Mathematics and Statistics Vol. 7(4), pp. 129 - 134
DOI: 10.13189/ms.2019.070406
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Ehrlich-type Methods with King's Correction for the Simultaneous Approximation of Polynomial Complex Zeros

Roselaine Neves Machado ¹, Luiz Guerreiro Lopes ^2,*
1 Federal Institute of Rio Grande do Sul, Bento Gonçalves Campus, 95700-206 Bento Gonçalves, RS, Brazil
² Faculty of Exact Sciences and Engineering, University of Madeira, Penteada Campus, 9020-105 Funchal, Madeira Is., Portugal

ABSTRACT

There are many simultaneous iterative methods for approximating complex polynomial zeros, from more traditional numerical algorithms, such as the well-known third order Ehrlich–Aberth method, to the more recent ones. In this paper, we present a new family of combined iterative methods for the simultaneous determination of simple complex zeros of a polynomial, which uses the Ehrlich iteration and a correction based on King's family of iterative methods for nonlinear equations. The use of King's correction allows increasing the convergence order of the basic method from three to six. Some numerical examples are given to illustrate the convergence behaviour and effectiveness of the proposed sixth order Ehrlich-like family of combined iterative methods for the simultaneous approximation of simple complex polynomial zeros.

KEYWORDS
Polynomial Zeros, Simultaneous Iterative Methods, Combined Methods, Ehrlich Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Roselaine Neves Machado , Luiz Guerreiro Lopes , "Ehrlich-type Methods with King's Correction for the Simultaneous Approximation of Polynomial Complex Zeros," Mathematics and Statistics, Vol. 7, No. 4, pp. 129 - 134, 2019. DOI: 10.13189/ms.2019.070406.

(b). APA Format:
Roselaine Neves Machado , Luiz Guerreiro Lopes (2019). Ehrlich-type Methods with King's Correction for the Simultaneous Approximation of Polynomial Complex Zeros. Mathematics and Statistics, 7(4), 129 - 134. DOI: 10.13189/ms.2019.070406.