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A family of Ehrlich-type accelerated methods with King’s correction for the simultaneous approximation of polynomial complex zeros
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Orientador(es)
Resumo(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.
Descrição
Palavras-chave
Polynomial zeros Simultaneous iterative methods Combined methods Accelerated convergence Ehrlich method . Faculdade de Ciências Exatas e da Engenharia
Contexto Educativo
Citação
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.
Editora
Research India Publications