polyroot

0th

Percentile

Find Zeros of a Real or Complex Polynomial

Find zeros of a real or complex polynomial.

Keywords
math
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.