Parallel Monte Carlo computations for solving SLAE with minimum communications

In this paper we introduce a new development of Monte Carlo methods for solving system of linear algebraic equations. We discuss compressing the data and we consider a suitable statistical distribution to generate the non zero elements of the coefficient matrix in the system given by x = Ax + f. In this way we eliminate sending all elements of the matrix and even the compressed partitioned matrix in parallel implementation. We obtain only the parameters of the distribution of non zero elements of the coefficient matrix and we just send these parameters. Therefore, we minimize the amount of data sent during the computation.