摘要
介绍了矩形区域上由迭代函数系(iterated function system,IFS)生成的二元分形插值函数的不定积分.首先证明二元插值函数的不定积分也是由迭代函数系迭代生成的,并得到了其迭代函数系.其次,证明了二元插值函数的不定积分的2阶混合偏导数等于其二元插值函数本身的充要条件,并推广到2N阶的情形.
On the rectangular grids, the indefinite integral of binary fractal interpolating function generated by IFS is discussed. At first, the indefinite integral of binary fractal interpolating function generated by IFS is proved, and its IFS is given. Second, the sufficient and necessary condition for second-order partial derivative of binary fractal interpolating function equaling itself is obtained. The sufficient and necessary condition is extended to 2N-th order partial derivative.
出处
《江苏大学学报（自然科学版）》
EI
CAS
北大核心
2005年第B12期113-115,共3页
Journal of Jiangsu University：Natural Science Edition
基金
国家自然科学基金资助项目(1007103350074032)
关键词
迭代函数系
分形插值曲面
二元分形插值函数
积分
iterated function systems
fractal interpolating surface
binary fractal interpolating
integral
