@article{Chen2022, 
author = {Cairong Chen},
title = {A structure-preserving doubling algorithm for solving a class of quadratic matrix equation with  M-matrix},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {2},
pages = {574-584},
keywords = {Quadratic matrix equation, structure-preserving doubling algorithm, M-matrix, maximal nonpositive solvent, quadratic convergence},
url = {https://www.sciopen.com/article/10.3934/era.2022030},
doi = {10.3934/era.2022030},
abstract = {Consider the problem of finding the maximal nonpositive solvent  Φ of the quadratic matrix equation (QME)  X2+BX+C=0 with  B being a nonsingular  M-matrix and  C an  M-matrix such that  B−1C≥0. Such QME arises from an overdamped vibrating system. Recently, under the condition that  B−C−I is a nonsingular  M-matrix, Yu et al. (Appl. Math. Comput., 218 (2011): 3303–3310) proved that  ρ(Φ)≤1 for this QME. In this paper, under the same condition, we slightly improve their result and prove that  ρ(Φ)<1, which is important for the quadratic convergence of the structure-preserving doubling algorithm. Then, a new globally monotonically and quadratically convergent structure-preserving doubling algorithm for solving the QME is developed. Numerical examples are presented to demonstrate the feasibility and effectiveness of our method.}
}