Abstract:
The convergence rate of the pure greedy algorithm (PGA) is considered. Upper bounds for the convergence rate of the PGA are obtained in the case of the target function in the classes ^Aγ(D), γ⩾0, which are extensions of the class ^A1(D). This bound is shown to be sharp in order for γ⩾2.
Bibliography: 14 titles.
\Bibitem{Liv07}
\by E.~D.~Livshits
\paper Optimality of the greedy algorithm for some function classes
\jour Sb. Math.
\yr 2007
\vol 198
\issue 5
\pages 691--709
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This publication is cited in the following 7 articles:
M. G. Grigoryan, K. A. Navasardyan, “Universal functions in ‘correction’ problems guaranteeing the convergence of Fourier–Walsh series”, Izv. Math., 80:6 (2016), 1057–1083
Grigoryan M.G., “Nonlinear Approximation By the Trigonometric System in Weighted l (Mu) (P) Spaces”, J. Contemp. Math. Anal.-Armen. Aca., 50:3 (2015), 128–140
M. G. Grigoryan, “Modifications of functions, Fourier coefficients and nonlinear approximation”, Sb. Math., 203:3 (2012), 351–379
E. D. Livshits, “The convergence of the greedy algorithm with respect to the Haar system in the space Lp(0,1)”, Sb. Math., 201:2 (2010), 253–288
E. D. Livshits, “Lower bounds for the rate of convergence of greedy algorithms”, Izv. Math., 73:6 (2009), 1197–1215
M. G. Grigoryan, A. A. Sargsyan, “Non-linear approximation of continuous functions
by the Faber-Schauder system”, Sb. Math., 199:5 (2008), 629–653
V. N. Temlyakov, “Greedy approximation”, Acta Numerica, 17 (2008), 235–409
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