The best \(m\)-term approximations on generalized Besov classes \(M\, B_{q, \theta}^{\Omega}\) with regard to orthogonal dictionaries

DOI10.1016/J.JAT.2010.05.005zbMath1209.41007OpenAlexW2068346149MaRDI QIDQ619046

Liqin Duan

Publication date: 21 January 2011

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2010.05.005

zbMATH Keywords

greedy algorithmgeneralized Besov classbest \(m\)-term approximationorthogonal dictionary

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Best approximation, Chebyshev systems (41A50) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (5)

Kolmogorov and Linear Widths on Generalized Besov Classes in the Monte Carlo Setting ⋮ Nonlinear wavelet approximation of periodic function classes with generalized mixed smoothness ⋮ Best \(m\)-term trigonometric approximation for periodic functions with low mixed smoothness from the Nikol'skii-Besov-type classes ⋮ Approximative characteristics of functions from the classes \( {S}_{p,\theta}^{\Omega } B(\mathbb R^d)\) with a given majorant of mixed moduli of continuity ⋮ Representation and \(m\)-term approximation for anisotropic Besov classes

Cites Work

• Representation and approximation of periodic functions of several variables with given mixed modulus of continuity
• Greedy algorithms with regard to multivariate systems with special structure
• Universal bases and greedy algorithms for anisotropic function classes
• On best \(m\)-term approximations and the entropy of sets in the space \(L^ 1\)
• Continuous algorithms in \(n\)-term approximation and nonlinear widths
• Greedy algorithm for functions with low mixed smoothness
• Linear widths of the classes B p,θ Ω of periodic functions of many variables in the space L q
• Best Approximations and Kolmogorov and Trigonometric Widths of the Classes B Ω p,θ of Periodic Functions of Many Variables
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