  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.
