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Aveiro method in reproducing kernel Hilbert spaces under complete dictionary
Mai, Weixiong; Qian, Tao

Aveiro method is a sparse representation method in reproducing kernel Hilbert spaces, which gives orthogonal projections in linear combinations of reproducing kernels over uniqueness sets. It, however, suffers from determination of uniqueness sets in the underlying reproducing kernel Hilbert space. In fact, in general spaces, uniqueness sets are not easy to be identified, let alone the convergence speed aspect with Aveiro method. To avoid those difficulties, we propose an new Aveiro method based on a dictionary and the matching pursuit idea. What we do, in fact, are more: The new Aveiro method will be in relation to the recently proposed, the so-called pre-orthogonal greedy algorithm involving completion of a given dictionary. The new method is called Aveiro method under complete dictionary. The complete dictionary consists of all directional derivatives of the underlying reproducing kernels. We show that, under the boundary vanishing condition bring available for the classical Hardy and Paley-Wiener spaces, the complete dictionary enables an efficient expansion of any given element in the Hilbert space. The proposed method reveals new and advanced aspects in both the Aveiro method and the greedy algorithm.

KeywordAveiro Method Pre-orthogonal Greedy Algorithm Reproducing Kernel
URLView the original
Indexed BySCIE
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000419218900069
The Source to ArticleWOS
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Cited Times [WOS]:4   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorMai, Weixiong
AffiliationDepartment of Mathematics, University of Macau, Macau, China
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Mai, Weixiong,Qian, Tao. Aveiro method in reproducing kernel Hilbert spaces under complete dictionary[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2017,40(18):7240-7254.
APA Mai, Weixiong,&Qian, Tao.(2017).Aveiro method in reproducing kernel Hilbert spaces under complete dictionary.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,40(18),7240-7254.
MLA Mai, Weixiong,et al."Aveiro method in reproducing kernel Hilbert spaces under complete dictionary".MATHEMATICAL METHODS IN THE APPLIED SCIENCES 40.18(2017):7240-7254.
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