Pretreatment Technology Research, The Iterative Method Of Linear Equations

In order to solving the non-singular linear algebra equations Ax=b,the preconditioned technique is the valid method that resolves the convergent problem, become a heating problem.This thesis mainly deals with the iterative method to solve the linear system of equations and discuss how to accelerate the rate of convergence in the condition ofprecondion.In the first part the paper mainly introduces that the iterative solving method has much superiority in solving the linear system of equations and introduces the development in preconditioned theory in recent years.The matrices we involved are usually large-scale sparse matrices,so we end this chapter by introducing the storage technology of large-scale sparse matrices.In the same time the writer provides the basic knowledge and the basic lemma required in this paper.And simply summarize the present research status of solving linear systems by preconditioning iteration method.In the second part we obtain some theorem and corollary(it is the essence of this thesis).It discusses the preconditioner P_C(α)=I+C(α) accelerate the convergence of the AOR iterative method when the matix A is an L-matrix.At Last it gives the parameterω=γ=α_i=1(i=2,3,…,n),the convergence of the AOR iterative method is the quickest one in preconditioner P_C(α)=I+C(α).We give some numerical instance to explain the conclusions of this thesis.