The FZ_ROOTS function is used to find the roots of an m-degree complex polynomial, using Laguerre’s method.
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.
Result = FZ_ROOTS(C [, /DOUBLE] [, EPS=value] [, /NO_POLISH] )
Returns an m-element complex vector containing the roots of an m-degree complex polynomial.
A vector of length m+1 containing the coefficients of the polynomial, in ascending order (see example). The type can be real or complex.
Set this keyword to force the computation to be done in double-precision arithmetic.
The desired fractional accuracy. The default value is 2.0 x 10-6.
Set this keyword to suppress the usual polishing of the roots by Laguerre’s method.
Example 1: Real coefficients yielding real roots.
Find the roots of the polynomial:
P (x) = 6x3 - 7x2 - 9x - 2
The exact roots are -1/2, -1/3, 2.0.
coeffs = [-2.0, -9.0, -7.0, 6.0]
roots = FZ_ROOTS(coeffs)
PRINT, roots
IDL prints:
( -0.500000, 0.00000)( -0.333333, 0.00000)( 2.00000, 0.00000)
Example 2: Real coefficients yielding complex roots.
Find the roots of the polynomial:
P (x) = x4 + 3x2 + 2
The exact roots are:
coeffs = [2.0, 0.0, 3.0, 0.0, 1.0]
roots = FZ_ROOTS(coeffs)
PRINT, roots
IDL Prints:
(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.
Find the roots of the polynomial:
P (x) = x3 + (-4 - i4)x2 + s (-3 + i4)x + (18 + i24)
The exact roots are –2.0, 3.0, (3.0 + i4.0)
coeffs = [COMPLEX(18,24), COMPLEX(-3,4), COMPLEX(-4,-4), 1.0]
roots = FZ_ROOTS(coeffs)
PRINT, roots
IDL Prints:
( -2.00000, 0.00000) ( 3.00000, 0.00000) ( 3.00000, 4.00000)
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4.0 |
Introduced |