A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics
Geum, Young Hee
Kim, Young Ik
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Under the assumption of the known multiplicity of zeros of nonlinear equations, a class of two-point sextic-order multiple-zero finders and their dynamics are investigated in this paper by means of extensive analysis of modified double-Newton type of methods. Wit the introduction of a bivariate weight function dependent on function-to-function and derivative-to-derivative ratios, higher-order convergence is obtained. Additional investigation is carried out for extraneous fixed points of the iterative maps associated with the proposed methods along with a comparison with typically selected cases. Through a variety of test equations, numerical experiments strongly support the theory developed in this paper. In addition, relevant dynamics of the proposed methods is successfully explored for various polynomials with a number of illustrative basins of attraction.
The article of record as published may be found at http://dx.doi.org/10.1016/j.amc.2015.08.039
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