correct

[kahina_paper1.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 4e2180ed5999a9c5274090d36b28ded8edbb0262..b3e3076c085c43d6067814158e10073a3f180407 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -183,7 +183,7 @@ drastically increases like the degrees of high polynomials. It is expected that
 parallelization of these algorithms will improve the convergence
 time.
 
 parallelization of these algorithms will improve the convergence
 time.
 

-Many authors have dealt with the parallelisation of
+Many authors have dealt with the parallelization of

 simultaneous methods, i.e. that find all the zeros simultaneously. 
 Freeman~\cite{Freeman89} implemeted and compared DK, EA and another method of the fourth order proposed
 by Farmer and Loizou~\cite{Loizon83}, on a 8- processor linear
 simultaneous methods, i.e. that find all the zeros simultaneously. 
 Freeman~\cite{Freeman89} implemeted and compared DK, EA and another method of the fourth order proposed
 by Farmer and Loizou~\cite{Loizon83}, on a 8- processor linear


@@ -194,7 +194,7 @@ Freeman and Bane~\cite{Freemanall90}  considered asynchronous
 algorithms, in which each processor continues to update its
 approximations even though the latest values of other $z_i((k))$
 have not been received from the other processors, in contrast with synchronous algorithms where it would wait those values before making a new iteration.
 algorithms, in which each processor continues to update its
 approximations even though the latest values of other $z_i((k))$
 have not been received from the other processors, in contrast with synchronous algorithms where it would wait those values before making a new iteration.

-Couturier and al~\cite{Raphaelall01} proposed two methods of parallelisation for
+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 polynomials of degree 10000 in 430 seconds with only 8
 personal computers and 2 communications per iteration. Comparing to the sequential implementation
 a shared memory architecture and for distributed memory one. They were able to
 compute the roots of polynomials of degree 10000 in 430 seconds with only 8
 personal computers and 2 communications per iteration. Comparing to the sequential implementation


@@ -365,7 +365,7 @@ R = exp(log(DBL_MAX)/(2*n) );
 \label{secStateofArt}   
 The main problem of simultaneous methods is that the necessary
 time needed for convergence is increased when we increase
 \label{secStateofArt}   
 The main problem of simultaneous methods is that the necessary
 time needed for convergence is increased when we increase

-the degree of the polynomial. The parallelisation of these
+the degree of the polynomial. The parallelization of these

 algorithms is expected to improve the convergence time.
 Authors usually adopt one of the two following approaches to parallelize root
 finding algorithms. The first approach aims at reducing the total number of
 algorithms is expected to improve the convergence time.
 Authors usually adopt one of the two following approaches to parallelize root
 finding algorithms. The first approach aims at reducing the total number of