Greedy algorithm with gaps

We generalize the well-known greedy approximation algorithm, by allowing gaps in the approximating sequence. We give examples of bases which are “quasi-greedy with gaps,” in spite of failing to be quasi-greedy in the usual sense. However, we also show that for some classical bases (such as the norma...

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Bibliographic Details
Published inJournal of approximation theory Vol. 225; pp. 176 - 190
Main Author Oikhberg, T.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2018
Subjects
Basis
Greedy algorithm
Greedy algorithm
Basis
Online AccessGet full text
ISSN0021-9045
1096-0430
DOI10.1016/j.jat.2017.10.006

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Summary:We generalize the well-known greedy approximation algorithm, by allowing gaps in the approximating sequence. We give examples of bases which are “quasi-greedy with gaps,” in spite of failing to be quasi-greedy in the usual sense. However, we also show that for some classical bases (such as the normalized Haar basis in L1, and the trigonometric basis in Lp for p≠2), the greedy algorithm may diverge, even if gaps are introduced into the approximating sequence.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2017.10.006