polyroot                package:base                R Documentation

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.

Details:

     A polynomial of degree n - 1,

              p(x) = z1 + z2 * x + ... + 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.

     As from R 2.8.0 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 and Traub (1972) TOMS Algorithm 419. _Comm. ACM_, *15*,
     97-99.

See Also:

     'uniroot' for numerical root finding of arbitrary functions;
     'complex' and the 'zero' example in the demos directory.

Examples:

     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

