Monte Carlo Algorithms for Solving Linear Systems

This paper presents two different monte carlo algorithms for obtaining thesolution of vector x in linear system x=ax+f, where a is a given non singular matrixand f is a known vector with the same size as a. in this paper, we consider twoindividual transition probabilities for our monte carlo computations. consideringdifferent statistical nature for generating the random walk to select the nonzero entriesof the coefficient matrix a, are caused different accuracy and computational times forour employed algorithms.we first make monte carlo estimator for the elements of the solution vector x, then wedetermine the monte carlo estimation of the solution vector x based on its unbiasedestimator. finally, we present the computational results obtained by two differenttransition probabilities.