A structure-preserving doubling algorithm for solving a class of quadratic matrix equation with $ M $-matrix

<abstract><p>Consider the problem of finding maximal nonpositive solvent $ \varPhi quadratic matrix equation (QME) X^2 + BX C = 0 with B being a nonsingular M $-matrix and an such that B^{-1}C\ge $. Such QME arises from overdamped vibrating system. Recently, under condition - I is $-matrix, Yu et al. (<italic>Appl. Math. Comput.</italic>, 218 (2011): 3303–3310) proved \rho(\varPhi)\le 1 for this QME. In paper, same condition, we slightly improve their result prove \rho(\varPhi) < $, which important convergence structure-preserving doubling algorithm. Then, new globally monotonically quadratically convergent algorithm solving developed. Numerical examples are presented to demonstrate feasibility effectiveness our method.</p></abstract>