Sufficient Conditions For Symmetric MSOR Convergence Of A Class Of 2 - Cyclic Coefficient Matrices

Solution of the system of linear equations Ax=b, the commonly used method is divided into direct method and iterative method two kinds, direct method, as the name implies, iteration method is a kind of continuous with the old values of vari-ables recursive New value cycle. Relatively simple equation, we will choose the direct method to solve equation, but when the complex problems, especially the unknown quantity is large, the iteration method is used to solve the large Linear equation (group) one of the most main method. The main have Jacobi iteration method in the study of, Gauss-Seidel, SOR, AOR, SIP, PE, incomplete decomposition method and iterative method. Iterative method research lies in the convergence of iterative method and convergence speed. No convergence of the iterative format no research value, and slow convergence speed of iteration will inevitably be replaced by the iteration method of fast convergence speed. So choose the appropriate iteration method and determine the involved in the iterative format Some of the parameters of the size of the range to achieve the optimal iterative convergence. In addition, the convergence of iterative method is closely connected with the nature of the co-efficient matrix of linear equations are linked, such as when the coefficient matrix of the M, H, L, Nonnegative matrix and a cyclic matrix, the irreducible matrix, and so on, with the properties of matrix, the iteration method of study will also have different restrictions.This article main research is in the coefficient matrix of linear equations for2-circulation coefficient matrix under the condition of large, when the coefficient matrix of Jacobi iteration matrix eigenvalues of square for pure imaginary, The sufficient conditions for symmetric MSOR iteration convergence method. Chapter structure and arrangement of specific content is as follows:Chapter1:Preliminaries. we give the basic concepts which will be used in this paper.Chapter2:2-circulation coefficient matrix is symmetrical MSOR iteration method is introduced and2-the basic equations of circulation coefficient matrix is symmetrical MSOR iteration method to set up and proved.Chapter3:Symmetric MSOR law under the special relaxation parameter con-vergence under the sufficient conditions and general relaxation parameters of suffi- cient conditions for the convergence of symmetric MSOR method. The main dis-cussion in different relaxation parameters Convergence under the condition of the limit value, makes the symmetric MSOR convergence.Chapter4:about the thesis puts forward the unsolved problem for further analysis and elaboration.