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| 研究生： |
張天財 Chang, Tian-Tsair |
|---|---|
| 論文名稱： |
有關賈可比矩陣數值建構上的討論 On the Numerical Construction of a Jacobi Matrix |
| 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： | 1999 |
| 畢業學年度： | 87 |
| 語文別： | 英文 |
| 論文頁數： | 32 |
| 中文關鍵詞： | 賈可比矩陣 、蘭可修斯過程 |
| 外文關鍵詞： | Jacobi matrix, Lanczos process |
| 相關次數： | 點閱：88 下載：0 |
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這篇論文使用前人所提出的七種方法LMGS、ITQR、imITQR、CB、HH、TLD和TLS，去造一個賈可比(Jacobi)矩陣。文中我們使用已知的特徵值(eigenvalue)和特徵向量的第一個成份，去運作這些演算法，並列出數值的結果，以比較這六種方法造出來的賈可比矩陣之準確性。
In this thesis seven methods LMGS、ITQR、imITQR、CB、HH、TLS and TLD developed in the past are applied to construct a Jacobi matrix. We use the known eige-envalues and the first components of eigenvctors of a Jacobi matrix to execute thes-e algorithms and list the numerical results and compare the accuracy of the computed Jacobi matrix.
1.Introduction.........................................................................................1
1.1 Lanczos Process...............................................................................1
1.2 Orthogonal Polynomials..................................................................4
1.3 Lanczos-type Methods.....................................................................6
1.4 DG Method......................................................................................10
1.5 HH Method......................................................................................12
1.6 TQR Methods..................................................................................14
2. Examples and Numerical Results...................................................... 16
2.1 Examples......................................................................................16
2.2 Comparison of the Algorithms ........................................................17
3. Conclusion..........................................................................................20
Bibliography..........................................................................................21
Appendix................................................................................................22
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