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Derivative-Free Conformable Iterative Methods for Solving Nonlinear Equations
Fractal and Fractional, 2023 In this manuscript, we use approximations of conformable derivatives for designing iterative methods to solve nonlinear algebraic or trascendental equations.
Giro Candelario +3 more
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Two Optimal Eighth-Order Derivative-Free Classes of Iterative Methods [PDF]
Abstract and Applied Analysis, 2012 Optimization problems defined by (objective) functions for which derivatives are unavailable or available at an expensive cost are emerging in computational science.
F. Soleymani, S. Shateyi
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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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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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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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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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A derivative-free Gauss–Newton method [PDF]
Mathematical Programming Computation, 2019 We present DFO-GN, a derivative-free version of the Gauss-Newton method for solving nonlinear least-squares problems. As is common in derivative-free optimization, DFO-GN uses interpolation of function values to build a model of the objective, which is then used within a trust-region framework to give a globally-convergent algorithm requiring $O(ε^{-2})
Roberts, L, Cartis, C
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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.
Larson, Jeffrey +2 more
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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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A Derivative-Free Method for Structured Optimization Problems [PDF]
SIAM Journal on Optimization, 2021 Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given function. In the present paper, we want to minimize a black-box function over the convex hull of a given set of ...
Cristofari A., Rinaldi F.
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