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Title: 三對角QR算則之位移策略
Shifts of origin for the real symmetric tridiagonal QR algorithm
Authors: 黃建發
Contributors: 王太林
Date: 1990
Issue Date: 2016-05-03 14:17:43 (UTC+8)
Abstract: QR 算則是目前常用的一種計算矩陣特徵值的方法,而適當的運用位移可增加比算則的收斂速度,本文探討五種己知的位移,並提出二種新位移.我們首先對各種位移做摘要性的探討及其收斂性的研究,其次舉出一些例子以說明各位移的利弊及其相互間的比較,並就下列三類方式對位移做排行:
Reference: [Da] Bernard Danloy (1986). "Improved Strategies of Shift for the QL Algorithm and for Inverse Iteration in the Symmetric Case,"Department of Pure and Applied Mathematics Chemin du Cyclotron,2, 1348 Louvain-la-Neuve Belgium, unpublished paper.
[DT] T. J. Dekker and J. F. Traub (1971). "The Shifted QR Algorithm for Hermitian Matrices," 1. Linear Algebra Appl. 4, p137--54.
[HP] W. Hoffman and B. N. Parlett (1978). "A New Proof of Global Convergence for the Tridiagonal QL Algorithm," SIAM. J. Numer.Anal. 15, p929-37.
[JZ] Jiang Erxiong and Zhang Zhenyue (1985). "A New shift of the QL Algorithm for Irreducible Symmetric Tridiagonal Matrices," J. Linear Algebra Appl. 65, p261-72.
[Pa] B. N. Parlett (1980). The Symmetric Eigenvalue Problem, PrenticeHall, Englewood Cliffs, N.J.
[Sa] Youcef Saad (1974). "Shifts of Origin for the QR Algorithm,"Toronto: Pro. IFIP Congress.
[Wa] Tai-Lin Wang (1988). Unpublished manuscripts.
[Wi1] J. H. Wilkinson (1965). The Algebraic Eigenvalue Problem,Clarendon Press, Oxford.
[Wi2] J. H. Wilkinson (1968). "Global Convergence of Tridiagonal QR Algorithm with Origin Shifts," 1. Linear Algebra Appl. I, p409-20.
Description: 碩士
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Data Type: thesis
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