Greedy algorithm with gaps

T. Oikhberg

doi:10.1016/j.jat.2017.10.006

Greedy algorithm with gaps

T. Oikhberg

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 L_p for p≠2), the greedy algorithm may diverge, even if gaps are introduced into the approximating sequence.

Original language	English (US)
Pages (from-to)	176-190
Number of pages	15
Journal	Journal of Approximation Theory
Volume	225
DOIs	https://doi.org/10.1016/j.jat.2017.10.006
State	Published - Jan 2018

Keywords

Basis
Greedy algorithm

ASJC Scopus subject areas

Analysis
Numerical Analysis
General Mathematics
Applied Mathematics

Online availability

10.1016/j.jat.2017.10.006

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abstract = "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.",

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KW - Basis

KW - Greedy algorithm

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ER -

Greedy algorithm with gaps

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

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