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Affine zipper fractal interpolation functions

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Abstract

This paper introduces a univariate interpolation scheme using a binary parameter called signature such that the graph of the interpolant—which we refer to as affine zipper fractal interpolation function—is obtained as an attractor of a suitable affine zipper. The scaling vector function is identified so that the graph of the corresponding affine zipper fractal interpolation function can be inscribed within a prescribed rectangle. Convergence analysis of the proposed affine zipper fractal interpolant is carried out. It is observed that for a fixed choice of discrete scaling factors, the box counting dimension of the graph of an affine zipper fractal interpolant is independent of the choice of a signature. Several examples of affine zipper fractal interpolants are presented to supplement our theory.

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Authors and Affiliations

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

    A. K. B. Chand

  2. Department of Basic Sciences and Engineering, Indian Institute of Information Technology Nagpur, Nagpur, India

    N. Vijender

  3. Department of Mathematics, Indian Institute of Technology Delhi, Delhi, India

    P. Viswanathan

  4. Department of Mathematics and Physics, Novosibirsk state university and Gorno-Altaisk State University, Gorno-Altaisk, Russia

    A. V. Tetenov

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  1. A. K. B. Chand
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  2. N. Vijender
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  3. P. Viswanathan
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  4. A. V. Tetenov
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Correspondence to A. K. B. Chand.

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A.K.B. Chand is thankful for the Project: MTR/2017/000574 - MATRICS from the Science and Engineering Research Board (SERB), Government of India. A part of the paper has been presented as a short communication at the International Congress of Mathematician (ICM -2018), Brazil. A.V. Tetenov is supported by Russian Foundation of Basic Research project 18-01-00420 A, and thanks to IIT Madras for facilitating two visits for this joint work.

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Chand, A.K.B., Vijender, N., Viswanathan, P. et al. Affine zipper fractal interpolation functions. Bit Numer Math 60, 319–344 (2020). https://doi.org/10.1007/s10543-019-00774-3

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