Caratheodory-Tchakaloff Subsampling

TL;DR

This paper surveys Caratheodory-Tchakaloff subsampling for measure compression, discusses its implementation via optimization, and introduces an algorithm for computing CATCH points and weights for polynomial approximation on complex sets.

Contribution

It provides a comprehensive survey, details on implementation methods, and introduces a new algorithm for computing CATCH points and weights in multivariate polynomial spaces.

Findings

Effective measure compression using Caratheodory-Tchakaloff subsampling.

Algorithm for computing CATCH points on 2D and 3D manifolds.

Application to multivariate polynomial least squares approximation.

Abstract

We present a brief survey on the compression of discrete measures by Caratheodory-Tchakaloff Subsampling, its implementation by Linear or Quadratic Programming and the application to multivariate polynomial Least Squares. We also give an algorithm that computes the corresponding Caratheodory-Tchakaloff (CATCH) points and weights for polynomial spaces on compact sets and manifolds in 2D and 3D.