A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation
文献类型：期刊论文
| 作者 | Guo, XX; Lin, WW; Xu, SF |
| 刊名 | NUMERISCHE MATHEMATIK
 |
| 出版日期 | 2006-05-01 |
| 卷号 | 103期号:3页码:393-412 |
| 关键词 | nonsymmetric algebraic Riccati equation minimal nonnegative solution structure-preserving doubling algorithm |
| ISSN号 | 0029-599X |
| DOI | 10.1007/s00211-005-0673-7 |
| 英文摘要 | In this paper, we propose a structure-preserving doubling algorithm (SDA) for the computation of the minimal nonnegative solution to the nonsymmetric algebraic Riccati equation (NARE), based on the techniques developed for the symmetric cases. This method allows the simultaneous approximation to the minimal nonnegative solutions of the NARE and its dual equation, requiring only the solutions to two linear systems and several matrix multiplications per iteration. Similar to Newton's method and the fixed-point iteration methods for solving NAREs, we also establish global convergence for SDA under suitable conditions, using only elementary matrix theory. We show that sequences of matrices generated by SDA are monotonically increasing and quadratically convergent to the minimal nonnegative solutions of the NARE and its dual equation. Numerical experiments show that the SDA algorithm is feasible and effective, and outperforms Newton's iteration and the fixed-point iteration methods. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000237189800003 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/2497]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Guo, XX |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100080, Peoples R China 2.Natl Tsing Hua Univ, Dept Math, Hsinchu 300, Taiwan 3.Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China |
| 推荐引用方式 GB/T 7714 | Guo, XX,Lin, WW,Xu, SF. A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation[J]. NUMERISCHE MATHEMATIK,2006,103(3):393-412. |
| APA | Guo, XX,Lin, WW,&Xu, SF.(2006).A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation.NUMERISCHE MATHEMATIK,103(3),393-412. |
| MLA | Guo, XX,et al."A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation".NUMERISCHE MATHEMATIK 103.3(2006):393-412. |
入库方式： OAI收割
来源：数学与系统科学研究院
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