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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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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 \
Sanjay Kumar Khattri, Trond Steihaug
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Objective-derivative-free methods for constrained optimization
Mathematical Programming, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
LUCIDI, Stefano, M. Sciandrone, P. Seng
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A family of derivative-free methods for nonlinear equations
Revista Matemática Complutense, 2010The 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, 2013From 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. +3 more
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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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Methods to Derive the Differential Equation of the Free Surface Boundary
Groundwater, 2010Comment in Ground Water. 2010 Jul-Aug;48(4):486-490; discussion 490-493 & Ground Water. 2011 Mar-Apr;49(2):133-142; discussion 142-143.
Kuang, X, Chen, C, Jiao, JJ
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Modified Halley’s method free from second derivative
Applied Mathematics and Computation, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jisheng Kou, Yitian Li, Xiuhua Wang 0002
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Derivative-Free Optimization Via Proximal Point Methods
Journal of Optimization Theory and Applications, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Warren L. Hare, Yves Lucet
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On a family of second-derivative-free variants of Chebyshev’s method
Applied Mathematics and Computation, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jisheng Kou, Yitian Li, Xiuhua Wang 0002
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