Interpolation by ridge polynomials and its application in neural networks
type: Item
instance of: scholarly article
title: Interpolation by ridge polynomials and its application in neural networks
zbMATH Open document ID: 0999.41003
DOI: 10.1016/S0377-0427(01)00560-X
author: Xin Li
published in: Journal of Computational and Applied Mathematics
publication date: 2002-08-22T00:00:00Z
review text: In this paper the author studies a computational algorithm for training feedforward neural networks through multivariate interpolation by polynomials and explicitly constructive procedure. However, first the author considers multivariate interpolation at arbitrary points by ridge polynomials. Then several effective interpolation formulas are derived using effective ridge polynomials. A set of ridge polynomials with least degree of interpolation is also provided.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A30
zbMATH DE Number: 1787656
zbMATH Keywords: polynomial interpolation
zbMATH Keywords: ridge functions
zbMATH Keywords: neural networks
zbMATH Keywords: Kergin interpolation
reviewed by: Ganesh Datta Dikshit
MaRDI profile type: Publication
cites work: Universal approximation bounds for superpositions of a sigmoidal function
cites work: On multivariate polynomial interpolation
cites work: Computational Aspects of Polynomial Interpolation in Several Variables
cites work: On Lattices Admitting Unique Lagrange Interpolations
cites work: Approximation by superpositions of a sigmoidal function
cites work: Polynomial interpolation in several variables
cites work: Nonlinearity creates linear independence
cites work: Q4885199
cites work: A natural interpolation of \(C^ k \)functions
cites work: Construction of lattices for Lagrange interpolation in projective space
cites work: Simultaneous approximations of multivariate functions and their derivatives by neural networks with one hidden layer
cites work: On simultaneous approximations by radial basis function neural networks
cites work: Interpolation of scattered data: distance matrices and conditionally positive definite functions
cites work: A formula for Kergin interpolation in \(R^ k\).
cites work: Q4938227
cites work: Networks and the best approximation property
cites work: On Multivariate Lagrange Interpolation
cites work: Deterministic convergence of an online gradient method for neural networks
full work available at URL: s0377-0427(01)00560-x
OpenAlex ID: W2056554781
description: scientific article; zbMATH DE number 1787656