a

[desynchronisation-controle.git] / IWCMC14 / convergence.tex

diff --git a/IWCMC14/convergence.tex b/IWCMC14/convergence.tex
index ea4d4c223a2e597bf7f319f08c9dd60b8cfb30b2..13b3b2d6a14c0a7394fd2df507baba0a2a0c472e 100644 (file)
--- a/IWCMC14/convergence.tex
+++ b/IWCMC14/convergence.tex
@@ -1,8 +1,8 @@
-Let us first have a discussion on the stop criterion of the citted algorithm.
+Let us first have a discussion on the stop criterion of the cited algorithm.

 We claim that even if the variation of the dual function is less than a given 
 We claim that even if the variation of the dual function is less than a given 

-threeshold, this does not ensure that the lifetime has been maximized.
+threshold, this does not ensure that the lifetime has been maximized.

 Minimizing a function on a multiple domain (as the dual function)
 Minimizing a function on a multiple domain (as the dual function)

-may indeed easilly fall into a local trap because some of introduced 
+may indeed easily fall into a local trap because some of introduced 

 variables may lead to uniformity of the output.
 
 \begin{figure}
 variables may lead to uniformity of the output.
 
 \begin{figure}


@@ -11,7 +11,7 @@ variables may lead to uniformity of the output.
   \label{fig:convergence:scatterplot}
 \end{figure}  
 
   \label{fig:convergence:scatterplot}
 \end{figure}  
 

-Experimentations have indeed shown that even if the dual
+Experiments have indeed shown that even if the dual

 function seems to be constant 
 (variations between two evaluations of this one is less than $10^{-5}$) 
 not all the $q_i$ have the same value.
 function seems to be constant 
 (variations between two evaluations of this one is less than $10^{-5}$) 
 not all the $q_i$ have the same value.


@@ -20,15 +20,15 @@ a scatter plot.
 
 The maximum amplitude rate  of the sequence of $q_i$ --which is 
 $\frac{\max_{i \in N} q_i} {\min_{i \in N}q_i}-1$--
 
 The maximum amplitude rate  of the sequence of $q_i$ --which is 
 $\frac{\max_{i \in N} q_i} {\min_{i \in N}q_i}-1$--

-is represented in $y$-coordonates 
+is represented in $y$-coordinate 

  with respect to the
  with respect to the

-value of the threeshold for dual function that is represented in 
-$x$-coordonates.
+value of the threshold for dual function that is represented in 
+$x$-coordinate.

 This figure shows that a very small threshold is a necessary condition, but not 
 a sufficient criteria to observe convergence of $q_i$.
 
 In the following, we consider the system are $\epsilon$-stable  if both 
 This figure shows that a very small threshold is a necessary condition, but not 
 a sufficient criteria to observe convergence of $q_i$.
 
 In the following, we consider the system are $\epsilon$-stable  if both 

-maximum amplitude rate and the dual function are less than a threeshold 
+maximum amplitude rate and the dual function are less than a threshold 

 $\epsilon$.
 
 
 $\epsilon$.