Re: FixedPoint vs. FixedPointList
- To: mathgroup at smc.vnet.net
- Subject: [mg24428] Re: [mg24384] FixedPoint vs. FixedPointList
- From: BobHanlon at aol.com
- Date: Tue, 18 Jul 2000 00:58:26 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 7/12/2000 11:43:32 PM, linsuain+ at andrew.cmu.edu writes:
>Hi all. I need to know the fixed point of a function (to a certain
>accuracy) starting from a certain value of the arguement, say:
>
> x = FixedPoint[ f, x, SameTest -> ( #2-#1 < somesmallnumber &) ]
>
> I do not care about the intermediate results, but I would like to know
>how many iterations it takes for the process to converge. FixedPointList
>will do, for example:
>
> {n,x}={Length[#],Last[#]}& @ FixedPointList[....]
>
> However I believe this would cause problems. The reason is that x is
>really a very long list (FixedPoint works for lists too), and it could
>take many iterations for this to settle. Mathematica, I believe, stores
>only a maximum of two values at any given moment when executing
>FixedPoint, but it stores all intermediate values for FixedPointList,
>and most certainly would run out of memory.
>
> Could any think of how to trick Mathematica to count the iteration
>without trying to store all the results?
>
poly[x_] := x^5 - x^4 + 2 x^3 - x^2 + 3;
n = 1;
FixedPoint[(n++; # - poly[#]/poly'[#]) &, 2.]
-0.8574417862415682
n
23
Length[FixedPointList[(n++; # - poly[#]/poly'[#]) &, 2.]]
23
Bob Hanlon