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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/151280


    Title: The Orthogonal flows for orthogonal iteration
    Authors: 郭岳承
    Kuo, Yueh-Cheng;Lin, Huey-Er;Shieh, Shih-Feng
    Contributors: 應數系
    Keywords: Orthogonal iteration;Invariant subspace;Orthogonal flow;Riccati differential equation (RDE)
    Date: 2023-12
    Issue Date: 2024-05-24 11:34:30 (UTC+8)
    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.
    Relation: Linear Algebra and its Applications, Vol.679, pp.67-85
    Data Type: article
    DOI link: https://doi.org/10.1016/j.laa.2023.09.002
    DOI: 10.1016/j.laa.2023.09.002
    Appears in Collections:[Department of Mathematical Sciences] Periodical Articles

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