# [Trilinos-Users] How does Anasazi internally treat preconditioners ?

Davood Ansari david.ansari at gmail.com
Fri Feb 22 20:45:17 MST 2008

```*Hi everyone

The basic idea for krylov subspace eigen solvers is to find the largest
eigen value(s) of a problem A x = lambda B x
by  repeated application of the operation B^(-1) A on an initial
vector (very roughly speaking).
This means a multiplication by A and a linear solve by B is involved.
When smallest eigenvalue(s) are sought, the two are interchanged (A and B)
to solve B x = (1 / lambda) A x.

In trilinos, when an eigen problem is being defined  through either the
BasicEigenproblem or the Eigenproblem class, a preconditioner
can be introduced. I guess this is going to be used for the linear solve???
Based on this interpretation, when largest eigenvalues of **A x = lambda B x

are sought, one should (for example) produce an incomplete factorization
of A. On the other hand, for the case with the smallest eigenvalues, one
should take the incomplete factorization of B as the preconditioner???

Is that right ?