Numerical solution of a class of quadratic matrix equations

Quadratic matrix equations arise in many fields of scientific computing and engineering applications. In this paper, we study a class of quadratic matrix equations. Firstly, we prove the existence of minimal nonnegative solution for this quadratic matrix equation under a certain condition. Then, we propose some numerical methods for solving it. Finally, convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.