Monte-Carlo algorithm for solution of a systems of linear algebraic equations by the Seidel’s method

Abstract

For solution of a system of linear algebraic equations by the Monte Carlo method a method of the successive approximations is used. The next in turn iteration is modeled as a random vector, the expectation of which coincides with the corresponding Seidel’s iteration. The existence and the boundedness of dispersions of the limiting vector is proved. The system of linear equations, to which satisfy the cross-correlations of the limiting vector, and the limiting correlations of two successive approximations is delivered. All these correlations are unknowns of the common linear system and may be found only simultaneously. The boundedness of dispersions of the limiting vector leads to the stochastic stability of algorithm. The number of iterations giving the desirable exactness is estimated. As an examples, the systems of the orders of n = 3 and n = 100 are studied. Refs 7. Tables 1.