The orthogonal flows for orthogonal iteration

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


研究成果: 雜誌貢獻期刊論文同行評審


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.

頁(從 - 到)67-85
期刊Linear Algebra and Its Applications
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


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