X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/blobdiff_plain/7b00f9048df407936aee5458d1d219bbe59844ba..c90f146cdefa047c69990e5c0d1891ef6def1bc2:/paper.tex

diff --git a/paper.tex b/paper.tex
index 276c50a..c78df7b 100644
--- a/paper.tex
+++ b/paper.tex
@@ -312,8 +312,7 @@ The convergence condition determines the termination of the algorithm. It consis
 
 \begin{equation}
 \label{eq:Aberth-Conv-Cond}
-\forall i \in
-[1,n];\frac{z_{i}^{k}-z_{i}^{k-1}}{z_{i}^{k}}<\xi
+\forall i \in [1,n];\vert\frac{z_{i}^{k}-z_{i}^{k-1}}{z_{i}^{k}}\vert<\xi
 \end{equation}
 
 
@@ -348,7 +347,7 @@ Using the logarithm (eq.~\ref{deflncomplex}) and the exponential (eq.~\ref{defex
 manipulate lower absolute values and the roots for large polynomial's degrees can be looked for successfully~\cite{Karimall98}.
 
 Applying this solution for the Ehrlich-Aberth method we obtain the
-iteration function with logarithm:
+iteration function with exponential and logarithm:
 %%$$ \exp \bigl(  \ln(p(z)_{k})-ln(\ln(p(z)_{k}^{'}))- \ln(1- \exp(\ln(p(z)_{k})-ln(\ln(p(z)_{k}^{'})+\ln\sum_{i\neq j}^{n}\frac{1}{z_{k}-z_{j}})$$
 \begin{equation}
 \label{Log_H2}