The curse of dimensionality for the class of monotone functions and for the class of convex functions
نویسندگان
چکیده
We study the integration and approximation problems for monotone or 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 ". ∗This author was supported by the DFG Heisenberg grant HI 584/3-2. †This author was partially supported by the DFG, SPP 1324 ‡This author was partially supported by the National Science Foundation.
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ورودعنوان ژورنال:
- Journal of Approximation Theory
دوره 163 شماره
صفحات -
تاریخ انتشار 2011