# Computing Minimal Interpolants in C^1,1(R^d)

- Apr 12, 2017
- News, Publications

*Article:*

"**Computing Minimal Interpolants in C ^{1,1}(R^{d})**"

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

*Revista Mathematica Iberoamericana Vol. 33, Issue 1, *(2017), *pp. 29-66 *

Link: __http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=33&iss=1&rank=2__

**Abstract**

We consider the following interpolation problem. Suppose one is given a finite set E ⊂ R^{d}, a function f: E → R, and possibly the gradients of f at the points of E. We want to interpolate the given information with a function F ∈ C^{1,1}(R^{d}) 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.