https://doi.org/10.1140/epjs/s11734-025-01797-4
Regular Article
Recurrent rational fractal modeling
VIT-AP University, Amaravati, India
Received:
14
March
2025
Accepted:
7
July
2025
Published online:
22
July
2025
The paper introduces a novel approach to recurrent rational fractal modeling through a recurrent iterated function system. This method employs rational functions with cubic numerators and quadratic denominators polynomials. The recurrent fractal model is intended to enhance flexibility and efficiency in curve construction compared to traditional cubic spline techniques. We derive the convergence results for a recurrent cubic fractal interpolation function towards an original function, which involves rigorous mathematical analysis and proof techniques. We propose the sufficient constraints that an interpolant must satisfy to uphold the recurrent rational relationship (i) between two piecewise functions, (ii) between two straight lines, and (iii) within a bounded rectangular region. We illustrate recurrent rational fractal interpolation models with several numerical examples to better understand how these models work and their potential applications.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
