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

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


"Computing Minimal Interpolants in C1,1(Rd)"

Ariel Herbert-Voss, Matthew J. Hirn, Frederick McCollum
Revista Mathematica Iberoamericana Vol. 33, Issue 1, (2017), pp. 29-66 



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 f 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.