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

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 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. © 2010 Cambridge Philosophical Society.

author list (cited authors)

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

citation count

  • 1

publication date

  • January 2010