From: couturie <couturie@extinction>
Date: Wed, 8 Jan 2014 17:25:22 +0000 (+0100)
Subject: new
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/Krylov_multi.git/commitdiff_plain/5e3a7342021a720e17be4f147b4e73e5ad5396b9?ds=inline;hp=ed256d49ed3a06f1ca791baf04262e8775091cd0

new
---

diff --git a/biblio.bib b/biblio.bib
index 55c4a93..e45f5d6 100644
--- a/biblio.bib
+++ b/biblio.bib
@@ -77,7 +77,14 @@
 @TechReport{prace-multi,
 	author = 			 {Nick Brown and J. Mark Bull and Iain Bethune},
 	title = 			 {Solving Large Sparse Linear Systems using Asynchronous Multisplitting},
-	institution =  {PRACE White paper n°WP84},
+	institution =  {PRACE White paper number WP84},
 	year = 				 {2013},
 }
 
+@Book{S96,
+        author =         {Y. Saad},
+        title =          {Iterative Methods for Sparse Linear Systems},
+        publisher =      {PWS Publishing},
+        year =           {1996},
+        address =        {New York},
+}
diff --git a/krylov_multi.tex b/krylov_multi.tex
index 40380d0..91e4745 100644
--- a/krylov_multi.tex
+++ b/krylov_multi.tex
@@ -38,9 +38,14 @@ classical GMRES both in terms of number of iterations and execution times.
 
 Iterative methods are used to solve  large sparse linear systems of equations of
 the form  $Ax=b$ because they are  easier to parallelize than  direct ones. Many
-iterative  methods have  been proposed  and  adapted by  many researchers.  When
-solving large  linear systems  with many cores,  iterative methods  often suffer
-from  scalability  problems.    This  is  due  to  their   need  for  collective
+iterative  methods have  been proposed  and  adapted by  many researchers.   For
+example, the GMRES method and the  Conjugate Gradient method are very well known
+and  used by  many researchers  ~\cite{S96}. Both  the method  are based  on the
+Krylov subspace which consists in forming  a basis of the sequence of successive
+matrix powers times the initial residual.
+
+When  solving large  linear systems  with  many cores,  iterative methods  often
+suffer  from scalability problems.   This is  due to  their need  for collective
 communications  to  perform  matrix-vector  products and  reduction  operations.
 Preconditionners can be  used in order to increase  the convergence of iterative
 solvers.   However, most  of the  good preconditionners  are not  sclalable when