We use the same grid spacing and
get two sparse symmetric positive definite
matrices
and
of order
. They have a very regular sparse band
structure, now with at most 9 nonzero elements filled in each row.
We used the shift
to seek the 8 smallest eigenvalues.
The residual estimates (5.21)
at each step
are plotted in Figure 5.1.
When we compare the results on this generalized problem
to those for the standard Hermitian
eigenproblem of the same order in Figure 4.4
(p. ) in §4.4.6, we have
to bear in mind that this 9-point
approximation is a more accurate one to the partial
differential equation than the 5-point approximation used there.