Continuous-time algebraic Riccati equations can be found in many disciplines in different forms. In the case of small-scale dense coefficient matrices, stabilizing solutions can be computed to all possible formulations of the Riccati equation. This is not the case when it comes to large-scale sparse coefficient matrices. In this paper, we provide a reformulation of the Newton-Kleinman iteration scheme for continuous-time algebraic Riccati equations using indefinite symmetric low-rank factorizations. This allows the application of the method to the case of general large-scale sparse coefficient matrices. We provide convergence results for several prominent realizations of the equation and show in numerical examples the effectiveness of the approach.

翻译：连续时间代数Riccati方程以不同形式出现在众多学科中。对于小规模稠密系数矩阵，可计算所有可能形式的Riccati方程的镇定解；但当涉及大规模稀疏系数矩阵时则无法实现。本文通过使用不定对称低秩分解，对连续时间代数Riccati方程的牛顿-克莱因曼迭代格式进行了重新表述，使得该方法适用于一般大规模稀疏系数矩阵情形。我们给出了该方程若干重要实现形式的收敛性结果，并通过数值算例展示了该方法的有效性。