Re: Sparse Eigenvalues

[Chaman Singh Verma]

On Sat, Dec 20, 2008 at 9:16 PM, John W. Eaton <address@hidden> wrote:

On 20-Dec-2008, Chaman Singh Verma wrote:

| Does anyone know any performance results of Sparse-Eigenvalue solver (i.e.
| eigs ) ? My observation
| is that it is too slow.

What is the purpose of sending a message like this?  Do you think that
it helps in some way?  If you think that there is something that could
be improved, then I suggest helping our community by working on the
problem and submitting a patch, not just complaining in vague terms
that something doesn't meet your expectations.

jwe

Hello, 

Sorry, if my sentence hurt in any way somebody's feelings, it was unintentional.
but you are correct that I should have been more objective. I will be careful next time.
But surely, I was not critical about Octave, it is WONDERFUL software.

Well, here is my sincere question. It is my observation that eigs ( which probably 
based on ARPACK code) seems to take atleast "N" sparse-matrix-vector operations,
which could be quite expensive for reasonably large matrices. One of the application
where someone may need second eigenvalue is for graph partitioning ( and famous
Google rank Matrix).  For typical graph of 200,000 rows and 100-200 columns, it takes
more than 45-50 minutes on single node machine, which is not competitive to other
graph partitioning methods such as METIS.

Here is my query to all the knowledge people.

(1)  What is the most competitive  algorithms for finding few eigenvalues/eigenvectors
      compared to ARPACK. Has somebody done any study and have some number to show its
      superiority.
(2)  Can we reduce the number of Matrix-Vec Operations ?
(3)  Can spectral decomposition beat METIS type decompositions ?

Thanks.
csv