On the Convergence of Greedy Algorithms for Initial Segments of the Haar Basis

Author(s)

S J. Dilworth, University of South Carolina - ColumbiaFollow
E Odell, University of Texas at AustinFollow
TH Schlumprecht, Texas A & M University - College StationFollow
Andras Zsak, Lancaster UniversityFollow

Document Type

Article

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 < 1) 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.

Publication Info

Mathematical Proceedings of the Cambridge Philosophical Society, Volume 148, 2010, pages 519-529.

Dilworth, S. J., Odell, E., Schlumprecht, Th., & Zsak, A. (2010). On the Convergence of Greedy Algorithms for Initial Segments of the Haar Basis. Math. Proc. Camb. Phil. Soc., 148, 519-529.

©Mathematical Proceedings of the Cambridge Philosophical Society 2010, Cambridge University Press

Rights

Dilworth, S. J., Odell, E., Schlumprecht, Th., & Zsak, A. (2010). On the Convergence of Greedy Algorithms for Initial Segments of the Haar Basis. Math. Proc. Camb. Phil. Soc., 148, 519-529.

©Mathematical Proceedings of the Cambridge Philosophical Society 2010, Cambridge University Press