How many steps still left to x*?
Abstract The high speed of \(x_{k}\rightarrow x^\ast\in{\mathbb R}\) is usually measured using the C-, Q- or R-orders: \begin{equation}\tag{$C$} \lim \frac…
secant/chord method
Methods of Newton and Newton-Krylov type
Book summaryLocal convergence results on Newton-type methods for nonlinear systems of equations are studied. Solving of large linear systems by…
A unified treatment of the modified Newton and chord methods
Abstract The aim of this paper is to obtain a unified treatment of some iterative methods. We obtain some conditions…
A note on inexact secant methods
Abstract The inexact secant method \([x_{k-1},x_{k};F]s_{k}=-F(x_k) +r_k\), \( x_{k+1}=x_k+s_k\), \( k=1,2,\ldots\), \( x_0,x_1 \in {\mathbb R}^n\) is considered for solving the nonlinear…
On some iterative methods for solving nonlinear equations
Abstract Consider the nonlinear equation \(H(x):=F(x)+G(x)=0\), with \(F\) differentiable and \(G\) continuous, where \(F,G,H:X \rightarrow X\), \(X\) a Banach space. The…
On some interpolatory iterative methods for the second degree polynomial operators (I)
Abstract In this note we consider the chord (secant) method and the Steffensen method for solving polynomial operators of degree…