Sampling inequalities for sparse grids
The authors use a construction technique (Smolyak algorithm) to build a multivariate operator on a sparse grid having almost the same convergence properties as the univariate operator from which it was constructed. Polynomial reproductions are used. Then some sampling inequalities for functions from mixed regularity Sobolev spaces on sparse grids are derived. For classical sparse grids built from Chebyshev points, both cases of oversampling and non-oversampling are taken into account. In the end, the derived sampling inequalities are used for obtaining error estimates for stable reconstruction processes as norm-minimal kernel-based interpolation and penalized least-squares approximation in mixed order Sobolev spaces.
scientific article; zbMATH DE number 6728588
scientific article