If we can factor
for a shift
, we can generalize the inverse iteration to
compute eigenvalues of the problem (5.1) near
as shown in Algorithm 5.2.
Here are some comments on this algorithm.
In step (3) we multiply by , while in step (5) we solve
a system with the shifted matrix
. In a practical case, we perform
an initial sparse Gaussian elimination and use
its
and
factors while operating.
Step (4) makes sure that the vector
is of unit
norm. The quantity
is a
Rayleigh quotient,