A New Monte Carlo Algorithm for Linear Algebraic Systems Based on the “Walk on Equations” Algorithm

A new Monte Carlo algorithm for solving systems of Linear Algebraic (LA) equations is presented and studied. The algorithm is based on the “Walk on Equations” Monte Carlo method recently developed by Ivan Dimov, Sylvain Maire and Jean Michel Sellier [4]. The algorithm is optimized by choosing the appropriate values for the relaxation parameters which leads to dramatic reduction in time and lower relative errors for a given number of iterations. Numerical tests are performed for examples with matrices of different size and on a system coming from a finite element approximation of a problem describing a beam structure in constructive mechanics.