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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 Lp[0, 1] (1< p < 1) 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.


Dilworth, S. J., Odell, E., Schlumprecht, Th., & Zsak, A. (2010). On the Convergence of Greedy Algorithms for Initial Segments of the Haar Basis. Math. Proc. Camb. Phil. Soc., 148, 519-529.

©Mathematical Proceedings of the Cambridge Philosophical Society 2010, Cambridge University Press

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