On constrained uniform approximation
Let \(f\) be a function on the unit interval \([0,1]\), and let \(\{x_i\}\) be a finite set of distinct points in \([0,1]\). Let \(m\) be a sufficiently large integer, and let \(S\) be the polynomials of degree \(m\) or less that interpolate to \(f\) on \(\{x_i\}\), and which also have designated higher derivatives that assume prescribed values on \(\{x_i\}\). The general problem is to find the member of \(S\) that is the best uniform approximation to \(f\). The problem, in various forms has a distinguished history that includes classical Hermite interpolation. Here a setting is presented in which the author proves the best approximation is unique.
scientific article; zbMATH DE number 1780406