Two Types Of Matrix Preconditioned Iterative Method Convergence

Mathematics, physics, mechanics and engineering disciplines, such as many problems are attributed to the final solution of one or a number of large-scale sparse matrix of linear equations, which are generally solved by using iterative methods. Therefore iterative methods for solving large computing problems are playing an important role. Non-convergence or slow convergence of the iterative format has no practical value. Therefore, in order to seek the rapid convergence for iterative scheme ,we need to seek the rapid convergence tfor iterative scheme,we need to determine the parameter in certain iterative scheme, and so on in the modern time.For solving these large sparse linear algebraic equations, the first iteration what have found are Jacobi iterative method and Gauss-Seidel iterative method. With the introduction of relaxation factor and the acceleration factor, such as SOR iterative method, AOR iterative method have emerged , we call these methods as the basic iterative method. They are constructed through the iterative series, check out the limits of a few to be exact solutions of the equations. These methods give us a big convenience when resolve the large-scale system of linear equations .Here are the structure and main contents of this paper.The first part is the introduction. We give methods of pre-conditions for the background, as well as the basic SOR iterative method, AOR iterative method for iterative matrix, the introduction of pre-conditions for the matrix P, and give a pre-condition of SOR, preconditioned AOR iterative method for the Diego generation matrix.The second part is the prior knowledge. Part of this is the fourth part of and the fifth part of the preparation, it mainly gives some important definitions, lemmas, such as H-matrix, Z-matrix and matrix splitting definition.The third part is that there are already conclusions. Briefly describes the pre-conditions in recent years and the development of the theory as well as some important results have been achieved.Part IV is one of the main conclusions of this article. This part of the main discussion of linear equations when the coefficient matrix is the H-matrix at the preconditioned SOR iterative method and preconditioned AOR iterative method of convergence, and discussed the H-matrix and the H-matrix comparison matrix at SOR iterative method under the conditions of the convergence rate of the comparison theorem.Part V is the other one of the main conclusions of this article. It majorly studies two different preconditioned AOR iterative method of convergence when the coefficient matrix of linear equations is non-singular Z-matrix. Even then the two preconditioned AOR iterative method with the classical AOR iterative method for the comparison theorem will be discussed.Part VI is a summary and outlook. Of this article has done a summary of certain preconditions for the iterative method of outlook.