Ehrlich-type methods with king’s correction for the simultaneous approximation of polynomial complex zeros

• Autor(a) principal: Neves Machado, Roselaine
• Data de Publicação: 2019
• Outros Autores: Lopes, Luiz Guerreiro
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.13/3761
• topic: Polynomial zeros; Simultaneous iterative methods; Combined methods; Ehrlich method; .; Faculdade de Ciências Exatas e da Engenharia

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. the advantage of being inherently parallel and avoid the pro cess of deflation, although these iterative methods usually need good initial approximations for all the zeros in order to con verge. In this work, a new family of numerical methods for the si multaneous approximation of simple complex polynomial ze ros is presented. The proposed simultaneous methods are con structed on the basis of the well-known third order Ehrlich– Aberth iteration [1, 6], combined with an iterative correction from the optimal fourth order two-step King’s method for solv ing nonlinear equations [10]