| 有限区间内四阶样条小波的构造 |
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| 引用本文： | 段继伟,李启光.有限区间内四阶样条小波的构造[J].应用数学和力学,2000,21(4):393-401. |
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| 作者姓名： | 段继伟 李启光 |
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| 作者单位： | 1.浙江工业大学土木系, 杭州 310014; |
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| 摘 要： | 用有限区间上的截断4阶B样条,构造了有限区间上的4阶样条小波。这些小波由边界小波和内部小波组成,对某一尺度,它们组成了有限维的小波空间。于是,任何有限区间上的函数皆可表示为该区间上的尺度函数和小波函数的有限和,即小波级数,这克服了用无穷区间上的小波进行有限信号处理时,在边界上误差较大的不足,同时将该小波用于偏微分方程具有同样重要的意义。
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| 关 键 词： | B样条 小波 有限区间 |
| 收稿时间： | 1997-09-22 |
| 修稿时间： | 1997-09-22 |
4th Order Spline Wavelets on a Bounded Interval |
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| Duan Jiwei,Peter Kai-kwong Lee.4th Order Spline Wavelets on a Bounded Interval[J].Applied Mathematics and Mechanics,2000,21(4):393-401. |
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| Authors: | Duan Jiwei Peter Kai-kwong Lee |
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| Institution: | 1.Department of Civil Engineering, Zhejiang University of Technology, Hangzhou 310014, P R China;2.Department of Civil Engineering, The University of Hong Kong, Hong Kong, P R China |
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| Abstract: | The 4th order spline wavelets on a bounded interval are constructed by the 4th order trun- cated B-spline functions. These wavelets consist of inner and boundary wavelets. They are bases of wavelet space with finite dimensions. Any function on an interval will be expanded as the sum of fi- nite items of the scaling functions and wavelets. It plays an important role for numerical analysis of partial differential equations, signal processes, and other similar problems. |
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| Keywords: | B-spline: wavelet bounded interval |
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