Geodesic
Example of Divergence of a Greedy Algorithm with Respect to an Asymmetric Dictionary
Matematičeskie zametki, Tome 109 (2021) no. 3, pp. 352-360 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : convergence. 
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P. A. Borodin. Example of Divergence of a Greedy Algorithm with Respect to an Asymmetric Dictionary. Matematičeskie zametki, Tome 109 (2021) no. 3, pp. 352-360. http://geodesic.mathdoc.fr/item/MZM_2021_109_3_a2/

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