From: couturie <couturie@extinction>
Date: Mon, 2 Nov 2015 15:50:32 +0000 (-0500)
Subject: new
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/commitdiff_plain/7b00f9048df407936aee5458d1d219bbe59844ba?hp=-c

new
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7b00f9048df407936aee5458d1d219bbe59844ba
diff --git a/paper.tex b/paper.tex
index 76b626e..276c50a 100644
--- a/paper.tex
+++ b/paper.tex
@@ -308,7 +308,7 @@ but we prefer the latter one because we can use it to improve the
 Ehrlich-Aberth method and find the roots of very high degrees polynomials. More
 details are given in Section ~\ref{sec2}.
 \subsection{Convergence Condition}
-The convergence condition determines the termination of the algorithm. It consists in stopping from running the iterative function  when the roots are sufficiently stable. We consider that the method converges sufficiently when:
+The convergence condition determines the termination of the algorithm. It consists in stopping the iterative function  when the roots are sufficiently stable. We consider that the method converges sufficiently when:
 
 \begin{equation}
 \label{eq:Aberth-Conv-Cond}
@@ -319,7 +319,8 @@ The convergence condition determines the termination of the algorithm. It consis
 
 \section{Improving the Ehrlich-Aberth Method for high degree polynomials with exp.log formulation}
 \label{sec2}
-The Ehrlich-Aberth method implementation suffers of overflow problems. This
+With high degree polynomial, the Ehrlich-Aberth method implementation,
+as well as the Durand-Kerner implement, suffers from overflow problems. This
 situation occurs, for instance, in the case where a polynomial
 having positive coefficients and a large degree is computed at a
 point $\xi$ where $|\xi| > 1$, where $|x|$ stands for the modolus of a complex $x$. Indeed, the limited number in the