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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Symmetric integration rules for hypercubes. II. Rule projection and rule extension
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by J. N. Lyness PDF
Math. Comp. 19 (1965), 394-407 Request permission

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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Additional Information
  • © Copyright 1965 American Mathematical Society
  • Journal: Math. Comp. 19 (1965), 394-407
  • MSC: Primary 65.55
  • DOI: https://doi.org/10.1090/S0025-5718-1965-0201068-5
  • MathSciNet review: 0201068