Databases Reference
In-Depth Information
FIGURE 9.9
Completed overdetermined case Worksheet.
The following are topics of interest with respect to the overdetermined solutions given in
the sample. Notice that any solution to an overdetermined system can only approximately satisfy
all of the equations in the system. This is self-evident in that the residuals are nonzero, indicative
of deviation. Also notice that, for perfect conditioning, the function
rcond
will return unity (1).
The higher the value rcond returns, the worse the conditioning of the matrix. Notice that, in this
instance, omitting the
a
0
term will produce a better-conditioned matrix to work with, and thus
the residuals solved for without an
a
0
term will generally be smaller than those solved for with
an
a
0
term.
This tool is also capable of solving a system of equations where the opposite condition exists —
that of the underdetermined system. If the user loads the “MatlabMLRDataUnder.xlt” sample file from
the CD-ROM in location Chapter 9\Samples, the Worksheet template shown in Figure 9.10 will appear.
Here, an underdetermined system is presented with two areas reserved for results. The top area is
for the case where the
a
0
term is omitted from the solution, and the bottom area is for the case
where the
a
0
term is included in the returned solution. The result areas have designated places for
FIGURE 9.10
The underdetermined case example template.
