Greedy algorithms and best \(m\)-term approximation with respect to biorthogonal systems

DOI10.1007/BF02514500zbMath1003.41020OpenAlexW1983701661MaRDI QIDQ5943952

Peter Oswald

Publication date: 20 January 2003

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/59686

zbMATH Keywords

Haar systembiorthogonal systems in Banach spacesgreedy algorithmsnonlinear \(m\)-term approximationuncondionality

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (7)

Embeddings and Lebesgue-type inequalities for the greedy algorithm in Banach spaces ⋮ New parameters and Lebesgue-type estimates in greedy approximation ⋮ Lebesgue inequalities for the greedy algorithm in general bases ⋮ Bidemocratic bases and their connections with other greedy-type bases ⋮ Democracy functions and optimal embeddings for approximation spaces ⋮ Best \(m\)-term approximation and Lizorkin-Triebel spaces ⋮ Lebesgue constants for the weak greedy algorithm

Cites Work

• The Franklin system is an unconditional basis in \(H_ 1\)
• The best \(m\)-term approximation and greedy algorithms
• Greedy algorithm and \(m\)-term trigonometric approximation
• Greedy algorithms and \(M\)-term approximation with regard to redundant dictionaries
• Nonlinear approximation in finite-dimensional spaces
• Some remarks on greedy algorithms
• Weak greedy algorithms
• Greedy algorithm for general biorthogonal systems
• Tree approximation and optimal encoding
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