Geodesic
Example of Divergence of a Greedy Algorithm with Respect to an Asymmetric Dictionary
Matematičeskie zametki, Tome 109 (2021) no. 3, pp. 352-360.

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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/

[1] V. Temlyakov, Greedy Approximation, Cambridge Univ. Press, Cambridge, 2018 | MR

[2] L. Jones, “On a conjecture of Huber concerning the convergence of projection pursuit regression”, Ann. Statist., 15:2 (1987), 880–882 | DOI | MR

[3] P. A. Borodin, “Zhadnye priblizheniya proizvolnym mnozhestvom”, Izv. RAN. Ser. matem., 84:2 (2020), 43–59 | DOI

[4] E. D. Livshits, “O vozvratnom zhadnom algoritme”, Izv. RAN. Ser. matem., 70:1 (2006), 95–116 | DOI | MR | Zbl

[5] E. D. Livshits, “Ob $n$-chlennom priblizhenii s neotritsatelnymi koeffitsientami”, Matem. zametki, 82:3 (2007), 373–382 | DOI | MR | Zbl