An improvement on Nourein's method for the simultaneous determination of the zeroes of a polynomial (An algorithm)

摘要

In a recent paper [2], Nourein derived an iteration formula, which exhibited cubic convergence for the simultaneous determination of the zeroes of a polynomial. In this paper - following quite a different appraoch - we derive a method which can be viewed as an improvement on that of [2]. The derivation is based on the approximation of the polynomial in question by a Lagrange interpolation formula. We give the algorithm in ALGOL 60. For a given real polynomial, the algorithm caters for the general case of complex zeroes.