Results 251 to 260 of about 10,995,154 (282)

Theory of Multivariate Secant Methods

SIAM Journal on Numerical Analysis, 1979
We study multivariate secant methods for the solution off systems of nonlinear equations in complex n-dimensional space $(1 \leqq n < \infty )$. We prove a quantitative theorem about the convergence of such methods and consider the dependence of the order of convergence on the position of the iteration points by using the concept of a set of admissible
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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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Secant-like methods

2017
Capítulo del libro "Iterative Methods and Their Dynamics with Applications"
Argyros, Ioannis K, Magreñán, Á. Alberto   +1 more
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On the local convergence of secant-type methods

International Journal of Computer Mathematics, 2004
In this article, we carry out a local convergence study for Secant-type methods. Our goal is to enlarge the radius of convergence, without increasing the necessary hypothesis. Finally, some numerical tests and comparisons with early results are analyzed.
Sergio Amat, Sonia Busquier, José Manuel Gutiérrez Jiménez   +2 more
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Convergence analysis of the secant type methods

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jinhai Chen, Zuhe Shen
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Secant-type methods and nondiscrete induction

Numerical Algorithms, 2012
For solving the equation \(f(x)= 0\), where \(f\) is a Fréchet-differentiable operator defined on a subset \(D\) of a Banach space \(X\) with values in a Banach space \(Y\), the authors consider secant-type methods based on the concept of nondiscrete mathematical induction.
Ioannis K. Argyros, Saïd Hilout
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Extending the applicability of Secant methods and nondiscrete induction

Applied Mathematics and Computation, 2011
Nondiscrete mathematical induction is used to extend the applicability of secant methods for solving nonlinear operator equations in a Banach space setting. This approach has the following advantages over earlier works under the same information: weaker sufficient convergence conditions; tighter error bounds on the distances involved and more ...
Ioannis K. Argyros, Saïd Hilout
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The Secant Method and the Golden Mean

The American Mathematical Monthly, 1993
The rate at which the sequence {Xk} converges to a root a depends on the multiplicity of a. Recall that a is a root of multiplicity m of the function f if f(x) can be written as f(x) (x a) m(x), where 4 is bounded at a and ( a) = 0. (2) It is well known (see [2]) that if a is simple root, that is, if m = 1, then there will be a nonzero asymptotic error
Melvin J. Maron, Robert J. Lopez
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A class of modified Secant methods for unconstrained optimization

Applied Mathematics and Computation, 2008
This short article introduces a class of modified secant methods to solve the univariate minimization problem. The first section provides a brief overview of the background on this problem, followed by an outline of the secant method which avoids evaluations of second order derivatives at each step of the Newton iterative method.
Hongmin Ren, Qingbiao Wu
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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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