Kernel Interpolation for Geometric Problems

We will demonstrate how ideas from kernel interpolation can be extended for use as a tool to understand the geometry of point clouds and perform analysis for functions defined on it. Reformulating the relevant interpolation problems as optimization problems also suggests natural a natural regularization that proves effective when the data is noisy. The regularization parameter admits a probabilistic interpretation that clarifies its meaning. Numerical experiments will be presented.

The link for participation in the event is the following: https://fernuni.zoom.us/j/64536503562.

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