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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/88452

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/88452

Title:	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
Authors:	鄧起文 Deng, Qi Wen
Contributors:	蔡隆義 Cai, Long Yi 鄧起文 Deng, Qi Wen
Keywords:	波包多重解析度分析角錐圖解快速週期性波包轉換 Wavelet Multiresolution Analysis Pyramid Scheme Fast Periodic Wavelet Transform
Date:	1995 1994
Issue Date:	2016-04-29 15:59:57 (UTC+8)
Abstract:	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.
Description:	碩士國立政治大學應用數學系
Source URI:	http://thesis.lib.nccu.edu.tw/record/#B2002003514
Data Type:	thesis
Appears in Collections:	[Department of Mathematical Sciences] Theses

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