Annals of Mathematical Sciences and Applications

Volume 4 (2019)

Number 2

Projection methods for rational Riccati equations arising in stochastic optimal control

Pages: 83 – 105



Eric King-Wah Chu (School of Mathematics, Monash University, Melbourne, Victoria, Australia)

Hung-Yuan Fan (Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan)

Liping Zhang (Department of Mathematics, Zhejiang University of Technology, Hangzhou, China)


We consider the numerical methods of large-scale rational Riccati equations, arising in stochastic optimal control. We propose a projection method or a Krylov subspace interpretation of the generalized Smith method. More importantly, we prove that some solvability conditions of the rational Riccati equation and their linearizations are inherited by the projected equation.


Krylov subspace, projection method, rational Riccati equation

2010 Mathematics Subject Classification

15A24, 65F30, 93C05

The last two authors were supported respectively by the Ministry of Science and Technology, RoC, and the National Natural Science Foundation, China (Grants MOST-105-2115-M-003-003 and 11601484).

Received 6 March 2019

Published 2 October 2019