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| 研究生： |
鄧起文 Deng, Qi Wen |
|---|---|
| 論文名稱： |
關於週期性波包近似值的理論與應用 On the Theory and Applications of Periodic Wavelet Approximation |
| 指導教授： |
蔡隆義
Cai, Long Yi |
| 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： | 1995 |
| 畢業學年度： | 83 |
| 語文別： | 英文 |
| 論文頁數： | 65 |
| 中文關鍵詞： | 波包 、多重解析度分析 、角錐圖解 、快速週期性波包轉換 |
| 外文關鍵詞： | Wavelet, Multiresolution Analysis, Pyramid Scheme, Fast Periodic Wavelet Transform |
| 相關次數： | 點閱：255 下載：0 |
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在本篇論文裏，我們將使用所謂的週期化(periodization)的裝置作用於Daubechies' compactly supported wavelets上而得到一族構成L<sup>2</sup>([0,1])和H<sup>s</sup>-periodic (the space of periodic function locally in H<sup>s</sup>)基底的正交的週期性波包(orthonormal periodic wavelets)。然後我們給出了對於一函數的波包近似值的誤差估計（參閱定理6）以及對於週期性邊界值的常微分方程問題的解的波包近似值的誤差估計（參閱定理7）。對於Burger equation的數值解也當作一個應用來討論。
In this thesis,we shall construct a family of orthonormal periodic wavelets which form a basis of L<sup>2</sup>([0,l]) and H<sup>s</sup>-periodic (the space of periodic functions locally in H<sup>s</sup>) by using a device called periodization ([10,7]) on Daubechies' compactly supported wavelets.We then give the error estimates for the wavelet approximation to a given function (see theorem 6) and to a solution of periodic boundary value problem for ordinary differential equation(see theorem 7). Numerical solution for Burger equation is also discussed as an application.
摘要
Contents-----1
Abstract-----2
1 Introduction-----3
2 Multiresolution analysis-----5
2.1 Multiresolution analysis-----5
2.2 Examples of orthogonal wavelets-----10
3 Periodic wavelets-----14
4 The fast periodic wavelet transform-----18
4.1 Wavelets with finitely many non-zero filter coefficients-----18
4.2 Decomposition algorithm-----19
4.3 Reconstruction algorithm-----22
4.4 The pyramid scheme-----24
4.5 Two-dimensional periodic wavelets-----29
5 Approximation and error estimates-----33
6 Applications-----37
6.1 Application to ordinary differential equation with periodic boundary conditions-----37
6.2 Application to Burgers' equation with periodic boundary conditions-----40
7 Conclusions-----44
References-----45
Appendix-----46
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