## 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.

原文 | 英語 |
---|---|

頁（從 - 到） | 291-313 |

頁數 | 23 |

期刊 | Numerical Linear Algebra with Applications |

卷 | 23 |

發行號 | 2 |

DOIs | |

出版狀態 | 已發佈 - 2016 3月 1 |

## ASJC Scopus subject areas

- 代數與數理論
- 應用數學