Abstract

Fractal interpolation provides an efficient way to describe a smooth or non-smooth structure associated with nature and scientific data. The aim of this paper is to introduce a bivariate Hermite fractal interpolation formula that generalizes the classical Hermite interpolation formula for two variables. It is shown here that the proposed Hermite fractal interpolation function and its derivatives of all orders are good approximations of original function even if the partial derivatives of original function are non-smooth in nature.

中文翻译：

---

广义二元 Hermite 分形插值函数

摘要

分形插值提供了一种描述与自然和科学数据相关的平滑或非平滑结构的有效方法。本文的目的是介绍一个二元 Hermite 分形插值公式，它推广了两个变量的经典 Hermite 插值公式。这里表明，即使原始函数的偏导数本质上是非平滑的，所提出的 Hermite 分形插值函数及其所有阶的导数也是原始函数的良好近似。