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Approximation by the linear fractal interpolation functions with the same fractal dimension

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Abstract

A continuous function defined on a closed interval can be of unbounded variation with certain fractal dimension. Fractal interpolation functions are often used to approximate such functions whose structure seem self affine. In the present paper, a continuous function with non-integer Box dimension has been approximated by certain linear fractal interpolation functions. Both the original function and the linear fractal interpolation functions have the same Box dimension. The interpolation approximation of integer dimensional continuous functions has also been discussed elementary.

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Acknowledgements

Research is supported by National Natural Science Foundation of China with Grant no. 12071218 and Natural Science Foundation of Jiangsu Province with Grant no. BK20161492.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, 210094, China

    Y. S. Liang

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  1. Y. S. Liang
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Correspondence to Y. S. Liang.

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Framework of Fractals in Data Analysis: Theory and Interpretation. Guest editors: Santo Banerjee, A. Gowrisankar.

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Liang, Y.S. Approximation by the linear fractal interpolation functions with the same fractal dimension. Eur. Phys. J. Spec. Top. 232, 1071–1076 (2023). https://doi.org/10.1140/epjs/s11734-023-00866-w

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  • DOI: https://doi.org/10.1140/epjs/s11734-023-00866-w

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