[SciPy-dev] Example of eig not converging

David Goldsmith d_l_goldsmith@yahoo....
Fri Jul 3 15:05:53 CDT 2009


Thanks, Pauli. In that case, I won't worry about it (I thought there was some "well-known" condition, like w/ the condition number and numerical invertibility, but if not, then there's no point in illustrating it w/ an example).

DG

--- On Fri, 7/3/09, Pauli Virtanen <pav@iki.fi> wrote:

> From: Pauli Virtanen <pav@iki.fi>
> Subject: Re: [SciPy-dev] Example of eig not converging
> To: scipy-dev@scipy.org
> Date: Friday, July 3, 2009, 11:38 AM
> On 2009-07-03, David Goldsmith <d_l_goldsmith@yahoo.com>
> wrote:
> > What has to be true of `a` so that eig(a) fails to
> converge?
> 
> The approximate answer is: in practice, it always
> converges.
> 
> Mathematically, the eigenvalue problem of an n x n matrix
> is 
> well-defined (modulo floating-point accuracy). So the
> actual 
> answer is very much implementation-dependent. LAPACK is a
> widely 
> used library, and I suppose its eigenvalue routines are
> quite 
> robust. So, failing matrices are probably difficult to
> find, and 
> constructing them probably requires looking carefully at
> the 
> algorithm itself, unless LAPACK authors themselves have
> listed 
> some examples somewhere. (I didn't find any with a quick
> search.)
> 
> So, I don't know the answer, and I suppose it would take
> quite a 
> bit of work to find out.
> 
> -- 
> Pauli Virtanen
> 
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