A counter-example to the general convergence of partially greedy algorithms

JOURNAL OF APPROXIMATION THEORY

卷:111

Article

Gribonval, R

关键词: nonlinear approximation;    greedy algorithms;    redundant dictionary;    convergence;   

DOI  :  10.1006/jath.2001.3566

来源: Elsevier

【 摘 要 】

In a separable Hilbert space H, greedy algorithms iteratively define nz-term approximants to a given vector from a complete redundant dictionary D. With very large dictionaries, the pure greedy algorithm cannot be implemented and must be replaced with a weak greedy algorithm. In numerical applications, partially greedy algorithms have been introduced to reduce the numerical complexity. A conjecture about their convergence arises naturally from the observation of numerical experiments. We introduce, study and disprove this conjecture. (C) 2001 Academic Press.

【 授权许可】

Free