Inexact Iterative Methods for Solving Matrix Riccati Equations Arising in Stochastic Control

摘要

In this paper, we consider the matrix Riccati equation arising in stochastic control. Newton's method is very expensive since the matrices in applications can be very large. In [1], Guo proposed a much less expensive iteration. We propose an inexact variant which allows one to control the number of the inner iterations, and also give the conditions under which the monotonicity and global convergence results also hold for the inexact method. Numerical tests report the effectiveness of this proposed method.