期刊论文详细信息
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 卷:237
Solving large-scale continuous-time algebraic Riccati equations by doubling
Article
Li, Tiexiang1  Chu, Eric King-wah2  Lin, Wen-Wei3  Weng, Peter Chang-Yi2 
[1] Southeast Univ, Dept Math, Nanjing 211189, Jiangsu, Peoples R China
[2] Monash Univ, Sch Math Sci, Clayton, Vic 3800, Australia
[3] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu 300, Taiwan
关键词: Continuous-time algebraic Riccati equation;    Doubling algorithm;    Krylov subspace;    Large-scale problem;   
DOI  :  10.1016/j.cam.2012.06.006
来源: Elsevier
PDF
【 摘 要 】

We consider the solution of large-scale algebraic Riccati equations with numerically low-ranked solutions. For the discrete-time case, the structure-preserving doubling algorithm has been adapted, with the iterates for A not explicitly computed but in the recursive form A(k) = A(k-1)(2) - (DkSk-1)-S-(1)[D-k((2))](T), with D-k((1)) and D-k((2)) being low-ranked and S-k(-1) being small in dimension. For the continuous-time case, the algebraic Riccati equation will be first treated with the Cayley transform before doubling is applied. With n being the dimension of the algebraic equations, the resulting algorithms are of an efficient O(n) computational complexity per iteration, without the need for any inner iterations, and essentially converge quadratically. Some numerical results will be presented. For instance in Section 5.2, Example 3, of dimension n = 20 209 with 204 million variables in the solution X, was solved using MATLAB on a MacBook Pro within 45 s to a machine accuracy of O(10(-16)). (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free   

【 预 览 】
附件列表
Files Size Format View
10_1016_j_cam_2012_06_006.pdf 249KB PDF download
  文献评价指标  
  下载次数:0次 浏览次数:0次