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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - P. A. Borodin
AU  - S. V. Konyagin
TI  - Projection Greedy Algorithm
JO  - Matematičeskie zametki
PY  - 2021
SP  - 17
EP  - 28
VL  - 110
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a1/
LA  - ru
ID  - MZM_2021_110_1_a1
ER  - 
%0 Journal Article
%A P. A. Borodin
%A S. V. Konyagin
%T Projection Greedy Algorithm
%J Matematičeskie zametki
%D 2021
%P 17-28
%V 110
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_110_1_a1/
%G ru
%F MZM_2021_110_1_a1
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/

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

[2] V. N. Temlyakov, “Weak greedy algorithms”, Adv. Comput. Math., 12:2-3 (2000), 213–227 | DOI | MR

[3] A. Yu. Popov, “Novye dvustoronnie otsenki gamma-funktsii i chisel sochetanii iz $2n$ po $n$. Usilennoe obvertyvanie asimptoticheskim ryadom”, Matem. zametki, 103:5 (2018), 785–789 | DOI | MR