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Re: Eigenvalues of sparse arrays

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102302] Re: Eigenvalues of sparse arrays
  • From: "Kevin J. McCann" <kjm at KevinMcCann.com>
  • Date: Tue, 4 Aug 2009 04:30:44 -0400 (EDT)
  • References: <h4uetk$iof$1@smc.vnet.net>

You might also try Singular Value Decomposition (SVD):

SingularValueList[dat]

This is a list of the non-zero eigenvalues. As you will see there are 
154 of these for your matrix, which indicates that two of the 
eigenvalues are zero to machine accuracy.

Kevin

gopher wrote:
> I am computing the eigenvalues of a matrix 's'.
> ----------------------------------------------------------------------
> In[164]:= SparseArray[s] == s
> 
> Out[164]= True
> 
> In[165]:= Eigenvalues[s, -6] // Chop
> 
> Out[165]= {0.382326, -0.382326, 0.350062, -0.350062, 0, 0}
> 
> In[166]:= Eigenvalues[SparseArray[s], -6] // Chop
> 
> Out[166]= {0.38245, -0.352447, 0.351011, 1.26736*10^-7, 0, 0}
> ----------------------------------------------------------------------
> 
> Why are the two results different? Is there an issue with precision
> when computing eigenvalues of sparse arrays? The matrix is such that
> the eigenvalues are symmetric about 0 so I'm pretty sure that the
> first result is correct.
> 


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