Geodesic
Rate of convergence of Thresholding Greedy Algorithms
Sbornik. Mathematics, Tome 215 (2024) no. 2, pp. 275-289

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The rate of convergence of the classical Thresholding Greedy Algorithm with respect to some bases is studied. We bound the error of approximation by the product of two norms, the norm of $f$ and the $A_1$-norm of $f$. We obtain some results for greedy bases, unconditional bases and quasi-greedy bases. In particular, we prove that our bounds for the trigonometric basis and Haar basis are optimal. Bibliography: 16 titles.
Keywords: greedy algorithm, rate of convergence.
Mots-clés : bases 
@article{SM_2024_215_2_a7,
     author = {V. N. Temlyakov},
     title = {Rate of convergence of {Thresholding} {Greedy} {Algorithms}},
     journal = {Sbornik. Mathematics},
     pages = {275--289},
     publisher = {mathdoc},
     volume = {215},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2024_215_2_a7/}
}
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V. N. Temlyakov. Rate of convergence of Thresholding Greedy Algorithms. Sbornik. Mathematics, Tome 215 (2024) no. 2, pp. 275-289. http://geodesic.mathdoc.fr/item/SM_2024_215_2_a7/