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Mathematics of Computation

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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
MathSciNet review: 0201070
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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.

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Article copyright: © Copyright 1965 American Mathematical Society