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iteration question

  • To: mathgroup at
  • Subject: [mg122583] iteration question
  • From: Francisco Gutierrez <fgutiers2002 at>
  • Date: Wed, 2 Nov 2011 06:21:44 -0500 (EST)
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  • Reply-to: Francisco Gutierrez <fgutiers2002 at>

Dear Group:

I have a function, and I iterate it using fixedpoint. Something of this sort:

 function[arg1,arg2,arg3, #] &, arg4, 
 SameTest -> (Max[Abs[Flatten[#1] - Flatten[#2]]] < 0.01 &)]

I would like to know how many steps it takes this function to converge. I have tried with EvaluationMonitor to no avail:

Block[{veamos, c = 0}, 
  veamos = FixedPoint[
    function[arg1,arg2,arg3, #] &, arg4, 
    SameTest -> (Max[Abs[Flatten[#1] - Flatten[#2]]]< 0.01 &)]; 
  EvaluationMonitor :> c++; {veamos, c}] 

The iterator c simply does not move, and the previous function works ok but returns the value of c as 0.

I tried if this was true with Length[FixedPointList[...]] and the answer was 20 (which should be the value of c in the immediately previous function). In principle, this would solve my problem, but it seems
rather inefficient, especially when the convergence criterion is severe (not 0.01, but say 10^-4).

Is there an efficient and nice way to solve this?



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