nonlinear equations in R

On an Aitken type method

Abstract In this note we study the convergence of a generalized Aitken type method for approximating the solutions of nonlinear…

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How many steps still left to x*?

Emil Cătinaş
(original), (survey), Convergence orders, Fixed point theory, history, ISI/JCR, iterative methods, local convergence, Newton method, nonlinear equations in R, Numerical Analysis, paper, secant/chord method, successive approximations
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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 {|x^\ast – x_{k+1}|}{|x^\ast – x_k|^{p_0}}\in(0,+\infty), \end{equation} \begin{equation}\tag{$Q$} \lim \frac {\ln…
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