A modified Newton's method for rational Riccati equations arising in stochastic control

@article{Chu2011AMN,
  title={A modified Newton's method for rational Riccati equations arising in stochastic control},
  author={Eric King-Wah Chu and Tiexiang Li and Wen-Wei Lin and Chang-Yi Weng},
  journal={2011 International Conference on Communications, Computing and Control Applications (CCCA)},
  year={2011},
  pages={1-6}
}
We consider the solution of the rational matrix equations, or generalized algebraic Riccati equations with rational terms, arising in stochastic optimal control in continuous- and discrete-time. Fixed-point iteration and (modified) Newton's methods will be considered. In particular, the convergence results of a new modified Newton's method, for both continuous- and discrete-time rational Riccati equations, will be presented.