Graphics Programs Reference
In-Depth Information
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The zeros areobtainedbycalculating the eigenvalues of the
n
n
“companion
matrix”
⎡
⎣
⎤
⎦
−
a
2
/
a
1
−
a
3
/
a
1
···
−
a
n
/
a
1
−
a
n
+
1
/
a
1
1
0
···
0
0
0
1
0
0
A
=
.
.
.
.
.
.
.
0
0
···
1
0
The characteristicequation (see Art. 9.1)ofthis matrix is
a
2
a
n
a
1
x
a
n
+
1
a
1
x
n
a
1
x
n
−
1
+
+···
+
=
0
which isequivalentto
P
n
(
x
)
0. Thus the eigenvalues of
A
are the zeroes of
P
n
(
x
). The
eigenvalue methodis robust, butconsiderably slower than Laguerre's method.
=
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