A characterization of optimal points for integration on manifolds

Mathias Sonnleitner (JKU, Linz)

Jan 21. 2022, 15:45 — 16:25

For numerical integration on compact Riemannian manifolds one may use cubature rules weighting function values at a suitable point set to approximate the integral with respect to the Riemannian volume. Building on our earlier work on bounded convex domains, we present a characterization of point sets with asymptotically optimal worst-case error in Sobolev spaces on such manifolds. Applied to random points, our result closes (except for boundary cases) a logarithmic gap left open by Ehler, Gräf and Oates [Stat. Comput. 29, 2019]. Using a well-known relation on the sphere connected to Stolarsky's principle, we apply the Hilbert space case to weighted spherical L2-discrepancy. This talk is based on joint work with D. Krieg.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Optimal Point Configurations on Manifolds (Workshop)
Christine Bachoc (U Bordeaux)
Henry Cohn (Microsoft, Redmond)
Peter Grabner (TU Graz)
Douglas Hardin (Vanderbilt U, Nashville)
Edward Saff (Vanderbilt U, Nashville)
Achill Schürmann (U of Rostock)
Robert Womersley (UNSW, Sydney)