polyroot: Find Zeros of a Real or Complex Polynomial

Description

Find zeros of a real or complex polynomial.

Usage

polyroot(z)

Arguments

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.

Examples

Run this code

# 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
# }

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