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is the unit eigenvector corresponding to
. We
need this vector in the hard case (see the paragraph containing
equation 4.15 ). Since
is the eigenvector
corresponding to
, we can write:
We will try to find a vector
which minimizes
. This is equivalent to find a
vector
which maximize
. We will choose the component of
between
and
in order to make
large. This is achieved by
ensuring that at each stage of the forward substitution
, the sign of
is chosen to make
as large as
possible. In particular, suppose we have determined the first
components of
during the forward substitution, then
the
component satisfies:
and we pick
to be
depending on which of
is larger. Having
found
,
is simply
. The vector
found this way has the useful property that

as
Next: The Rayleigh quotient trick
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Frank Vanden Berghen
2004-04-19