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Optimizing fixed point iteration

• To: mathgroup at smc.vnet.net
• Subject: [mg83070] Optimizing fixed point iteration
• From: Yaroslav Bulatov <yaroslavvb at gmail.com>
• Date: Fri, 9 Nov 2007 05:17:59 -0500 (EST)

Can anyone see the trick to speed up the following code significantly?

depth;step=.02;
Table[(c = 0;
   NestWhile[-4 (# - a) (# - b) &, .51, (c++; Abs[#1 - #2] > .1) &, 2,
     depth]; c), {a, -1., 0., step}, {b, 0., 1., step}] // ArrayPlot

This makes a plot of the number of iterations needed for the quadratic
fixed point iterations to converge, as a function of quadratic
parameters, however it's too slow to get sufficient granularity

• Follow-Ups:
  • Re: Optimizing fixed point iteration
    • From: Murray Eisenberg <murray@math.umass.edu>