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Bicubic partially blended rational fractal surface for a constrained interpolation problem

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Abstract

This paper investigates some univariate and bivariate constrained interpolation problems using fractal interpolation functions. First, we obtain rational cubic fractal interpolation functions lying above a prescribed straight line. Using a transfinite interpolation via blending functions, we extend the properties of the univariate rational cubic fractal interpolation function to generate surfaces that lie above a plane. In particular, the constrained bivariate interpolation discussed herein includes a method to construct fractal interpolation surfaces that preserve positivity inherent in a prescribed data set. Uniform convergence of the bivariate fractal interpolant to the original function which generates the data is proven.

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Acknowledgments

The first two authors wish to thank the Science and Engineering Research Council (SERC), Department of Science and Technology (DST) India (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

  2. Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India

    P. Viswanathan

  3. Department of Mathematics, VIT University, Chennai Campus, Chennai, 600127, India

    N. Vijender

Authors
  1. A. K. B. Chand
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  2. P. Viswanathan
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  3. N. Vijender
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Correspondence to A. K. B. Chand.

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Communicated by Antonio José Silva Neto.

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Chand, A.K.B., Viswanathan, P. & Vijender, N. Bicubic partially blended rational fractal surface for a constrained interpolation problem. Comp. Appl. Math. 37, 785–804 (2018). https://doi.org/10.1007/s40314-016-0373-1

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  • DOI: https://doi.org/10.1007/s40314-016-0373-1

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