Estimates of ‖MGN‖ and Their Applications to the Convergence of Splitting Methods of Linear Interval Equations

Using the properties of diagonally dominant interval matrices defined in a previous paper, a group of conditions and criteria are given for estimating ‖MGN‖ (MGis the Gauss-inverse ofM), which are more useful than those of the well-known estimate of ‖MG‖. By applying these results to the convergence of splitting methods used for solving linear interval equations such as the Jacobi, Gauss–Seidel, SOR, and regular splitting equations, we obtain some new results.