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

Han, Hai-Shan; Del Popolo, Antonino; Xia, Zun-Quan

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

Authors

Han, Hai-Shan

Del Popolo, Antonino

Xia, Zun-Quan

Description

This paper is to explore a model of the ABS Algorithms dealing with the solution of a class of systems of linear stochastic equations $Aξ=η$ when $η$ is a $m$-dimensional normal distribution. It is shown that the stepsize $α_i$ is distributed as $N(u_i,σ_i)$ (being $u_i$ the expected value of $α_i$ and $σ_i$ its variance) and the approximation to the solutions $ξ_{i}$ is distributed as $N_n(U_i,Σ_i)$ (being $U_i$ the expected value of $ξ_i$ and $Σ_i$ its variance), for this algorithm model.
14 pages; in prin in JAMC (Journal of Applied Mathematics and Computing)