一类α-分形函数的误差估计

Error Estimation of a Class of α - Fractal Functions

对任意给定的二元连续函数,在R3中运用分形插值迭代函数系生成相应的α-分形函数。研究分形函数与原二元连续函数之间的关系及性质,给出在L2范数及无穷大范数意义下,任一二元连续函数与其分形函数之间的误差估计,得到它们的矩量误差上界。

For any given bivariate continuous function,an α-fractal function in the three-dimensional space is generated with the iterated function system of fractal interpolation.Errors between the α-fractal function and the corresponding continuous function in the sense of L2-norm and infinity norm are estimated.Errors of their moments are also studied,and the error upperbound is obtained.