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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:	王太林黃建發
Date:	1990 1989
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in the Symmetric Case,"Department of Pure and Applied Mathematics Chemin du Cyclotron,2, 1348 Louvain-la-Neuve Belgium, unpublished paper.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 Unpublished manuscripts.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:	碩士國立政治大學應用數學系
Source URI:	http://thesis.lib.nccu.edu.tw/record/#B2002005455
Data Type:	thesis
Appears in Collections:	[應用數學系] 學位論文

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