Specifications

11 Reliable Computations
11-16
entries are the smallest deviations that are significant to each variable. An
excellent discussion of scaling is given in the introduction to the LINPACK
Users’ Guide, [1].
Choose scaling based upon physical insight to the problem at hand. If you
choose not to scale, and for many small problems scaling is not necessary, be
aware that this choice affects the accuracy of your answers.
Finally, note that the function
ssbal performs automatic scaling of the state
vector. Specifically, it seeks to minimize the norm of
by using diagonal scaling matrices . Such diagonal scaling is an economical
way to compress the numerical range and improve the conditioning of
subsequent state-space computations.
N
x
1–
AN
x
N
x
1–
B
CN
x
0
N
x