Diagonal update method for a quadratic matrix equation.

The quadratic matrix equation A X 2 + B X + C = 0 has been studied in many researches. The sufficient condition for the existence of the primary solution is already provided where the equation arose from an overdamped vibrating system with M-matrix coefficients. The Bernoulliu0027s method can not be modified by relaxation in this equation. In this paper, we will introduce the diagonal update method and modify the Bernoulliu0027s method.