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Constructing cubature formulae of degree 5 with few points

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
237
Issue
1
Identifiers
DOI: 10.1016/j.cam.2012.06.004
Keywords
  • Fifth Degree Formula
  • Cubature Formula
  • Product Region
  • Spherically Symmetric Region
  • Numerical Integration

Abstract

Abstract This paper is devoted to construct a family of fifth degree cubature formulae for n-cube with symmetric measure and n-dimensional spherically symmetrical region. The formula forn-cube contains at most n2+5n+3 points and for n-dimensional spherically symmetrical region contains only n2+3n+3 points. Moreover, the numbers can be reduced to n2+3n+1 and n2+n+1 if n=7 respectively, the latter of which is minimal.

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