Minimax nonlinear approximation by approximation on subsets

A possible algorithm for minimax approximation on an infinite set X consists in choosing a sequence of finite point sets { X k } which fill out X and taking a limit of minimax approximations on X k as k → ∞. Such a procedure is considered by Rice [4, pp. 12-15]. In the case of linear approximation such a procedure has been shown to converge [1, pp. 84-88]. It has been claimed by Watson [5] that the procedure works for approxition by nonlinear families.