Jacobi Method, Gauss-Siedel Method, and Successive Over-Relaxation Method for Solving Linear Systems

Abstract

This review article discusses iterative methods for linear systems. We explain general ideas of iterations and focus on three famous iterative methods, namely, Jacobi method, Gauss-Siedel method, and successive over-relaxation (SOR) method. We present ideas behind the formulas of iterations, make convergence analysis, illustrate examples, and discuss related iterative methods. In conclusion, Jacobi and Gauss-Siedel methods guarantee convergences when the matrix coefficients of the linear system are strictly diagonally dominant. The SOR method is convergent if we
apply it to positive definite matrices and choose an appropriate value of weighted factor.