On best uniform approximation of finite sets by linear combinations of real valued functions using linear programming

2022/04/17 by Damelin, Steven B., Werman, Michael
#41 #49 #68 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2204.07949

Abstract

We study the best approximation problem: min_{α∈ \mathbb R^m}max_{1≤ i≤ n}|y_i -∑_j=1^m α_j Γ_j (\bf x_i) |. Here: Γ:=\Γ₁,...,Γ_m\ is a list of functions where for each 1≤ j≤ m, Γ_j:Δ→ \mathbb R with Δ a set of evaluation points \\bf x₁,...,\bf x_n\. \y₁,...,y_n\ is a set of real values and \mathbb R^m:=\(α₁,...,α_m), α_j∈ \mathbb R, 1≤ j≤ m\.

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