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arXiv · 0905.3036

On the convergence of greedy algorithms for initial segments of the Haar basis

S. J. Dilworth·E. Odell·Th. Schlumprecht·A. Zsak
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Abstract

We consider the $X$-Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial segment of the Haar basis in $L_p[0,1]$ ($1 < p < \infty$) then the algorithms terminate after finitely many iterations and that the number of iterations is bounded by a function of the length of the initial segment. We also prove a more general result for a class of strictly monotone bases.

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S. J. Dilworth, E. Odell, Th. Schlumprecht, A. Zsak. 2009-05-19. On the convergence of greedy algorithms for initial segments of the Haar basis. https://doi.org/10.1017/s0305004109990478

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