Results 211 to 220 of about 3,149 (256)

SOR-Secant Methods

SIAM Journal on Numerical Analysis, 1994
The paper introduces the families of (block) successive overrelaxation (SOR) quasi-Newton methods and (block) SOR-least-change secant updated (LCSU) methods for solving large systems of nonlinear equations. These are decomposition methods in the sense that different components of the system are evaluated at different points, and each iteration is a ...
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On a higher order Secant method

Applied Mathematics and Computation, 2003
A modified secant method is introduced for solving a nonlinear equation \(f(x)=0\). The secant of \(f(x)\) at \(x_{k}\) is replaced by a higher order approximation. It is show that this method can have quadratic convergence as the Newton method. Global monotonic convergence is proven for real functions.
Amat, Sergio, Busquier, Sonia
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Secant methods for semismooth equations

Numerische Mathematik, 1998
The authors present some generalizations of the secant method to semismooth equations. After a review of relevant results about semismooth operators, the superlinear convergence of the classical secant method for one-dimensional, general semismooth equations is proved and a new quadratically convergent method is proposed.
Potra, Florian A., Qi, Liqun, Sun, Defeng   +2 more
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A modified Secant method for unconstrained optimization

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kahya, Emin, Chen, Jinhai
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The secant–homotopy continuation method

Chaos, Solitons & Fractals, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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