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

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