This paper proposes an effective low-rank alternating direction doubling algorithm (R-ADDA) for computing numerical low-rank solutions to large-scale sparse continuous-time algebraic Riccati matrix equations. The method is based on the alternating direction doubling algorithm (ADDA), utilizing the low-rank property of matrices and employing Cholesky factorization for solving. The advantage of the new algorithm lies in computing only the $2^k$-th approximation during the iterative process, instead of every approximation. Its efficient low-rank formula saves storage space and is highly effective from a computational perspective. Finally, the effectiveness of the new algorithm is demonstrated through theoretical analysis and numerical experiments.

翻译：本文提出了一种有效的低秩交替方向加倍算法（R-ADDA），用于计算大规模稀疏连续时间代数Riccati矩阵方程的数值低秩解。该方法基于交替方向加倍算法（ADDA），利用矩阵的低秩特性，并采用Cholesky分解进行求解。新算法的优势在于迭代过程中仅计算第$2^k$次近似值，而非每次近似值。其高效的低秩公式节省了存储空间，并从计算角度展现出高效性。最后，通过理论分析和数值实验验证了新算法的有效性。