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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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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.
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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