Efficient Algorithms for Approximate Smooth Selection

  • Charles Fefferman
  • Bernat Guillén PeguerolesEmail author


In this paper, we provide efficient algorithms for approximate \({\mathcal {C}}^m({\mathbb {R}}^n, {\mathbb {R}}^D)-\)selection. In particular, given a set E, a constant \(M_0 > 0\), and convex sets \(K(x) \subset {\mathbb {R}}^D\) for \(x \in E\), we show that an algorithm running in \(C(\tau ) N \log N\) steps is able to solve the smooth selection problem of selecting a point \(y \in (1+\tau )\blacklozenge K(x)\) for \(x \in E\) for an appropriate dilation of K(x), \((1+\tau )\blacklozenge K(x)\), and guaranteeing that a function interpolating the points (xy) will be \({\mathcal {C}}^m({\mathbb {R}}^n, {\mathbb {R}}^D)\) with norm bounded by CM.


Smooth selection Approximate algorithms Efficient algorithms Partition of unity 

Mathematics Subject Classification




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© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.Princeton UniversityPrincetonUSA

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