Optimal, random and constructive sampling for high-dimensional approximation
Faculty of Informatics - Academic Studies Administration
Date: 13 January 2026 / 14:30 - 15:30
USI East Campus, Room D0.02
Speaker: Dr. Ullrich Mario, Johannes Kepler University Linz
Abstract: I consider the approximation of functions based on function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were obtained only recently. I will discuss some of these insights, including the optimality of least squares in a worst-case setting and corresponding (random) sampling strategies. I will also present a semi-constructive algorithm that is provably superior to sparse grid interpolation for L2-approximation in 'tensor product spaces'.
Biography: Mario Ullrich is a mathematician who works in theoretical numerical analysis and complexity theory, with an emphasis on high-dimensional approximation. Mario did his PhD in mathematics at the Friedrich Schiller University of Jena and Università Roma Tre, and his habilitation at Johannes Kepler University Linz, where he is a senior scientist. He is the recipient of the "Joseph F. Traub Prize for Achievement in Information-based Complexity" and the author of the upcoming Acta Numerica article "Approximation of functions: optimal sampling and complexity".
Host: Prof. Michael Multerer