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Multiple Rank-1 Lattices as Sampling Schemes for Approximation

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ASCW01 - Challenges in optimal recovery and hyperbolic cross approximation

The approximation of functions using sampling values
along single rank-1 lattices leads to convergence rates of the approximation
errors that are far away from optimal ones in spaces of dominating mixed
smoothness.

A recently published idea that uses sampling
values along several rank-1 lattices in order to reconstruct multivariate
trigonometric polynomials accompanied by fast methods for the construction of
these sampling schemes as well as available fast Fourier transform algorithms
motivates investigations on the approximation properties of the arising
sampling operators applied on functions of specific smoothness, in particular
functions of dominating mixed smoothness which naturally leads to hyperbolic
cross approximations.

This talk is part of the Isaac Newton Institute Seminar Series series.

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