Mathematical Notes

, Volume 61, Issue 5, pp 614–620 | Cite as

Invariant cubature formulas for the hyperoctahedron

  • S. B. Stoyanova
Article

Abstract

Cubature formulas for calculating integrals over the hyperoctahedron that are invariant under the group of all of its orthogonal transformations are obtained. Two of them are exact for all polynomials of degree no greater than seven and one is exact for all polynomials of degree no greater than five.

Key words

cubature formulas polynomials invariance under symmetries hyperoctahedron 

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References

  1. 1.
    I. P. Mysovskikh,Interpolational Cubature Formulas [in Russian], Nauka, Moscow (1981).Google Scholar
  2. 2.
    A. H. Stroud,Approximate Calculation Of Multiple Integrals, Prentice-Hall, Englewood Cliffs, New Jersey (1971).Google Scholar
  3. 3.
    S. L. Sobolev, “On formulas of mechanical cubatures on the surface of the sphere,”Sibirsk. Mat. Zh. [Siberian Math. J.],3, No. 4, 769–796 (1962).MATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • S. B. Stoyanova
    • 1
  1. 1.Technical UniversityVarnaBulgaria

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