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Efficient Speed-Up of Radial Basis Functions Approximation and Interpolation Formula Evaluation

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Computational Science and Its Applications – ICCSA 2020 (ICCSA 2020)

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Abstract

This paper presents a method for efficient Radial basis function (RBF) evaluation if compactly supported radial basis functions (CSRBF) are used. Application of CSRBF leads to sparse matrices, due to limited influence of radial basis functions in the data domain and thus non-zero weights (coefficients) are valid only for some areas in the data domain. The presented algorithm uses space subdivision which enables us to use only relevant weights for efficient RBF function evaluation. This approach is applicable for 2D and 3D case and leads to a significant speed-up. This approach is applicable in cases when the RBF function is evaluated repeatably.

The research was supported by projects Czech Science Foundation (GACR) No. GA17-05534S, by Ministry of Education, Youth, and Sport of Czech Republic - University spec. research - 1311, and partially by SGS 2019-016.

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Notes

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Acknowledgments

The authors would like to thank their colleagues at the University of West Bohemia, Plzen, for their discussions and suggestions. Also, great thanks belong to our colleague Martin Cervenka for his hints and ideas. The research was supported by projects Czech Science Foundation (GACR) No. GA17-05534S, by the Ministry of Education, Youth, and Sport of Czech Republic - University spec. research - 1311, and partially by SGS 2019-016.

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Authors and Affiliations

  1. Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic

    Michal Smolik & Vaclav Skala

Authors
  1. Michal Smolik
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  2. Vaclav Skala
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Corresponding author

Correspondence to Michal Smolik .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Chair- Center of ICT/ICE, Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Clayton School of Information Technology, Monash University, Clayton, VIC, Australia

    David Taniar

  7. Department of Information Science, Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

  11. Department of Neurology, University of Massachusetts Medical School, Worcester, MA, USA

    Yeliz Karaca

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Smolik, M., Skala, V. (2020). Efficient Speed-Up of Radial Basis Functions Approximation and Interpolation Formula Evaluation. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science(), vol 12249. Springer, Cham. https://doi.org/10.1007/978-3-030-58799-4_12

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  • DOI: https://doi.org/10.1007/978-3-030-58799-4_12

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  • Online ISBN: 978-3-030-58799-4

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