new

diff --git a/biblio.bib b/biblio.bib
index 55c4a932db5b6579d0abfd30c66f040e635f46ca..e45f5d6dde0823081b05ba1b56beaede7a6f99b6 100644 (file)
--- 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 40380d0f50678f162ca474373e64278fbf915124..91e47458d85749235dbe5d7e5106fecee13efcf2 100644 (file)
--- 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