ISSN:
1572-9044
Keywords:
ill-posed problems
;
least-squares collocation
;
neural networks
;
network training
;
regularization
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper is devoted to the analysis of network approximation in the framework of approximation and regularization theory. It is shown that training neural networks and similar network approximation techniques are equivalent to least-squares collocation for a corresponding integral equation with mollified data. Results about convergence and convergence rates for exact data are derived based upon well-known convergence results about least-squares collocation. Finally, the stability properties with respect to errors in the data are examined and stability bounds are obtained, which yield rules for the choice of the number of network elements.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1016641629556
