On the convergence of Monte Carlo method to solve system of linear algebraic equations

In this study, after reviewing the Monte Carlo method for solving system of linear algebraic equations and convergence theorems, we discuss more the convergence of the Monte Carlo method using the Ulam-von Neumann algorithm related to selection the transition probability matrix. Moreover we investigate the convergence conditions in the special cases of the introduced transition probability matrix. Finally, we represent numerical results to illustrate the efficiency of the theoretical results