2022/05/18 by Aparna MP, MP, Aparna, P. Paramanathan +1
Computer Science · Mathematics · #28A80 #41A10 #65D05 #Digital Filter Design and Implementation #FOS: Mathematics #G.0 #General Mathematics (math.GM) #Iterative Methods for Nonlinear Equations #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.2206.07657
openalex publication_date 2022/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fractal interpolation technique is an alternative to the classical interpolation methods especially when a chaotic signal is involved. The logic behind the formulation of an iterated function system for the construction of fractal interpolation functions is to divide the entire interpolating domain into subdomains and define functions on each subdomain piecewisely. The objective of this paper is to explore the significance of the end point conditions on the graphical representation of the resultant functions and their numerical integration. The central problem in the formulation of the IFS, the continuity of the fractal interpolation functions, is addressed with an explanation on the techniques implemented to resolve the problem. Instead of an analytical expression, the fractal interpolation functions are always represented in terms of recursive relations. This paper further presents the derivation of these recursive relations and proposes a straightforward method to find the approximating function, involved in these relations.