扰动细分的光滑性研究
Research on the Smoothness of Perturbed Subdivision
DOI: 10.12677/AAM.2023.121045, PDF,   
作者: 亓万锋*, 王 影：辽宁师范大学数学学院，辽宁 大连
关键词: 细分；特征值；H?lder指数；光滑性；Subdivision； Eigenvalue； H?lder Exponent； Smoothness
摘要: 细分在小波分析和计算机图形学中起着重要作用。本文对一类特殊的二重细分格式乘以一个简单的多项式作为扰动，提出了得到扰动后细分格式光滑性更高的充分条件。通过Mathematica对理论结果加以分析。结果表明，在该条件下扰动后的细分光滑性明显提高。
Abstract: Subdivision plays an important role in wavelet analysis and computer graphics. In this paper, a class of special subdivision schemes is multiplied by a simple polynomial as a perturbation, and a sufficient condition for higher smoothness of the subdivision scheme after perturbation is proposed. The theoretical results are analyzed by Mathematica. The results show that the subdivision smoothness is improved obviously after perturbation under this condition.
文章引用：亓万锋, 王影. 扰动细分的光滑性研究[J]. 应用数学进展, 2023, 12(1): 428-434. https://doi.org/10.12677/AAM.2023.121045

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