Algorithms for Nonnegative $C^2({\mathbb{R}}^2)$ Interpolation

Abstract

Let $E\subset {\mathbb{R}}^2$ be a finite set, and let $f:E\to [0,\infty )$. In this paper, we address the algorithmic aspects of nonnegative $C^2$ interpolation in the plane. Specifically, we provide an efficient algorithm to compute a nonnegative $C^2({\mathbb{R}}^2)$ extension of $f$ with norm within a universal constant factor of the least possible. We also provide an efficient algorithm to approximate the trace norm.

38 pages