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Second-derivative-free variants of Cauchy’s method
Applied Mathematics and Computation, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Derivative-free method for singular systems
2019 IEEE 17th International Symposium on Intelligent Systems and Informatics (SISY), 2019This paper presents algorithm for solving singular nonlinear system. Since the convergence rate of any method to singular solution drops down, the convergence can be accelerated by forming the bordered system. Singular vectors of the Jacobian can be used for the construction of the bordered system.
Buhmiler, Sandra +5 more
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Hydrodynamic design using a derivative-free method
Structural and Multidisciplinary Optimization, 2004A derivative-free shape optimization tool for computational fluid dynamics (CFD) is developed in order to facilitate the implementation of complex flow solvers in the design procedure. A modified Rosenbrock’s method is used, which needs neither gradient evaluations nor approximations.
Duvigneau, R., Visonneau, Michel
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On Chebyshev‐type methods free from second derivative
Communications in Numerical Methods in Engineering, 2007AbstractIn this paper, we present a new Chebyshev‐type method free from second derivative. An analysis of convergence shows that the new method has fourth‐order convergence. Per iteration, the method requires one evaluation of the function and two of its first derivative and therefore this method has the efficiency index equal to 1.587.
Kou, Jisheng, Li, Yitian
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Constructing third-order derivative-free iterative methods
International Journal of Computer Mathematics, 2011In this work, we develop nine derivative-free families of iterative methods from the three well-known classical methods: Chebyshev, Halley and Euler iterative methods. Methods of the developed families consist of two steps and they are totally free of derivatives.
Sanjay Kumar Khattri, Torgrim Log
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Nonmonotone derivative-free methods for nonlinear equations
Computational Optimization and Applications, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
L. GRIPPO, SCIANDRONE, MARCO
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Algorithm for forming derivative-free optimal methods
Numerical Algorithms, 2013The Newton method is the best known method for solving a nonlinear equation \(f(x)=0\) which is given as \[ x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}, \qquad n=0,1,2,\dots, \qquad |f'(x_n)|\neq 0. \] A scheme for constructing optimal derivative free iterative methods is the main aim of the article. The derivative in Newton's method is approximated as follows \
Khattri, Sanjay K., Steihaug, Trond
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Modified Chebyshev–Halley methods free from second derivative
Applied Mathematics and Computation, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A drift‐free simulation method for pricing commodity derivatives
Applied Stochastic Models in Business and Industry, 2014Having in view the pricing of commodity derivatives in Libor Market Model (LMM) setting, we first analyze the set of basic rates we need to formulate the model by using the spanning tree concept taken from graph theory. Next, we present an efficient procedure for Monte Carlo simulation of the dynamics of the rates associated to LMM, avoiding the ...
Fernández, José Luis +2 more
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On second derivative-free zero finding methods
Proceedings of the 2010 American Control Conference, 2010High order root-finding algorithms are constructed from formulas for approximating higher order logarithmic and standard derivatives. These formulas are free of derivatives of second order or higher and use only function evaluation and/or first derivatives at multiple points. Richardson extrapolation technique is applied to obtain better approximations
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