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.

翻译：本文针对具有稀疏低秩矩阵的大规模随机连续时间代数Riccati方程，提出了一种RADI型求解方法。该RADI型方法的新变体通过将原始RADI方法的核心思想与随机连续时间代数Riccati方程中左半张量积的隐式表现形式相结合而构建。该方法采用不同位移加速收敛，并运用压缩技术降低存储需求与计算复杂度。与牛顿型方法、同伦方法等现有大规模问题求解方法不同，本方法能以较低代价计算残差，且无需难以获取的稳定化初始近似。数值实验验证了该方法的有效性。