polyroot: 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.

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.

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.