polyroot {base} | R Documentation |
Find zeros of a real or complex polynomial.
polyroot(z)
z |
the vector of polynomial coefficients in increasing order. |
A polynomial of degree n - 1,
p(x) = z1 + z2 * x + … + 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.
A complex vector of length n - 1, where n is the position
of the largest non-zero element of z
.
C translation by Ross Ihaka of Fortran code in the reference, with modifications by the R Core Team.
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.
uniroot
for numerical root finding of arbitrary
functions;
complex
and the zero
example in the demos
directory.
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