On the Kung-Traub Conjecture for Iterative Methods for Solving Quadratic Equations
Algorithms, 2015 Kung-Traub’s conjecture states that an optimal iterative method based on d function evaluations for finding a simple zero of a nonlinear function could achieve a maximum convergence order of 2 d−1.
D. Babajee
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New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 A new family of eighth-order derivative-free methods for solving nonlinear equations is presented. It is proved that these methods have the convergence order of eight.
Rajinder Thukral
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Four-Point Optimal Sixteenth-Order Iterative Method for Solving Nonlinear Equations [PDF]
Journal of Applied Mathematics, 2013 We present an iterative method for solving nonlinear equations. The proposed iterative method has optimal order of convergence sixteen in the sense of Kung-Traub conjecture (Kung and Traub, 1974); it means that the iterative scheme uses five functional ...
Malik Zaka Ullah +2 more
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On a 4-Point Sixteenth-Order King Family of Iterative Methods for Solving Nonlinear Equations
International Journal of Mathematics and Mathematical Sciences, 2012 A one-parameter 4-point sixteenth-order King-type family of iterative methods which satisfy the famous Kung-Traub conjecture is proposed. The convergence of the family is proved, and numerical experiments are carried out to find the best member of the ...
Diyashvir Kreetee Rajiv Babajee +1 more
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On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics [PDF]
Discrete Dynamics in Nature and Society, 2015 With an error corrector via principal branch of the mth root of a function-to-function ratio, we propose optimal quartic-order multiple-root finders for nonlinear equations.
Young Ik Kim, Young Hee Geum
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Optimal Algorithms for Nonlinear Equations with Applications and Their Dynamics
Complexity, Volume 2022, Issue 1, 2022., 2022 In the present work, we introduce two novel root‐finding algorithms for nonlinear scalar equations. Among these algorithms, the second one is optimal according to Kung‐Traub’s conjecture.
Amir Naseem, M. A. Rehman, N. Ide
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An optimal eighth order derivative free multiple root finding scheme and its dynamics [PDF]
AIMS Mathematics, 2023 The problem of solving a nonlinear equation is considered to be one of the significant domain. Motivated by the requirement to achieve more optimal derivative-free schemes, we present an eighth-order optimal derivative-free method to find multiple zeros ...
F. Zafar +3 more
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A Family of Three-Point Methods of Ostrowski's Type for Solving Nonlinear Equations [PDF]
Journal of Applied Mathematics, 2012 A class of three-point methods for solving nonlinear equations of eighth order is constructed. These methods are developed by combining two-point Ostrowski's fourth-order methods and a modified Newton's method in the third step, obtained by a suitable ...
Jovana Džunić, Miodrag S. Petković
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Efficient iterative scheme for solving non-linear equations with engineering applications
Applied Mathematics in Science and Engineering, 2022 A family of three-step optimal eighth-order iterative algorithm is developed in this paper in order to find single roots of nonlinear equations using the weight function technique.
Mudassir Shams +3 more
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Family of fourth-order optimal classes for solving multiple-root nonlinear equations [PDF]
Journal of Mathematical Chemistry, 2022 We present a new iterative procedure for solving nonlinear equations with multiple roots with high efficiency. Starting from the arithmetic mean of Newton’s and Chebysev’s methods, we generate a two-step scheme using weight functions, resulting in a ...
F. Chicharro +3 more
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