Convergence Analysis Of The Aor Iterative Method And Gaor Iterative Method

The method and theory of matrix calculation have become an indispensable tool of treating various mathematical problems in science and technology, a core problem of numerical algebra’s research is presented to solve the large scale sparse linear systems, it has become very important to study the efficient solution of linear equations. In this paper, we investigate some iterative methods of large sparse linear system.Firstly, we introduce the background. Then, we introduce some iterative methods for the solution of linear systems of equations.Firstly, we study the convergence of AOR method and we give the area of convergence when the coefficient matrix of a linear system is a strictly double a chain diagonally dominant matrix and a strictly double sum α diagonally dominant matrix, respectively.Secondly, we analyze the convergence of GAOR iterative method when the coefficient matrix is a strictly doubly a diagonally dominant matrix.Finally, we analyze the preconditioned GAOR iterative method, and we compare it with GAOR iterative method. And we prove that the convergence speed of preconditioned GAOR iterative method is faster than GAOR iterative method and we give one numerical example.