Geodesic
Comparison of Purely Greedy and Orthogonal Greedy Algorithm
Matematičeskie zametki, Tome 115 (2024) no. 1, pp. 43-50.

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Conditions for a dictionary in a Hilbert space are obtained that are necessary or sufficient for the coincidence of purely greedy and orthogonal greedy algorithms with respect to this dictionary.
Keywords: greedy approximation, $m$-term approximation, Hilbert space, coherence parameter. 
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K. S. Vishnevetskiy. Comparison of Purely Greedy and Orthogonal Greedy Algorithm. Matematičeskie zametki, Tome 115 (2024) no. 1, pp. 43-50. http://geodesic.mathdoc.fr/item/MZM_2024_115_1_a3/

[1] V. Temlyakov, Greedy Approximation, Cambridge Monogr. Appl. Comput. Math., 20, Cambridge Univ. Press, Cambridge, 2011 | MR

[2] V. N. Temlyakov, “Relaxation in greedy approximation”, Constr. Approx., 28:1 (2008), 1–25 | DOI | MR

[3] K. S. Vishnevetskii, “O sovpadenii chisto zhadnykh i nailuchshikh $m$-chlennykh priblizhenii”, Matem. zametki, 111:2 (2022), 202–210 | DOI | MR