A new two-phase structure-preserving doubling algorithm for critically singular M-matrix algebraic Riccati equations

Tsung Ming Huang, Wei Qiang Huang, Ren Cang Li*, Wen Wei Lin

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

2 引文 斯高帕斯(Scopus)

摘要

Summary: Among numerous iterative methods for solving the minimal nonnegative solution of an M-matrix algebraic Riccati equation, the structure-preserving doubling algorithm (SDA) stands out owing to its overall efficiency as well as accuracy. SDA is globally convergent and its convergence is quadratic, except for the critical case for which it converges linearly with the linear rate 1/2. In this paper, we first undertake a delineatory convergence analysis that reveals that the approximations by SDA can be decomposed into two components: the stable component that converges quadratically and the rank-one component that converges linearly with the linear rate 1/2. Our analysis also shows that as soon as the stable component is fully converged, the rank-one component can be accurately recovered. We then propose an efficient hybrid method, called the two-phase SDA, for which the SDA iteration is stopped as soon as it is determined that the stable component is fully converged. Therefore, this two-phase SDA saves those SDA iterative steps that previously have to have for the rank-one component to be computed accurately, and thus essentially, it can be regarded as a quadratically convergent method. Numerical results confirm our analysis and demonstrate the efficiency of the new two-phase SDA. Copyright

原文英語
頁(從 - 到)291-313
頁數23
期刊Numerical Linear Algebra with Applications
23
發行號2
DOIs
出版狀態已發佈 - 2016 三月 1

ASJC Scopus subject areas

  • 代數與數理論
  • 應用數學

指紋

深入研究「A new two-phase structure-preserving doubling algorithm for critically singular M-matrix algebraic Riccati equations」主題。共同形成了獨特的指紋。

引用此