Geodesic
On the Coincidence of Pure Greedy and Best $m$-Term Approximations
Matematičeskie zametki, Tome 111 (2022) no. 2, pp. 202-210 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain conditions on a dictionary in a Hilbert space that are necessary or sufficient for the coincidence of pure greedy and best $m$-term approximations.
Keywords: greedy approximation, $m$-term approximation, coherence parameter, Hilbert space. 
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K. S. Vishnevetskiy. On the Coincidence of Pure Greedy and Best $m$-Term Approximations. Matematičeskie zametki, Tome 111 (2022) no. 2, pp. 202-210. http://geodesic.mathdoc.fr/item/MZM_2022_111_2_a2/

[1] V. Temlyakov, Greedy Approximation, Cambridge Univ. Press, Cambridge, 2011 | MR | Zbl

[2] R. A. DeVore, V. N. Temlyakov, “Some remarks on greedy algorithms”, Adv. Comp. Math., 5 (1996), 173–187 | DOI | Zbl

[3] G. Davis, S. Mallat, M. Avellaneda, “Adaptive greedy approximations”, Construct. Approx., 13 (1997), 57–98 | DOI | Zbl

[4] M. Donahue, L. Gurvits, C. Darken, E. Sontag, “Rate of convex approximation in non-Hilbert spaces”, Construct. Approx., 13 (1997), 187–220 | DOI | Zbl

[5] E. Schmidt, “Zur Theorie der linearen und nichtlinearen Integralgleichungen”, Math. Ann., 63 (1906), 433–476 | DOI

[6] S. B. Stechkin, “Ob absolyutnoi skhodimosti ortogonalnykh ryadov”, Dokl. AN SSSR, 102:1 (1955), 37–40 | MR | Zbl