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Synergetics section 260.42

• To: mathgroup at smc.vnet.net
• Subject: [mg58228] Synergetics section 260.42
• From: "Clifford J. Nelson" <cjnelson9 at verizon.net>
• Date: Thu, 23 Jun 2005 05:34:20 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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?

The Mathematica notebook Synegetics Coordinates Applications is at:

http://library.wolfram.com/infocenter/MathSource/600/

What is the closest to Synergetics Section 260.42? at:

http://mathworld.wolfram.com/topics/Root-Finding.html

  Cliff Nelson

Dry your tears, there's more fun for your ears,
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