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.

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.

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.