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Symmetric cubature formulas for a truncated octahedron

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Abstract

For a truncated octahedron, which can be used to fill the whole space R3 by translating it, we construct symmetric cubature formulas, exact for polynomials of degrees 3, 5, and 7. We furnish estimates of the remainder terms, and we discuss the problem of numerical integration over an arbitrary bounded domain D ⊂ R3.

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Authors and Affiliations

  1. V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, USSR

    A. V. Yakovlev

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  1. A. V. Yakovlev
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Translated from Matematicheskie Zametki, Vol. 14, No. 5, pp. 667–675, November, 1973.

In conclusion I wish to thank S. B. Stechkin for his statement of the problem and for his constant interest in the course of its solution.

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Yakovlev, A.V. Symmetric cubature formulas for a truncated octahedron. Mathematical Notes of the Academy of Sciences of the USSR 14, 943–947 (1973). https://doi.org/10.1007/BF01462254

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  • DOI: https://doi.org/10.1007/BF01462254

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