correct

[kahina_paper1.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index bfbbc31349c304500abb364668186d5df10ad28a..1a307883c303d75f16d1073e57c98899c90aefd6 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -195,10 +195,11 @@ iterations  before making a new one.
 Couturier and al.~\cite{Raphaelall01} proposed two methods of parallelization for
 a shared memory architecture and for distributed memory one. They were able to
 compute the roots of sparse polynomials of degree 10,000 in 430 seconds with only 8
 Couturier and al.~\cite{Raphaelall01} proposed two methods of parallelization for
 a shared memory architecture and for distributed memory one. They were able to
 compute the roots of sparse polynomials of degree 10,000 in 430 seconds with only 8

-personal computers and 2 communications per iteration. Comparing to the sequential implementation
-where it takes up to 3,300 seconds to obtain the same results, the authors show an interesting speedup.
+personal computers and 2 communications per iteration. Compared to sequential implementations
+where it takes up to 3,300 seconds to obtain the same results, the
+authors' work experiment show an interesting speedup.

 
 

-Very few works had been performed since this last work until the appearing of
+Few works have been conducted after those works until the appearance of

 the Compute Unified Device Architecture (CUDA)~\cite{CUDA10}, a
 parallel computing platform and a programming model invented by
 NVIDIA. The computing power of GPUs (Graphics Processing Unit) has exceeded that of CPUs. However, CUDA adopts a totally new computing architecture to use the
 the Compute Unified Device Architecture (CUDA)~\cite{CUDA10}, a
 parallel computing platform and a programming model invented by
 NVIDIA. The computing power of GPUs (Graphics Processing Unit) has exceeded that of CPUs. However, CUDA adopts a totally new computing architecture to use the


@@ -230,8 +231,11 @@ topic.
 
 \section{Ehrlich-Aberth method}
 \label{sec1}
 
 \section{Ehrlich-Aberth method}
 \label{sec1}

-A cubically convergent iteration method for finding zeros of
-polynomials was proposed by O. Aberth~\cite{Aberth73}. The Ehrlich-Aberth method contain 4 main steps, presented in the following. 
+A cubically convergent iteration method to find zeros of
+polynomials was proposed by O. Aberth~\cite{Aberth73}. The
+Ehrlich-Aberth method contains 4 main steps, presented in what
+follows.
+

 %The Aberth method is a purely algebraic derivation. 
 %To illustrate the derivation, we let $w_{i}(z)$ be the product of linear factors 
 
 %The Aberth method is a purely algebraic derivation. 
 %To illustrate the derivation, we let $w_{i}(z)$ be the product of linear factors