An RADI-type method for stochastic continuous-time algebraic Riccati equations

Abstract: In this paper, we propose an RADI-type method for large-scale stochastic continuous-time algebraic Riccati equations with sparse and low-rank matrices. This new variant of RADI-type methods is developed by integrating the core concept of the original RADI method with the implicit appearance of the left semi-tensor product in stochastic continuous-time algebraic Riccati equations.The method employs different shifts to accelerate convergence and uses compression techniques to reduce storage requirements and computational complexity.Unlike many existing methods for large-scale problems such as Newton-type methods and homotopy method, it calculates the residual at a low cost and does not require a stabilizing initial approximation, which can often be challenging to find. Numerical experiments are provided to demonstrate its efficiency.