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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 連結:	https://doi.org/10.1016/j.laa.2023.09.002
DOI:	10.1016/j.laa.2023.09.002
Appears in Collections:	[應用數學系] 期刊論文

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