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Re: Inverse of a Big Matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96894] Re: Inverse of a Big Matrix
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Thu, 26 Feb 2009 08:02:51 -0500 (EST)

On 2/25/09 at 4:06 AM, gregory.lypny at videotron.ca (Gregory Lypny)
wrote:

>I'm computing the inverse of a big matrix, 500 x 500.  Well, maybe
>not that big, but I'm getting the error message

>"General::luc: Result for `1` of badly conditioned matrix `2` may
>contain significant numerical errors. >>"

>and I'm wondering if anyone can suggest a workaround.  All I can say
>is that the determinant is very small (-4.327475016428501*10^-1947),

If the determinant is that small, why do you think it isn't
truly 0? Recall, a matrix with a determinant of 0 is singular
and has no inverse. In fact, such a small determinant is the
reason you are getting a warning about a badly conditioned
matrix. If the matrix is singular there is no workaround.

But why are you computing the inverse? Computing the inverse of
a general matrix is computationally expensive (a n^3 problem).
There are a variety of algorithms for solving matrix problems
that avoid explicitly computing a matrix inverse and are much
more efficient. Many of these are built in to Mathematica already.

>and that I can compute the inverse of various submatrices of size
>100 x100.

Being able to compute the inverse of submatrices of some given
matrix says nothing about whether the given matrix is singular
or not.




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