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Sobolev Algorithm for Local Smoothness Analysis (SALSA) via Sharp Direct and Inverse Statements

MCML Authors

Tizian Wenzel

Dr.

→ Group Holger Rauhut
Mathematical Data Science and Artificial Intelligence

Abstract

We extend sharp direct and inverse approximation statements for kernel-based methods for finitely smooth kernels, i.e. those whose native spaces are norm-equivalent to Sobolev spaces. In particular, our inverse results are now formulated for a broad class of approximation schemes beyond interpolation, extending existing theory. Building on these results, we propose a novel Sobolev Algorithm for Local Smoothness Analysis (SALSA) for detecting local smoothness properties of target data, including their degree of smoothness and non-smoothness. The method is rigorously grounded based on the sharp direct and inverse statements. Numerical experiments in various settings highlight the effectiveness of the proposed algorithm.

misc ALM+25