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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2021 Volume 109, Issue 3, Pages 352–360 (Mi mzm12577)

This article is cited in 3 papers

Example of Divergence of a Greedy Algorithm with Respect to an Asymmetric Dictionary

P. A. Borodin

Moscow Center for Fundamental and Applied Mathematics

Abstract: We construct an example of an asymmetric dictionary $D$ in a Hilbert space $H$ such that the linear combinations of elements of $D$ with positive coefficients are dense in $H$, but the greedy algorithm with respect to $D$, in which inner product with the elements of $D$ (not the modulus of this inner product) is maximized at each step, diverges for some initial element.

Keywords: Hilbert space, greedy approximations, asymmetric dictionary, convergence.

UDC: 517.518.8

Received: 07.10.2019

DOI: 10.4213/mzm12577


 English version:
Mathematical Notes, 2021, 109:3, 379–385

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© Steklov Math. Inst. of RAS, 2025