Research On Diagonally Dominant Matrix,Block Diagonally Dominant Matrix And The Relevant Special Matrices

Several kinds of diagonally dominant matrices and block diagonally dominant matrices play an important role in numerical mathematics, economics and statistics, many scholars have gotten important conclusions on them. In this paper, further research are carried out on their identification, properties and applications.In chapter one, firstly, we introduced several kinds of diagonally dominant matrices' definition and their connection. Secondly, the relationship between those kinds of matrices and the convergence of some basic iteration methods (such as Jacobi, Seidel and SOR iteration methods) are also mentioned. Thirdly, several kinds of block diagonally dominant matrices' definition and their connection are introduced.In chapter two, we recommend some methods for how to identify generalized diagonally dominant matrices, point out the relationship between generalized diagonally dominant matrices and generalized subdiagonally dominant matrices, and besides, we give a succinct proof to an equivalence condition of the generalized diagonally dominant matrices.In chapter three, we discussed some properties of Kronecker sum of some matrices, such as M-matrices, H-matrices, diagonally dominant matrices and a - diagonally dominant matrices, and study the solution of the matrix equation AX+XB=C.In chapter four, block diagonally dominant matrices and block diagonally dominant matrices are combined, some important results are got.