Algorithms for Nonnegative C²(ℝ²) Interpolation

2021/02/28 by Fushuai Jiang, Garving K. Luli · 1 citation
Mathematics · #math.CA #math.OC #msc:41A29 #msc:41A05

paper · pdf · doi:10.1016/j.aim.2021.107756

published as Algorithms for nonnegative C2(R2) interpolation, Advances in Mathematics, 385:107756, 2021 · 38 pages

arxiv created 2021/07/15 · arxiv updated 2021/07/19

Abstract

Let E ⊂ ℝ² be a finite set, and let f : E → [0,∞) . In this paper, we address the algorithmic aspects of nonnegative C² interpolation in the plane. Specifically, we provide an efficient algorithm to compute a nonnegative C²(ℝ²) 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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• C² Interpolation with Range Restriction