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.
This software is also peer reviewed by journal TOMS.
Keywords for this software
References in zbMATH (referenced in 11 articles , 1 standard article )
Showing results 1 to 11 of 11.
Sorted by year (- Li, Tiancheng; Robinson, Ian: Algorithm 906: \textitelrint3d -- a three-dimensional nonadaptive automatic cubature routine using a sequence of embedded lattice rules (2010)
- Cools, Roland; Nuyens, Dirk: A Belgian view on lattice rules (2008)
- Sidi, Avram: Further extension of a class of periodizing variable transformations for numerical integration (2008)
- Li, Tiancheng; Robinson, Ian: The search for a good lattice augmentation sequence in three dimensions (2007) ioport
- Li, Tiancheng; Robinson, Ian; Hill, Michael: The index of merit of (k)th-copy integration lattices (2007)
- Sidi, Avram: A novel class of symmetric and nonsymmetric periodizing variable transformations for numerical integration (2007)
- Hill, M.; Robinson, I.: Quadrature using 64-bit IEEE arithmetic for integrands over [0,1] with a singularity at 1 (2006)
- Sidi, Avram: Extension of a class of periodizing variable transformations for numerical integration (2006)
- Sidi, Avram: Numerical integration over smooth surfaces in (\mathbbR^3) via class (\mathcalI_m) variable transformations. I: Smooth integrands (2005)
- Hill, Michael; Robinson, Ian: A comparison of strategies for the automatic computation of two-dimensional integrals over infinite domains (2003)
- Robinson, Ian; Hill, Michael: Algorithm 816: \textitr2d2lri: an algorithm for automatic two-dimensional cubature (2002)