Efficient Algorithms for Approximate Smooth Selection

Charles Fefferman, Bernat Guillén Pegueroles

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper, we provide efficient algorithms for approximate Cm(Rn, RD) - selection. In particular, given a set E, a constant M> 0 , and convex sets K(x) ⊂ RD for x∈ E, we show that an algorithm running in C(τ) Nlog N steps is able to solve the smooth selection problem of selecting a point y∈ (1 + τ) ⧫K(x) for x∈ E for an appropriate dilation of K(x), (1 + τ) ⧫K(x) , and guaranteeing that a function interpolating the points (x, y) will be Cm(Rn, RD) with norm bounded by CM.

Original languageEnglish (US)
Pages (from-to)6530-6600
Number of pages71
JournalJournal of Geometric Analysis
Issue number7
StatePublished - Jul 2021

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


  • Approximate algorithms
  • Efficient algorithms
  • Partition of unity
  • Smooth selection


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