Computing minimal interpolants in C1,1(Rd)

• Ariel Herbert-Voss ^[1] ; Matthew J. Hirn ^[2] ; Frederick McCollum ^[3]
  1. [1] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
  2. [2] Michigan State University

     Michigan State University

     City of East Lansing, Estados Unidos

     
  3. [3] New York University

     New York University

     Estados Unidos

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 33, Nº 1, 2017, págs. 29-66
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We consider the following interpolation problem. Suppose one is given a finite set E⊂Rd, a function f:E→R, and possibly the gradients of ff at the points of E. We want to interpolate the given information with a function F∈C1,1(Rd) with the minimum possible value of Lip(∇F). We present practical, efficient algorithms for constructing an F such that Lip(∇F) is minimal, or for less computational effort, within a small dimensionless constant of being minimal.