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QEP with Cayley Transform.
With the so-called Cayley transform,
where the parameters
,
, and
are chosen such that
, the original QEP (9.1) becomes
![\begin{displaymath}
\left(\mu^2 \widehat{M} + \mu \widehat{C} + \widehat{K} \right) x = 0,
\end{displaymath}](img3345.png) |
(262) |
where
,
, and
.
Eigenvalues
of the original QEP (9.1)
close to the antishift
are
transformed into large (in modulus) eigenvalues
of the QEP
(9.18). Eigenvalues
close to the shift
correspond to eigenvalues
of (9.17) close to
.
Note that the triple
is symmetric
if that is the case for the real triple
and if
,
,
and
are real.
Susan Blackford
2000-11-20