杨守志,申培萍,杨建伟.矩阵的正交扩充与多正交小波[J].数学研究及应用,2003,23(3):525~534
矩阵的正交扩充与多正交小波
Matrix Orthogonal Extension and Orthogonal Multiwavelets with Scale=a
投稿时间:2000-11-24  
DOI:10.3770/j.issn:1000-341X.2003.03.025
中文关键词:  紧支撑函数  多尺度函数  正交多小波  两尺度矩阵方程  两尺度矩阵符号  两尺度矩阵序列
英文关键词:compactly supported function  multiscaling function  Orthogonal multiwavelets  two-scale matrix equation  two-scale matrix sequence  two-scale matrix symbol.
基金项目:河南省自然科学基金(984051900)和河南省教委自然科学基金(98110015)资助项目.
作者单位
杨守志 汕头大学数学系,广东,汕头,515063 
申培萍 西安交通大学理学院,陕西,西安,710049 
杨建伟 西安交通大学理学院,陕西,西安,710049 
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中文摘要:
      给出一种由a尺度紧支撑正交多尺度函数构造短支撑正交多小波的方法,其过程仅仅应用矩阵的正交扩充和求解方程组。如果r重尺度函数的支撑区间较大,可以将其转化为ar重短支撑情形,从而使得本文的方法适用于任意紧支撑正交多小波的构造,文后给出多小波的构造算例。
英文摘要:
      There are perfect formulas for the constructions of orthogonal uni-wavelet with scale = 2. However, as yet there has not been a general method to obtain orthogonal multi-wavelets with scale = a (a∈Z, a≥2 ). In this paper, we will give an approach for constructing compactly supported orthogonal multiwavelets with scale = a, which makes construction of orthogonal multiwavelets easy like in the construction of orthogonal uni-wavelet. Finally, an example for construction multiwavelets is given.
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