Mathematical Software (TOMS)
Certification of algorithm 145: adaptive numerical integration by Simpson's rule
Communications of the ACM
Algorithm 706: DCUTRI: an algorithm for adaptive cubature over a collection of triangles
ACM Transactions on Mathematical Software (TOMS)
Algorithm 720: An algorithm for adaptive cubature over a collection of 3-dimensional simplices
ACM Transactions on Mathematical Software (TOMS)
Implementation of a lattice method for numerical multiple integration
ACM Transactions on Mathematical Software (TOMS)
Algorithm 764: Cubpack++: a C++ package for automatic two-dimensional cubature
ACM Transactions on Mathematical Software (TOMS)
Local error estimates and regularity tests for the implementation of double adaptive quadrature
ACM Transactions on Mathematical Software (TOMS)
An adaptive numerical cubature algorithm for simplices
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Algorithm 868: Globally doubly adaptive quadrature—reliable Matlab codes
ACM Transactions on Mathematical Software (TOMS)
Vectorized adaptive quadrature in MATLAB
Journal of Computational and Applied Mathematics
Generalisations of the compound trapezoidal rule
Applied Numerical Mathematics
Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants
ACM Transactions on Mathematical Software (TOMS)
Edge Detection by Adaptive Splitting
Journal of Scientific Computing
A review of error estimation in adaptive quadrature
ACM Computing Surveys (CSUR)
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A new algorithm for estimating the error in quadrature approximations is presented. Based on the same integrand evaluations that we need for approximating the integral, one may, for many quadrature rules, compute a sequence of null rule approximations. These null rule approximations are then used to produce an estimate of the local error. The algorithm allows us to take advantage of the degree of precision of the basic quadrature rule. In the experiments we show that the algorithm works satisfactorily for a selection of different quadrature rules on all test families of integrals.