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MathGroup Archive 2006

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Re: calculate Recurrence Equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68785] Re: [mg68713] calculate Recurrence Equations
  • From: Sseziwa Mukasa <mukasa at jeol.com>
  • Date: Fri, 18 Aug 2006 03:12:43 -0400 (EDT)
  • References: <200608170818.EAA24918@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On Aug 17, 2006, at 4:18 AM, 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...

The difficulties are subtle, for starters use anteil[0]:=1, also if  
you are not evaluating the series for large values of n, cache the  
values of intermediate n eg:

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

{0.0014070000000003802 Second,
   
4909085745117164100520051333566036654601/1342177280000000000000000000000 
000000000}

Regards,

Ssezi


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