Newton's method for solving cross-coupled sign-indefinite algebraic Riccati equations for weakly coupled large-scale systems
Newton's method for solving cross-coupled sign-indefinite algebraic Riccati equations for weakly coupled large-scale systems
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DOI：
10.1016/j.amc.2006.09.100
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发表时间：
2007-05
期刊：
影响因子：
--
通讯作者：
H. Mukaidani
中科院分区：
文献类型：
--
作者：
H. Mukaidani
提出了一种求解弱耦合大系统交叉耦合符号不定代数Riccati方程的新算法。结果表明，由于所提出的算法是基于牛顿法，达到二次收敛。此外，研究了CSARE收敛解的局部唯一性。最后，为了克服牛顿法计算大型稀疏矩阵的困难，将不动点算法与交替方向隐式（ADI）方法相结合。
In this paper, a new algorithm for solving cross-coupled sign-indefinite algebraic Riccati equations (CSAREs) for weakly coupled large-scale systems is proposed. It is shown that since the proposed algorithm is based on the Newton’s method, the quadratic convergence is attained. Moreover, the local uniqueness of the convergence solutions for the CSAREs is investigated. Finally, in order to overcome the computation of large- and sparse-matrix related to the Newton’s method, the fixed point algorithm and the alternating direction implicit (ADI) method are combined.