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MathGroup Archive 1998

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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
dreissNOSPAM@nospam.earthlink.net
http://home.earthlink.net/~dreiss
To send personal email, remove the words  "nospam" and "NOSPAM" from the
email address



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