@inproceedings{Griebel:2005,
author = {M.~Griebel},
title = {Sparse grids and related approximation schemes for higher
dimensional problems},
booktitle = {Foundations of Computational Mathematics (FoCM05),
Santander},
editor = {L. Pardo and A. Pinkus and E. Suli and M.J. Todd},
year = {2006},
pages = {106-161},
publisher = {Cambridge University Press},
annote = {series,C2,ALM,1145},
abstract = {The efficient numerical treatment of high dimensional
problems is hampered by the curse of dimensionality. We
review approximation techniques which overcome this problem
to some extent. Here, we focus on methods stemming from
Kolmogorov's theorem, the ANOVA decomposition and the
sparse grid approach and discuss their prerequisites and
properties. Moreover, we present energy-norm based sparse
grids and demonstrate that, for functions with bounded
mixed derivatives on the unit hypercube, the associated
approximation rate in terms of the involved degrees of
freedom shows no dependence on the dimension at all,
neither in the approximation order nor in the order
constant.},
pdf = {http://wissrech.ins.uni-bonn.de/research/pub/griebel/focm.pdf 1}
}
