Results 11 to 20 of about 305,961 (299)
Basin attractors for derivative-free methods to find simple roots of nonlinear equations
Journal of Numerical Analysis and Approximation Theory, 2020 Many methods exist for solving nonlinear equations. Several of these methods are derivative-free. One of the oldest is the secant method where the derivative is replaced by a divided difference.
Beny Neta
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Comparison of some optimal derivative-free three-point iterations
Journal of Numerical Analysis and Approximation Theory, 2020 We show that the well-known Khattri et al. methods and Zheng et al. methods are identical. In passing, we propose a suitable calculation formula for Khattri et al. methods.
Thugal Zhanlav, Khuder Otgondorj
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Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations
European Journal of Mathematical Analysis, 2023 In nonlinear problems where function’s derivatives are difficult or expensive to compute, derivative-free iterative methods are good options to find the numerical solution.
Sunil Kumar +3 more
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Derivative-free optimization methods [PDF]
Acta Numerica, 2019 In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization.
Jeffrey Larson 0001 +2 more
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A New Derivative-Free Method to Solve Nonlinear Equations
Mathematics, 2021 A new high-order derivative-free method for the solution of a nonlinear equation is developed. The novelty is the use of Traub’s method as a first step. The order is proven and demonstrated.
Beny Neta
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Extended Seventh Order Derivative Free Family of Methods for Solving Nonlinear Equations
Mathematics, 2023 A plethora of applications from Computational Sciences can be identified for a system of nonlinear equations in an abstract space. These equations are mostly solved with an iterative method because an analytical method does not exist for such problems ...
Ramandeep Behl +3 more
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Barekeng, 2022 The variant of Chebyshev-Halley’s method is an iterative method used for solving a nonlinear equation with third order of convergence. In this paper, we present some new variants of three steps Chebyshev-Halley’s method free from second derivative with ...
Yuslenita Muda +3 more
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Derivative-Free Optimal Iterative Methods
Computational Methods in Applied Mathematics, 2010 AbstractIn this study, we develop an optimal family of derivative-free iterative methods. Convergence analysis shows that the methods are fourth order convergent, which is also verified numerically. The methods require three functional evaluations during each iteration. Though the methods are independent of derivatives, computa-
Sanjay Kumar Khattri, Ravi P. Agarwal
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Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation
Mathematics, 2019 Finding a simple root for a nonlinear equation f ( x ) = 0 , f : I ⊆ R → R has always been of much interest due to its wide applications in many fields of science and engineering.
Moin-ud-Din Junjua +2 more
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A Note on Traub’s Method for Systems of Nonlinear Equations
Mathematics, 2021 Traub’s method was extended here to systems of nonlinear equations and compared to Steffensen’s method. Even though Traub’s method is only of order 1.839 and not quadratic, it performed better in the 10 examples.
Beny Neta
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