Results 1 to 10 of about 3,102,564 (352)
Nonlinear Approximation via Compositions [PDF]
Neural Networks, 2019 Given a function dictionary $\cal D$ and an approximation budget $N\in\mathbb{N}^+$, nonlinear approximation seeks the linear combination of the best $N$ terms $\{T_n\}_{1\le n\le N}\subseteq{\cal D}$ to approximate a given function $f$ with the minimum approximation error\[\varepsilon_{L,f}:=\min_{\{g_n\}\subseteq{\mathbb{R}},\{T_n\}\subseteq{\cal D}}\
Zuowei Shen, Haizhao Yang, Shijun Zhang
semanticscholar +5 more sources
Nonlinear quasi-normal modes: uniform approximation
Journal of High Energy Physics, 2023 Recent works have suggested that nonlinear (quadratic) effects in black hole perturbation theory may be important for describing a black hole ringdown.
Bruno Bucciotti +3 more
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Optimal Runge approximation for nonlocal wave equations and unique determination of polyhomogeneous nonlinearities. [PDF]
Calc Var Partial Differ EquLin YH, Tyni T, Zimmermann P.
europepmc +3 more sources
Nonlinear approximation spaces for inverse problems [PDF]
Analysis and Applications, 2022 This paper is concerned with the ubiquitous inverse problem of recovering an unknown function u from finitely many measurements possibly affected by noise. In recent years, inversion methods based on linear approximation spaces were introduced in [MPPY15,
A. Cohen +3 more
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Multiscale regression on unknown manifolds
Mathematics in Engineering, 2022 We consider the regression problem of estimating functions on $ \mathbb{R}^D $ but supported on a $ d $-dimensional manifold $ \mathcal{M} ~~\subset \mathbb{R}^D $ with $ d \ll D $.
Wenjing Liao +2 more
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Nonlinear Approximation Theory
Mathematics and Computers in Simulation, 2016 S. Kuester
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A Functional Characterization of Almost Greedy and Partially Greedy Bases in Banach Spaces
Mathematics, 2021 In 2003, S. J. Dilworth, N. J. Kalton, D. Kutzarova and V. N. Temlyakov introduced the notion of almost greedy (respectively partially greedy) bases. These bases were characterized in terms of quasi-greediness and democracy (respectively conservativeness)
Pablo Manuel Berná, Diego Mondéjar
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Incrementally Solving Nonlinear Regression Tasks Using IBHM Algorithm
Journal of Telecommunications and Information Technology, 2023 This paper considers the black-box approximation problem where the goal is to create a regression model using only empirical data without incorporating knowledge about the character of nonlinearity of the approximated function.
Paweł Zawistowski, Jarosław Arabas
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators [PDF]
Nature Machine Intelligence, 2019 It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator.
Lu Lu +4 more
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Structural And Multidisciplinary Optimization, 2021 Nonlinear dynamic structural optimization is a real challenge, in particular for problems that require the use of explicit solvers, e.g., crash. Here, the number of design variables is typically very limited.
J. Triller +3 more
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