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Nonmonotone derivative-free methods for nonlinear equations

Computational Optimization and Applications, 2007
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L. GRIPPO, SCIANDRONE, MARCO
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New Subspace Method for Unconstrained Derivative-Free Optimization

ACM Transactions on Mathematical Software, 2023
This article defines an efficient subspace method, called SSDFO , for unconstrained derivative-free optimization problems where the gradients of the objective function are Lipschitz continuous but only exact function values are available.
Morteza Kimiaei, Arnold Neumaier, Parvaneh Faramarzi   +2 more
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Derivative Free Inclusion Methods for Polynomial Zeros

Computing, 2005
Iterative methods for the simultaneous inclusion of complex zeros of polynomials realized in circular arithmetic without use of polynominal derivatives are presented. A short review of definitions and operations of circular arithmetic which are necessary to describe the methods and their convergence analysis are given. A two-stage method as combination
Miodrag S. Petkovic, Dusan M. Milosevic
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Derivative-free method for singular systems

2019 IEEE 17th International Symposium on Intelligent Systems and Informatics (SISY), 2019
This 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, Rapajić, Sanja, Lukić, Milan, Medić, Slavica, Duraković, Nataša, Grbić, Tatjana   +5 more
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Algorithm for forming derivative-free optimal methods

Numerical Algorithms, 2013
The 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 \
Sanjay Kumar Khattri, Trond Steihaug
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Objective-derivative-free methods for constrained optimization

Mathematical Programming, 2002
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LUCIDI, Stefano, M. Sciandrone, P. Seng
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A family of derivative-free methods for nonlinear equations

Revista Matemática Complutense, 2010
The authors review a few third order convergent iteration methods for solving nonlinear scalar equations and propose a new family of derivative-free third order methods. Convergence and error estimates of the proposed methods are discussed and illustrated with some numerical examples.
Wang, Haijun, Li, Subei
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CONSTRUCTION OF DERIVATIVE-FREE ITERATIVE METHODS FROM CHEBYSHEV'S METHOD

Analysis and Applications, 2013
From some modifications of Chebyshev's method, we consider a uniparametric family of iterative methods that are more efficient than Newton's method, and we then construct two iterative methods in a similar way to the Secant method from Newton's method. These iterative methods do not use derivatives in their algorithms and one of them is more efficient ...
Ezquerro, J. A., Grau, A., Grau-Sánchez, M., Hernández, M. A.   +3 more
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