Optimal nonlinear approximation Academic Article uri icon

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.

author list (cited authors)

  • DeVore, R. A., Howard, R., & Micchelli, C.

citation count

  • 98

publication date

  • December 1989