Computing minimal interpolants in C1,1(Rd)C^{1,1}(\mathbb R^d)

  • Ariel Herbert-Voss

    Harvard University, Cambridge, USA
  • Matthew J. Hirn

    Michigan State University, East Lansing, USA
  • Frederick McCollum

    New York University, USA
Computing minimal interpolants in $C^{1,1}(\mathbb R^d)$ cover
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We consider the following interpolation problem. Suppose one is given a finite set ERdE \subset \mathbb R^d, a function f ⁣:ERf \colon E \to \mathbb R, and possibly the gradients of ff at the points of EE. We want to interpolate the given information with a function FC1,1(Rd)F \in C^{1,1}(\mathbb R^d) with the minimum possible value of Lip(F)(\nabla F). We present practical, efficient algorithms for constructing an FF such that Lip(F)(\nabla F) is minimal, or for less computational effort, within a small dimensionless constant of being minimal.

Cite this article

Ariel Herbert-Voss, Matthew J. Hirn, Frederick McCollum, Computing minimal interpolants in C1,1(Rd)C^{1,1}(\mathbb R^d). Rev. Mat. Iberoam. 33 (2017), no. 1, pp. 29–66

DOI 10.4171/RMI/927