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Re: calculate Recurrence Equations


Frank Hechtner schrieb:
> 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
> 

Hi Frank,

Mathematika doesn't remeber the values it has alraedy calculated. So 
anteil[30] leads to 2^30 ~ 10^9 calls to anteil[]. If you store the 
calculated values, the calls to anteil[] are 31:

In[1]:=
anteil[0] = 1;
anteil[n_] := anteil[n] = anteil[n - 1] + (anteil[n - 1]*5 - 1)/100;
AbsoluteTiming[anteil[30]]
Out[3]=
{0.*Second, 
4909085745117164100520051333566036654601/1342177280000000000000000000000000000000}

But I prefer using RSolve[]:

In[1]:=
<< "DiscreteMath`RSolve`"
anteil = a /. First[RSolve[{a[0] == 1,
       a[n] == a[n - 1] + (a[n - 1]*5 - 1)/100}, a, n]]
anteil[30]
N[%]

Out[2]=
Function[{n}, (1/5)*(1 + 4^(1 - n)*(21/5)^n)]
Out[3]=
4909085745117164100520051333566036654601/
   1342177280000000000000000000000000000000
Out[4]=
3.6575539001205297

HTH,
Peter


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