Low-rank alternating direction doubling algorithm for solving large-scale continuous time algebraic Riccati equations
<|reference_start|>Low-rank alternating direction doubling algorithm for solving large-scale continuous time algebraic Riccati equations: 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.<|reference_end|>
@article{zhang2024low-rank,
    title={Low-rank alternating direction doubling algorithm for solving
  large-scale continuous time algebraic Riccati equations},
    author={Juan Zhang and Wenlu Xun},
    journal={arXiv preprint arXiv:2404.12155},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.12155},
    primaryClass={math.NA cs.NA}
}