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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Symmetric integration rules for hypercubes. II. Rule projection and rule extension

Author: J. N. Lyness
Journal: Math. Comp. 19 (1965), 394-407
MSC: Primary 65.55
MathSciNet review: 0201068
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Abstract: A theory is described which facilitates the construction of highdimensional integration rules. It is found that, for large $ n$, an $ n$-dimensional integration rule of degree $ 2t + 1$ man be constructed requiring a number of function evaluations of order $ {2^t}{n^t}/t!$. In an example we construct a $ 15$-dimensional rule of degree 9 which requires 52,701 function evaluations. The corresponding number for the product Gaussian is $ 3 \times {10^{10}}$.

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PII: S 0025-5718(1965)0201068-5
Article copyright: © Copyright 1965 American Mathematical Society

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