Results 311 to 320 of about 3,102,564 (352)

Nonlinear Approximation and (Deep) ReLU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {ReLU}$$\end{document}

Constructive approximation, 2019
This article is concerned with the approximation and expressive powers of deep neural networks. This is an active research area currently producing many interesting papers.
I. Daubechies, Ronald A. DeVore, S. Foucart, Boris Hanin, G. Petrova   +4 more
semanticscholar   +1 more source

Nonlinear Approximation of Random Functions

SIAM Journal on Applied Mathematics, 1997
Summary: Given an orthonormal basis and a certain class \(X\) of vectors in a Hilbert space \(H\), consider the following nonlinear approximation process: approach a vector \(x\in X\) by keeping only its \(N\) largest coordinates, and let \(N\) go to infinity.
A. Cohen, Jean-Pierre D'Ales
semanticscholar   +2 more sources

Nonlinear Nonnested Spline Approximation

Constructive Approximation, 2016
Linear and in particular non-linear spline approximation is a most useful tool in the approximation of for instance two-dimensional functions. Usually, piecewise polynomial splines with more and more refined knot-sequences are considered as elements of nested spaces spanned by splines. Generalising from this point of view, it is interesting to consider
Lind, Martin, Petrushev, Pencho
openaire   +1 more source

Nonlinear Wavelet Approximation in BMO

Constructive Approximation, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ivanov, Kamen G., Petrushev, Pencho
openaire   +1 more source

Nonlinear smoothing: approximate algorithms

Applied Mathematics and Computation, 1979
In this paper the method of stochastic linearization is employed to develop new approximate algorithms for nonlinear smoothing. Both fixed-point and fixed-interval smoothing cases are considered. An example is included to illustrate the use of the algorithms.
Chan, W. K., Kumar, K. S. P.
openaire   +1 more source

Nonlinear system approximations

26th IEEE Conference on Decision and Control, 1987
We are interested in approximating a nonlinear system by a feedback linearizable system instead of a linear system. Two approaches presently exist in the literature. One involves the concept of involutivity to a certain order, and the other considers a canonical expansion and pure feedback approximation.
Richard Goldthwait, L. Hunt
openaire   +1 more source

Fuzzy-Approximation-Based Adaptive Output-Feedback Control for Uncertain Nonsmooth Nonlinear Systems

IEEE transactions on fuzzy systems, 2018
This paper proposes a solution to adaptive output-feedback control for a class of nonsmooth nonlinear systems. First, the concept of semiglobally uniformly ultimately bounded (SGUUB) stability that has been widely used for smooth nonlinear systems with ...
Xudong Zhao, Xinyong Wang, Guangdeng Zong, Hongmin Li   +3 more
semanticscholar   +1 more source

Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation

arXiv.org
Accurate approximation of complex nonlinear functions is a fundamental challenge across many scientific and engineering domains. Traditional neural network architectures, such as Multi-Layer Perceptrons (MLPs), often struggle to efficiently capture ...
SS Sidharth, R. Gokul
semanticscholar   +1 more source

Nonlinear Methods of Approximation

Foundations of Computational Mathematics, 2003
This extensive survey paper is, according to its author, complementary to the survey by \textit{R. A. DeVore} [Acta Numerica 7, 51--150 (1998; Zbl 0931.65007)]. The central concept is \(m\)-term approximation, that is, approximation of a given element \(f\) of a Banach space \(X\) by linear combinations of \(\leq m\) elements \(g_k\) taken from some ...
openaire   +2 more sources

Discrete Nonlinear Mean Approximation

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1977
AbstractBest approximation on a finite set by a non‐linear family of functions with respect to a general sum “norm”, which includes as a special case the Lp norms (1 < p < ∞), is considered. Properties of best approximations are given. It is shown that a local minimum of the error may not be a global minimum. Computation of best approximations is
openaire   +2 more sources