COunting approximate values

[Peter Cameron]

On Mon, Nov 03, 2003 at 04:02:11PM +0000, Leonard Soicher wrote:
> How do you propose to represent multiplicities of, say, distinct eigenvalues 
> when we know the exact multiplicities, but only know approximations to the 
> (not neccesarily rational) eigenvalues? Do we do something like 
> (0.683, at 2),(0.683, at 3) which we were discussing yesterday to mean that 
> an eigenvalue x approximated by 0.683 occurs with multiplicity 2
> and an eigenvalue y also approximated by 0.683 but not equal to x
> has multiplicity 3? 
>
My first answer would be that actually most people won't really be
interested in this information. Also, it is likely to apply only to
eigenvalues, not to pairwise variances (which are rational anyway, so
real values for these would only mean that we hadn't done an exact
computation).

My second answer is that this is interesting information which we can
think at leisure about how to include. Perhaps there can be a value-count
list of eigenvalues and a separate list of eigenvalue multiplicities,
the latter only given when the first has been calculated by an approximate
method but the multiplicities are known exactly.

Peter.