Abstract: Firstly, we properly divided the row index sets of the matrix by utilizing the theory of α-diagonally dominant matrices. Secondly, by selecting the progressive coefficients to construct the positive diagonal matrix, we gave some determination conditions of generalized strictly α-diagonally dominant matrices, and then some determination criteria for nonsingular H-matrices were obtained. A numerical example shows that these determination criteria are effective.

Key words: diagonally dominant matrix, α-diagonally dominant matrix, nonsingular H-matrix