A modified secant method for semismooth equations

Secant methods for semismooth equations

Some generalizations of the secant method to semismooth equations are presented. In the one-dimensional case the superlinear convergence of the classical secant method for general semismooth equations is proved. Moreover a new quadratically convergent method is proposed that requires two function values per iteration. For the n-dimensional cases, we discuss secant methods for two classes of com...

A modified secant method for unconstrained minimization

Newton - Secant method for solving operator equations ∗

where F is a Fréchet-differentiable operator defined on an open subset D of a Banach space X with values in a Banach space Y . Finding roots of Eq.(1) is a classical problem arising in many areas of applied mathematics and engineering. In this study we are concerned with the problem of approximating a locally unique solution α of Eq.(1). Some of the well known methods for this purpose are the f...

A MODIFIED STEFFENSEN'S METHOD WITH MEMORY FOR NONLINEAR EQUATIONS

In this note, we propose a modification of Steffensen's method with some free parameters. These parameters are then be used for further acceleration via the concept of with memorization. In this way, we derive a fast Steffensen-type method with memory for solving nonlinear equations. Numerical results are also given to support the underlying theory of the article.  

On a Secant-like Method for Solving Generalized Equations

In the paper by Hilout and Piétrus (2006) a semilocal convergence analysis was given for the secant-like method to solve generalized equations using Hölder-type conditions introduced by the first author (for nonlinear equations). Here, we show that this convergence analysis can be refined under weaker hypothesis, and less computational cost. Moreover finer error estimates on the distances invol...