Several Classes Of Iterative Determination Methods For Generalized Strictly Diagonally Dominant Matrices

Generalized strictly diagonally dominant matrices(i.e.non-singular Hmatrices)is a very important class of matrices in matrix theory.It has a wide range of applications in computational mathematics,power system theory and mathematical physics problems.Since many problems in applications are attributed to the determination of generalized strictly diagonally dominant matrices.Therefore,it is important to study the problem of determining generalized strictly diagonally dominant matrices.In this paper,we use the ideas of subdivision and iteration to construct new positive diagonal transformation matrices,several classes of new criteria and new iterative algorithm s for determining generalized strictly diagonally dominant matrices are given.In this paper,we use the ideas of subdivision and iteration to construct new positive diagonal transformation matrices,several classes of new criteria and new iterative algorithm s for determining generalized strictly diagonally dominant matrices are given.In chapter 1,introduces the background and current status of the study of the decision problem of generalized strictly diagonally dominant matrices,and gives the basic notation,definitions,lemmas and properties related to the study of this paper.In Chapter 2,a new recursive criterion for determining generalized strictly diagonally dominant matrices is given by constructing a recursive positive diagonal factor based on the properties related to the determination of generalized strictly diagonally dominant matrices,and a numerical example is used to illustrate that the new criterion has a wider range of determination than some existing results.In Chapter 3,a new positive diagonal transformation matrix is obtained by partitioning the matrix elements,subdividing the set of non-prevailing row indicators of the matrix and constructing new iteration factors,and giving a criterion for determining the subdivision iteration of generalized strictly diagonally dominant matrices.In Chapter 4,using the properties of generalized strictly diagonally dominant matrices and the relationship between the α-chain diagonally dominant matrices and it,we give a new class of subdivided and iterative criteria for generalized strictly diagonally dominant matrices by subdividing the set of non-dominant rows of the matrix and constructing new progression coefficients,which improves some recent results.In Chapter 5,based on generalized strictly diagonally dominant matrices decision criterion given earlier,two types of iterative decision algorithm s for generalized strictly diagonally dominant matrices are given,and the superiority of the algorithm s is verified by numerical examples.