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Zipper Rational Quadratic Fractal Interpolation Functions

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Proceedings of the Fifth International Conference on Mathematics and Computing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1170))

Abstract

In this article, we propose an interpolation method using a binary parameter called signature such that the graph of the interpolant is an attractor of a suitable zipper rational iterated function system. The presence of scaling factors and signature in the proposed zipper rational quadratic fractal interpolation functions (ZRQFIFs) gives the flexibility to produce a wide variety of interpolants. Using suitable conditions on the scale factor and shape parameter, we construct a \(\mathcal {C}^1\)-continuous ZRQFIF from a \(\mathcal {C}^0\)-continuous ZRQFIF. We also establish the uniform convergence of ZRQFIF to an original data-generating function. Further, we deduce suitable conditions on the IFS parameters and shape parameters to retain the positivity feature associated with a prescribed data by the proposed interpolant.

A. K. B. Chand is thankful for the project: MTR/2017/000574—MATRICS from the Science and Engineering Research Board (SERB), Government of India.

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Authors and Affiliations

  1. Department of Mathematics, NIT Rourkela, Rourkela, Odisha, 769008, India

    Sangita Jha

  2. Department of Mathematics, IIT Madras, Chennai, 600036, India

    A. K. B. Chand

Authors
  1. Sangita Jha
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  2. A. K. B. Chand
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Corresponding author

Correspondence to A. K. B. Chand .

Editor information

Editors and Affiliations

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

    Debasis Giri

  2. Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, UK

    Anthony T. S. Ho

  3. Indian Institute of Technology Madras, Chennai, India

    S. Ponnusamy

  4. Department of Information Management, National Taiwan University of Science and Technology, Taipei City, Taiwan

    Nai-Wei Lo

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Jha, S., Chand, A.K.B. (2021). Zipper Rational Quadratic Fractal Interpolation Functions. In: Giri, D., Ho, A.T.S., Ponnusamy, S., Lo, NW. (eds) Proceedings of the Fifth International Conference on Mathematics and Computing. Advances in Intelligent Systems and Computing, vol 1170. Springer, Singapore. https://doi.org/10.1007/978-981-15-5411-7_18

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