X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/Krylov_multi.git/blobdiff_plain/1aae0aa7fe4cab80db08382a65985baef5853fb1..09702354d347f9bf651fba24d04f262c757e2cc5:/krylov_multi.tex?ds=sidebyside

diff --git a/krylov_multi.tex b/krylov_multi.tex
index 3482e92..7a7e809 100644
--- a/krylov_multi.tex
+++ b/krylov_multi.tex
@@ -345,7 +345,12 @@ implement: a 3 dimension Poisson problem.
 \end{equation}
 
 After discretization, with a finite  difference scheme, a seven point stencil is
-obtained.
+used. It  is well-known that the  spectral radius of  matrices representing such
+problems are very close to 1.  Moreover, the larger the number of discretization
+points is,  the closer to 1  the spectral radius  is.  Hence, to solve  a matrix
+obtained for  a 3D Poisson  problem, the number  of iterations is high.  Using a
+preconditioner  it  is   possible  to  reduce  the  number   of  iterations  but
+preconditioners are not scalable when using many cores.
 
 \section{Conclusion and perspectives}
 
