## 留言板

 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.
Duan Jiwei, Li Qiguan. 4th Order Spline Wavelets on a Bounded Interval[J]. Applied Mathematics and Mechanics, 2000, 21(4): 393-401.
 Citation: Duan Jiwei, Li Qiguan. 4th Order Spline Wavelets on a Bounded Interval[J]. Applied Mathematics and Mechanics, 2000, 21(4): 393-401.

## 有限区间内四阶样条小波的构造

###### 作者简介:段继伟(1964-.),男,云南蒙自,副教授,博士,研究方向为软基处理、桩基的数值分析、计算土力学、小波理论.
• 中图分类号: O242.29;O241.82

## 4th Order Spline Wavelets on a Bounded Interval

• 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。
•  [1] Chen Mingquayer,Hwang Chyi,Shih Yenping.A wavelet-Galerkin method for solving population balance equations[J].Computers Chem Engng,1996,20(2):131～145. [2] Chen Mingquayer,Hwang Chyi,Shin Yehping.The computation of wavelet-Galerkin approximation on a bounded interval[J].International Journal for Numerical Methods in Engineering,1996,39:2921～2944. [3] Williams John R,Amaratunga Kevin.Introduction to wavelets in engineering[J].International Journal for Numerical Method in Engineering,1994,37(14):2365～2388. [4] Chen W H,Wu C W.A spline wavelet element method for frame structure vibration[J].Computational Mechanics,1995,16(1):11～12. [5] Daubechies Ingrid.Two recent results on wavelets:wavelet bases for the interval,and biothogonal wavelets diagonalizing the derivative operator[A].In:Larry L Schumaker,Glenn Webb Eds.Recent Advances in Wavelet Analysis,Academic Press,Incorporeted,1993. [6] Quak Ewald,Weyrich Norman.Wavelets on the interval[A].In:Singh S P Ed.Approximation Theory Wavelets and Applications[C].1995. [7] Quak Ewald,Weyrich Norman.Decomposition and reconstruction algorithms for spline wavelets on a bounded interval[J].Applied and Computational Harmonic Analysis,1994,1:217～231. [8] 关履泰.有限区间截断B样条小波及其消失矩性质[J].中山大学学报(自然科学版),1996,35(3):28～33.
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##### 出版历程
• 收稿日期:  1997-09-22
• 修回日期:  1998-09-10
• 刊出日期:  2000-04-15

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