| dc.contributor.advisor | 王太林 | zh_TW |
| dc.contributor.advisor | Wang ,Tai-Lin | en_US |
| dc.contributor.author (Authors) | 蔡淑芬 | zh_TW |
| dc.contributor.author (Authors) | Tsai ,Shu-Fen | en_US |
| dc.creator (作者) | 蔡淑芬 | zh_TW |
| dc.creator (作者) | Tsai ,Shu-Fen | en_US |
| dc.date (日期) | 2003 | en_US |
| dc.date.accessioned | 18-Sep-2009 18:28:39 (UTC+8) | - |
| dc.date.available | 18-Sep-2009 18:28:39 (UTC+8) | - |
| dc.date.issued (上傳時間) | 18-Sep-2009 18:28:39 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0090751008 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/36398 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學研究所 | zh_TW |
| dc.description (描述) | 90751008 | zh_TW |
| dc.description (描述) | 92 | zh_TW |
| dc.description.abstract (摘要) | 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. | zh_TW |
| dc.description.abstract (摘要) | 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. | en_US |
| dc.description.abstract (摘要) | 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 | - |
| dc.description.tableofcontents | 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 | zh_TW |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0090751008 | en_US |
| dc.subject (關鍵詞) | QR Algorithm | en_US |
| dc.subject (關鍵詞) | Tridiagonal | en_US |
| dc.title (題名) | 移位QR算則在三對角矩陣上之收斂 | zh_TW |
| dc.title (題名) | Convergence of the Shifted QR Algorithm on Tridiagonal Matrices | en_US |
| dc.type (資料類型) | thesis | en |
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