Comparison Of Jacobi Iteration Method And Gauss-Seidel Iteration Method In Solving Fuzzy Linear Equation Systems Using A Computer

Abstract

A linear equation with n variables x1, x2, x3,..... xn as an equation with the form a1 x1 + a2 x2 +..... an xn = b, where a1, a2,.....an and b are real constants. A system of linear equations is a finite collection of linear equations in the variables x1, x2,.... xn. A solution to a system of equations is a sequence of integers s1, s2,....= sn that solves each of the system's equations. The goal of this research is to compare the Jacobi Iteration Method with the Gauss-Seidel Iteration Method in order to find the solution to the Fuzzy Linear Equation System. The Jacobi iteration technique is an indirect method that begins with a rough estimate. A approach for solving a system of linear equations is the Jacobi method. A convergent approach is the Jacobi method. As a result, each equation must be adjusted such that the absolute value coefficients are the highest. The most recently computed values are utilized in all computations in the Gauss-Seidel iteration technique. The next step is to compare the two approaches by looking at the number of iterations and which error value is superior in solving the Fuzzy Linear Equation System after receiving the results of the iteration of the two ways.