The theory of splines is a well studied topic, but the kinship of splines with fractals is novel.
We introduce a simple explicit construction for a-cubic Hermite Fractal Interpolation Function …

Fractal interpolation is a modern technique in approximation theory to fit and analyze
scientific data. We develop a new class of\mathcal C^ 1-rational cubic fractal interpolation …

This paper is devoted to a hierarchical approach of constructing a class of fractal
interpolants with trigonometric basis functions and to preserve the geometric behavior of …

Let a data set Δ={(ti, yi)∈ R× Y: i= 0, 1,⋯, N} be given, where t 0< t 1< t 2<⋯< t N and Y is a
complete metric space. In this article, fractal interpolation functions (FIFs) on I=[t 0, t N] …

One of the main tasks in the problems of machine learning and curve fitting is to develop
suitable models for given data sets. It requires to generate a function to approximate the data …

We propose a new type of C 1-rational cubic spline Fractal Interpolation Function (FIF) for
convexity preserving univariate interpolation. The associated Iterated Function System (IFS) …

Generating a function from its finite set of samples is widely studied in data fitting problems.
The theory of nonparametric modeling has been developed by many researchers, and …

Fractal interpolation is an advanced technique for analysis and synthesis of scientific and
engineering data. We introduce the 𝒞1‐rational quadratic fractal interpolation functions …

This paper introduces a rational Fractal Interpolation Function (FIF), in the sense that it is
obtained using a rational cubic spline transformation involving two shape parameters, and …

In this paper, we discuss the construction of 𝐶¹-rational cubic fractal interpolation function
(RCFIF) and its application in preserving the constrained nature of a given data set. The 𝐶¹ …