Generalized Alternating Iterative Method And The Schur Complement

This paper investigates alternating iterative method and generalized alternating method for the solution of a large linear system, extend the convergence theorem and comparison theorem for generalized or alternating iterative method when the coefficient are Hermitian positive definite systems. At the same time, this paper investigates Schur complements and diagonal-Schur complements of generalized doubly diagonally dominant matrices. The thesis consists of three chapters.In chapter 1, we mainly introduced the paper selected topic background, simultaneously made the outline to the iterative methods and Schur complements.In chapter 2, we sets up the convergence theory of the alternating method for solving Hermitian positive definite systems of linear equations, and establishes the corresponding comparison theorem on its asymptotic convergence rate. On the other hand, we introduce the convergence theories for generalized alternating method, parallel synchronous iterative methods and parallel alternating synchronous iterative methods when the coefficient matrix are Hermitian positive definite matrices.In chapter 3, we obtain a theorem on the distribution of eigenvalues for Schur complements of generalized doubly diagonally dominant matrices. Futher, we give a property of diagonal-Schur complements on generalized doubly diagonally dominant matrices.