[petsc-users] estimation of max and min eigenvalues in SLEPc

[Xujun Zhao]

Hi Jose,

Thank you for your reply. How about the computational cost compared to one
EPSSolve() with all eigenvalues? what methods does SLEPc use for each
solve? Because it may be cheaper for largest eigenvalue if the power method
is used, but I don't if it is still so for smallest eigenvalue?

Xujun

On Wed, Jun 3, 2015 at 2:24 AM, Jose E. Roman <jroman at dsic.upv.es> wrote:

>
> El 03/06/2015, a las 01:00, Xujun Zhao escribió:
>
> > Hi Jed,
> >
> > Here is my problem:
> >
> > I want to evaluate a vector  u = B*dw where B and dw are a matrix and a
> stochastic vector. However, B = D^(-1/2) in which D is not explicitly
> assembled, so it is expensive to directly evaluate B. One solution is to
> make a Chebyshev approximation on B w.r.t. D, which is
> > B = sum(c_k*D_k)
> >
> > Then, the problem becomes u = B*dw = sum(c_k*y_k)  where y_k = D_k*dw
> can be obtained from my solver.
> >
> > Note c_k is the coefficient that is a function of approximate(not exact)
> max and min eigenvalues of D matrix. So I need an approximate range [
> lambda_min, lambda_max ] to calculate c_k. If this range is accurate, then
> Chebyshev approximation can converge faster, otherwise may be slow or even
> never.
> >
> > Xujun
> >
>
> SLEPc does not support computing eigenvalues from both ends of the
> spectrum with the same call. You have to call EPSSolve() twice, one with
> EPS_LARGEST_REAL and the other with EPS_SMALLEST_REAL.
>
> Jose
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20150603/351e9d9c/attachment.html>