This is an announcement for the paper "On the convergence of greedy algorithms for initial segments of the Haar basis" by S.J. Dilworth, E. Odell, Th. Schlumprecht, and A. Zsak.

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.

Archive classification: math.FA

Mathematics Subject Classification: 41A65 ;42A10

The source file(s), dosz_greedy.tex: 33654 bytes, is(are) stored in gzipped form as 0905.3036.gz with size 11kb. The corresponding postcript file has gzipped size 102kb.

Submitted from: schlump@math.tamu.edu

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