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With the so-called Cayley transform,
QEP with Cayley Transform.
where the parameters , , and are chosen such that
, the original QEP (9.1) becomes
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
if that is the case for the real triple and if , ,
and are real.