Testing multidimensional integration routines
Proc. of international conference on Tools, methods and languages for scientific and engineering computation
Lattice methods for multiple integration: theory, error analysis and examples
SIAM Journal on Numerical Analysis
The accuracy of floating point summation
SIAM Journal on Scientific Computing
ParInt: a software package for parallel integration
ICS '96 Proceedings of the 10th international conference on Supercomputing
Minimal cubature formulae of trigonometric degree
Mathematics of Computation
The Mathematica book (4th edition)
The Mathematica book (4th edition)
d2lri: a nonadaptive algorithm for two-dimensional cubature
Journal of Computational and Applied Mathematics - Numerical evaluation of integrals
Algorithm 816: r2d2lri: an algorithm for automatic two-dimensional cubature
ACM Transactions on Mathematical Software (TOMS)
Algorithm 824: CUBPACK: a package for automatic cubature; framework description
ACM Transactions on Mathematical Software (TOMS)
Quadrature using 64-bit IEEE arithmetic for integrands over [0,1] with a singularity at 1
Theoretical Computer Science - Real numbers and computers
The index of merit of kth-copy integration lattices
Journal of Computational and Applied Mathematics
Practical Extrapolation Methods: Theory and Applications
Practical Extrapolation Methods: Theory and Applications
The search for a good lattice augmentation sequence in three dimensions
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part III
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A three-dimensional automatic cubature routine, called elrint3d, is described and numerical results are presented that demonstrate its applicability across a wide range of domains and integrand types. The underlying algorithm is based on a 2s-copy lattice augmentation sequence, the seed lattice for which has been determined by exhaustive search based on optimization of index of merit and trigonometric degree of precision.