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Some results on the space of rational cubic fractal interpolation functions

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Abstract

In this article, rational cubic fractal interpolation function (RCFIF) with three shape parameters is constructed. We develope the orthonormal basis consists of cardinal RCFIFs for the space of RCFIFs with fixed parameters. We show the space RCFIFs with fixed parameters is a reproducing kernel Hilbert space and we study the curve fitting problem. Also, we discuss the orthogonal projection on the space of RCFIFs with fixed parameters. Further, we study the constrained aspects of cardinal RCFIFs. Numerical results are provided to support theoretical results.

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Acknowledgements

The authors thank the unknown referees for their valuable comments and suggestions, which helps to improve the presentation. The second author work was supported by the Ministry of Science and Technology, R.O.C., under Grant MOST 111-2115-M-214-001.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620015, India

    N. Balasubramani

  2. Department of Data Science and Analytics, I-Shou University, Kaohsiung, 84001, Taiwan

    Dah-Chin Luor

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  1. N. Balasubramani
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  2. Dah-Chin Luor
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Correspondence to N. Balasubramani.

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Balasubramani, N., Luor, DC. Some results on the space of rational cubic fractal interpolation functions. J Anal (2024). https://doi.org/10.1007/s41478-024-00734-3

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  • DOI: https://doi.org/10.1007/s41478-024-00734-3

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