论文标题
关于可数数据和相关的非线性分形操作员的双变量分形插值
On Bivariate Fractal Interpolation for Countable Data and Associated Nonlinear Fractal Operator
论文作者
论文摘要
我们提供了一个通用框架，用于构建分形插值表面（FIS），用于在矩形网格上设置的规定的无限数据。以此为重要的工具，我们获得了同时插值并近似规定的双变量连续函数的双变量分形函数的参数化家族。建立了相关的非线性（不一定是线性）分形操作员的某些基本特性，从而启动了分形插值与非线性操作员理论的相互作用。
We provide a general framework to construct fractal interpolation surfaces (FISs) for a prescribed countably infinite data set on a rectangular grid. Using this as a crucial tool, we obtain a parameterized family of bivariate fractal functions simultaneously interpolating and approximating a prescribed bivariate continuous function. Some elementary properties of the associated nonlinear (not necessarily linear) fractal operator are established, thereby initiating the interaction of the notion of fractal interpolation with the theory of nonlinear operators.
