Durand-Kerner method for the real roots (Q5960870)

The Durand-Kerner method for calculating all zero-points of a univariate polynomial is modified for simultaneous calculation of all real zero-points of a real univariate polynomial. Techniques of choosing initial values for both real and complex zero-points are discussed. It is shown that the proposed method converges locally quadratically. Even for multiple zero-points, a quadratic convergence is established for the ``center'' of their approximations. Comparison with the original Durand-Kerner method and Newton method shows effectiveness of the proposed methods.