Find Zeros of a Complex Polynomial

Usage

polyroot(z)

Arguments

z the vector of polynomial coefficients in decreasing order.

Description

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.

Value

A complex vector of length n - 1, where n is length(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)

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