Continuous Algorithms in n-Term Approximation and Non-Linear Widths Original Research Article

In the present paper we investigate optimal continuous algorithms in n-term approximation based on various non-linear n-widths, and n-term approximation by the dictionary V formed from the integer translates of the mixed dyadic scales of the tensor product multivariate de la Vallée Poussin kernel, for the unit ball of Sobolev and Besov spaces of functions with common mixed smoothness. The asymptotic orders of these quantities are given. For each space the asymptotic orders of non-linear n-widths and n-term approximation coincide. Moreover, these asymptotic orders are achieved by a continuous algorithm of n-term approximation by V, which is explicitly constructed.