On the convergence of greedy algorithms for initial segments of the Haar basis
On the convergence of greedy algorithms for initial segments of the Haar basis
复制标题
Haar基初始段贪心算法的收敛性
DOI：
--
复制
发表时间：
2009
影响因子：
0.8
通讯作者：
A. Zsák
中科院分区：
文献类型：
--
作者：
S. Dilworth;E. Odell;T. Schlumprecht;A. Zsák
摘要本文研究了以严格单调基为字典的有限维Banach空间中的X-贪婪算法和对偶贪婪算法。我们证明了当字典是Lp[0，1]（1 < p < ∞）中Haar基的初始段时，算法在多次迭代后终止，且迭代次数受初始段长度的函数限制.我们还证明了一类严格单调基的一个更一般的结果。
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.