[petsc-dev] strangness in Chebyshev estimate of eigenvalues

[Jed Brown]

Mark Adams <mfadams at lbl.gov> writes:
> I've not looked at it, and it would be hard to because it is not a well
> defined problem.  But, if the initial guess is low frequency then it will
> give a poor estimate for the highest eigen value.  

This is true.

> It is not clear to me what the relationship is, generally, of an
> initial guess and the solution, spectrally.  Initial guesses will
> change as the problem evolves but we don't update the eigen estimates.
> If the user's initial guess happens to be zero then god knows what
> happens. 

The right hand side is used.  You have to explicitly ask to use a
nonzero initial guess.

> (This is actually the case for the XGC1 code!!!)  It adds one more
> variable in debugging AMG, which is hard enough as it is.

I agree that we should be using a random starting vector for spectral
estimates.  I'm not overly concerned whether it's a hash of the global
ID or a deterministic seed, but let's use something that has been
studied.  Your suggested "hash function" is way hokey.  I'm fine with
guaranteeing drand48 and a deterministic seed.
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