Databases Reference
In-Depth Information
FIGURE 9.13
Underdetermined case solutions.
The solutions to both cases for the underdetermined set of equations are shown in Figure 9.13.
Some points are worth mentioning here. Underdetermined systems typically have an infinite number
of solutions that can typically be described with a series of curves. Matlab will return only one
solution to the underdetermined system, and no warning is given to the user to indicate that the
returned solution is merely one of many.
Notice in this instance that Matlab randomly chose to assign x
2
to zero. It could have just as
easily picked x
1
or x
3
to fix at zero, or any other constant for that matter. In an underdetermined
case, arbitrary assignments must be made to some variables in order to converge on a solution for
the other variables. Because this system of equations has 3 unknowns and 2 equations, only one
of the variables to be solved for had to be arbitrarily assigned a value. If the system consisted of
4 unknowns and 2 equations, two of the variables would have to be fixed for convergence.
The last case for consideration is that of the consistent system, where the number of equations
equals the number of unknowns. If the user loads the “MatlabMLRConsistent.xlt” sample file from
the CD-ROM
in location Chapter 9\Samples, the Worksheet template shown in Figure 9.14 will appear.
FIGURE 9.14
Consistent system sample template.
