Numerical methods for a class of quadratic matrix equations

Abstract

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