eigenvalues from dot-product

[Daniel Oberhoff]

Hi,

This is not directly linked to octave, but I assume that there are  
enough people on this who know about such stuff:

Is there an efficient way to compute the eigenvalues of a matrix  
given it's dot product with an aribtrary vector?

The problem is that the matrix M is nxn  with n=O(10,000), which  
simply blows memory, but there is a relatively quick way to get those  
dot products M*v. The sparsity of this matrix is at about 50%, on top  
of this it is symmetric, and probably positive definite.

An octave solution (or pointers) would be nice of course ;).

Daniel