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.

Susan Blackford 2000-11-20