Symmetric quadrature formulae for simplexes

Author:
P. Silvester

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

MSC:
Primary 65.55

MathSciNet review:
0258283

Full-text PDF Free Access

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 3 for simplexes*, Math. Comp.**18**(1964), 590–597. MR**0169378**, 10.1090/S0025-5718-1964-0169378-7**[2]**Preston C. Hammer and Arthur H. Stroud,*Numerical integration over simplexes*, Math. Tables Aids Comput.**10**(1956), 137–139. MR**0086390**, 10.1090/S0025-5718-1956-0086390-2**[3]**P. C. Hammer, O. J. Marlowe, and A. H. Stroud,*Numerical integration over simplexes and cones*, Math. Tables Aids Comput.**10**(1956), 130–137. MR**0086389**, 10.1090/S0025-5718-1956-0086389-6**[4]**Eugene Isaacson and Herbert Bishop Keller,*Analysis of numerical methods*, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR**0201039****[5]**Gilbert C. Best,*Helpful formulas for integrating polynomials in three dimensions*, Math. Comp.**18**(1964), 310–312. MR**0185801**, 10.1090/S0025-5718-1964-0185801-6

Retrieve articles in *Mathematics of Computation*
with MSC:
65.55

Retrieve articles in all journals with MSC: 65.55

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