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

Steven B. Damelin, Michael Werman

We study the best approximation problem: \[ \displaystyle \min_{α\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m α_j Γ_j ({\bf x}_i) \right|. \] Here: $Γ:=\left\{Γ_1,..…