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On the validity of the variational approximation in discrete nonlinear Schrödinger equations
Physica D: Nonlinear Phenomena, 2012Dmitry E Pelinovsky, Guido Schneider
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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}}\
Zuowei Shen +2 more
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Nonlinear Approximations in Cryptanalysis Revisited [PDF]
IACR Transactions on Symmetric Cryptology, 2018 This work studies deterministic and non-deterministic nonlinear approximations for cryptanalysis of block ciphers and cryptographic permutations and embeds it into the well-understood framework of linear cryptanalysis.
Christof Beierle +2 more
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On-line Nonlinear Sparse Approximation of Functions [PDF]
2007 IEEE International Symposium on Information Theory, 2007 This paper provides new insights into on-line nonlinear sparse approximation of functions based on the coherence criterion. We revisit previous work, and propose tighter bounds on the approximation error based on the coherence criterion. Moreover, we study the connections between the coherence criterion and both the approximate linear dependence ...
Paul Honeiné +2 more
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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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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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Mathematics, 2021 A method for identification of structures of a complex signal and noise suppression based on nonlinear approximating schemes is proposed. When we do not know the probability distribution of a signal, the problem of identifying its structures can be ...
Oksana Mandrikova +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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