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# Re: Math Problem in Mathematica
In article <694bda$kp6@smc.vnet.net>, Daniel <koheleth@ix.netcom.com>
wrote:
> The problem I would like to formulate in Mathematica is: Let f[i,j] =
> Abs[Sqrt[1-(i/n)^2]-j/n]. i and j run from 1 to n, and n is a fixed
> integer >=1. I want to find the sum S of the minimum of f over j, for
> each i for given n.
>
> Example: n=7. Min (i=1, j from 1 to 7)= .01
> Min (i=2, """ )= .04
> Min (i=3, ... = .05
> etc.
>
> and the sum S = 0.20.
>
> FindMinimum seemed like the right idea, but I don't know how to make it
> work for a function of discrete values.
>
> The problem appears as Problem 10365 in AMM.
>
> Daniel Tisdale
This simple implementation seems to be what you want (it used the
function Min); but, I dont seem to get exactly the same numerical
results that you note in your post. Perhaps I misunderstood...or...?
In[1]:=
Clear[f,MinfOverj,SumMins];
f[i_,j_,n_] :=Abs[Sqrt[1-(i/n)^2]-j/n];
MinfOverj[i_,n_]:=Min[Table[ f[i,j,n], {j,1,n}]];
SumMins[n_]:=Sum[MinfOverj[i,n],{i,1,n}];
Here are the minima for n=7 for i=1 to 7
In[2]:= Table[MinfOverj[i,7],{i,1,7}]//N
Out[2]
{0.0102567,0.0416852,0.046365,0.0364911,0.0144315,0.0563498,0.142857}
And this is the sum:
In[3]:= SumMins[7]//N
Out[3]= 0.348436
--
David Reiss
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http://home.earthlink.net/~dreiss
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