H-matrix Equations Preconditioned Iterative Method And The Preconditioned Diagonally Dominant

This paper mainly includes three parts:1. In chapter 2, we proposed a method to construct diagonally dominant matrix and point out that If the coefficient matrix A is an H-matrix, then PAQ is also an diagonally dominant matrix, Also we discuss the relation between diagonally dominance and parameters when A is an M-matrix. Numerical examples are also given, which show the effectiveness of our method.2. In chapter 3, the preconditioning matrix P based on preconditioner I +S is introduced. If the coefficient matrix A is an H-matrix, then PA is also an H-matrix by appropriate taking parameters.3. In chapter 4, we consider a preconditioned iterative method for solving linear system Ax = b, which is a generalization of method proposed by Zhang et al., and prove its convergence for the case when A is a nonnegative H-matrix. Numerical examples are also given, which show the effectiveness of our method.