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The direct iteration methods for the HEP
can be generalized to the GHEP (5.1).
First we assume that a Cholesky factorization of
is easily obtainable.
We then reformulate (5.1) as a standard Hermitian eigenvalue
problem with the matrix as described
in the previous subsection (5.5),
possibly after making positive definite as noted
in the introduction (5.2).
The power method of §4.3 now takes the following form.
In step (3),
the computation can be executed into three
Hence, no explicit knowledge of the matrix is needed for
the power method. The power method converges under
conditions similar to those for the standard HEP.