中文摘要：

在矩形区域上使用具有变量自由参数的迭代函数系，构造了一类新的分形插值曲面，并研究了这类曲面的若干性质．证明了这类变参数的迭代函数系能生成连续的二元分形插值曲面，指出该类曲面可用作任意数据点上的自仿射和非自仿射的分形插值模型．在两种度量意义下，导出了能刻画这类分形曲面敏感性的一些不等式．给出了相应的分形插值函数与数据生成函数之间的误差估计．最后，在一定条件下，证明了这类分形插值函数序列一致收敛于数据生成函数．

英文摘要：

A new construction of fractal interpolation surfaces （FISs） on rectangular grids using iterated function systems （IFSs） is proposed and some of their properties arestudied in this paper. The IFSs employed are endowed with variable free parameters and are proved that they can generate continuous bivariate FISs, which can be used as self-affine and non-self-affine fractal interpolation models on arbitrary data points. Some inequalities concerning the sensitivity of the resulting bivariate fractal interpo lation functions （FIFs） are deduced in two metric senses. The estimation of the error between the bivariate FIF and a bivariate data generating function is given. Finally, under certain conditions, the uniform convergence of the bivariate FIFs to the data generating function is proved.