A criterion for generalized doubly α-chain diagonally dominant matrix

Let A=(aij)∈Cn×n,if there exists α∈(0,1) which can make |aii| |ajj|≥Riα(A)Rαj(A)S1-αj(A)S1-αj(A) be right for i,j∈N,i≠j,then A is called a doubly α-chain diagonally dominant matrix.In order to obtain some simple determinate conditions for nonsingular H-matrix,the concept to generalized doubly α-chain diagonally dominant matrix was extended,the concept generalized doubly α-chain diagonally dominant matrix to obtain a new criteria condition was applied for a matrix to be a generalized doubly α-chain diagonally dominant matrix.The theory of doubly α-chain diagonally dominant matrix and nonsingular H-matrix are improved and completed.