https://doi.org/10.1140/epjs/s11734-023-00780-1
Regular Article
Rational quadratic trigonometric spline fractal interpolation functions with variable scalings
Department of Mathematics, Indian Institute of Technology Madras, 600036, Chennai, Tamil Nadu, India
Received:
26
July
2022
Accepted:
25
January
2023
Published online:
17
February
2023
Fractal interpolation function (FIF) constructed through an iterated function system is more versatile than any classical spline interpolation. In this paper, we propose a novel 
-rational quadratic trigonometric spline FIF with variable scaling, where the numerator and denominator of rational function are quadratic trigonometric polynomials with two shape parameters in every subinterval. The error and convergence analysis of the proposed rational trigonometric fractal interpolant are studied for data generating function in 
. We deduce sufficient conditions based on the parameters of the rational quadratic trigonometric spline FIF to preserve positivity, monotonicity, and range restrictions features of the concerned data sets. Numerical examples are presented to supplement the shape preserving results based on a restricted class of scaling functions and minimum values of the shape parameters.
Framework of Fractals in Data Analysis: Theory and Interpretation. Guest editors: Santo Banerjee, A. Gowrisankar.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. 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.
