new

[GMRES2stage.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 16beac7e509d9b87c1bd444249ad71a7807fe5cd..25f1393e95bfd5d65094c8a57eb03211344bb34b 100644 (file)
--- 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 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:}
     \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
 
 
 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}
 
 \begin{table}[htbp]
 \begin{center}