A family of Ehrlich-type accelerated methods with King’s correction for the simultaneous approximation of polynomial complex zeros

Machado, Roselaine Neves; Lopes, Luiz Guerreiro

http://hdl.handle.net/10400.13/3744

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Authors

Machado, Roselaine Neves

Lopes, Luiz Guerreiro

Abstract(s)

In 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.

Keywords

Polynomial zeros Simultaneous iterative methods Combined methods Accelerated convergence Ehrlich method . Faculdade de Ciências Exatas e da Engenharia

URI

http://hdl.handle.net/10400.13/3744

Citation

Machado, R. N., & Lopes, L. G. (2019). A Family of Ehrlich-type Accelerated Methods with King’s Correction for the Simultaneous Approximation of Polynomial Complex Zeros. Global Journal of Pure and Applied Mathematics, 15(6), 789-802.