具有函数纵向尺度因子的分形插值函数的分析特性

王宏勇, 樊昭磊

数学学报 ›› 2011, Vol. 54 ›› Issue (1) : 147-158.

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数学学报 ›› 2011, Vol. 54 ›› Issue (1) : 147-158. DOI: 10.12386/A2011sxxb0016
论文

具有函数纵向尺度因子的分形插值函数的分析特性

    王宏勇, 樊昭磊
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Analytical Characteristics of Fractal Interpolation Functions with Function Vertical Scaling Factors

    Hong Yong WANG, Zhao Lei FAN
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摘要

研究一类具有函数纵向尺度因子的分形插值函数的光滑性、稳定性和敏感性等分析特性.给出了这类分形插值函数的光滑性结果, 证明了它们的稳定性. 同时, 考虑这类分形插值函数及其矩量的敏感性问题,证明了当生成这类分形插值函数的迭代函数系有小的扰动时, 相应的分形插值函数及其矩量也有小的扰动, 给出了相应扰动误差的上估计.

 

Abstract

The analytical characteristics of a class of fractal interpolation functions (FIFs) with function vertical scaling factors, including smoothness, stability and sensitivity, are studied in this work. The results on smoothness of such FIFs are presented, and their stability is proved. In addition, the sensitivity and moments for the class of FIFs are discussed. It is shown that if a small perturbation occurs in the iterated function systems (IFSs) generating the class of FIFs, then a small perturbation is also produced in the corresponding FIFs and their moments. The upper estimates of the perturbation errors are given.

 

关键词

迭代函数系 / 光滑性 / 稳定性 / 敏感性 / 分形插值函数

Key words

fractal interpolation function / iterated function system / smoothness / stability / sensitivity

引用本文

导出引用
王宏勇, 樊昭磊. 具有函数纵向尺度因子的分形插值函数的分析特性. 数学学报, 2011, 54(1): 147-158 https://doi.org/10.12386/A2011sxxb0016
Hong Yong WANG, Zhao Lei FAN. Analytical Characteristics of Fractal Interpolation Functions with Function Vertical Scaling Factors. Acta Mathematica Sinica, Chinese Series, 2011, 54(1): 147-158 https://doi.org/10.12386/A2011sxxb0016

参考文献


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基金

国家自然科学基金资助项目(11071152)

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