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5.3. EFFICIENCY OF THE ND-SYSTEMS APPROACH 77
Figure 5.16: Points required by the linear, diagonal, equalizing and the axis method
for computing state vectors at time instants (0, 500), (125, 375), (250, 250), (375, 125),
and (500, 0) with a 3 × 3 initial state
in Tables 5.3 and 5.4. An increase by a factor 2 in two dimensions indicates, for
example, the increase of stored points when comparing the points (0, 50) and (0, 100)
or the points (50, 50) and (100, 100). An increase factor of 5 in three dimensions
concerns the increase of stored points when moving from (10, 10, 10) to (50, 50, 50),
or from (0, 0, 10) to (0, 0, 50).
Table 5.3: Increase in the number of stored points along the diagonal
Increase factor Diagonal method Linear/Equalizing method Axis method
n =2/n =3 n =2and n =3 n =2/n =3
2 3.9 / 7.6 2.0 3.5 / 5.1
5 19.4 / 86.9 4.8 12.0 / 29.6
10 75.0 / 662.3 9.4 41.6 / 150.9
From the Tables 5.3 and 5.4 it is concluded that for the equalizing method the
number of points required for the computation of points with almost equal coordinates
indeed grows linearly with the increase factor. For the axis method a similar statement