Inverse rational \(L^ 1\) approximation
Considering the nonlinear approximating family \(\mathbb{R}^n_m\) of rational expressions over a given interval, the author studies the question as to which elements of the family may arise as best approximation to continuous functions from outside the family. It is shown that there exist continuous functions not in the above family which do have any given defect on functions, as their best \(L^1\) approximation [cf. \textit{C. B. Dunham}, J. Approximation Theory 4, 269-273 (1971; Zbl 0217.42501)]. Variational techniques from \textit{J. M. Wolfe} [J. Approximation Theory 17, 166-176 (1976; Zbl 0373.41025)] are used for the proof.
scientific article; zbMATH DE number 810859