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

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.