Solving Systems of Linear Equations Via Gradient Systems With Discontinuous Righthand Sides: Application to LS-SVM

A gradient system with discontinuous righthand side that solves an underdetermined system of linear equations in the L/sub 1/ 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.