Geodesic
Projection Greedy Algorithm
Matematičeskie zametki, Tome 110 (2021) no. 1, pp. 17-28

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We introduce and study a new type of greedy algorithms, namely, the projection greedy algorithm with respect to a given dictionary in a Hilbert space. We prove its convergence and estimate the rate of convergence for initial elements from the convex hull of the dictionary. Several specific examples of dictionaries are used to compare the introduced algorithm with the orthogonal greedy algorithm.
Keywords: greedy approximations, Hilbert space, rate of convergence. 
@article{MZM_2021_110_1_a1,
     author = {P. A. Borodin and S. V. Konyagin},
     title = {Projection {Greedy} {Algorithm}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {17--28},
     publisher = {mathdoc},
     volume = {110},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a1/}
}
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P. A. Borodin; S. V. Konyagin. Projection Greedy Algorithm. Matematičeskie zametki, Tome 110 (2021) no. 1, pp. 17-28. http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a1/