Mathematics – Numerical Analysis
Scientific paper
2010-11-16
Mathematics
Numerical Analysis
Scientific paper
We study the integration and approximation problems for monotone and convex bounded functions that depend on $d$ variables, where $d$ can be arbitrarily large. We consider the worst case error for algorithms that use finitely many function values. We prove that these problems suffer from the curse of dimensionality. That is, one needs exponentially many (in $d$) function values to achieve an error $\epsilon$.
Hinrichs Aicke
Novak Erich
Woźniakowski Henryk
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