X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/1d3b67d64fd41314640caf3d2ff71f52d7b71181..9c62a07698805bbb6ab383b37818dc1974f58425:/paper.tex

diff --git a/paper.tex b/paper.tex
index 49480a8..6f1cc96 100644
--- a/paper.tex
+++ b/paper.tex
@@ -154,7 +154,7 @@ iteration without having to wait for the data dependencies coming from its
 neighbors. Both communications and computations are \textit{asynchronous}
 inducing that there is no more idle time, due to synchronizations, between two
 iterations~\cite{bcvc06:ij}. This model presents some advantages and drawbacks
-that we detail in Section~\ref{sec:asynchro} but even if the number of
+that we detail in Section~\ref{sec:asynchro}. Even if the number of
 iterations required to converge is generally  greater  than for the synchronous
 case, it appears that the asynchronous  iterative scheme  can significantly
 reduce  overall execution times by  suppressing idle  times due to
@@ -181,7 +181,7 @@ multisplitting  algorithm   with  the   GMRES  (Generalized   Minimal  RESidual)
 solver~\cite{saad86} in  synchronous mode.  The simulation  results allow  us to
 determine  which method  to choose  for a given multi-core  architecture.
 Moreover the  obtained results  on different simulated  multi-core architectures
-confirm the  real results  previously obtained  on non  simulated architectures.
+confirm the  real results  previously obtained  on real physical architectures.
 More precisely the simulated results are in accordance (i.e. with the same order
 of magnitude)  with the works  presented in~\cite{couturier15}, which  show that
 the synchronous  Krylov multisplitting method  is more efficient  than GMRES  for large
@@ -209,7 +209,7 @@ concluding remarks and perspectives.
 Asynchronous iterative methods have been  studied for many years theoretically and
 practically. Many methods have been considered and convergence results have been
 proved. These  methods can  be used  to solve, in  parallel, fixed  point problems
-(i.e. problems  for which  the solution is  $x^\star =f(x^\star)$.  In practice,
+(i.e. problems  for which  the solution is  $x^\star =f(x^\star)$).  In practice,
 asynchronous iteration  methods can be used  to solve, for example,  linear and
 non-linear systems of equations or optimization problems, interested readers are
 invited to read~\cite{BT89,bahi07}.
@@ -219,8 +219,8 @@ studied. Otherwise, the  application is not ensure to reach  the convergence. An
 algorithm that supports both the synchronous or the asynchronous iteration model
 requires very few modifications  to be able to be executed  in both variants. In
 practice, only  the communications and  convergence detection are  different. In
-the synchronous  mode, iterations are  synchronized whereas in  the asynchronous
-one, they are not.  It should be noticed that non-blocking communications can be
+the synchronous  mode iterations are  synchronized, whereas in  the asynchronous
+one they are not.  It should be noticed that non-blocking communications can be
 used in both  modes. Concerning the convergence  detection, synchronous variants
 can use  a global convergence procedure  which acts as a  global synchronization
 point. In the  asynchronous model, the convergence detection is  more tricky as
@@ -239,8 +239,8 @@ optimize since the financial and deployment costs on large scale multi-core
 architectures are often very important. So, prior to deployment and tests it
 seems very promising to be able to simulate the behavior of asynchronous
 iterative algorithms. The problematic is then to show that the results produced
-by simulation are in accordance with reality i.e. of the same order of
-magnitude. To our knowledge, there is no study on this problematic.
+by simulation are in accordance with reality (i.e. of the same order of
+magnitude). To our knowledge, there is no study on this problematic.
 
 \section{SimGrid}
 \label{sec:simgrid}