r2d2lri

$r2d2lri$ is a non-adaptive algorithm implemented in C++ for performing automatic cubature over a wide variety of finite and non-finite two-dimensional domains. The core integrator uses a sixth-order Sidi transformation applied to a sequence of embedded lattice rules in such a fashion as to incur virtually no computational overhead. Even for integrals over non-finite domains, for which several non-finite to finite transformations may be attempted, the algorithm remains very fast. Performance data are presented which demonstrate both the effectiveness and efficiency of $r2d2lri$, taking into account the number of function evaluations needed and the execution speed. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

Keywords for this software

Anything in here will be replaced on browsers that support the canvas element

References in zbMATH (referenced in 11 articles , 1 standard article )

Showing results 1 to 11 of 11.
Sorted by year (citations)

  1. Li, Tiancheng; Robinson, Ian: Algorithm 906: \textitelrint3d -- a three-dimensional nonadaptive automatic cubature routine using a sequence of embedded lattice rules (2010)
  2. Cools, Roland; Nuyens, Dirk: A Belgian view on lattice rules (2008)
  3. Sidi, Avram: Further extension of a class of periodizing variable transformations for numerical integration (2008)
  4. Li, Tiancheng; Robinson, Ian: The search for a good lattice augmentation sequence in three dimensions (2007) ioport
  5. Li, Tiancheng; Robinson, Ian; Hill, Michael: The index of merit of (k)th-copy integration lattices (2007)
  6. Sidi, Avram: A novel class of symmetric and nonsymmetric periodizing variable transformations for numerical integration (2007)
  7. Hill, M.; Robinson, I.: Quadrature using 64-bit IEEE arithmetic for integrands over [0,1] with a singularity at 1 (2006)
  8. Sidi, Avram: Extension of a class of periodizing variable transformations for numerical integration (2006)
  9. Sidi, Avram: Numerical integration over smooth surfaces in (\mathbbR^3) via class (\mathcalI_m) variable transformations. I: Smooth integrands (2005)
  10. Hill, Michael; Robinson, Ian: A comparison of strategies for the automatic computation of two-dimensional integrals over infinite domains (2003)
  11. Robinson, Ian; Hill, Michael: Algorithm 816: \textitr2d2lri: an algorithm for automatic two-dimensional cubature (2002)