Factorization of a polynomial into quadratic factors by Newton method
In this paper the method for simultaneous finding of all the roots of a polynomial is derived. The method is based on the factorization of a polynomial into quadratic factors. The method is designed for the polynomial with real coefficients. It is derived by using the Newton method. The quadratic convergence of this method is proved for given good guesses of the roots and for the polynomial with distinct roots. Algorithm of the method is described in Algol 60.