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Rational quadratic trigonometric spline fractal interpolation functions with variable scalings

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Abstract

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 \(C^1\)-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 \(C^3\). 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.

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Acknowledgements

AKB Chand would like to acknowledge ICSR, IIT Madras for the funding support from the IoE research project [Project Number = SB20210848MAMHRD 008558].

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  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, Tamil Nadu, 600036, India

    Vijay & A. K. B. Chand

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  1. Vijay
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Correspondence to Vijay.

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Framework of Fractals in Data Analysis: Theory and Interpretation. Guest editors: Santo Banerjee, A. Gowrisankar.

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Vijay, Chand, A.K.B. Rational quadratic trigonometric spline fractal interpolation functions with variable scalings. Eur. Phys. J. Spec. Top. 232, 1001–1013 (2023). https://doi.org/10.1140/epjs/s11734-023-00780-1

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