Abstract: Nonsingular $H$-matrices, as an essential special matrices in the area of matrix theory, has been widely used in many fields such as computational mathematics, statistics, elastic mechanics and neural networks. Therefore, it is important to study its determination criteria. This paper is focused on the direct criteria for nonsingular $H$-matrix. A set of simple and novel practical criteria for nonsingular $H$-matrices are obtained through forming different positive diagonal factors and new parameters. The obtained results improve some recent studies and expand the range of determination criteria for nonsingular $H$-matrices. Three numerical examples illustrate the advantages of the proposed new conditions.

Key words: diagonally dominant matrix, nonsingular $H$-matrix, irreducible, nonzero elements chain