The Optimum Convergence Condition for the Durand-Kerner Type Simultaneous Inclusion Method

In order to solve the algebraic equation, where the complex polynomial has only simple zeros, one can use the simultaneous inclusion methods. The quadratic convergence condition for the Durand-Kerner simultaneous inclusion method, using point estimation theory is w⁽⁰⁾ < d⁽⁰⁾/(an+b), where n is the polynomial degree, d⁽⁰⁾ the minimum distance between the initial iterations and w⁽⁰⁾ is the absolute maximum of the Weierstrass factors. This paper determines the optimum quadratic convergence condition for a generalized Durand-Kerner type simultaneous inclusion method