Fitting a Sobolev function to data I

• Charles Fefferman ^[2] ; Arie Israel ^[1] ; Garving K. Luli ^[3]
  1. [1] University of Texas at Austin

     University of Texas at Austin

     Estados Unidos

     
  2. [2] Princeton University

     Princeton University

     Estados Unidos

     
  3. [3] University of California at Davis

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 1, 2016, págs. 275-376
• Idioma: inglés
• DOI: 10.4171/RMI/887
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.