On the convergence of greedy algorithms for initial segments of the Haar basis
Dilworth, S. J. · Odell, E. · Schlumprecht, Th. · Zsak, A.
Original · EN
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 < ∞) 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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