Optimal nonlinear approximation

Abstract

We introduce a definition of nonlinear n-widths and then determine the n-widths of the unit ball of the Sobolev space Wpr in Lq. We prove that in the sense of these widths the manifold of splines of fixed degree with n free knots is optimal for approximating functions in these Sobolev spaces. © 1989 Springer-Verlag.