Neural network operators: constructive interpolation of multivariate functions

DOI10.1016/j.neunet.2015.02.002zbMath1396.41019OpenAlexW2041793405WikidataQ41087570 ScholiaQ41087570MaRDI QIDQ1669090

Danilo Costarelli

Publication date: 30 August 2018

Published in: Neural Networks (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.neunet.2015.02.002

zbMATH Keywords

order of approximationmultivariate approximationmultivariate interpolationsigmoidal functionsneural networks operatorsirregular sampling scheme

Mathematics Subject Classification ID

Linear operator approximation theory (47A58) Approximation by operators (in particular, by integral operators) (41A35) Approximation by other special function classes (41A30)

Related Items (25)

Approximation theorems for a family of multivariate neural network operators in Orlicz-type spaces ⋮ Approximation by max-product neural network operators of Kantorovich type ⋮ Max-product neural network and quasi-interpolation operators activated by sigmoidal functions ⋮ DENSITY RESULTS BY DEEP NEURAL NETWORK OPERATORS WITH INTEGER WEIGHTS ⋮ Degree of Approximation for Nonlinear Multivariate Sampling Kantorovich Operators on Some Functions Spaces ⋮ Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation ⋮ Neural network interpolation operators activated by smooth ramp functions ⋮ Solving polynomial systems using a fast adaptive back propagation-type neural network algorithm ⋮ On the approximation by single hidden layer feedforward neural networks with fixed weights ⋮ Probabilistic lower bounds for approximation by shallow perceptron networks ⋮ Saturation classes for MAX-product neural network operators activated by sigmoidal functions ⋮ A note on the applications of one primary function in deep neural networks ⋮ Pointwise and uniform approximation by multivariate neural network operators of the max-product type ⋮ Approximation by a class of neural network operators on scattered data ⋮ Detection of thermal bridges from thermographic images by means of image processing approximation algorithms ⋮ A novel recursive method to reconstruct multivariate functions on the unit cube ⋮ Convergence for a family of neural network operators in Orlicz spaces ⋮ Estimates for the neural network operators of the max-product type with continuous and \(p\)-integrable functions ⋮ Approximation results in Orlicz spaces for sequences of Kantorovich MAX-product neural network operators ⋮ Quantitative estimates involving K-functionals for neural network-type operators ⋮ Approximation by exponential sampling type neural network operators ⋮ Limitations of shallow nets approximation ⋮ On multidimensional Urysohn type generalized sampling operators ⋮ Approximate solutions of Volterra integral equations by an interpolation method based on ramp functions ⋮ The construction and approximation of ReLU neural network operators

Cites Work

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