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math.NA2013★ 24 cited
Complexity of Oscillatory Integration for Univariate Sobolev Spaces
Erich Novak, Mario Ullrich, Henryk Woźniakowski
We analyze univariate oscillatory integrals for the standard Sobolev spaces of periodic and non-periodic functions with an arbitrary integer . We find matching lower a…
math.NA2013★ 47 cited
The Curse of Dimensionality for Numerical Integration of Smooth Functions II
Aicke Hinrichs, Erich Novak, Mario Ullrich +1
We prove the curse of dimensionality in the worst case setting for numerical integration for a number of classes of smooth -variate functions. Roughly speaking, we consider diff…