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Nonnegative C2(ℝ2) interpolation

2019/01/28 by Fushuai Jiang, Jiang, Fushuai, Garving K. Luli +1
Computer Science · Mathematics · #26B05 #26B35 #41A05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #cs.NA #math.CA #math.NA #math.OC #msc:26B05 #msc:26B35 #msc:41A05

paper · pdf · doi:10.48550/arxiv.1901.09876

56 pages

arxiv created 2020/07/30 · arxiv updated 2020/07/31

Abstract

In this paper, we prove two improved versions of the Finiteness Principle for nonnegative C2(ℝ2) interpolation, previously proven by Fefferman, Israel, and Luli. The first version sharpens the finiteness constant to 64 , and the second version carries better computational practicality. Along the way, we also provide detailed construction of nonnegative C2 interpolants in one-dimension, and prove the nonexistence of a bounded linear C2 -extension operator that preserves nonnegativity.

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