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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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Some fourth degree integration formulas for simplexes
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by A. H. Stroud PDF
Math. Comp. 30 (1976), 291-294 Request permission

Abstract:

A fourth degree integration formula is given for the n-dimensional simplex for $n = 3,4,5,6,7,8,10,11,12$. The formula contains $({n^2} + 3n + 4)/2$ points.
References
    T. M. BYKOVA, "Cubature formulas for computing triple integrals which are exact for fourth degree polynomials and have eleven nodes," Vesci Akad. Navuk BSSR Ser Fīz.-Mat. Navuk, no. 1, v. 1970, pp. 51-54. (Russian)
  • R. Lauffer, Interpolation mehrfacher Integrale, Arch. Math. 6 (1955), 159–164 (German). MR 68307, DOI 10.1007/BF01900222
  • J. N. Lyness and D. Jespersen, Moderate degree symmetric quadrature rules for the triangle, J. Inst. Math. Appl. 15 (1975), 19–32. MR 378368
  • A. H. Stroud, Approximate calculation of multiple integrals, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0327006
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 291-294
  • MSC: Primary 65D30
  • DOI: https://doi.org/10.1090/S0025-5718-1976-0391484-0
  • MathSciNet review: 0391484