An Abs Algorithm for a Class of Systems of Stochastic Linear Equations

Abstract

This paper is to explore a model of the ABS Algorithms dealing with the solution of a class of systems of linear stochastic equations $A\xi=\eta$ when $\eta$ is a $m$-dimensional normal distribution. It is shown that the stepsize $\alpha_i$ is distributed as $N(u_i,\sigma_i)$ (being $u_i$ the expected value of $\alpha_i$ and $\sigma_i$ its variance) and the approximation to the solutions $\xi_{i}$ is distributed as $N_n(U_i,\Sigma_i)$ (being $U_i$ the expected value of $\xi_i$ and $\Sigma_i$ its variance), for this algorithm model.