link to my thesis

116 CHAPTER 7. NUMERICAL EXPERIMENTS
Figure 7.2: Residuals before and after projection during 250 iterations of the JD
eigenvalue solver
with RQI expansion with projection.
Table 7.8: Results for the projection with JD: # MVs (mean±stdev) and the error
JD RQI & No projection RQI & Projection
# #MVs Error #MVs Error #MVs Error
1 109.3 ± 6.789 5.63 × 10 −7 1661 ± 1088 4.45 × 10 −5 71.93 ± 7.741 4.69 × 10 −7
2 36 2.09 × 10 −7 34.53 ± 3.871 1.23 × 10 −6 36 2.46 × 10 −7
3 91.60 ± 6.957 5.61 × 10 −8 82.07 ± 9.721 2.92 × 10 −6 85.73 ± 7.741 5.26 × 10 −6
4 60.07 ± 9.721 6.99 × 10 −7 57.87 ± 7.039 6.46 × 10 −7 57.13 ± 7.039 3.26 × 10 −7
5 68.87 ± 5.680 9.12 × 10 −8 69.60 ± 9.109 2.73 × 10 −7 66.93 ± 5.470 6.46 × 10 −8
This table does not show a difference between the three approaches except for
the first test case. This first test case requires a relatively large number of operator
actions with the original JD implementation. If the expansion method is changed to
RQI then the number of operator actions increases more than tenfold to a level that is
comparable with the JDQZ implementation. However, if the projection is applied with
the RQI expansion then the required number of operator actions decreases below
the number of operator actions required with the original implementation. This
means that significantly less iterations of the eigenvalue solver are required because
an iteration with projection requires two additional operator actions compared to a
standard iteration: (i) an operator action for the Rayleigh quotient (6.3) to determine
the new approximate eigenvalue and (ii) an operator action for the residual check in
Equation (6.48).
Although no additional improvements can be seen with the presented settings,