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Some fourth degree integration formulas for simplexes

Author: A. H. Stroud
Journal: Math. Comp. 30 (1976), 291-294
MSC: Primary 65D30
MathSciNet review: 0391484
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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 [Enhancements On Off] (What's this?)

  • [1] 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)
  • [2] R. Lauffer, Interpolation mehrfacher Integrale, Arch. Math. 6 (1955), 159–164 (German). MR 0068307
  • [3] J. N. Lyness and D. Jespersen, Moderate degree symmetric quadrature rules for the triangle, J. Inst. Math. Appl. 15 (1975), 19–32. MR 0378368
  • [4] A. H. Stroud, Approximate calculation of multiple integrals, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. Prentice-Hall Series in Automatic Computation. MR 0327006

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Keywords: Numerical integration, integration formulas, simplexes
Article copyright: © Copyright 1976 American Mathematical Society