On Linear Versus Nonlinear Approximation in the Average Case Setting

DOI10.1007/978-3-319-72456-0_46zbMath1405.41014OpenAlexW2804654011MaRDI QIDQ4611839

Leszek Plaskota

Publication date: 22 January 2019

Published in: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-72456-0_46

Mathematics Subject Classification ID

Gaussian processes (60G15) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46) Approximation by arbitrary linear expressions (41A45)

Uses Software

• Wavelet and Multiscale Library

Cites Work

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• Average best \(m\)-term approximation
• Gaussian measures in Banach spaces
• Nonlinear methods of approximation
• Average-case analysis of numerical problems
• Adaptive wavelet methods for the stochastic Poisson equation
• Information-based nonlinear approximation: an average case setting
• Optimal nonlinear approximation
• Free-knot spline approximation of stochastic processes
• Noisy Information and Computational Complexity
• Nonlinear Approximation of Random Functions
• On the importance of combining wavelet-based nonlinear approximation with coding strategies
• Compressed sensing
• Complexity of neural network approximation with limited information: A worst case approach

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