Re: Optimizing fixed point iteration

*To*: mathgroup at smc.vnet.net*Subject*: [mg83128] Re: Optimizing fixed point iteration*From*: m.r at inbox.ru*Date*: Mon, 12 Nov 2007 05:14:05 -0500 (EST)*References*: <fh1ckb$csj$1@smc.vnet.net>

On Nov 9, 4:26 am, Yaroslav Bulatov <yarosla... at gmail.com> wrote: > 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 Here's a compiled version: f = Compile[{a, b, {d, _Integer}}, Module[{c = 1, x = .51, x2}, While[x2 = -4 (x - a) (x - b); c < d - 1 && Abs[x - x2] > .1, If[Abs[x] > 1.5, Return[d - 1]]; c++; x = x2]; c]] DynamicModule[{d = 50, u, gr}, gr = Graphics[Raster[ Reverse[ d - 1 - Table[f[a, b, d], {a, -1, 0, .001}, {b, 0, 1, .001}]], {{0, 0}, {1, 1}}, Dynamic@{u, d - 1}]]; Manipulate @@ {gr, {u, 1, d - 2, 1}} ] Maxim Rytin m.r at inbox.ru