Prof. David Levin, Some Remarks on Multivariate Approximation

Berliner Colloquium für wissenschaftliche Visualisierung

Donnerstag, 4. Juli 2019, 17:15 Uhr
Zuse-Institut Berlin (ZIB)
Takustrasse 7, 14195 Berlin
Großer Hörsaal (Rundbau, Erdgeschoss)

Prof. (emiritus) David Levin,

Tel Aviv University, Raymond & Beverly Sackler Faculty of Exact Sciences

My talk will present some ideas on scattered data multivariate approximation. I will start by suggesting a graphical visualization of the approximation power of linear bivariate approximation methods. This will lead us to the notion of quasi-interpolation and to the method of Moving Least-Squares. Approximation errors are usually larger near singularities of the approximated function and also near the boundary of the approximation domain. It turns out that by analyzing the approximation errors at the data points we can improve the approximation near singularities and near the boundary.

Other interesting issues are the approximation of low dimensional manifolds, and the approximation of a function over manifolds.

I will present the idea of approximation by projection, first for the approximation of surfaces in 3D, and then for the approximation of general low dimensional manifolds in high dimension. To get a feeling of this approach, please see a short video on approximating a curve in 3D from noisy samples at: https://youtu.be/K_TzGinrexM.