Convergence of Jacobi and Gauss-Seidel Method and Error Reduction Factor
HarpinderKaur HarpinderKaur · IOSR Journal of Mathematics · 2012
In this paper, it is shown that neither of the iterative methods always converges.That is, it is possible to apply the Jacobi method or the Gauss-Seidel method to a system of linear equations and obtain a divergent sequence of approximations.In such cases, it is said that the method diverges.So for convergence, the Diagonal Dominance of the matrix is necessary condition before applying any iterative methods.Moreover, also discussed about the error reduction factor in each iteration in Jacobi and Gauss-Seidel method.