[petsc-users] Best slepc solvers to compute the eigenvectors corresponding to the m smallest eigenvalues

[Jose E. Roman]

> El 1 oct 2017, a las 17:41, Frederic Nataf <nataf at ann.jussieu.fr> escribió:
> 
> Hi to everyone, 
> 
> 
>   I’d like to compute a basis for the vector space of a given dimension m (say m=10) that corresponds to the m smallest eigenvalues. You might as well say I want to compute the eigenvectors corresponding to the m smallest eigenvalues but actually I am only interested in vector space they span. I’d like as well to be able initialize the computation with some approximate guess vector space. My matrix is real symmetric definite positive and of moderate size so that I do not need a parallel version. 
> 
> What are the best and most reliable methods to do it. 
> 
>   Many thanks,
> 
>       Frédéric Nataf
> 

In SPD matrices, the smallest eigenvalues are the leftmost ones, so the default solver (Krylov-Schur) with -eps_smallest_real should give you the answer. However, this solver cannot exploit the knowledge of the initial guess subspace. In this case, it may be more effective to use GD or LOBPCG, especially if a good preconditioner is available. If the problem has multiple eigenvalues, I would suggest LOBPCG.

Jose