link to my thesis

5.3. EFFICIENCY OF THE ND-SYSTEMS APPROACH 75
Figure 5.13: Points required by the Diagonal method for computing state vectors at
time instants (0, 500), (250, 250), and (125, 375) with a 3 × 3 initial state
Figure 5.14: Points required by the Equalizing method for computing state vectors
at time instants (0, 500), (250, 250), and (125, 375) with a 3 × 3 initial state
for points located near the diagonal and Figure 5.15 shows that the axis method is
only efficient for points located near the coordinate axes.
Performance worsens if one wants to compute a whole set of state vectors involving
several different time instants at once, such as required, for example, for the operator
A T r when r involves several terms. In Figure 5.16 the points are displayed which
are computed by the linear, diagonal, equalizing, and axis method to facilitate the
computation of five requested state vectors at the time instants (0, 500), (125, 375),
(250, 250), (375, 125), and (500, 0) simultaneously. In the upper left corner the points
computed by the linear method are plotted. This way of computing simultaneous
paths to the requested time instants clearly is the most efficient (for this small example
where n = 2). Using the inefficient diagonal method, obviously too many points are
computed. The bottom part of the plot displays the points required by the equalizing
method and the axis method. The number of points evaluated by these four methods