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Acceleration of the Robust Newton Method by the Use of the S-iteration

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Computational Science – ICCS 2021 (ICCS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12742))

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Abstract

In this paper, we propose an improvement of the Robust Newton’s Method (RNM). The RNM is a generalisation of the known Newton’s root finding method restricted to polynomials. Unfortunately, the RNM is slow. Thus, in this paper, we propose the acceleration of this method by replacing the standard Picard iteration in the RNM by the S-iteration. This leads to an essential acceleration of the modified method. We present the advantages of the proposed algorithm over the RNM using polynomiagraphs and some numerical measures. Moreover, we present its possible application to the generation of artistic patterns.

W. Kotarski—Independent Researcher.

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Authors and Affiliations

  1. Institute of Computer Science, University of Silesia, Bȩdzińska 39, 41–200, Sosnowiec, Poland

    Krzysztof Gdawiec & Agnieszka Lisowska

  2. Katowice, Poland

    Wiesław Kotarski

Authors
  1. Krzysztof Gdawiec
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  2. Wiesław Kotarski
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  3. Agnieszka Lisowska
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Corresponding author

Correspondence to Krzysztof Gdawiec .

Editor information

Editors and Affiliations

  1. AGH University of Science and Technology, Krakow, Poland

    Maciej Paszynski

  2. Ludwig-Maximilians-Universität München, Munich, Germany

    Dieter Kranzlmüller

  3. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

  4. University of Tennessee at Knoxville, Knoxville, TN, USA

    Jack J. Dongarra

  5. University of Amsterdam, Amsterdam, The Netherlands

    Peter M. A. Sloot

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Gdawiec, K., Kotarski, W., Lisowska, A. (2021). Acceleration of the Robust Newton Method by the Use of the S-iteration. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12742. Springer, Cham. https://doi.org/10.1007/978-3-030-77961-0_28

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  • DOI: https://doi.org/10.1007/978-3-030-77961-0_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-77960-3

  • Online ISBN: 978-3-030-77961-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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