Stability of Coalescence Hidden variable Fractal Interpolation Surfaces

TL;DR

This paper establishes the stability of Coalescence Hidden variable Fractal Interpolation Surfaces (CHFIS), showing that small data perturbations lead to small changes in the interpolated surface, useful for modeling natural textures.

Contribution

It provides the first stability analysis of CHFIS, quantifying how data perturbations affect the interpolation of multi-variable natural surfaces.

Findings

Small perturbations in data cause only small changes in CHFIS

Error estimates for approximation of the data generating function

Applicable to modeling natural textures like rocks and clouds

Abstract

In the present paper, the stability of Coalescence Hidden variable Fractal Interpolation Surfaces(CHFIS) is established. The estimates on error in approximation of the data generating function by CHFIS are found when there is a perturbation in independent, dependent and hidden variables. It is proved that any small perturbation in any of the variables of generalized interpolation data results in only small perturbation of CHFIS. Our results are likely to be useful in investigations of texture of surfaces arising from the simulation of surfaces of rocks, sea surfaces, clouds and similar natural objects wherein the generating function depends on more than one variable.