Limits on the number of function evaluations required by certain high-dimensional integration rules of hypercubic symmetry
HTML articles powered by AMS MathViewer
- by J. N. Lyness PDF
- Math. Comp. 19 (1965), 638-643 Request permission
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
- J. N. Lyness, Symmetric integration rules for hypercubes. I. Error coefficients, Math. Comp. 19 (1965), 260–276. MR 201067, DOI 10.1090/S0025-5718-1965-0201067-3
- J. N. Lyness, Symmetric integration rules for hypercubes. II. Rule projection and rule extension, Math. Comp. 19 (1965), 394–407. MR 201068, DOI 10.1090/S0025-5718-1965-0201068-5
- J. N. Lyness, Symmetric integration rules for hypercubes. III. Construction of integration rules using null rules, Math. Comp. 19 (1965), 625–637. MR 201069, DOI 10.1090/S0025-5718-1965-0201069-7
- J. N. Lyness, Integration rules of hypercubic symmetry over a certain spherically symmetric space, Math. Comp. 19 (1965), 471–476. MR 201070, DOI 10.1090/S0025-5718-1965-0201070-3
- A. H. Stroud and Don Secrest, Approximate integration formulas for certain spherically symmetric regions, Math. Comp. 17 (1963), 105–135. MR 161473, DOI 10.1090/S0025-5718-1963-0161473-0
Additional Information
- © Copyright 1965 American Mathematical Society
- 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