polyroot
Find Zeros of a Real or Complex Polynomial
Find zeros of a real or complex polynomial.
- Keywords
- math
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.
References
Jenkins, M. A. and Traub, J. F. (1972). Algorithm 419: zeros of a complex polynomial. Communications of the ACM, 15(2), 97--99. 10.1145/361254.361262.
See Also
uniroot for numerical root finding of arbitrary
functions;
complex and the zero example in the demos
directory.
Examples
library(base)
# NOT RUN {
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
# }