### 摘要

We consider the projected Lyapunov and Stein equations arising in model order reduction and optimal control of descriptor systems. The projected Lyapunov equation is transformed to an equivalent projected Stein equation then solved by a generalized Smith iterative method. For a projected general Stein equation with a singular matrix "E", a double Cayley transform is devised to remove the singularity, and then the generalized Smith method is applied. Numerical examples are provided to demonstrate the feasibility and efficiency of our approach.

原文 | 英語 |
---|---|

頁（從 - 到） | 191-204 |

頁數 | 14 |

期刊 | UPB Scientific Bulletin, Series A: Applied Mathematics and Physics |

卷 | 80 |

發行號 | 2 |

出版狀態 | 已發佈 - 2018 一月 1 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Applied Mathematics

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## 引用此

Yu, B., Fan, H. Y., & Chu, E. K. W. (2018). Smith method for projected Lyapunov and Stein equations.

*UPB Scientific Bulletin, Series A: Applied Mathematics and Physics*,*80*(2), 191-204.