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MathGroup Archive 2006

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Strange Det function behavior.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65445] Strange Det function behavior.
  • From: "Alexander" <beginning.physst at mail.ru>
  • Date: Sun, 2 Apr 2006 05:00:05 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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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