X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/d40f73fb29cd99acadda6620fc198fc09066584e..ea64cb6b221dd87ee5567d67d8063a023f43330a:/paper.tex

diff --git a/paper.tex b/paper.tex
index 16beac7..25f1393 100644
--- a/paper.tex
+++ b/paper.tex
@@ -652,7 +652,7 @@ appropriate than a single direct method in a parallel context.
   \State Set the initial guess $x_0$
   \For {$k=1,2,3,\ldots$ until convergence (error$<\epsilon_{tsirm}$)} \label{algo:conv}
     \State  $[x_k,error]=Solve(A,b,x_{k-1},max\_iter_{kryl})$   \label{algo:solve}
-    \State $S_{k \mod s}=x_k$ \label{algo:store}
+    \State $S_{k \mod s}=x_k$ \label{algo:store} \Comment{update column (k mod s) of S}
     \If {$k \mod s=0$ {\bf and} error$>\epsilon_{kryl}$}
       \State $R=AS$ \Comment{compute dense matrix} \label{algo:matrix_mul}
             \State $\alpha=Least\_Squares(R,b,max\_iter_{ls})$ \label{algo:}
@@ -800,10 +800,12 @@ than the one of the GMRES method.
 
 
 In order to see the influence of our algorithm with only one processor, we first
-show  a comparison  with the  standard version  of GMRES  and our  algorithm. In
-Table~\ref{tab:01},  we  show  the  matrices  we  have used  and  some  of  them
-characteristics. For all  the matrices, the name, the field,  the number of rows
-and the number of nonzero elements are given.
+show a comparison with GMRES or FGMRES and our algorithm. In Table~\ref{tab:01},
+we  show the  matrices we  have  used and  some of  them characteristics.  Those
+matrices  are   chosen  from   the  Davis  collection   of  the   University  of
+Florida~\cite{Dav97}. They are matrices arising in real-world applications.  For
+all the  matrices, the name,  the field,  the number of  rows and the  number of
+nonzero elements are given.
 
 \begin{table}[htbp]
 \begin{center}
