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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}}\
Haizhao Yang, Shijun Zhang, Zuowei Shen
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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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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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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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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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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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Deep Residual Learning for Nonlinear Regression
Entropy, 2020 Deep learning plays a key role in the recent developments of machine learning. This paper develops a deep residual neural network (ResNet) for the regression of nonlinear functions.
Dongwei Chen +3 more
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Nonlinear Bivariate Bernstein–Chlodowsky Operators of Maximum Product Type
Journal of Mathematics, 2022 The positive nonlinear operators with maximum and product were introduced by Bede. In this study, nonlinear maximum product type of bivariate Bernstein–Chlodowsky operators is defined and the approximation properties are investigated with the help of new
Özge Özalp Güller +2 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 ...
Olvi L. Mangasarian, Edward W. Wild
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