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A New Family of Fourth-Order Optimal Iterative Schemes and Remark on Kung and Traub’s Conjecture
Journal of Mathematics, 2021 Kung and Traub conjectured that a multipoint iterative scheme without memory based on m evaluations of functions has an optimal convergence order p=2m−1.
Chein-Shan Liu, Tsung-Lin Lee
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Journal of Applied MathematicsA new family of fourth-order iterative methods for solving nonlinear equations is proposed using the weight function procedure. This family is optimal in the sense of the Kung–Traub conjecture, as it requires three function evaluations per iteration. Due
Ali Zein
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Comment on: On the Kung-Traub Conjecture for Iterative Methods for Solving Quadratic Equations. Algorithms 2016, 9, 1 [PDF]
Algorithms, 2016 Kung-Traub conjecture states that an iterative method without memory for finding the simple zero of a scalar equation could achieve convergence order 2 d − 1 , and d is the total number of function evaluations. In an article “Babajee, D.K.R.
Fayyaz Ahmad
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On a New Three-Step Class of Methods and Its Acceleration for Nonlinear Equations [PDF]
The Scientific World Journal, 2014 A class of derivative-free methods without memory for approximating a simple zero of a nonlinear equation is presented. The proposed class uses four function evaluations per iteration with convergence order eight.
T. Lotfi +4 more
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Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots [PDF]
The Scientific World Journal, 2014 We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen.
Fiza Zafar +3 more
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An Optimal Thirty-Second-Order Iterative Method for Solving Nonlinear Equations and a Conjecture [PDF]
Qualitative Theory of Dynamical Systems, 2022 Many multipoint iterative methods without memory for solving non-linear equations in one variable are found in the literature. In particular, there are methods that provide fourth-order, eighth-order or sixteenth-order convergence using only ...
J. Varona
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AxiomsThis paper introduces an iterative method with a remarkable level of accuracy, namely fourth-order convergence. The method is specifically tailored to meet the optimality condition under the Kung–Traub conjecture by linear combination.
Sania Qureshi +5 more
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Mathematics, 2020 In this study, we construct the one parameter optimal derivative-free iterative family to find the multiple roots of an algebraic nonlinear function.
Munish Kansal +4 more
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AxiomsThis study introduces a novel, iterative algorithm that achieves fourth-order convergence for solving nonlinear equations. Satisfying the Kung–Traub conjecture, the proposed technique achieves an optimal order of four with an efficiency index (I) of 1 ...
Shahid Abdullah +4 more
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An optimal family of methods for obtaining the zero of nonlinear equation [PDF]
Mathematics and Computational Sciences, 2022 This manuscript presents a developed fourth-order iterative familyof methods for determining the zero of nonlinear equations that isoptimal in line with Kung-Traub conjecture. The family of methodswas constructed by using weight function technique.
Oghovese Ogbereyivwe, John Emunefe
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