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Re: calculate Recurrence Equations

• To: mathgroup at smc.vnet.net
• Subject: [mg68781] Re: calculate Recurrence Equations
• From: "Norbert Marxer" <marxer at mec.li>
• Date: Fri, 18 Aug 2006 03:12:38 -0400 (EDT)
• References: <ec1a1u$omo$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hello

If you modify (your expression) to:

anteil[0] = 1;
anteil[n_] := (anteil[n] = anteil[n - 1] + (anteil[n - 1]*5 - 1)/100 )
anteil[30]//N

you can save the intermediate calculations. But even with this
modification you will run into problems for large n (a few 100),
because you build up your expression starting with the last index = n
and you will get a deeply nested expression (which might use up the
memory of your computer).

I would rather use the following command (which forward calculates the
expression starting with the starting value=1):

n=1000;Nest[(# + (#*5 - 1)/100) &, 1, n]//N

Even 1000 iterations work and need less than a second (on my computer).

Best Regards
Norbert Marxer
www.mec.li


Frank Hechtner wrote:
> hi,
>
> i?m in trouble with my Recurrence Equations:
>
> i?ve defined the following function
>
> anteil[0] = 1
> anteil[n_] := anteil[n - 1] + (anteil[n - 1]*5 - 1)/100
>
> i want mathematica to calculate the values for anteil[30] and so on.
>
> Unfortunately mathematica needs for this calculation over 2 hours (and
> is still running, athlon x2 4600, 2 gb ram).
>
> I don?t see where are the difficulties for mathematica...
> 
> Thanx for your help
> 
> frank