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Ehrlich-type methods with king’s correction for the simultaneous approximation of polynomial complex zeros
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Advisor(s)
Abstract(s)
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]
Description
Keywords
Polynomial zeros Simultaneous iterative methods Combined methods Ehrlich method . Faculdade de Ciências Exatas e da Engenharia
Citation
Machado, R. N., & Lopes, L. G. (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
Publisher
Horizon Research Publishing (HRPUB)