基于马特科夫斯基收缩法构建加权分形插值面

Fractals Pub Date : 2024-01-18 DOI:10.1142/s0218348x24500130

QIAN-RUI Zhong, HONG-YONG Wang

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引用次数: 0

摘要

本文构建了一种新的加权递归迭代函数系统（IFS），并基于马特科夫斯基定点定理证明了该类 IFS 唯一吸引子的存在。我们证实该吸引子是一个双变量分形插值面（FIS），它可以对给定的数据集进行插值。此外，我们还提供了由权重变化引起的此类 FIS 的误差上限估计值。最后，我们还给出了特定类型 FIS 的盒尺寸估计值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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CONSTRUCTION OF A WEIGHTED FRACTAL INTERPOLATION SURFACE BASED ON MATKOWSKI CONTRACTIONS

In this paper, we construct a new kind of weighted recursive iteration function system (IFS) and prove the existence of the unique attractor for the kind of IFS based on the Matkowski fixed point theorem. We confirm that the attractor is a bivariate fractal interpolation surface (FIS), which interpolates a given set of data. In addition, we also provide an upper error estimate of such FISs caused by changes of weights. Finally, we give their box dimension estimates for a specific type of the FISs.

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Fractals

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