Symmetric quadrature formulae for simplexes

Author:
P. Silvester

Journal:
Math. Comp. **24** (1970), 95-100

MSC:
Primary 65.55

DOI:
https://doi.org/10.1090/S0025-5718-1970-0258283-6

MathSciNet review:
0258283

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Abstract | References | Similar Articles | Additional Information

Abstract: Symmetrie interpolation polynomials are defined for -dimensional simplexes with the aid of a symmetric coordinate notation. These polynomials are used to produce symmetric interpolatory quadrature formulae of arbitrary degree of precision over simplexes of arbitrary dimensionality. Tabulated values of weight coefficients are given for triangles and tetrahedra.

**[1]**A. H. Stroud, "Approximate integration formulas of degree for simplexes,"*Math. Comp.*, v. 18, 1964, pp. 590-597. MR**29**#6628. MR**0169378 (29:6628)****[2]**P. C. Hammer & A. H. Stroud, "Numerical integration over simplexes,"*MTAC*, v. 10, 1956, pp. 137-139. MR**19**, 177. MR**0086390 (19:177f)****[3]**P. C. Hammer, O. J. Marlowe & A. H. Stroud, "Numerical integration over simplexes and cones,"*MTAC*, v. 10, 1956, pp. 130-137. MR**19**, 177. MR**0086389 (19:177e)****[4]**E. Isaacson & H. B. Keller,*Analysis of Numerical Methods*, Wiley, New York, 1966. MR**34**#924. MR**0201039 (34:924)****[5]**G. C. Best, "Helpful formulas for integrating polynomials in three dimensions,"*Math. Comp.*, v. 18, 1964, pp. 310-312. MR**32**#3261. MR**0185801 (32:3261)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0258283-6

Keywords:
Quadrature formulae,
interpolation polynomials,
Newton-Cotes quadrature,
multivariate interpolation,
multivariate quadrature

Article copyright:
© Copyright 1970
American Mathematical Society