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

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

2009-05-19

arxiv.org/abs/0905.3036v1

Mathematics

Functional Analysis

Scientific paper

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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