[SciPy-dev] Example of eig not converging
Pauli Virtanen
pav@iki...
Fri Jul 3 13:38:55 CDT 2009
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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