On the convergence of greedy algorithms for initial segments of the Haar basis Academic Article uri icon

abstract

  • AbstractWe 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.

published proceedings

  • Mathematical Proceedings of the Cambridge Philosophical Society

author list (cited authors)

  • DILWORTH, S. J., ODELL, E., SCHLUMPRECHT, T. H., & ZSK, A.

citation count

  • 1

complete list of authors

  • DILWORTH, SJ||ODELL, E||SCHLUMPRECHT, TH||ZSÁK, ANDRÁS

publication date

  • May 2010