Convergence of Solutions to Equations Arising in Neural Networks

A. Leizarowitz

Journal of Optimization Theory and Applications, 1997, vol. 94, issue 3, No 1, 533-560

Abstract: Abstract We study polynomial ordinary differential systems $$\dot M(t) = QM - M(M'QM){\text{, }}M(0) = M_0 ,t \geqslant 0,$$ whereQ≥0 is an n×n matrix and M(t) is an n×k matrix. It is proven that, as t grows to infinity, the solution M(t) tends to a limit BU, where U is a k×k orthogonal matrix and B is an n×k matrix whose columns are k pairwise orthogonal, normalized eigenvectors of Q. Moreover, for almost every M 0, these eigenvectors correspond to the k maximal eigenvalues of Q; for an arbitrary Q with independent columns, we provide a procedure of computing B by employing elementary matrix operations on M 0. This result is significant for the study of certain neural network systems, and in this context it shows that M(∞) provides a principal component analyzer.

Keywords: Polynomial differential equations; convergence of solutions; neural network systems; optimal control (search for similar items in EconPapers)
Date: 1997
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1022633615273 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:94:y:1997:i:3:d:10.1023_a:1022633615273

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1023/A:1022633615273

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().