Criteria for nonsingular H-matrices

Abstract—Nonsingular H − matrices play a very important role in matrix analysis and numerical algebra. Based on the concept and properties of the generalized strictly diagonal dominance matrices, we partition the row and column index set of square matrix, construct a positive diagonal matrix according to the elements and row sum, column sum of the matrix as well, then obtain several new criteria for the nonsingular H − matrices, and extend the criteria of nonsingular H − matrices. Finally, advantages are illustrated by a numerical example. Keywords- H − matrices, α − diagonally dominant matrices, strictly diagonally dominant matrix. I