Error expansions for multidimensional trapezoidal rules with Sidi transformations |
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| Authors: | Verlinden P. Potts D.M. Lyness J.N. |
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| Affiliation: | (1) Departement Computerwetenschappen, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium;(2) The James Franck Institute and the Department of Chemistry, The University of Chicago, Chicago, IL 60637, USA;(3) Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Argonne, IL 60439, USA |
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| Abstract: | In 1993, Sidi introduced a set of trigonometric transformations x = ψ(t) that improve the effectiveness of the one-dimensional trapezoidal quadrature rule for a finite interval. In this paper, we extend Sidi's approach to product multidimensional quadrature over [0,1] N . We establish the Euler–Maclaurin expansion for this rule, both in the case of a regular integrand function f(x) and in the cases when f(x) has homogeneous singularities confined to vertices. This revised version was published online in August 2006 with corrections to the Cover Date. |
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| Keywords: | quadrature multidimensional integration cubature Euler– Maclaurin expansion vertex singularity Sidi transformation extrapolation 65D30 |
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