Preconditioned Iterative Method Of Solving Linear Equations

With the development of the computers, numerical analysis concerned with the solution of linear systems of equations is always used in the practical and mathematic problems. For a linear system, we study the several preconditioning method in this paper. It is quite common to use preconditioning to accelerate the convergence of a basic iterative scheme which is very useful to solve the large sparse coefficient matrix.We improve the preconditioned AOR iterative scheme for irreducible L-matrices considered and then we prove the convergence of our method. Lastly, numerical experiments to illustrate the theoretical results are provided. When choosing the approximately optimal parameters, our scheme has small spectral radii of the iterative matrices than the spectral radii of AOR iterative scheme, which is shown through numerical examples.We present the relaxed nonstationary two-stage multisplitting method using an outer splitting and the SSOR multisplitting as inner splitting. Then, we study the convergence of the proposed method for solving the linear system whose coefficient matrix is an H -matrix. At last, we give the specific convergence of this method of argumentation and its application. Chosen the approximately optimal parameters, the proposed method gets faster convergent rate than the convergent rate of relaxed SSOR multisplitting method, which will be shown through numerical example.