Fitting a Sobolev function to data i

Charles Fefferman, Arie Israel, Garving Luli

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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 ⊆ ℝn and a function f : E → ℝ, compute an extension F of f belonging to the Sobolev space Wm,p(ℝn) 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 CNlogN, where N denotes the cardinality of E, and C depends only on m, n, and p.

Original languageEnglish (US)
Pages (from-to)275-376
Number of pages102
JournalRevista Matematica Iberoamericana
Volume32
Issue number1
DOIs
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Algorithm
  • Interpolation
  • Sobolev spaces

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