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Constrained 2D Data Interpolation Using Rational Cubic Fractal Functions

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Mathematical Analysis and its Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 143))

Abstract

In this paper, we construct the \(\mathscr {C}^1\)-rational cubic fractal interpolation function (RCFIF) and its application in preserving the constrained nature of a given data set. The \(\mathscr {C}^1\)-RCFIF is the fractal design of the traditional rational cubic interpolant of the form \(\frac{p_i(\theta )}{q_i(\theta )}\), where \(p_i(\theta )\) and \(q_i(\theta )\) are the cubic polynomials with three tension parameters. We derive the uniform error bound between the RCFIF with the original function in \(\mathscr {C}^3[x_1,x_n]\). When the data set is constrained between two piecewise straight lines, we deduce the sufficient conditions on the parameters of the RCFIF so that it lies between those two lines. Numerical examples are given to support that our method is interactive and smooth.

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Acknowledgments

The first author is thankful to the Department of Science & Technology, India for the SERC DST Project No. SR/S4/MS: 694/10.

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Authors and Affiliations

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

    A. K. B. Chand & K. R. Tyada

Authors
  1. A. K. B. Chand
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  2. K. R. Tyada
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Corresponding author

Correspondence to A. K. B. Chand .

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Editors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    P. N. Agrawal

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    R. N. Mohapatra

  3. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Uaday Singh

  4. Dept. of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

    H. M. Srivastava

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Chand, A.K.B., Tyada, K.R. (2015). Constrained 2D Data Interpolation Using Rational Cubic Fractal Functions. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_49

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