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Shift-and-Invert QEP.
Combining the above shift-and-invert spectral transformations (SI),
the so-called shift-and-invert QEP becomes
![\begin{displaymath}
\left(\mu^2 \widehat{M} + \mu \widehat{C} + \widehat{K} \right) x = 0,
\end{displaymath}](img3345.png) |
(261) |
where
and
,
, and
.
The exterior eigenvalues
of the QEP (9.17)
approximate the eigenvalues
of the original QEP (9.1)
closest to the shift
. These eigenvalues
are given by
Again, the corresponding generalized ``linear'' eigenvalue problem
in terms of
, rather than
, is
or
if the Hermitian of the matrix triplet
wants to be preserved.
Susan Blackford
2000-11-20