Riemann sums over polytopes
Victor Guillemin[1]; Shlomo Sternberg[2]
- [1] MIT Department of Mathematics Cambridge, MA 02139 (USA)
- [2] Harvard University Department of Mathematics Cambridge, MA 02140 (USA)
Annales de l’institut Fourier (2007)
- Volume: 57, Issue: 7, page 2183-2195
- ISSN: 0373-0956
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topGuillemin, Victor, and Sternberg, Shlomo. "Riemann sums over polytopes." Annales de l’institut Fourier 57.7 (2007): 2183-2195. <http://eudml.org/doc/10294>.
@article{Guillemin2007,
abstract = {It is well-known that the $N$-th Riemann sum of a compactly supported function on the real line converges to the Riemann integral at a much faster rate than the standard $O(1/N)$ rate of convergence if the sum is over the lattice, $Z/N$. In this paper we prove an n-dimensional version of this result for Riemann sums over polytopes.},
affiliation = {MIT Department of Mathematics Cambridge, MA 02139 (USA); Harvard University Department of Mathematics Cambridge, MA 02140 (USA)},
author = {Guillemin, Victor, Sternberg, Shlomo},
journal = {Annales de l’institut Fourier},
keywords = {Riemann sums; Euler-Maclaurin formula for polytopes; Ehrhart’s theorem; Ehrhart's theorem},
language = {eng},
number = {7},
pages = {2183-2195},
publisher = {Association des Annales de l’institut Fourier},
title = {Riemann sums over polytopes},
url = {http://eudml.org/doc/10294},
volume = {57},
year = {2007},
}
TY - JOUR
AU - Guillemin, Victor
AU - Sternberg, Shlomo
TI - Riemann sums over polytopes
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 7
SP - 2183
EP - 2195
AB - It is well-known that the $N$-th Riemann sum of a compactly supported function on the real line converges to the Riemann integral at a much faster rate than the standard $O(1/N)$ rate of convergence if the sum is over the lattice, $Z/N$. In this paper we prove an n-dimensional version of this result for Riemann sums over polytopes.
LA - eng
KW - Riemann sums; Euler-Maclaurin formula for polytopes; Ehrhart’s theorem; Ehrhart's theorem
UR - http://eudml.org/doc/10294
ER -
References
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