Analytic properties of hidden variable recurrent fractal interpolation function with function contractivity factors

TL;DR

This paper studies the smoothness and stability of hidden variable recurrent fractal interpolation functions with function contractivity factors, highlighting their flexibility and potential for practical applications.

Contribution

It provides a detailed analysis of the analytic properties, including smoothness and stability, of HVRFIFs with function contractivity factors, extending prior work.

Findings

HVRFIFs exhibit local self-similar or self-affine structures.

The stability of HVRFIFs is proven under dataset perturbations.

HVRFIFs offer greater flexibility than constant contractivity fractal functions.

Abstract

In this paper, we analyze the smoothness and stability of hidden variable recurrent fractal interpolation functions (HVRFIF) with function contractivity factors introduced in Ref. 1. The HVRFIF is a hidden variable fractal interpolation function (HVFIF) constructed by recurrent iterated function system (RIFS) with function contractivity factors. An attractor of RIFS has a local self-similar or self-affine structure and looks more naturally than one of IFS. The contractivity factors of IFS(RIFS) determine fractal characteristic and shape of its attractor. Therefore, the HVRFIF with function contractivity factors has more flexibility and diversity than the HVFIF constructed by iterated function system (IFS) with constant contractivity factors. The analytic properties of the interpolation functions play very important roles in determining whether these functons can be applied to the practical problems or not. We analyze the smoothness of the one variable HVRFIFs in Ref. 1 and prove their stability according to perturbation of the interpolation dataset.