Diagonal update method for a quadratic matrix equation

The quadratic matrix equation AX2+BX+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 Bernoulli's method can not be modified by relaxation in this equation. In this paper, we will introduce the diagonal update method and modify the Bernoulli's method.