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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
June 22, 1998. Date revised: March 26, 1999. Date accepted: March 22, 1999.
Rights and permissions
About this article
Cite this article
Temlyakov, V. Greedy Algorithms with Regard to Multivariate Systems with Special Structure. Constr. Approx. 16, 399–425 (2000). https://doi.org/10.1007/s003659910017
Published:
Issue Date:
DOI: https://doi.org/10.1007/s003659910017