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MathGroup Archive 2006

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Re: Strange Det function behavior

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65474] Re: Strange Det function behavior
  • From: bsyehuda at gmail.com
  • Date: Mon, 3 Apr 2006 06:59:46 -0400 (EDT)
  • References: <200604020900.FAA01592@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
This has nothing to do with the fact that you are running on celeron.
It seems that the problem is at the accuracy of the floating numbers
generated by the random number generator (RNG).
If you are willing to overcome this just try
 f[x_Integer] := Det[ Table[ Random[Integer,{0,1000000}]/1000000*t + i/j,
{i, x}, {j, x} ] ]
and then it will work with infinite precision.
Then N[f[12]] (or any other index) will give you good results.
You can also change the one milion that I used with another number (I also
tried 100000000 with very good results).
Remember that Mathematicas RNG for integers is different from the RNG for
floats (reals).
regards
yehuda

On 4/2/06, Alexander <beginning.physst at mail.ru> wrote:
>
> Dear MathGroup!
>
> Suppose we have defined the following function:
>
> f[x_Integer] := Det[ Table[ Random[]*t + i/j, {i, x}, {j, x} ] ];
>
> Now try to make a table for different values of argument (matrix
> dimension):
>
> Table[f[i], {i, 12}] // TableForm
>
> It takes a considerable time on my Celeron 1700 with Mathematica 5.2
> under WinXP to make such a table.
>
> Once we made this table we see very strange bihavior, all results
> before x=12 dimension are polynoms,
> but starting from x=12 result become very big and very
> strange, and in fact it's not even a polynom.
>
> I spend several hours try to understand why system acts so strange, and
> finally came to idea that the answer is in numbers representation and
> inner
> system algorithms used to evaluate Det function.
>
> It would be very interesting to see explanations of this result.
>
> Thanks for your answers!
>
> Alexander.
>
>


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