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arXiv · 2102.05777

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

Fushuai Jiang·Garving K. Luli
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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.

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Fushuai Jiang, Garving K. Luli. 2021-02-10. Algorithms for Nonnegative $C^2(\mathbb{R}^2)$ Interpolation. https://doi.org/10.1016/j.aim.2021.107756

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