X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/6f7da323faf523827b19731b7fcedde8f8e8fbea..0152824d3e001a7084c17325a1171e9efe4c51ec:/paper.tex

diff --git a/paper.tex b/paper.tex
index 8085604..fe7fa39 100644
--- a/paper.tex
+++ b/paper.tex
@@ -425,16 +425,17 @@ Email: lilia.ziane@inria.fr}
 
 
 \begin{abstract}
-In  this article,  a  two-stage  iterative algorithm is proposed to improve  the
-convergence of Krylov based iterative methods,  typically those of GMRES variants. The
-principle of  the proposed approach  is to  build an external  iteration over  the Krylov
-method, and to  frequently store its current  residual   (at  each
-GMRES restart for instance). After a given number of outer iterations, a minimization
-step  is applied  on the  matrix composed by the  saved residuals,  in  order to
-compute a better solution and to make  new iterations if required.  It is proven that
-the proposal has  the same convergence properties than the  inner embedded method itself. 
-Experiments using up  to 16,394 cores also show that the proposed algorithm
-runs around 5 or 7 times faster than GMRES.
+In  this article, a  two-stage iterative  algorithm is  proposed to  improve the
+convergence  of  Krylov  based  iterative  methods,  typically  those  of  GMRES
+variants.  The  principle of  the  proposed approach  is  to  build an  external
+iteration over the  Krylov method, and to frequently  store its current residual
+(at each GMRES restart for instance).  After a given number of outer iterations,
+a least-squares minimization step is applied on the matrix composed by the saved
+residuals, in order  to compute a better solution and to  make new iterations if
+required.  It  is proven that the  proposal has the  same convergence properties
+than the  inner embedded  method itself.  Experiments  using up to  16,394 cores
+also  show that the  proposed algorithm  runs around  5 or  7 times  faster than
+GMRES.
 \end{abstract}
 
 \begin{IEEEkeywords}
@@ -897,7 +898,7 @@ corresponds to 30*12, there are $max\_iter_{ls}$ which corresponds to 15.
 \begin{figure}[htbp]
 \centering
   \includegraphics[width=0.45\textwidth]{nb_iter_sec_ex15_juqueen}
-\caption{Number of iterations per second with ex15 and the same parameters than in Table~\ref{tab:03}}
+\caption{Number of iterations per second with ex15 and the same parameters than in Table~\ref{tab:03} (weak scaling)}
 \label{fig:01}
 \end{figure}
 
@@ -965,6 +966,13 @@ In Table~\ref{tab:04}, some experiments with example ex54 on the Curie architect
 \end{center}
 \end{table*}
 
+\begin{figure}[htbp]
+\centering
+  \includegraphics[width=0.45\textwidth]{nb_iter_sec_ex54_curie}
+\caption{Number of iterations per second with ex54 and the same parameters than in Table~\ref{tab:05} (strong scaling)}
+\label{fig:02}
+\end{figure}
+
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