Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

Limits on the number of function evaluations required by certain high-dimensional integration rules of hypercubic symmetry


Author: J. N. Lyness
Journal: Math. Comp. 19 (1965), 638-643
MSC: Primary 65.55
DOI: https://doi.org/10.1090/S0025-5718-1965-0199961-5
MathSciNet review: 0199961
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider an $ n$-dimensional integration rule $ R_t^{(n)}$ of degree $ 2t - 1$ and of hypercubic symmetry. We derive theorems which set a lower bound in terms of $ n$ and $ t$ on the number of function evaluations such a rule requires. These results apply to spaces of integration which have hypercubic symmetry. In certain cases this bound is very close to the number of points required by a known rule.


References [Enhancements On Off] (What's this?)

  • [1] J. N. Lyness, "Symmetric integration rules for hypercubes. I. Error coefficients," Math. Comp., v. 19, 1965, pp. 260-276. MR 0201067 (34:952)
  • [2] 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)
  • [3] J. N. Lyness, "Symmetric integration rules for hypercubes. III. Construction of integration rules using null rules," Math. Comp., v. 19, 1965, pp. 625-637. MR 0201069 (34:954)
  • [4] J. N. Lyness, "Integration rules of hypercubic symmetry over a certain spherically symmetric space," Math. Comp., v. 19, 1965 pp. 471-476. MR 0201070 (34:955)
  • [5] A. H. Stroud & D. Secrest, "Approximate integration formulas for certain spherically symmetric regions," Math. Comp., v. 17, 1963, pp. 105-135. MR 28 #4677. MR 0161473 (28:4677)

Similar Articles

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/S0025-5718-1965-0199961-5
Article copyright: © Copyright 1965 American Mathematical Society

American Mathematical Society