Some New Criteria Of Generalized H-matrices

H-matrices have a wide range of applications in economics,statistics,engi-neering and other fields. As a generalization of H-matrices under positive definite condition, generalized H-matrices play important roles in the numerical solution of 2-D or 3-D Euler equations in fluid flow computations, invariant tori of dynamical systems and matrices theory etc.In this paper,we obtain a new set of criteria for generalized H-matrices by us-ing the relation between generalized eigenvalues and generalized Rayleigh quotien-t,the relation between generalized M-matrices and M-matrices,and submatrices spectral radius estimation techniques of block matrices, which improve and gen-eralize some recent related results. In chapter one, we introduce some theoretical background, application background knowledge and recent research of generalized M-matrices. Some notations, definitions, lemmas are also given in this paper.In chapter two, by applying the relation between generalized M-matrices and M-matrices, the relationship between generalized eigenvalue and generalized rayleigh quotient, and some techniques of inequalities, we obtain several simple criterion for generalized H-matrices. At the same time, several numerical example for effective of the methods are provided.In chapter three, based on the early results, we obtain some new criteria for generalized H-matrices by constructing positive diagonal matrix D in a progressive way such that AD is block strictly diagonally dominant matrix with the partial order, which provide a theoretical basis for some iterative algorithms in chapter four.In chapter four, on the basis of the theory of the third chapter, several some iterative algorithms for distinguishing generalized H-matrices are obtained by con-structing corresponding iterative matrices, the convergence of the presented algo-rithms are also proved. Finally, we illustrate the effectiveness of each algorithm by using appropriate numerical examples.