From d3e87f59ffa2ba8a54513a8a8713280dda780920 Mon Sep 17 00:00:00 2001 From: Kahina Date: Thu, 5 Nov 2015 10:14:18 +0100 Subject: [PATCH] new --- paper.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/paper.tex b/paper.tex index a2102e7..f227762 100644 --- a/paper.tex +++ b/paper.tex @@ -268,7 +268,7 @@ The initialization of a polynomial $p(z)$ is done by setting each of the $n$ com \subsection{Vector $Z^{(0)}$ Initialization} \label{sec:vec_initialization} -As for any iterative method, we need to choose $n$ initial guess points $z^{(0)}_{i}, i = 1, . . . , n.$ +As for any iterative method, we need to choose $n$ initial guess points $z^{0}_{i}, i = 1, . . . , n.$ The initial guess is very important since the number of steps needed by the iterative method to reach a given approximation strongly depends on it. In~\cite{Aberth73} the Ehrlich-Aberth iteration is started by selecting $n$ @@ -299,7 +299,7 @@ Here we give a second form of the iterative function used by Ehrlich-Aberth meth \begin{equation} \label{Eq:Hi} -EA2: z^{k+1}=z_{i}^{k}-\frac{\frac{p(z_{i}^{k})}{p'(z_{i}^{k})}} +EA2: z^{k+1}_{i}=z_{i}^{k}-\frac{\frac{p(z_{i}^{k})}{p'(z_{i}^{k})}} {1-\frac{p(z_{i}^{k})}{p'(z_{i}^{k})}\sum_{j=1,j\neq i}^{j=n}{\frac{1}{(z_{i}^{k}-z_{j}^{k})}}}, i=0,. . . .,n \end{equation} It can be noticed that this equation is equivalent to Eq.~\ref{Eq:EA}, -- 2.39.5