From: Christophe Guyeux <guyeux@gmail.com>
Date: Fri, 10 Oct 2014 11:23:33 +0000 (+0200)
Subject: Je sais pas trop
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/commitdiff_plain/e22868ab5dffa57e6db9bb8d6c9c21ae84411e2a?hp=6ee06aaa241c211c1fbd5d1efd3697c9e1e20b41

Je sais pas trop

Merge branch 'master' of ssh://info.iut-bm.univ-fcomte.fr/GMRES2stage
---

diff --git a/paper.tex b/paper.tex
index a2a3e9d..e512018 100644
--- a/paper.tex
+++ b/paper.tex
@@ -649,15 +649,15 @@ appropriate than a single direct method in a parallel context.
 \begin{algorithmic}[1]
   \Input $A$ (sparse matrix), $b$ (right-hand side)
   \Output $x$ (solution vector)\vspace{0.2cm}
-  \State Set the initial guess $x^0$
+  \State Set the initial guess $x_0$
   \For {$k=1,2,3,\ldots$ until convergence (error$<\epsilon_{tsirm}$)} \label{algo:conv}
-    \State  $x^k=Solve(A,b,x^{k-1},max\_iter_{kryl})$   \label{algo:solve}
+    \State  $x_k=Solve(A,b,x_{k-1},max\_iter_{kryl})$   \label{algo:solve}
     \State retrieve error
-    \State $S_{k \mod s}=x^k$ \label{algo:store}
+    \State $S_{k \mod s}=x_k$ \label{algo:store}
     \If {$k \mod s=0$ {\bf and} error$>\epsilon_{kryl}$}
       \State $R=AS$ \Comment{compute dense matrix} \label{algo:matrix_mul}
-            \State $\alpha=Solve\_Least\_Squares(R,b,max\_iter_{ls})$ \label{algo:}
-      \State $x^k=S\alpha$  \Comment{compute new solution}
+            \State $\alpha=Least\_Squares(R,b,max\_iter_{ls})$ \label{algo:}
+      \State $x_k=S\alpha$  \Comment{compute new solution}
     \EndIf
   \EndFor
 \end{algorithmic}
@@ -704,19 +704,21 @@ less the same principle but it takes more place, so we briefly explain the paral
 \begin{algorithmic}[1]
   \Input $A$ (matrix), $b$ (right-hand side)
   \Output $x$ (solution vector)\vspace{0.2cm}
-  \State $r=b-Ax$
-  \State $p=A'r$
-  \State $s=p$
-  \State $g=||s||^2_2$
-  \For {$k=1,2,3,\ldots$ until convergence (g$<\epsilon_{ls}$)} \label{algo2:conv}
-    \State $q=Ap$
-    \State $\alpha=g/||q||^2_2$
-    \State $x=x+alpha*p$
-    \State $r=r-alpha*q$
-    \State $s=A'*r$
-    \State $g_{old}=g$
-    \State $g=||s||^2_2$
-    \State $\beta=g/g_{old}$
+  \State Let $x_0$ be an initial approximation
+  \State $r_0=b-Ax_0$
+  \State $p_1=A^Tr_0$
+  \State $s_0=p_1$
+  \State $\gamma=||s_0||^2_2$
+  \For {$k=1,2,3,\ldots$ until convergence ($\gamma<\epsilon_{ls}$)} \label{algo2:conv}
+    \State $q_k=Ap_k$
+    \State $\alpha_k=\gamma/||q_k||^2_2$
+    \State $x_k=x_{k-1}+\alpha_kp_k$
+    \State $r_k=r_{k-1}-\alpha_kq_k$
+    \State $s_k=A^Tr_k$
+    \State $\gamma_{old}=\gamma$
+    \State $\gamma=||s_k||^2_2$
+    \State $\beta_k=\gamma/\gamma_{old}$
+    \State $p_{k+1}=s_k+\beta_kp_k$
   \EndFor
 \end{algorithmic}
 \label{algo:02}
@@ -837,17 +839,16 @@ scalable linear equations solvers:
 \begin{itemize}
 \item ex15  is an example  which solves in  parallel an operator using  a finite
   difference  scheme.   The  diagonal  is  equal to  4  and  4  extra-diagonals
-  representing the neighbors in each directions  is equal to -1. This example is
+  representing the neighbors in each directions  are equal to -1. This example is
   used  in many  physical phenomena, for  example, heat  and fluid  flow, wave
-  propagation...
+  propagation, etc.
 \item ex54 is another example based on 2D problem discretized with quadrilateral
   finite elements. For this example, the user can define the scaling of material
-  coefficient in embedded circle, it is called $\alpha$.
+  coefficient in embedded circle called $\alpha$.
 \end{itemize}
-For more technical details on  these applications, interested reader are invited
-to  read the  codes available  in the  PETSc sources.   Those problem  have been
-chosen because they  are scalable with many cores. We  have tested other problem
-but they are not scalable with many cores.
+For more technical details on  these applications, interested readers are invited
+to  read the  codes available  in the  PETSc sources.   Those problems  have been
+chosen because they  are scalable with many cores which is not the case of other problems that we have tested.
 
 In the following larger experiments are described on two large scale architectures: Curie and Juqeen... {\bf description...}\\