Fitting a sobolev function to data II

Charles Fefferman, Arie Israel, Garving Luli

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


In this paper and two companion papers, we produce efficient algorithms to solve the following interpolation problem. Let m ≥ 1 and p > n ≥ 1. Given a finite set E ⊂ ℝ n and a function f : E → ℝ , compute an extension F of f belonging to the Sobolev space Wm,p(ℝ n ) with norm having the smallest possible order of magnitude; secondly, compute the order of magnitude of the norm of F. The combined running time of our algorithms is at most CN log N, where N denotes the cardinality of E, and C depends only on m, n, and p.

Original languageEnglish (US)
Pages (from-to)649-750
Number of pages102
JournalRevista Matematica Iberoamericana
Issue number2
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Algorithm
  • Interpolation
  • Sobolev spaces.


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