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2010

Sampling inequalities for infinitely smooth functions, with applications to interpolation and machine learning

9 years 4 months ago
Sampling inequalities for infinitely smooth functions, with applications to interpolation and machine learning
Sampling inequalities give a precise formulation of the fact that a differentiable function cannot attain large values, if its derivatives are bounded and if it is small on a sufficiently dense discrete set. Sampling inequalities can be applied to the difference of a function and its reconstruction in order to obtain (sometimes optimal) convergence orders for very general possibly regularized recovery processes. So far, there are only sampling inequalities for finitely smooth functions, which lead to algebraic convergence orders. In this paper the case of infinitely smooth functions is investigated, in order to derive error estimates which lead to exponential convergence orders.
Christian Rieger, Barbara Zwicknagl
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2010
Where ADCM
Authors Christian Rieger, Barbara Zwicknagl
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