Integration rules of hypercubic symmetry over a certain spherically symmetric space

Author:
J. N. Lyness

Journal:
Math. Comp. **19** (1965), 471-476

MSC:
Primary 65.55

DOI:
https://doi.org/10.1090/S0025-5718-1965-0201070-3

MathSciNet review:
0201070

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A theory of integration rules suitable for integration over a hypercube and having hypercubic symmetry has recently been published. In this paper it is found that, with minor modification, this theory may be directly applied to obtain integration rules of hypercubic symmetry suitable for integration over a complete -dimensional space with the weight function . As in the case of integration over hypercubes, an -dimensional rule of degree may be constructed requiring a number of function evaluations of order , only.

**[1]**Z. Kopal,*Numerical Analysis*, Wiley, New York and Chapman and Hall, London, 1955. MR**17**, 1007. MR**0077213 (17:1007c)****[2]**J. N. Lyness, ``Symmetric integration rules for hypercubes. I, Error coefficients,''*Math. Comp.*, v. 19, 1965, pp. 260-276. MR**0201067 (34:952)****[3]**J. N. Lyness, ``Symmetric integration rules for hypercubes. II. Rule projection and rule extension,''*Math. Comp.*, v. 19, 1965, pp. 394-407. MR**0201068 (34:953)****[4]**A. H. Stroud & D. Secrest, ``Approximate integration formulas for certain spherically symmetric regions,''*Math. Comp.*, v. 17, 1963, pp. 105-135. MR**0161473 (28:4677)****[5]**H. C. Thacher, Jr., ``Optimum quadrature formulas in dimensions,''*MTAC*, v. 11, 1957, pp. 189-194.

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/S0025-5718-1965-0201070-3

Article copyright:
© Copyright 1965
American Mathematical Society