       Eigensystem bug in Mathematica 7.0.1 on Windows 7 (64 bit) for

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• Subject: [mg127949] Eigensystem bug in Mathematica 7.0.1 on Windows 7 (64 bit) for
• From: jdbates <batej6 at gmail.com>
• Date: Tue, 4 Sep 2012 05:48:26 -0400 (EDT)
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```Hello all,

I seem to have encounter a bug in the Eigensystem function in Mathematica 7.0.1 for Windows 7 (64 bit).

I'm attempting to solve for the eigenvectors of a covariance function on with support on a random lattice.  The process works up to 80 points in the lattice, but as soon as I include that 81st point the Eigensystem function fails (it generates spuriously negative eigenvalues and incorrect eigenvectors).

Here's an example code demonstrating this behavior:

**********************************

Cov[x_]=Exp[-x^2/a^2];

numx=81;
d=1;
a0=0.1;

xs=Table[RandomReal[{-d,d}],{n1,1,numx}]

CM=Table[Cov[xs[[n1]]-xs[[n2]]]/.{a->a0},{n1,1,numx},{n2,1,numx}];

{el,ev} = Eigensystem[CM]

**********************************

For numx <= 80, the Eigensystem command works fine.  For numx > 80, it fails.  This behavior seems to be independent of choice of lattice points (recomputing the xs numerous times did not change this behavior).  It also seems relatively independent of the width parameter a0, although I've found that if I make a0 sufficiently small such that the covariance matrix becomes sparse then the Eigensystem function seems to work correctly.

After searching this board, I've encountered a couple of threads regarding similar issues with Eigensystem for previous versions of Mathematica, but none for 7.0.1 or later.  Is this a known issue, and if so is there a workaround?

```

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