An expert driver is provided to compute all the eigenvalues and (optionally) the eigenvectors of the following types of problems:

where *A* and *B* are symmetric or Hermitian and *B* is positive definite.
For all these problems the eigenvalues are
real.
When *A* and *B* are symmetric, the matrices *Z*
of computed eigenvectors satisfy
(problem types 1 and 3) or
(problem type 2), where is a diagonal matrix with the eigenvalues
on the diagonal. *Z* also satisfies
(problem types 1 and 2) or (problem type 3).
When *A* and *B* are Hermitian, the matrices *Z*
of computed eigenvectors satisfy
(problem types 1 and 3) or
(problem type 2), where is a diagonal matrix with the eigenvalues
on the diagonal. *Z* also satisfies
(problem types 1 and 2) or (problem type 3).

The routine is listed in table 3.5.

**Table 3.5:** Driver routine for the generalized symmetric definite eigenvalue problems

Tue May 13 09:21:01 EDT 1997