Results 221 to 230 of about 66,291 (256)

Simultaneous approximations of multivariate functions and their derivatives by neural networks with one hidden layer

Neurocomputing, 1996
Let \(\sigma\) be a non-polynomial activation function of a neural network that has \(n\)th order continuous derivatives on \(R\). This paper shows that for any compact set \(K\) of \(R^s\), \(s\geq 1\), and any multivariate function \(f\) defined on an open set containing \(K\), a neural network with one hidden layer can be so constructed that \(f ...
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Multivariate numerical approximation using constructive $$ L^{2} (\mathbb{R}) $$ RBF neural network

Neural Computing and Applications, 2011
For the multivariate continuous function, using constructive feedforward $$ L^{2} (\mathbb{R}) $$ radial basis function (RBF) neural network, we prove that a $$ L^{2} (\mathbb{R}) $$ RBF neural network with n + 1 hidden neurons can interpolate n + 1 multivariate samples with zero error.
Muzhou Hou, Xuli Han
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Multivariate Error Function Based Neural Network Operators Approximation

2015
Here we present multivariate quantitative approximations of real and complex valued continuous multivariate functions on a box or \(\mathbb {R}^{N},\) \(N\in \mathbb {N}\), by the multivariate quasi-interpolation, Baskakov type and quadrature type neural network operators.
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Constructive Multivariate Approximation with Sigmoidal Functions and Applications to Neural Networks

1992
In this paper, we show how to use sigmoidal functions in order to generate approximation operators for multivariate functions of bounded variation. We start with Lebesgue-Stieltjes type convolution operators, then — via numerical quadrature — we pass over to point-evaluation operators and give local and global approximation results for them.
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Multivariate Fuzzy-Random Quasi-interpolation Neural Networks Approximation

2015
In this chapter we study the rate of multivariate pointwise and uniform convergence in the q-mean to the Fuzzy-Random unit operator of multivariate Fuzzy-Random Quasi-Interpolation neural network operators.
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Multivariate Quantitative Approximation by Perturbed Kantorovich–Shilkret Neural Network Operators

2018
This chapter deals with the determination of the rate of convergence to the unit of Perturbed Kantorovich–Shilkret multivariate normalized neural network operators of one hidden layer. These are given through the multivariate modulus of continuity of the engaged multivariate function or its high order partial derivatives and that appears in the ...
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Multivariate Fuzzy-Random Error Function Relied Neural Network Approximations

2015
In this chapter we deal with the rate of multivariate pointwise and uniform convergence in the q-mean to the Fuzzy-Random unit operator multivariate Fuzzy-Random Quasi-Interpolation error function based neural network operators.
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Deep Neural Network Approximation Theory

IEEE Transactions on Information Theory, 2021
Dmytro Perekrestenko, Philipp Grohs, Helmut Bölcskei   +2 more
exaly  

Rates of Approximation of Multivariable Functions by One-hidden-layer Neural Networks

1998
We investigate rates of approximation of multivariable functions by one-hidden-layer neural networks with a general hidden unit function. Under mild assumptions on hidden unit function we derive upper bounds on rates of approximation (measured by both the number of hidden units and the size of parameters) in terms of various norms of the function to be
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Rates of approximation by neural network interpolation operators

Applied Mathematics and Computation, 2022
Dansheng Yu
exaly