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\(C^1\)-Rational Quadratic Trigonometric Spline Fractal Interpolation Functions

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Mathematics and Computing (ICMC 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 415))

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Abstract

Trigonometric interpolation has an essential role in geometric modeling of conic data. In this paper, a novel \(C^{1}\)-rational quadratic trigonometric spline fractal interpolation function with variable scaling and two families of shape parameters is introduced. We have investigated the convergence analysis of this fractal interpolant to a data-generating function in \(C^3\) from the uniform error bound. When the conic data is positive and monotone, we have derived sufficient conditions based on the scaling functions and shape parameters so that the resultant trigonometric spline FIF preserves these fundamental shapes of conic data. The proposed results are verified by generating positive and monotonic trigonometric spline fractal interpolation functions.

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Authors and Affiliations

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

    Vijay & A. K. B. Chand

Authors
  1. Vijay
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  2. A. K. B. Chand
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Correspondence to Vijay .

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Editors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India

    B. Rushi Kumar

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

    S. Ponnusamy

  3. Department of Information Technology, Maulana Abul Kalam Azad University of Technology, Haringhata, West Bengal, India

    Debasis Giri

  4. Department of Computer Science, The University of Texas at Dallas, Richardson, TX, USA

    Bhavani Thuraisingham

  5. Department of Computer Science, Purdue University, West Lafayette, IN, USA

    Christopher W. Clifton

  6. Department of Theoretical and Applied Sciences, University of Insubria, Varese, Italy

    Barbara Carminati

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Vijay, Chand, A.K.B. (2022). \(C^1\)-Rational Quadratic Trigonometric Spline Fractal Interpolation Functions. In: Rushi Kumar, B., Ponnusamy, S., Giri, D., Thuraisingham, B., Clifton, C.W., Carminati, B. (eds) Mathematics and Computing. ICMC 2022. Springer Proceedings in Mathematics & Statistics, vol 415. Springer, Singapore. https://doi.org/10.1007/978-981-19-9307-7_20

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