A family of optimal quadratic-order multiple-zero finders with a weight function of the principal kth root of a derivative-to-derivative ratio and their basins of attraction
Young, Hee Geum
Kim, Young Ik
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Multiple-zero finders with optimal quartic convergence for nonlinear equations are proposed in this paper with a weight function of the principal kth root of a derivative-to-derivative ratio. The optimality of the proposed multiple-zero finders is checked for their consistency based on Kung–Traub’s conjecture established in 1974. Through various test equations, relevant numerical experiments strongly support the claimed theory in this paper. Also investigated are extraneous fixed points of the iterative maps associated with the proposed methods. Their dynamics is explored along with illustrated basins of attraction for various polynomials.
The article of record as published may be found at http://dx.doi.org/10.1016/j.matcom.2016.10.008
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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