From: Kahina <kahina@kahina-VPCEH3K1E.(none)>
Date: Thu, 5 Nov 2015 09:14:18 +0000 (+0100)
Subject: new
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/commitdiff_plain/d3e87f59ffa2ba8a54513a8a8713280dda780920

new
---

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},