small corrections

[kahina_paper1.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index c49a7052603cf95dc5ec785bea154dabfa93bbff..4e2180ed5999a9c5274090d36b28ded8edbb0262 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -136,7 +136,7 @@ two main groups: direct methods and iterative methods.
 Direct methods exist only for $n \leq 4$, solved in closed form by G. Cardano
 in the mid-16th century. However, N. H. Abel in the early 19th
 century showed that polynomials of degree five or more could not
 Direct methods exist only for $n \leq 4$, solved in closed form by G. Cardano
 in the mid-16th century. However, N. H. Abel in the early 19th
 century showed that polynomials of degree five or more could not

-be solved by  direct methods. Since then, mathmathicians have
+be solved by  direct methods. Since then, mathematicians have

 focussed on numerical (iterative) methods such as the famous
 Newton method, the Bernoulli method of the 18th, and the Graeffe method.
 
 focussed on numerical (iterative) methods such as the famous
 Newton method, the Bernoulli method of the 18th, and the Graeffe method.
 


@@ -346,7 +346,7 @@ where:
 
 \begin{equation}
 \label{Log_H1}
 
 \begin{equation}
 \label{Log_H1}

-Q(z^{k}_{i})=\exp\left( \ln (p(z^{k}_{i}))-\ln(p'(z^{k}^{i}))+\ln \left(
+Q(z^{k}_{i})=\exp\left( \ln (p(z^{k}_{i}))-\ln(p'(z^{k}_{i}))+\ln \left(

 \sum_{k\neq j}^{n}\frac{1}{z^{k}_{i}-z^{k}_{j}}\right)\right).
 \end{equation}
 
 \sum_{k\neq j}^{n}\frac{1}{z^{k}_{i}-z^{k}_{j}}\right)\right).
 \end{equation}