The
FZ_ROOTS
function is used to find the
roots of an *
m*
-degree
complex polynomial, using
Laguerre's method. The result is an *
m*
-element complex vector.

FZ_ROOTS is based on the routine ```
zroots
```

described in section 9.5 of *
Numerical Recipes in C: The Art of Scientific Computing*
(Second Edition), published by Cambridge University Press, and is used by permission.

EXAMPLE 1:" Real coefficients yielding real roots.

*
P *
(*
x*
) = 6*
x*
^{
3}
- 7*
x*
^{
2}
- 9*
x*
- 2 (The exact roots are -1/2, -1/3, 2.0)

coeffs = [-2.0, -9.0, -7.0, 6.0]

( -0.500000, 0.00000)( -0.333333, 0.00000)( 2.00000, 0.00000)

EXAMPLE 2: Real coefficients yielding complex roots.

*
P*
(*
x*
) = *
x*
^{
4}
+ 3*
x*
^{
2}
+ 2

coeffs = [2.0, 0.0, 3.0, 0.0, 1.0]

*
(0.00000, -1.41421)(0.00000, 1.41421)*

*
(0.00000, -1.00000)(0.00000, 1.00000)*

EXAMPLE 3: Real and complex coefficients yielding real and complex roots.

*
P*
(*
x*
) = *
x*
^{
3}
+ (-4 - *
i*
4)*
x*
^{
2}
+s (-3 + *
i*
4)*
x*
+ (18 + *
i*
24)

(The exact roots are -2.0, 3.0, (3.0 + *
i*
4.0))

coeffs = [COMPLEX(18,24), COMPLEX(-3,4), COMPLEX(-4,-4), 1.0]

( -2.00000, 0.00000) ( 3.00000, 0.00000) ( 3.00000, 4.00000)