Bounds for approximate solutions of Fredholm integral equations using kernel networks

Authors:
Giorgio Gnecco;Věra Kůrková;Marcello Sanguineti
Affiliations:
Department of Communications, Computer, and System Sciences, University of Genoa, Genova, Italy;Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 8, Czech Republic;Department of Communications, Computer, and System Sciences, University of Genoa, Genova, Italy
Venue:
ICANN'11 Proceedings of the 21th international conference on Artificial neural networks - Volume Part I
Year:
2011

Citing 12
Cited 0

Approximation and radial-basis-function networks

Neural Computation
Rate of approximation results motivated by robust neural network learning

COLT '93 Proceedings of the sixth annual conference on Computational learning theory
The nature of statistical learning theory

The nature of statistical learning theory
Approximation and learning of convex superpositions

Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Complexity of Gaussian-radial-basis networks approximating smooth functions

Journal of Complexity
Accuracy of suboptimal solutions to kernel principal component analysis

Computational Optimization and Applications
Approximate Minimization of the Regularized Expected Error over Kernel Models

Mathematics of Operations Research
Some comparisons of complexity in dictionary-based and linear computational models

Neural Networks
Numerical solution of the two-dimensional Fredholm integral equations using Gaussian radial basis function

Journal of Computational and Applied Mathematics
On the exponential convergence of matching pursuits in quasi-incoherent dictionaries

IEEE Transactions on Information Theory
Geometric Upper Bounds on Rates of Variable-Basis Approximation

IEEE Transactions on Information Theory
A neural network approach for solving Fredholm integral equations of the second kind

Neural Computing and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

Approximation of solutions of integral equations by networks with kernel units is investigated theoretically. There are derived upper bounds on speed of decrease of errors in approximation of solutions of Fredholm integral equations by kernel networks with increasing numbers of units. The estimates are obtained for Gaussian and degenerate kernels.