Displaying similar documents to “Convergence conditions for Secant-type methods”

Weaker convergence conditions for the secant method

Ioannis K. Argyros, Saïd Hilout (2014)

Applications of Mathematics

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We use tighter majorizing sequences than in earlier studies to provide a semilocal convergence analysis for the secant method. Our sufficient convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.

New sufficient convergence conditions for the secant method

Ioannis K. Argyros (2005)

Czechoslovak Mathematical Journal

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We provide new sufficient conditions for the convergence of the secant method to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses “Lipschitz-type” and center-“Lipschitz-type” instead of just “Lipschitz-type” conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than the earlier ones and under our convergence hypotheses we can cover cases where the earlier conditions are violated. ...

Convergence of a Lagrange-Galerkin method for a fluid-rigid body system in ALE formulation

Guillaume Legendre, Takéo Takahashi (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We propose a numerical scheme to compute the motion of a two-dimensional rigid body in a viscous fluid. Our method combines the method of characteristics with a finite element approximation to solve an ALE formulation of the problem. We derive error estimates implying the convergence of the scheme.