## Abstract

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.

Original language | English |
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Pages (from-to) | 67-85 |

Number of pages | 19 |

Journal | Linear Algebra and Its Applications |

Volume | 679 |

DOIs | |

Publication status | Published - 2023 Dec 15 |

## Keywords

- Invariant subspace
- Orthogonal flow
- Orthogonal iteration
- Riccati differential equation (RDE)

## ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics