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##

Inverse Iteration

Inverse iteration, described in Algorithm 4.2,
can also be used to solve the
NHEP without any apparent change.

As in the Hermitian case, assume that and
are an eigenvalue and eigenvector pair of so that
is the largest eigenvalue of
in magnitude. The inverse power method
converges if the starting vector
is not perpendicular to . The
convergence rate is
, where is an eigenvalue of
such that
is the second
largest eigenvalue of
in magnitude.
In general, inverse iteration tends to have
much more rapid convergence than the power method if
is chosen to be very close to a desired
eigenvalue. However, inverse iteration does require a
factorization of the matrix , making it less
attractive when this factorization is expensive.

Susan Blackford
2000-11-20