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- A family of Ehrlich-type accelerated methods with King’s correction for the simultaneous approximation of polynomial complex zerosPublication . Machado, Roselaine Neves; Lopes, Luiz GuerreiroIn this paper, we present a new family of accelerated iterative methods for the simultaneous approximation of simple complex zeros of a polynomial. These simultaneous methods are constructed on the basis of the third order Ehrlich iteration, accelerated by using the so-called Gauss–Seidel approach, and combined with a correction based on King’s family of optimal fourth order iterative methods for solving nonlinear equations. Using King’s correction, the R-order of convergence of the basic accelerated method is increased from at least 3 to at least 6. A numerical example is provided to illustrate the convergence and effectiveness of the proposed family of combined accelerated methods for the simultaneous approximation of simple polynomial zeros.