caa a22 4500 475743652 CHVBK 20180406123506.0 cr unu---uuuuu 170329e20000701xx s 000 0 eng 10.1007/s003659910017 doi (NATIONALLICENCE)springer-10.1007/s003659910017 Temlyakov V. N. Department of Mathematics, University of South Carolina, SC 29208, Columbia, USA aut Greedy Algorithms with Regard to Multivariate Systems with Special Structure [Elektronische Daten] [V. N. Temlyakov] Abstract. : The question of finding an optimal dictionary for nonlinear m -term approximation is studied in this paper. We consider this problem in the periodic multivariate (d variables) case for classes of functions with mixed smoothness. We prove that the well-known dictionary U d which consists of trigonometric polynomials (shifts of the Dirichlet kernels) is nearly optimal among orthonormal dictionaries. Next, it is established that for these classes near-best m -term approximation, with regard to U d , can be achieved by simple greedy-type (thresholding-type) algorithms. The univariate dictionary U is used to construct a dictionary which is optimal among dictionaries with the tensor product structure. Springer-Verlag New York Inc., 2000 Key words. Nonlinear approximation, Asymptotic estimates, Greedy algorithm, Orthogonal systems, Bilinear approximation. AMS Classification. 41A17, 41A25, 41A46, 41A63, 42A10 nationallicence https://doi.org/10.1007/s003659910017 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003659910017 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Temlyakov V. N. Department of Mathematics, University of South Carolina, SC 29208, Columbia, USA aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer