Bounds for Approximate Solutions of Fredholm Integral Equations Using Kernel Networks

Authors: G. Gnecco, Věra Kůrková, M. Sanguineti
Publication year: 2011
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Artificial Neural Networks and Machine Learning - ICANN 2011. Part I
Projects: Learning of functional relationships from high-dimensional data
Bibliographic citation: GNECCO, G., KŮRKOVÁ, Věra, SANGUINETI, M. Bounds for Approximate Solutions of Fredholm Integral Equations Using Kernel Networks. In: HONKELA, T., DUCH, W., GIROLAMI, M., KASKI, S., eds. Artificial Neural Networks and Machine Learning - ICANN 2011. Part I. Berlin: Springer, 2011, S. 126-133. Lecture Notes in Computer Science, 6791. ISBN 978-3-642-21734-0. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-642-21735-7_16
DOI: 10.1007/978-3-642-21735-7_16
ID: 359504

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.