Synergetics Section 260.42 root finding

[Clifford J. Nelson]

The last graphic in the section "Finding Roots Of Equations Numerically
With Bucky Numbers" at:

http://users.adelphia.net/~cnelson9/Links/index_lnk_11.html

which is one of the sections of "Synergetics Coordinates Applications"
at:

http://users.adelphia.net/~cnelson9/

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" at:

http://users.adelphia.net/~cnelson9/Links/index_lnk_10.html

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/Root-Finding.html

Cliff Nelson

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