Lebesgue-type inequalities in greedy approximation
Copyright policy )Lebesgue-type inequalities in greedy approximation
We present new results regarding Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces. We improve earlier bounds in Temlyakov (Forum Math Sigma 2014), for dictionaries satisfying a new property introduced here. We apply these results to derive optimal bounds in two natural examples of sequence spaces. In particular, optimality is obtained in the case of the multivariate Haar system in Lp with 1
33 pages, 1 figure
- Autonomous University of Madrid Spain
- University of South Carolina United States
- University of Illinois at Urbana–Champaign United States
- University of South Carolina System United States
- University of Murcia Spain
Approximation by arbitrary nonlinear expressions; widths and entropy, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, weak Chebyshev greedy algorithm, Rate of convergence, degree of approximation, non-linear approximation, uniformly smooth Banach space, Functional Analysis (math.FA), Mathematics - Functional Analysis, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Geometry and structure of normed linear spaces, Algorithms for approximation of functions, FOS: Mathematics, thresholding greedy algorithm
Approximation by arbitrary nonlinear expressions; widths and entropy, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, weak Chebyshev greedy algorithm, Rate of convergence, degree of approximation, non-linear approximation, uniformly smooth Banach space, Functional Analysis (math.FA), Mathematics - Functional Analysis, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Geometry and structure of normed linear spaces, Algorithms for approximation of functions, FOS: Mathematics, thresholding greedy algorithm
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