“Optimal Nonlinear Approximation”, Ronald A. DeVore, Ralph Howard, Charles Micchelli1989 (algorithms)⁠:

We introduce a definition of nonlinear n-widths and then determine the n-widths of the unit ball of the Sobolev space W_p^r in L_q.

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.