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The best m-term approximations on generalized Besov classes MBq,θΩ with regard to orthogonal dictionaries

By Liqin Duan


AbstractIn this paper, we investigate nonlinear m-term approximation with regard to orthogonal dictionaries. We consider this problem in the periodic multivariate case for generalized Besov classes MBq,θΩ under the condition Ω(t)=ω(t1⋅⋯⋅td) where ω(t)∈Ψl∗ is a univariate function. We prove that the well-known dictionary Ud which consists of trigonometric polynomials (shifts of the Dirichlet kernels) is nearly optimal among orthogonal dictionaries. Moreover, it is established that for these classes near-best m-term approximation, with regard to Ud, can be achieved by simple greedy-type algorithms

Publisher: Elsevier Inc.
Year: 2010
DOI identifier: 10.1016/j.jat.2010.05.005
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