Fast Root-Finding of Nonlinear Equations in Geometric Computation

Chang Chun Geng; Zhong Li; Tian He Zhou; Bin Yang

doi:10.4028/www.scientific.net/AMR.756-759.2808

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 756-759Fast Root-Finding of Nonlinear Equations in...

Fast Root-Finding of Nonlinear Equations in Geometric Computation

Abstract:

Computing the roots of polynomials is an important issue in various geometric problems. In this paper, we introduce a new family of iterative methods with sixth and seventh order convergence for nonlinear equations (or polynomials). The new method is obtained by combining a different fourth-order iterative method with Newtons method and using the approximation based on the divided difference to replace the derivative. It can improve the order of convergence and reduce the required number of functional evaluations per step. Numerical comparisons demonstrate the performance of the presented methods.

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Periodical:

Advanced Materials Research (Volumes 756-759)

Pages:

2808-2812

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.756-759.2808

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Online since:

September 2013

Authors:

Chang Chun Geng, Zhong Li, Tian He Zhou, Bin Yang

Keywords:

Convergence Order, Divided Difference, Newton Method, Non-Linear Equation

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References

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