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

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.

authors

• Schlumprecht, Thomas

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

publisher

• Cambridge University Press (CUP)  Publisher

published in

• Cambridge Philosophical Society: Mathematical Proceedings  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1017/s0305004109990478

start page

• 519

end page

• 529

volume

• 148

issue

• 3

URL

• http://dx.doi.org/10.1017/s0305004109990478