METHODS FOR ACCELERATION OF APPROXIMATE SOLUTION OF A SYSTEM OF LINEAR ALGEBRAIC EQUATIONS BY THE MONTE CARLO METHOD

Abstract

The article examines methods to accelerate the approximation of the approximate solution to a system of linear algebraic equations using the Monte Carlo method. Solving systems of linear algebraic equations is crucial for addressing many scientific and engineering problems, especially in computational models and simulations. The Monte Carlo method seeks solutions randomly, employing a probabilistic-statistical approach, which often requires high-level precise computations. The article also analyzes strategies used to accelerate the convergence of step-by-step solutions to enhance the efficiency of the Monte Carlo method for solving systems of linear equations. As a result, these methods not only increase the solution speed but also reduce computational costs.