Journal
MATHEMATICS OF COMPUTATION
Volume 83, Issue 290, Pages 2853-2863Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0025-5718-2014-02855-X
Keywords
Curse of dimensionality; numerical integration; high dimensional numerical problems
Categories
Funding
- DFG-Priority Program [1324]
- DFG GRK [1523]
- ERC Advanced Grant PTRELSS
- National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1215987] Funding Source: National Science Foundation
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We prove the curse of dimensionality for multivariate integration of C-r functions: The number of needed function values to achieve an error epsilon is larger than c(r)(1 + gamma)(d) for epsilon <= epsilon(0), where cr, gamma > 0. The proofs are based on volume estimates for r = 1 together with smoothing by convolution. This allows us to obtain smooth fooling functions for r > 1.
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