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https://ah.lib.nccu.edu.tw/handle/140.119/90190| 題名: | 三對角QR算則之位移策略 Shifts of origin for the real symmetric tridiagonal QR algorithm |
作者: | 黃建發 | 貢獻者: | 王太林 黃建發 |
日期: | 1990 | 上傳時間: | 3-May-2016 | 摘要: | 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: | 參考文獻: | [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the Symmetric Case,\"Department of Pure and Applied Mathematics Chemin du Cyclotron,2, 1348 Louvain-la-Neuve Belgium, unpublished paper.\r\n[DT] T. J. Dekker and J. F. Traub (1971). \"The Shifted QR Algorithm for Hermitian Matrices,\" 1. Linear Algebra Appl. 4, p137--54.\r\n[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.\r\n[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.\r\n[Pa] B. N. Parlett (1980). The Symmetric Eigenvalue Problem, PrenticeHall, Englewood Cliffs, N.J.\r\n[Sa] Youcef Saad (1974). \"Shifts of Origin for the QR Algorithm,\"Toronto: Pro. IFIP Congress.\r\n[Wa] Tai-Lin Wang (1988). Unpublished manuscripts.\r\n[Wi1] J. H. Wilkinson (1965). The Algebraic Eigenvalue Problem,Clarendon Press, Oxford.\r\n[Wi2] J. H. Wilkinson (1968). \"Global Convergence of Tridiagonal QR Algorithm with Origin Shifts,\" 1. Linear Algebra Appl. I, p409-20. | 描述: | 碩士 國立政治大學 應用數學系 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#B2002005455 | 資料類型: | thesis |
| Appears in Collections: | 學位論文 |
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