Integration over a simplex,truncated cubes,and Eulerian numbers |
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Authors: | I J Good T N Tideman |
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Institution: | (1) Virginia Polytechnic Institute and State University, 24061 Blacksburg, VA, USA |
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Abstract: | Summary A method of integrating a function over a simplex is described in which (i) the simplex is first transformed into a right-angled isosceles simplex; (ii) this simplex is dissected into small cubes and truncated cubes; (iii) the integration over the truncated cubes is performed by the centroid method or by Stroud's method, and this requires the use of formulae for the moments of a truncated cube. These formulae are developed and are expressed in terms of Eulerian numbers. In the special case when the truncated cube is itself a right-angled isoceles simplex a new algorithm is given, depending on the discrete Fourier transform, for calculating the moments as polynomials inn wheren is the dimensionality. |
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Keywords: | AMS: 65D30 05A19 41A55 42A68 50B30 60C05 CR: 5 16 |
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