Interpolation by ridge polynomials and its application in neural networks

Journal of Computational and Applied Mathematics

Volumn 144, Issue 1-2, 2002, Pages 197-209

  Li, Xin ^a  

^a UNIVERSITY OF NEVADA   (United States)

Author keywords

Neural networks; Polynomial interpolation; Ridge functions

Indexed keywords

CALCULATIONS; INTERPOLATION; POLYNOMIALS;

ARBITRARY POINTS;

NEURAL NETWORKS;

NEURAL NETWORK;

EID: 0036644587     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(01)00560-X     Document Type: Article

References (22)

1. Universal approximation bounds for superpositions of a sigmoidal function
2. On multivariate polynomial interpolation
3. Computational aspects of polynomial interpolation in several variables
4. Realization of neural networks with one hidden layer
5. On lattices admitting unique Lagrange interpolations
6. Approximation by superpositions of a sigmoidal function
7. Upper bounds on the number of hidden neurons in feedforward networks with arbitrary bounded nonlinear activation functions
8. Polynomial interpolation in several variables
9. Nonlinearity creates linear independence
10. Superposition of linearly independent functions and finite mappings by neural networks
11. k functions
12. Construction of lattices for Lagrange interpolation in projective space
13. Simultaneous approximations of multivariate functions and their derivatives by neural networks with one hidden layer
14. On simultaneous approximations by radial basis function neural networks
15. Interpolation of scattered data: Distance matrices and conditionally positive definite functions
16. k
17. Approximation theory of the MLP model in neural networks
18. A simple method to derive bounds on the size and to train multilayer neural networks
19. On multivariate Lagrange interpolation
20. Deterministic convergence of an on-line gradient method for neural networks, this issue