Analysis of the effectiveness of methods for solving systems of linear algebraic equations in calculating the integral characteristics of the functioning of distributed information processing systems
Abstract
Analysis of the effectiveness of methods for solving systems of linear algebraic equations in calculating the integral characteristics of the functioning of distributed information processing systems
Incoming article date: 22.01.2022The paper presents the results of numerical experiments on solving systems of linear algebraic equations (SLAE) with discharged matrices by the LU decomposition method, the Jacobi method, the Gauss-Seidel method, the modified Gauss-Seidel method and the modified Jacobi method with a relaxation parameter ω. In the course of numerical experiments on the solution of (SLAE) with test discharged matrices of various dimensions using the MATLAB package, it was found that the best results in the time of solving the problem were obtained by the modified Gauss-Seidel method with a relaxation parameter ω = 0.5 or a given accuracy of solutions ε= 10^-6. In the future, this method was used to calculate the integral characteristics of the functioning of distributed information processing systems for various practical applications.average system response time to user requests).
Keywords: distributed information processing system, a system of linear algebraic, equations, sparse matrix, LU decomposition, Jacobi method, Gauss-Seidel method, relaxation parameter