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International Conference on Computational Science and Its Applications

ICCSA 2020: Computational Science and Its Applications – ICCSA 2020 pp 30–43Cite as

Conditionality Analysis of the Radial Basis Function Matrix

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12250))

Abstract

The global Radial Basis Functions (RBFs) may lead to ill-conditioned system of linear equations. This contribution analyzes conditionality of the Gauss and the Thin Plate Spline (TPS) functions. Experiments made proved dependency between the shape parameter and number of RBF center points where the matrix is ill-conditioned. The dependency can be further described as an analytical function.

The research was supported by projects Czech Science Foundation (GACR) No. 17-05534S and partially by SGS 2019-016.

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Notes

  1. 1.

    The Delaunay triangulation has time complexity of \(O\left( n^{\lceil d/2\rceil +1}\right) \), where d is number of tesselated dimensions.

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Acknowledgement

The authors would like to thank their colleagues and students at the University of West Bohemia for their discussions and suggestions, and especially to Michal Smolik for valuable discussion and notes he provided. The research was supported by projects Czech Science Foundation (GACR) No. 17-05534S and partially by SGS 2019-016.

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Authors and Affiliations

  1. Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czechia

    Martin Červenka & Václav Skala

Authors
  1. Martin Červenka
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  2. Václav Skala
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Corresponding author

Correspondence to Martin Červenka .

Editor information

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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Červenka, M., Skala, V. (2020). Conditionality Analysis of the Radial Basis Function Matrix. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science(), vol 12250. Springer, Cham. https://doi.org/10.1007/978-3-030-58802-1_3

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  • DOI: https://doi.org/10.1007/978-3-030-58802-1_3

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