** Next:** Shift-Invert Mode
** Up:** Selecting a Symmetric Driver
** Previous:** Generalized Eigenvalue Problem

Driver `dsdrv3` uses the regular inverse mode to solve the
generalized eigenvalue problem. This mode is appropriate when
is symmetric and positive definite but it is not
feasible to compute a sparse direct
Cholesky factorization . It might also be appropriate if can be factored but
there is reason to think that is ill-conditioned.
To use `dsdrv3` the user must supply the action of
The action of is typically done with an iterative
solver such as pre-conditioned conjugate gradient. The use
of -inner products restores symmetry. If can be factored
and is reasonably well conditioned,
then direct conversion to a standard problem is recommended.
Also, note that if *A* is positive definite and the smallest
eigenvalues are sought, then it is best to reverse the roles of
and and compute the largest eigevalues of . The reciprocals of these will then be the eigenvalues of interest.

*Chao Yang*

*11/7/1997*