Algorithm 824: CUBPACK: a package for automatic cubature; framework description

ABSTRACT

CUBPACK aims to offer a collection of re-usable code for automatic n-dimensional (n ≥ 1) numerical integration of functions over a collection of regions, i.e., quadrature and cubature. The current version allows this region to consist of a union of n-simplices and n-parellellepids. The framework of CUBPACK is described as well as its user interface. The functionality of several well known routines is embedded. New features include integration algorithms using the ε-algorithm for extrapolation for regions other than triangles and the implementation of a new type of subdivision for 3-cubes.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.4 Quadrature and Numerical Differentiation
          Subjects: Adaptive and iterative quadrature

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.4 Quadrature and Numerical Differentiation
          Subjects: Multidimensional (multiple) quadrature
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Efficiency; Reliability and robustness

General Terms:
Algorithms

Keywords:
Automatic integration, cubature, quadrature