Algorithms and error bounds for multivariate piecewise constant approximation [PDF]
, 2010 We review the surprisingly rich theory of approximation of functions of many vari- ables by piecewise constants. This covers for example the Sobolev-Poincar´e inequalities, parts of the theory of nonlinear approximation, Haar wavelets and tree ...
Davydov, Oleg
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On the stability of a class of essentially nonlinear difference systems
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012 The problem of the zero solution stability for a certain class of essentially nonlinear difference systems is studied. Theorems on the stability by the inhomogeneous approximation are proved.
A. A. Sultanbekov
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Echo-State Restricted Boltzmann Machines: A Perspective on Information Compensation
IEEE Access, 2019 Feature learning has been introduced in the modeling of echo state networks (ESNs). However, the procedure of feature learning is generally accompanied by certain information loss.
Xiaochuan Sun +3 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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A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients [PDF]
Communications in Mathematical Sciences, 2018 In recent years deep artificial neural networks (DNNs) have been successfully employed in numerical simulations for a multitude of computational problems including, for example, object and face recognition, natural language processing, fraud detection ...
Arnulf Jentzen +2 more
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Justification of the log-KdV equation in granular chains: the case of precompression [PDF]
, 2014 For travelling waves with nonzero boundary conditions, we justify the logarithmic Korteweg-de Vries equation as the leading approximation of the Fermi-Pasta-Ulam lattice with Hertzian nonlinear potential in the limit of small anharmonicity.
Dumas, Eric, Pelinovsky, Dmitry
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Nonlinear Approximation by $q$-Favard-Sz{\'a}sz-Mirakjan Operators of Max-Product Kind
Communications in Advanced Mathematical Sciences, 2023 In this study, nonlinear $q$-Favard-Sz{\'a}sz-Mirakjan operators of max-product kind are defined and approximation properties of these operators are investigated. Classical approximation and $A$-statistical approximation theorems are given.
Ecem Acar, Döne Karahan
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Multidimensional Approximation of Nonlinear Dynamical Systems [PDF]
Journal of Computational and Nonlinear Dynamics, 2018 A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only.
Patrick Gelß +3 more
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Nonlinear magnetic response of the magnetized vacuum to applied electric field [PDF]
, 2012 We find first nonlinear correction to the field, produced by a static charge at rest in a background constant magnetic field. It is quadratic in the charge and purely magnetic.
Gitman, Dmitry M., Shabad, Anatoly E.
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Automatic rational approximation and linearization of nonlinear eigenvalue problems [PDF]
IMA Journal of Numerical Analysis, 2018 We present a method for solving nonlinear eigenvalue problems (NEPs) using rational approximation. The method uses the Antoulas–Anderson algorithm (AAA) of Nakatsukasa, Sète and Trefethen to approximate the NEP via a rational eigenvalue problem.
Pieter Lietaert +3 more
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