Adaptive quarklet tree approximation Adaptive quarklet tree approximation

This paper is concerned with near-optimal approximation of a given univariate function with elements of a polynomially enriched wavelet frame, a so-called quarklet frame. Inspired by hp -approximation techniques of Binev, we use the underlying tree structure of the frame elements to derive an adapti...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 50; no. 6
Main Authors Dahlke, Stephan, Hovemann, Marc, Raasch, Thorsten, Vogel, Dorian
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2024
Springer Nature B.V
Subjects
Adaptive algorithms
Approximation
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Visualization
Adaptive numerical algorithms
Wavelets
Tree-based algorithms
42C40
Near-best approximation
hp-refinement
65D15
Quarkonial decompositions
41A15
65T60
65D07
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Summary:This paper is concerned with near-optimal approximation of a given univariate function with elements of a polynomially enriched wavelet frame, a so-called quarklet frame. Inspired by hp -approximation techniques of Binev, we use the underlying tree structure of the frame elements to derive an adaptive algorithm that, under standard assumptions concerning the local errors, can be used to create approximations with an error close to the best tree approximation error for a given cardinality. We support our findings by numerical experiments demonstrating that this approach can be used to achieve inverse-exponential convergence rates.
Bibliography:ObjectType-Article-1
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-024-10205-9