Fitting a sobolev function to data II

Charles Fefferman, Arie Israel, Garving Luli

Research output: Contribution to journalArticle

4 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 ⊂ 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
Volume32
Issue number2
DOIs
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Algorithm
  • Interpolation
  • Sobolev spaces.

Fingerprint Dive into the research topics of 'Fitting a sobolev function to data II'. Together they form a unique fingerprint.

  • Cite this