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

Ariel Herbert-Voss; Matthew J. Hirn; Frederick McCollum

doi:10.4171/rmi/927

JournalsrmiVol. 33, No. 1pp. 29–66

Computing minimal interpolants in $C^{1, 1} (R^{d})$

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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Abstract

We consider the following interpolation problem. Suppose one is given a finite set $E \subset R^{d}$ , a function $f : E \to R$ , and possibly the gradients of $f$ at the points of $E$ . We want to interpolate the given information with a function $F \in C^{1, 1} (R^{d})$ with the minimum possible value of Lip $(\nabla F)$ . We present practical, efficient algorithms for constructing an $F$ such that Lip $(\nabla F)$ 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 $C^{1, 1} (R^{d})$ . Rev. Mat. Iberoam. 33 (2017), no. 1, pp. 29–66

DOI 10.4171/RMI/927