Solving systems of linear equations via gradient systems with discontinuous righthand sides: application to LS-SVM

Author

Ferreira, Leonardo V. ; Kaszkurewicz, Eugenius ; Bhaya, Amit

Author_Institution

Dept. of Electr. Eng., NACAD-COPPE/Fed. Univ. of Rio de Janeiro, Brazil

Volume

16

Issue

2

fYear

2005

fDate

3/1/2005 12:00:00 AM

Firstpage

501

Lastpage

505

Abstract

A gradient system with discontinuous righthand side that solves an underdetermined system of linear equations in the L₁ norm is presented. An upper bound estimate for finite time convergence to a solution set of the system of linear equations is shown by means of the Persidskii form of the gradient system and the corresponding nonsmooth diagonal type Lyapunov function. This class of systems can be interpreted as a recurrent neural network and an application devoted to solving least squares support vector machines (LS-SVM) is used as an example.

Keywords

Lyapunov methods; convergence; gradient methods; least squares approximations; optimisation; recurrent neural nets; support vector machines; Lyapunov function; discontinuous righthand side; finite time convergence; gradient system; least squares support vector machine; linear equations; recurrent neural network; Convergence; Equations; Least squares methods; Linear programming; Lyapunov method; Neural networks; Power system modeling; Support vector machine classification; Support vector machines; Upper bound; Diagonal type functions; Persidskii systems; gradient systems; least absolute deviation; neural networks; nonsmooth systems; support vector machines (SVMs); systems of linear equations;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/TNN.2005.844091

Filename

1402512