This paper introduces a new algorithm for solving large-scale continuous-time algebraic Riccati equations (CARE). The advantage of the new algorithm is in its immediate and efficient low-rank formulation, which is a generalization of the Cholesky-factored variant of the Lyapunov ADI method. We discuss important implementation aspects of the algorithm, such as reducing the use of complex arithmetic and shift selection strategies. We show that there is a very tight relation between the new algorithm and three other algorithms for CARE previously known in the literature—all of these seemingly different methods in fact produce exactly the same iterates when used with the same parameters: they are algorithmically different descriptions of the same approximation sequence to the Riccati solution.

中文翻译：

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RADI：一种用于大规模代数 Riccati 方程的低阶 ADI 类型算法

本文介绍了一种求解大规模连续时间代数 Riccati 方程 (CARE) 的新算法。新算法的优势在于其直接高效的低秩公式，它是 Lyapunov ADI 方法的 Cholesky-factored 变体的推广。我们讨论了算法的重要实现方面，例如减少复杂算术和移位选择策略的使用。我们表明，新算法与文献中先前已知的其他三种 CARE 算法之间存在非常紧密的关系——所有这些看似不同的方法实际上在使用相同参数时产生完全相同的迭代：它们在算法上是不同的描述与 Riccati 解相同的近似序列。