| 多元对偶尺度函数的最优逼近阶和最优光滑性 |
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| 引用本文： | 崔丽鸿,杨守志,杨建伟.多元对偶尺度函数的最优逼近阶和最优光滑性[J].信阳师范学院学报(自然科学版),2002,15(2):125-128. |
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| 作者姓名： | 崔丽鸿 杨守志 杨建伟 |
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| 作者单位： | 西安交通大学,理学院,陕西,西安,710049 |
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| 摘 要： | 双正交小波由尺度函数和其对偶尺度函数对产生的多分辨分析导出，高光滑性、小支撑、高消失矩是双正交小波的三大重要特征。本文讨论多元对偶尺度函数的支撑、逼近阶、光滑性之间的关系，并由此得出它的最优逼近阶和最优光滑性。
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| 关 键 词： | 多分辨分析 多元对偶尺度函数 最优逼近阶 最优光滑性 双正交小波 和规则 小波分析 支撑 |
| 文章编号： | 1003-0972(2002)02-0125-04 |
Optimal approximation order and optimal smoothness of a multivariate dual scaling functions |
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| CUI Li hong,YANG Shou zhi,YANG Jian wei.Optimal approximation order and optimal smoothness of a multivariate dual scaling functions[J].Journal of Xinyang Teachers College(Natural Science Edition),2002,15(2):125-128. |
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| Authors: | CUI Li hong YANG Shou zhi YANG Jian wei |
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| Abstract: | A biorthogonal wavelet is derived from a multiresolution analysis generated by a pair consisting of a scaling function and its dual scaling function.It is well known that high smoothness,small support,and high vanishing moments are the three most important features of a biorthogonal wavelet.In this paper,the relations among these three properties are discussed and the optimal approximation order and optimal smoothness of a multivariate dual scaling functions are obtained. |
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| Keywords: | biorthogonal wavelets scaling functions dual scaling functions sum rules approximation order smoothness support |
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