| polyroot {base} | R Documentation |
Find Zeros of a Real or Complex Polynomial
Description
Find zeros of a real or complex polynomial.
Usage
polyroot(z)
Arguments
z |
the vector of polynomial coefficients in increasing order. |
Details
A polynomial of degree n - 1,
p(x) = z_1 + z_2 x + \cdots + z_n x^{n-1}
is given by its coefficient vector z[1:n].
polyroot returns the n-1 complex zeros of p(x)
using the Jenkins-Traub algorithm.
If the coefficient vector z has zeroes for the highest powers,
these are discarded.
There is no maximum degree, but numerical stability may be an issue for all but low-degree polynomials.
Value
A complex vector of length n - 1, where n is the position
of the largest non-zero element of z.
Source
C translation by Ross Ihaka of Fortran code in the reference, with modifications by the R Core Team.
References
Jenkins, M. A. and Traub, J. F. (1972). Algorithm 419: zeros of a complex polynomial. Communications of the ACM, 15(2), 97–99. doi:10.1145/361254.361262.
See Also
uniroot for numerical root finding of arbitrary
functions;
complex and the zero example in the demos
directory.
Examples
polyroot(c(1, 2, 1))
round(polyroot(choose(8, 0:8)), 11) # guess what!
for (n1 in 1:4) print(polyroot(1:n1), digits = 4)
polyroot(c(1, 2, 1, 0, 0)) # same as the first