## 摘要

In the field of scientific computation, orthogonal iteration is an essential method for computing the invariant subspace corresponding to the largest r eigenvalues. In this paper, we construct a flow that connects the sequence of matrices generated by the orthogonal iteration. Such a flow is called an orthogonal flow. In addition, we show that the orthogonal iteration forms a time-one mapping of the orthogonal flow. A generalized orthogonal flow is constructed that has the same column space as the orthogonal flow. By using a suitable change of variables, the generalized orthogonal flow can be transformed into the solution of a Riccati differential equation (RDE). Conversely, an RDE can also be transformed into a flow that can be represented by a generalized orthogonal flow.

原文 | 英語 |
---|---|

頁（從 - 到） | 67-85 |

頁數 | 19 |

期刊 | Linear Algebra and Its Applications |

卷 | 679 |

DOIs | |

出版狀態 | 已發佈 - 2023 12月 15 |

## ASJC Scopus subject areas

- 代數與數理論
- 數值分析
- 幾何和拓撲
- 離散數學和組合