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Synergetics Section 260.42 root finding
Posted:
Nov 25, 2009 6:27 PM


Synergetics Section 260.42 root finding
I made a new updated Notebook called SynergeticsAppTen.nb with Mathematica Version 7 Home Edition. It presents the Synergetics coordinate system and Bucky Numbers.
SynergeticsApplication7.nb (2 MB)  Mathematica Version 4.1 Notebook at:
http://library.wolfram.com/infocenter/MathSource/600/
has been replaced with SynergeticsAppTen.nb (540 KB)  Mathematica Version 7.0 1.0 Notebook.
The last graphic in the Notebook is followed by a question about the speed of the convergence of a general root finding method. The guesses for the third iteration on, could be found with the vector equation method shown in the section "Solving Matrix Problems Using Bucky Numbers" or trigonometry.
I don't think Newton's method can be beat, I've tried and tried, but if anyone could beat Newton it would be Bucky Fuller. How does the speed of convergence compare for polynomials in general? What is the traditional name for this kind of root finding method? Has it been done with the Cartesian coordinate system?
What is the closest to Synergetics Section 260.42? at: http://mathworld.wolfram.com/topics/RootFinding.html
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