Results 1 to 10 of about 59,729 (100)
Optimal Stable Nonlinear Approximation [PDF]
Foundations of Computational Mathematics, 2021 While it is well known that nonlinear methods of approximation can often perform dramatically better than linear methods, there are still questions on how to measure the optimal performance possible for such methods. This paper studies nonlinear methods of approximation that are compatible with numerical implementation in that they are required to be ...
Cohen, Albert +3 more
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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}}\
Shen, Zuowei +2 more
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Numerical approximation of nonlinear SPDE’s
Stochastics and Partial Differential Equations: Analysis and Computations, 2022 AbstractThe numerical analysis of stochastic parabolic partial differential equations of the form $$\begin{aligned} du + A(u)\, dt = f \,dt + g \, dW, \end{aligned}$$ d u
Martin Ondreját +2 more
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A nonlinear quantum adiabatic approximation [PDF]
Nonlinearity, 2020 This paper is devoted to a generalisation of the quantum adiabatic theorem to a nonlinear setting. We consider a Hamiltonian operator which depends on the time variable and on a finite number of parameters and acts on a separable Hilbert space of which we select a fixed basis. We study an evolution equation in which this Hamiltonian acts on the unknown
Fermanian Kammerer, Clotilde +1 more
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Nonlinear Knowledge in Kernel Approximation [PDF]
IEEE Transactions on Neural Networks, 2007 Prior knowledge over arbitrary general sets is incorporated into nonlinear kernel approximation problems in the form of linear constraints in a linear program. The key tool in this incorporation is a theorem of the alternative for convex functions that converts nonlinear prior knowledge implications into linear inequalities without the need to ...
O L, Mangasarian, E W, Wild
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Nonlinear Approximation by Trigonometric Sums [PDF]
Journal of Fourier Analysis and Applications, 1995 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
DeVore, R.A., Temlyakov, V.N.
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Nonlinear eigenvalue approximation
Numerische Mathematik, 1988 For each \(\lambda\) in some domain D in the complex plane, let F(\(\lambda)\) be a linear, compact operator on a Banach space X and let F be holomorphic in \(\lambda\). Assuming that there is a \(\xi\) so that I- F(\(\xi)\) is not one-to-one, we examine two local methods for approximating the nonlinear eigenvalue \(\xi\).
Smith, P.W., Moss, W.F., Ward, J.D.
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Nonlinear Approximation with Redundant Dictionaries [PDF]
Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005., 2006 In this paper we study nonlinear approximation and data representation with redundant function dictionaries. In particular, approximation with redundant wavelet bi-frame systems is studied in detail. Several results for orthonormal wavelets are generalized to the redundant case. In general, for a wavelet bi-frame system the approximation properties are
Borup, Lasse +2 more
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Optimal nonlinear approximation
Manuscripta Mathematica, 1989 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
DeVore, R., Howard, R., Micchelli, C.
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Nonlinear approximation using Gaussian kernels
Journal of Functional Analysis, 2010 15 Pages; corrected typos; to appear in J.
Hangelbroek, Thomas, Ron, Amos
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