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Re: calculate Recurrence Equations

• To: mathgroup at smc.vnet.net
• Subject: [mg68768] Re: calculate Recurrence Equations
• From: "Stratocaster" <stotz1 at verizon.net>
• Date: Fri, 18 Aug 2006 03:12:14 -0400 (EDT)
• References: <ec1a1u$omo$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Frank Hechtner" <frank.hechtner at rub.de> wrote in message 
news:ec1a1u$omo$1 at smc.vnet.net...
> 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...

Short answer:

Redefine the function as follows.  (notice the extra = ???)

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

Longer Answer:

They way you've inputed it, Mathematica needs to recalculate a[0 through n], 
every time it increments "n".

Adding the extra syntax;     a[n_]:=a[n]= "the function"
forces Mathematica to commit all calculations to the cache, so as not to 
re-evaluate what has already been evaluated.  This will significantly 
decrease processing time.