Integration rules of hypercubic symmetry over a certain spherically symmetric space
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- by J. N. Lyness PDF
- Math. Comp. 19 (1965), 471-476 Request permission
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 $n$-dimensional space with the weight function $\exp ( - {x_1}^2 - {x_2}^2 \cdot \cdot \cdot - {x_n}^2)$. As in the case of integration over hypercubes, an $n$-dimensional rule of degree $2t + 1$ may be constructed requiring a number of function evaluations of order ${2^t}{n^t}/t!$, only.References
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- 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
- 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 H. C. Thacher, Jr., “Optimum quadrature formulas in $s$ dimensions,” MTAC, v. 11, 1957, pp. 189–194.
Additional Information
- © Copyright 1965 American Mathematical Society
- 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