Re: calculate Recurrence Equations

• To: mathgroup at smc.vnet.net
• Subject: [mg68750] Re: [mg68713] calculate Recurrence Equations
• From: Adriano Pascoletti <pascolet at dimi.uniud.it>
• Date: Fri, 18 Aug 2006 03:11:52 -0400 (EDT)
• References: <200608170818.EAA24918@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 17 ago 2006, at 10:18, 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...

Frank,
Your definition is memoryless. Let's make a slight modification that
adds memory
(note the = on the right hand side):

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

On an old 800MHz iMac it gives

In[3]:=
Timing[anteil[30]//InputForm]

Out[3]=
{0.004157 \
Second,4909085745117164100520051333566036654601/\
1342177280000000000000000000000000000000}

The same result via RSolve:

In[10]:=
ClearAll[anteil];
RSolve[{anteil[n]==anteil[n-1]+(anteil[n-1]*5-1)/100,anteil[0]
==1},anteil,
n]//InputForm

Out[11]//InputForm=
{{anteil -> Function[{n}, (1 + 4^(1 - n)*(21/5)^n)/5]}}

Extract the solution

In[22]:= sol=%[[1,1,2]];

and compute sol[30]

In[23]:= sol[30]//InputForm
Out[23]//InputForm=
4909085745117164100520051333566036654601/
1342177280000000000000000000000000000000

Hope it helps
Adriano Pascoletti

```

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