The Monte-Carlo algorithm for the solving of systems of linear algebraic equations by the Seidel method

Abstract

The iteration algorithm is used to solve systems of linear algebraic equations by the Monte-Carlo method. Each next iteration is simulated as a random vector such that its expectation coincides with the Seidel approximation of the iteration process. We deduce a system of linear equations such that mutual correlations of components of the limit vector and correlations of two iterations satisfy them. We prove that limit dispersions of the random vector of solutions of the system exist and are finite.