Details

Autor(en) / Beteiligte

• Rieger, Christian
• Zwicknagl, Barbara

Titel

Improved Exponential Convergence Rates by Oversampling Near the Boundary

Ist Teil von

• Constructive approximation, 2014-04, Vol.39 (2), p.323-341

Ort / Verlag

Boston: Springer US

Erscheinungsjahr

2014

Quelle

SpringerNature Journals

Beschreibungen/Notizen

• Sampling inequalities for smooth functions bound a continuous norm in terms of a discretized norm and an error term that tends to zero exponentially as the discrete data set becomes dense. Improved estimates are derived for discrete point sets that cluster near the boundary, in particular for scattered point sets that are distributed quadratically in a boundary layer, and for tensorized Chebyshev grids. If applied to residuals of stable reconstruction processes, such inequalities yield exponential convergence orders. Our results agree with the observation that exponential deterministic approximation rates are often improved globally if the data sets are distributed more densely near the boundary.