Abstract: Based on the generalized strictly α-diagonally dominant matrices and its related concepts and properties, by dividing the matrix index set, forming corresponding positive diagonal factors and setting new parameters, we gave  a set of practical new criteria for nonsingular H-matrices,  expanding the judgment range of nonsingular H-matrices. Finally, numerical examples were used to illustrate the effectiveness of the new criterion.

Key words: nonsingular H-matrix,  , generalized strictly α-diagonally dominant matrix, irreducible α-diagonally dominant matrix, α-diagonal dominant matrix with a nonzero elements chain