4th Order Spline Wavelets on a Bounded Interval

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 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.

Citation:

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

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

Abstract

The 4th order spline wavelets on a bounded interval are constructed by the 4th order truncated 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 finite 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.
- B-spline:wavelet,
- bounded interval,

[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.