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| 研究生： |
蔡淑芬 Tsai ,Shu-Fen |
|---|---|
| 論文名稱： |
移位QR算則在三對角矩陣上之收斂 Convergence of the Shifted QR Algorithm on Tridiagonal Matrices |
| 指導教授： |
王太林
Wang ,Tai-Lin |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2004 |
| 畢業學年度： | 92 |
| 語文別： | 英文 |
| 論文頁數： | 21 |
| 外文關鍵詞： | Tridiagonal |
| 相關次數： | 點閱：204 下載：19 |
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在計算矩陣的特徵值(eigenvalues)中,QR演算法是一種常見的技巧. 尤其如果使用適當的移位,將可以較快得到特徵值. 在本文中提出一種新的移位策略, 我們證明這各方法是可行的,而且可適用於任何矩陣. 換句說, 本篇論文主旨即是提出有關新的移位QR演算法的收斂.
The QR algorithm is a popular method for computing all the
eigenvalues of a dense matrix. If we use a proper shift, we can
accelerate convergence of the iterative process. Hence, we design a new shift strategy which includes an eigenvalue of the trailing principal 3-by-3 submatrix of the tridiagonal matrix. We prove the global convergence of the new strategy. In other words, the purpose of this thesis is to propose a theory of the convergence of a new shifted QR algorithm.
Abstract i
中文摘要 ii
1 Introduction 1
2 Preliminaries 2
2.1 Notation 2
2.2 The shifted QR algorithm 2
2.3 Shift strategies 4
2.4 The convergence of sequences 5
3 A Residual Estimate 5
4 Convergence of the QR Iteration 8
5 Conclusions and Future Work 11
Reference 12
Appendix 14
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J. H. Wilkinson, Global convergence of tridiagonal QR algorithm
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