The Research On The Relative Problems Of Two Classes Of Special Matrices

In this dissertation, some criterea of nonsingular H-matrix, some new basic properties of inverse H-matrix and the convergence theorems of some iterative methods for the system of linear equations are given. There are eight chapters altogether.In chapter 1, the background of this dissertation is introduced. In chapter 2, some critera for nonsingular H-matrix are given and some examples are presented to show the superiority of the critera. In chapter 3, the critera for the degree of stability of linear ordinary system are given. In chapter 4, some new basic propeties of inverse H-matrix are studied on the basis of paper [16]. In chapter 5, the convergence of generalized alterating iterative method for the system of linear equations is studied when the coefficient matrix is a nonsingular H-matrix and some comparison theorems of spectral radius of the iterative matrix are given when the coefficient matrix is a nonsingular M-matrix (a subclass of nonsingular H-matrix). In chapter 6, the convergence of parallel alterating iterative method for the system of linear equations is studied when the coefficient matrix is a nonsingular H-matrix and some comparison theorems of spectral radius of the iterative matrix are given when the coefficient matrix is a nonsingular M-matrix (a subclass of nonsingular H-matrix). In chapter 7, the convergence of two-stage multisplitting iterative method for the system of linear equations is studied when the coefficient matrix is a nonsingular H-matrix. In chapter 8, the convergence of the extrapolated iterative methods for the system of linear equations is studied when the coefficient matrix is a singular H-matrix and a singular Hermitian positive semidefinite matrix, respectively.