Optimal recovery and n-widths for convex classes of functions

Abstract

We study the problem of optimal recoveryin the case of a nonsymmetric convex class of functions. In particular we show that adaptive methods may be much better than nonadaptive methods. We define certain Gelfand-type widths that are useful for nonsymmetric classes and prove relations to optimal error bounds for adaptive and nonadaptive methods, respectively. © 1995 Academic Press, Inc.