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Mathematics of Computation

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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
MathSciNet review: 0199961
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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.

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Article copyright: © Copyright 1965 American Mathematical Society