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<p>In this paper, we propose an effective low-rank alternating direction doubling algorithm (R-ADDA) for computing numerical low-rank solutions of large-scale sparse continuous-time algebraic Riccati matrix equations. Our algorithm represents a further extension of the alternating direction doubling algorithm, utilizing the low-rank property of matrices. It is only required to compute one recursion and may apply the associated low-rank structures, solving large-scale problems efficiently. The low-rank formula can save storage space and computational complexity. Finally, we offer theoretical analysis and numerical experiments to illustrate the effectiveness of the derived algorithm.</p>

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Low-rank Alternating Direction Doubling Algorithm for Solving Large-scale Continuous Time Algebraic Riccati Equations

  • 期刊论文

  • 发表日期：

    2025年3月10日

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  • Juan Zhang,
  • Wenlu Xun

摘要

In this paper, we propose an effective low-rank alternating direction doubling algorithm (R-ADDA) for computing numerical low-rank solutions of large-scale sparse continuous-time algebraic Riccati matrix equations. Our algorithm represents a further extension of the alternating direction doubling algorithm, utilizing the low-rank property of matrices. It is only required to compute one recursion and may apply the associated low-rank structures, solving large-scale problems efficiently. The low-rank formula can save storage space and computational complexity. Finally, we offer theoretical analysis and numerical experiments to illustrate the effectiveness of the derived algorithm.