Sparse approximation using new greedy-like bases in superreflexive spaces
Fecha
2023Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Impacto
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10.4064/sm220506-3-2
Resumen
This paper is devoted to theoretical aspects of optimality of sparse approximation. We undertake a quantitative study of new types of greedy-like bases that have recently arisen in the context of non-linear m-term approximation in Banach spaces as a generalization of the properties that characterize almost greedy bases, i.e., quasi-greediness and democracy. As a means to compare the efficiency of ...
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This paper is devoted to theoretical aspects of optimality of sparse approximation. We undertake a quantitative study of new types of greedy-like bases that have recently arisen in the context of non-linear m-term approximation in Banach spaces as a generalization of the properties that characterize almost greedy bases, i.e., quasi-greediness and democracy. As a means to compare the efficiency of these new bases with already existing ones in regard to the implementation of the Thresholding Greedy Algorithm, we place emphasis on obtaining estimates for their sequence of unconditionality parameters. Using an enhanced version of the original Dilworth-Kalton-Kutzarova method (2003) for building almost greedy bases, we manage to construct bidemocratic bases whose unconditionality parameters satisfy significantly worse estimates than almost greedy bases even in Hilbert spaces. [--]
Materias
Bidemocratic bases,
Superreflexive Banach spaces,
Thresholding greedy algorithm,
Unconditionality constants
Editor
Instytut Matematyczny
Publicado en
Studia Mathematica 271 (3) (2023)
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2