Stability and Accuracy Assessments

The generalized eigenvalue problem for a Hermitian matrix pair
with one of and , or some linear combination of and , being
positive definite takes a unique position among all
generalized eigenvalue problems for matrix pairs
because it resembles in many ways the standard Hermitian eigenvalue
problem discussed in Chapter 4.
Matrix pairs as such are called *Hermitian definite pairs*.
We shall consider separately

- is definite and well-conditioned, meaning that
is not too
large.
^{} - Some combination of and is definite and well-conditioned.

For the treatment of error estimation of computed eigenvalues and
eigenvectors of dense generalized Hermitian eigenproblems,
see Chapter 4 of the *LAPACK Users' Guide* [12].