A simple estimation for the spectral radius of (block) H-matrices

Simple bounds for the spectral radius of an H-matrix and a block H-matrix are presented, respectively, i.e., ρ ( A ) < 2 max i | a ii | for an H-matrix A = ( a ij ) and ρ ( A ) < max i ( ∥ A ii ∥ + ∥ A ii - 1 ∥ - 1 ) for a block H-matrix A = ( A ij ) , where ρ ( A ) denote the spectral radius.