An optimal eighth order derivative free multiple root finding numerical method and applications to chemistry [PDF]
, 2023 [EN] In this paper, we present an optimal eighth order derivative-free family of methods for multiple roots which is based on the first order divided difference and weight functions.
Fiza Zafar +3 more
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Local convergence for composite Chebyshev-type methods
Communications in Advanced Mathematical Sciences, 2018 We replace Chebyshev's method for solving equations requiring the second derivative by a Chebyshev-type second derivative free method. The local convergence analysis of the new method is provided using hypotheses only on the first derivative in contrast ...
Santhosh George, İoannis K Argyros
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A method with inertial extrapolation step for convex constrained monotone equations
Journal of Inequalities and Applications, 2021 In recent times, various algorithms have been incorporated with the inertial extrapolation step to speed up the convergence of the sequence generated by these algorithms.
Abdulkarim Hassan Ibrahim +3 more
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StepDIRECT - A Derivative-Free Optimization Method for Stepwise Functions
, 2022 In this paper, we propose the StepDIRECT algorithm for derivative-free optimization (DFO), in which the black-box objective function has a stepwise landscape. Our framework is based on the well-known DIRECT algorithm. By incorporating the local variability to explore the flatness, we provide a new criterion to select the potentially optimal hyper ...
Dzung T. Phan +2 more
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Ain Shams Engineering Journal, 2021 In this note, we propose a modification as an alternative to remove the assumption of uniformly monotone as assumed in Aliyu et al. (2019). Numerical experiment shows that the modification improves the numerical performance of the method.
Abdulkarim Hassan Ibrahim, Poom Kumam
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Wedge trust region methods for derivative free optimization [PDF]
Mathematical Programming, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marcelo Marazzi, Jorge Nocedal
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An Efficient Class of Traub–Steffensen-Type Methods for Computing Multiple Zeros
Axioms, 2019 Numerous higher-order methods with derivative evaluations are accessible in the literature for computing multiple zeros. However, higher-order methods without derivatives are very rare for multiple zeros.
Deepak Kumar +2 more
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Efficient Derivative-Free Class of Seventh Order Method for Non-differentiable Equations
European Journal of Mathematical Analysis, 2023 Many applications from a wide variety of disciplines in the natural sciences and also in engineering are reduced to solving of an equation or a system of equations in a correspondingly chosen abstract area.
oannis K. Argyros +3 more
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Some Iterative Methods Free from Derivatives and Their Basins of Attraction for Nonlinear Equations
Discrete Dynamics in Nature and Society, 2013 First, we make the Jain's derivative-free method optimal and subsequently increase its efficiency index from 1.442 to 1.587. Then, a novel three-step computational family of iterative schemes for solving single variable nonlinear equations is given.
Farahnaz Soleimani +2 more
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An Efficient Derivative Free One-Point Method with Memory for Solving Nonlinear Equations
Mathematics, 2019 We propose a derivative free one-point method with memory of order 1.84 for solving nonlinear equations. The formula requires only one function evaluation and, therefore, the efficiency index is also 1.84.
Janak Raj Sharma +2 more
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