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144 2. Tutorial
of all terms by least influence. If only one design point is present, the sorting order is obvious, but
it is not obvious for two or more design points. For example, if removing matrix entry X causes a
magnitude error of in design point and an error of in design point while the error
values for matrix entry Y are and respectively, which entry should be removed first
Removing X first would introduce a very small error in design point but an excessively large one
in design point . On the other hand, Y has a much larger influence in design point than X but
the total error in both design points would be smaller if Y is removed first.
SortingMethod is an option which selects the sorting strategy that is applied to the influence list
to obtain the term rankings. By default, terms are ranked by least influence on the solution in
the primary design point, that is design point . In the above example, this strategy would give X
precedence over Y. The corresponding option setting in Options[ApproximateMatrixEquation] is
SortingMethod −> PrimaryDesignPoint
The other available strategy ranks terms by least arithmetic mean influence in all design points,
which would give Y precedence over X:
SortingMethod −> LeastMeanInfluence
Usually, LeastMeanInfluence is the better choice if the calculations involve more than one design
point. To examine the effect of selecting a different term ranking method we repeat the previous
approximation run with SortingMethod −> LeastMeanInfluence.
In[39]:= approxceamp4 = ApproximateMatrixEquation[ceampsta,
V$RL, dpceamp3, CompressEquations −> True,
SortingMethod −> LeastMeanInfluence]
Out[39]= DAEAC, 19 19
Solving these approximated equations now yields a much simpler expression.
In[40]:= voutsimp4 = V$RL /. First[Solve[approxceamp4, V$RL]]
Out[40]=
C1 C2 gm$Q1 R1 R2 RC RL Rpi$Q1 s 2 V1
1 C2 RL s R1 R2 gm$Q1 R1 RE Rpi$Q1
gm$Q1 R2 RE Rpi$Q1 C1 gm$Q1 R1 R2 RE Rpi$Q1 s
Here, we determined the approximation sequence by using the average of the design-point errors as
sorting criterion. In our first approximation run with two design points the term influences on the
second design point at Hz were not taken into consideration when the ranking was computed. The
error bound at design point was reached quickly because some terms were removed first which
had low influence in design point but large influence in design point .