| dc.contributor.advisor | 王太林 | zh_TW |
| dc.contributor.author (作者) | 黃建發 | zh_TW |
| dc.creator (作者) | 黃建發 | zh_TW |
| dc.date (日期) | 1990 | en_US |
| dc.date (日期) | 1989 | en_US |
| dc.date.accessioned | 3-五月-2016 14:17:43 (UTC+8) | - |
| dc.date.available | 3-五月-2016 14:17:43 (UTC+8) | - |
| dc.date.issued (上傳時間) | 3-五月-2016 14:17:43 (UTC+8) | - |
| dc.identifier (其他 識別碼) | B2002005455 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/90190 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系 | zh_TW |
| dc.description.abstract (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: | zh_TW |
| dc.description.tableofcontents | 0 Introduction.....................................1 1 Preliminary 1.1 The QR Algorithm............................2 1.2 The Importance of Shifts...........................3 2 Shift Strategies ...........................5 3 Analysis 3.1 The Optimal Shift...........................11 3.2 The Modified Optimal Shift...........................16 3.3 The Third-order Shift ...........................20 4 NumericaI Examples 4.1 The Mixed Shift...........................24 4.2 Comparison of Shifts ...........................25 4.3 Properties of Convergence ...........................27 4.4 Estimate of Eigenvalues ...........................28 5 Conclusions ...........................31 Appendix ...........................33 References...........................41 | zh_TW |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#B2002005455 | en_US |
| dc.title (題名) | 三對角QR算則之位移策略 | zh_TW |
| dc.title (題名) | Shifts of origin for the real symmetric tridiagonal QR algorithm | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (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in the Symmetric Case,"Department of Pure and Applied Mathematics Chemin du Cyclotron,2, 1348 Louvain-la-Neuve Belgium, unpublished paper. [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. | zh_TW |
