On convergence of weak thresholding greedy algorithm in \(L^{1}\)(0,1). (English) Zbl 1177.41032
The author studies a weak thresholding greedy algorithm in \(L^1 (0,1)\) with regard to the Haar system. He proves that the Haar system is a good “non quasi-greedy” basis.
Reviewer: Antonio López-Carmona (Granada)
MSC:
| 41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |
| 42A10 | Trigonometric approximation |
References:
| [1] | Dilworth, S. J.; Kutzarova, D.; Wojtaszczyk, P., On approximate \(l_1\) systems in Banach spaces, J. Approx. Theory, 114, N2, 214-241 (2002) · Zbl 1018.46006 |
| [2] | Gogyan, S., Greedy algorithm with regard to Haar subsystems, East J. Approx., v.11, N2, 221-236 (2005) · Zbl 1137.41002 |
| [3] | Gogyan, S.; Wojtaszczyk, P., On weak non-equivalence of wavelet-like systems in \(L^1\), Math. Proc. Cambridge Philos. Soc., 144, 2, 499-510 (2008) · Zbl 1213.42138 |
| [4] | Jones, L. K., On a conjecture of Huber concerning the convergence of projection pursuit regression, Ann. Statist., 15, 880-882 (1987) · Zbl 0664.62061 |
| [5] | Konyagin, S. V.; Temlyakov, V. N., A remark on greedy approximation in Banach spaces, East J. Approx., 5, 365-379 (1999) · Zbl 1084.46509 |
| [6] | Konyagin, S. V.; Temlyakov, V. N., Convergence of greedy approximation I. General systems, Studia Mathematica, 159, N1, 143-160 (2003) · Zbl 1050.46012 |
| [7] | Konyagin, S. V.; Temlyakov, V. N., Greedy approximation with regard to bases and general minimal systems, Serdica Math. J., 28, N4, 305-328 (2002) · Zbl 1040.41008 |
| [8] | Temlyakov, V. N., The best \(m\)-term approximation and Greedy algorithms, Adv. Comput. Math., 8, N3, 249-265 (1998) · Zbl 0905.65063 |
| [9] | Wojtaszczyk, P., Greedy algorithms for general biorthogonal systems, J. Approx Theory, 107, N2, 293-314 (2000) · Zbl 0974.65053 |
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