On the diagonally dominant ratio

P(論文)It is well known that if the coefficient matrix is a generalized diagonally dominant matrix, then the Jacobi and the Gauss-Seidel methods converge. We know in our experiments that the number of iteration of these iterative methods is inveresely proportional to the degree of diagonal dominance of the coefficient matrix. In this paper, our is to present the definition of the diagonally dominant ratio as the degree of the convergence rate, and we define the diagonal dominator to improve the diagonally dominant ratio.departmental bulletin pape