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Weak Convergence of a Greedy Algorithm and the WN-Property.
- Source :
-
Mathematical Notes . Apr2023, Vol. 113 Issue 3/4, p475-479. 5p. - Publication Year :
- 2023
-
Abstract
- We study the weak convergence of a greedy algorithm of approximation by a given set in a Banach space. It is proved that the greedy algorithm of approximation by a strongly norm-reducing set in a uniformly smooth Banach space with the WN-property weakly converges. In an arbitrary separable Banach space without the WN-property, we construct an example of a strongly norm-reducing set such that the greedy algorithm of approximation by this set does not weakly converge for some initial element. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BANACH spaces
*APPROXIMATION algorithms
*GREEDY algorithms
Subjects
Details
- Language :
- English
- ISSN :
- 00014346
- Volume :
- 113
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Mathematical Notes
- Publication Type :
- Academic Journal
- Accession number :
- 163121757
- Full Text :
- https://doi.org/10.1134/S0001434623030197