Prescribed cycles of König’s method for polynomials

摘要

We consider König’s method for finding roots of polynomials. Let Kf,n be the function defined in König’s method for polynomial f of order n (n≥2). For any given complex number λ∈C and any given set Ω≔{z1,z2,…,zk} of k (k≥2) distinct complex numbers, we present a procedure of constructing a polynomial fn,λ for which Ω is a k-cycle of Kfn,λ,n with multiplier λ.