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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

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Frank Vanden Berghen
2004-04-19