[SciPy-dev] Example of eig not converging

[Pauli Virtanen]

On 2009-07-03, David Goldsmith <d_l_goldsmith at 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