Section
4:
Using Matrix Operations
121
Example:
Use the
residual correction program
to
calculate
the
inverse
of
matrix
A for
33 16 72
-24
-10 -57
-8 -4 -17
The
theoretical inverse
of A is
-29/3 -8/3
-32
8
5/2
51/2
8/3 2/3 9
Find
the
inverse
by
solving
AX = B for X,
where
B is a 3 X 3
identity matrix.
First,
enter
the
program
from
above. Then,
in Run
mode, enter
the
elements into matrix
A
(the system matrix)
and
matrix
B
(the
right-hand, identity matrix).
Press
|
GSB
I
[A]
to
execute
the
program.
Recall
the
elements
of the
uncorrected solution, matrix
C:
C
=
-9.666666881 -2.666666726 -32.00000071
8.000000167
2.500000046 25.50000055
2.666666728
0.6666666836 9.000000203
This solution
is
correct
to
seven
digits.
The
accuracy
is
well within
that
predicted
by the
equation
on
page 103.
(number
of
correct digits)
^
9 -
log(||
A||
||C||)
-
log(3)«
4.8
.
Recall
the
elements
of
the
corrected solution, matrix
B:
B
=
-9.666666667
-2.666666667 -32.00000000
8.000000000
2.500000000 25.50000000
2.666666667
0.6666666667 9.000000000
One
iteration
of
refinement yields
10
correct digits
in
this
case.
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