Results 241 to 250 of about 30,661 (276)

GENERALIZED SECANT METHODS AND THEIR FRACTAL PATTERNS

Fractals, 2009
In this paper, a class of generalized secant methods was investigated. The convergence of these methods was discussed, and their striking fractal patterns are generated to represent the chaotic behavior of these methods in the complex plane.
Liu, Xiang-Dong, Zhang, Jin-Hai, Li, Zhi-Jie, Zhang, Jun-Xing   +3 more
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On the secant method

Publicationes Mathematicae Debrecen, 1993
The author uses the secant method for solving a nonlinear operator equation in a Banach space setting. Assuming that the derivative of the governing operator is Hölder continuous and that the initial divided difference operator is invertible, he proves that the sequence produced by the secant iteration method converges to a unique solution of the ...
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Variants of Steffensen-secant method and applications

Applied Mathematics and Computation, 2010
Let \(f:D \rightarrow\mathbb R\) be a sufficiently differentiable function with a simple root \(a \in D\), with \(D \subset\mathbb R\) an open set. The authors define a parametric variant of the Steffensen-secant method as follows. Let \(A_{n+1} = f(x_n)\) and \(B_{n+1} = f(x_n+\lambda_nA_{n+1})\).
Zheng, Quan, Zhao, Peng, Zhang, Li, Ma, Wenchao   +3 more
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The method of secants

Computers & Graphics, 1991
Abstract The method of secants is defined. The convergence of the method is discussed and illustrated for some simple examples.
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Directional Secant-Type Methods for Solving Equations

Journal of Optimization Theory and Applications, 2012
The article of I. K. Argyros and S. Hilout is a valuable contribution to the calculus of solving equations with a special motivation and application in optimization, especially. This investigation takes place in a wide model setting, and it employs numerical analysis by addressing some of its basic solution techniques in a rather advanced way.
Argyros, Ioannis K., Hilout, Saïd
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Modified Secant-type methods for unconstrained optimization

Applied Mathematics and Computation, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Some secant approximations for Rosenbrock W-methods

Applied Numerical Mathematics, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Monotone Enclosure Using Multi‐Point‐Secant Methods

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1982
AbstractMulti‐point‐secant methods are applied to systems of equations in order to obtain sequences of upper and lower bounds for the solution. It is shown that the sequences converge monotonically and the order of convergence is better than linear. The results are illustrated by an example.
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Stable symmetric secant methods with restart

Cybernetics, 1991
A secant type method for systems of nonlinear equations with symmetric Jacobi matrices utilizing a restart procedure to guarantee stability and superlinear rate of convergence is described. An algorithm is reported and its convergence is proved.
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Secant-Like Methods and Fractional Calculus

2015
We present local and semilocal convergence results for secant-like methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In the last part of the study we present some choices of the operators involved in fractional calculus where the operators satisfy the convergence conditions. It follows [5].
George A. Anastassiou, Ioannis K. Argyros   +1 more
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