The orthogonal flows for orthogonal iteration

Yueh Cheng Kuo, Huey Er Lin*, Shih Feng Shieh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)67-85
Number of pages19
JournalLinear Algebra and Its Applications
Publication statusPublished - 2023 Dec 15


  • 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


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