On the degree of nonlinear spline approximation in Besov-Sobolev spaces

AbstractThis paper is devoted to estimating the degree of nonlinear spline approximation in Besov-Sobolev spaces defined on the unit cube in RN. Good approximants with a given number of polynomial pieces and a given global smoothness are obtained from a certain decomposition of the functions under consideration into B-splines with respect to uniform dyadic partitions which, in turn, are constructed by means of a certain strategy of selecting terms with large coefficients. The general concept is applied to approximation by smooth splines with variable knots (N = 1) and smooth nonlinear piecewise polynomial approximation with respect to partitions into cubes and certain triangulations (N > 1)