Sampling recovery of multivariate functions

by Dr Kateryna Pozharska (Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)

Thursday 9 Sep 2021, 10:00 → 12:00 Europe/Kiev

https://zoom.us/j/91749209940?pwd=N2VZYUdFcm1ZdmhkTlkrK2tnVGEwZz09 (ONLINE)

 Abstract: We will discuss the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. We study a certain weighted least squares algorithm that uses the so-called ''standard information'', i.e., finite number of function values at some points. The main advantage of our approach is that the nodes are taken at random w.r.t. a tailored distribution and simultaneously for the whole class of functions. We show that the considered deterministic algorithm leads to near optimal results in several relevant situations. We additionally apply a recently introduced sub-sampling technique to further reduce the sampling budget.