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An improved rational cubic clipping method for computing real roots of a polynomial

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  • Li, Shi
  • Chen, Guang
  • Wang, Yigang

Abstract

The root-finding problem has wide applications in geometric processing and computer graphics. Previous rational cubic clipping methods are either of convergence rate 7/k with O(n2) complexity, or of convergence rate 5/k with linear complexity, where n and k are degree of the given polynomial and the multiplicity of the root, respectively. This paper presents an improved rational cubic clipping of linear complexity, which can achieve convergence rate 7/k, or a better one 7/(k−1) for a multiple root such that k ≥ 2. Numerical examples illustrate both efficiency and convergence rate of the new method.

Suggested Citation

  • Li, Shi & Chen, Guang & Wang, Yigang, 2019. "An improved rational cubic clipping method for computing real roots of a polynomial," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 207-213.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:207-213
    DOI: 10.1016/j.amc.2018.12.040
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    References listed on IDEAS

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    1. Chen, Xiao-diao & Ma, Weiyin, 2016. "Rational cubic clipping with linear complexity for computing roots of polynomials," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1051-1058.
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    Cited by:

    1. Kinga Kruppa & Roland Kunkli & Miklós Hoffmann, 2021. "Possibilities and Advantages of Rational Envelope and Minkowski Pythagorean Hodograph Curves for Circle Skinning," Mathematics, MDPI, vol. 9(8), pages 1-13, April.

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