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.

14 pages; in prin in JAMC (Journal of Applied Mathematics and Computing)