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Jenkins‐Traub

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Oscar Veliz edited this page Jul 25, 2024 · 3 revisions

Jenkins-Traub video

The video covering Jenkins-Traub can be found at https://youtu.be/3_yxAnhLiAk. Example code is given in JenkinsTraub.py file, written in Python. You can run the program online from Link_Coming_Soon. To run the program locally have Python installed (https://www.python.org/) then type python JenkinsTraub.py in the terminal in the directory where it is saved.

Special Installation Instructions

You may also need to install Python and NumPy, matplotlib, and SymPy which can be done by running the command pip install numpy matplotlib sympy once Python is installed.

Fractal Examples

z^3-1

z^3-1

z^8+15z^4-16

z^8+15z^4-16

Reference links:

  • NumPy polyroots
  • NumPy polycompanion
  • "A Three-Stage Variable-shift Iteration for Polynomial Zeros and its Relation to Generalized Rayleigh Iteration" by Jenkins & Traub Research Gate
  • "A Class of Globally Convergent Iteration Functions for the Solution of Polynomial Equations" by Traub ams.org
  • "The Calculation of Zeros of Polynomials and Analytic Functions" by Traub Research Gate
  • "A Generalization of the Jenkins-Traub Method" by Ford ams
  • "Three-Stage Variable-Shift Iterations for the Solution of Polynomial Equations with a posteriori Error Bounds for the Zeros" (Dissertation) by Jenkins ProQuest
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