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128 CHAPTER 7. NUMERICAL EXPERIMENTS
Figure 7.11: Eigenvalue spectra of the matrices A p1 and A xi , i =1,...,4
Table 7.18: Details of the performance of JD and JDCOMM with mindim = 10 and
maxdim = 100
Method MV A p1 MV A xi Flops ×10 9 Time (s) Global minimum
JD 5941 0 7.5 139.9 −206.5
JDCOMM A x1 237 1607 0.4 10.1 −206.5
JDCOMM A x2 302 2322 0.5 7.6 −206.5
JDCOMM A x3 725 6975 1.2 20.8 −206.5
JDCOMM A x4 636 5996 1.1 20.7 −206.5
to compute the requested eigenvalue; mindim is 10 and maxdim is 100 (last row of
Table 7.17).
Figure 7.12 shows the plot of the norms of the residuals in the eigenvalue equation
(at each JD outer step) against the number of matrix-vector products with A p1 . All
methods compute the same global minimum and the identical location.
To reveil the performance of a Krylov based eigenvalue solver, we also apply
the Matlab eigs method, which is an implicitly restarted Arnoldi method [95], to
this problem. This method computes the requested smallest real eigenvalue in 62
seconds as the 151th eigenvalue. We used no additional parameter settings here;