06-12-2014 v00

diff --git a/krylov_multi.tex b/krylov_multi.tex
index 1ab94c6f15f34cce6269b9ba1d8248f0ba8505cd..95e9dcd9e70c265c7f662998f4e4e389dad5f398 100644 (file)
--- a/krylov_multi.tex
+++ b/krylov_multi.tex
@@ -94,6 +94,8 @@ method. In opposition to traditional multisplitting method that suffer from slow
 convergence, as  proposed in~\cite{huang1993krylov},  the use of  a minimization
 process can drastically improve the convergence.
 
+In this work we develop a new parallel two-stage algorithm for large-scale clusters. Our objective is to mix between Krylov based iterative methods and the multisplitting method to improve the scalability. In fact Krylov subspace methods are well-known for their good convergence compared to others iterative methods. So our main contribution is to use the multisplitting method which splits the problem to solve into different sub-problems in order to reduce the large amount of communications and, to implement both inner and outer iterations as Krylov subspace iterations improving the convergence of the multisplitting algorithm.
+
 The present paper is  organized as follows. First, Section~\ref{sec:02} presents
 some  related  works and  the  principle  of  multisplitting methods.  Then,  in
 Section~\ref{sec:03}  the algorithm  of our  Krylov multisplitting

diff --git a/review.txt b/review.txt
index 173bfa2cc590e9ae31360056805a896266aa9b02..28fbe3f0cb9e85a10ec0c30cad788f8ddd857e5b 100644 (file)
--- a/review.txt
+++ b/review.txt
@@ -31,24 +31,22 @@ Reviewer #2: This work focus on an better algorithm that solves very large spars
 ,----
 |1. It is better to clearly state the major contributions of this paper in the introduction.
 `---
-In this work we develop a new parallel two-stage algorithm for large-scale clusters. Our objective is to mix between Krylov based iterative methods and the multisplitting method to improve the scalability. In fact Krylov subspace methods are well-known for their good convergence compared to others iterative methods. So our main contribution is to use the multisplitting method which splits the problem to solve into different sub-problems in order to reduce the communications and to implement both inner and outer iterations as Krylov subspace iterations improving the convergence of the multisplitting method.
+In this work we develop a new parallel two-stage algorithm for large-scale clusters. Our objective is to mix between Krylov based iterative methods and the multisplitting method to improve the scalability. In fact Krylov subspace methods are well-known for their good convergence compared to others iterative methods. So our main contribution is to use the multisplitting method which splits the problem to solve into different sub-problems in order to reduce the large amount of communications and, to implement both inner and outer iterations as Krylov subspace iterations improving the convergence of the multisplitting algorithm.
        
 
 
 ,----
-|2. Given that the focus of the paper is to provide a better solution on a well known problem with several well studied approaches. It is essential for the 
-|author to provide extensive comparison studies with those approaches. In Section 4 the paper provides some experiments with very limited scope (solving 
-|one simple problem and comparing with one well known problems). This seems not enough. Another way is to provide a qualitative comparison against other 
-|proposed approaches and explain why the proposed approach is better. But this is also not found.
+2. Given that the focus of the paper is to provide a better solution on a well known problem with several well studied approaches. It is essential for the author to provide extensive comparison studies with those approaches. In Section 4 the paper provides some experiments with very limited scope (solving one simple problem and comparing with one well known problems). This seems not enough. Another way is to provide a qualitative comparison against other proposed approaches and explain why the proposed approach is better. But this is also not found.
 `----
 
 ,----
-|3. It is better if the paper can provide a quantitative study on the speed-up achieved by the proposed algorithm so that the reader can get insights on how |much is the performance improvement in theory.
+3. It is better if the paper can provide a quantitative study on the speed-up achieved by the proposed algorithm so that the reader can get insights on how much is the performance improvement in theory.
 `----
 
 ,----
-|4. In Section 3. it is better if the paper can explain the intuition of multi-splitting. Currently it is more like "Here is what I did" presentation but |"why do we do this" is left for the reader to guess.
+4. In Section 3. it is better if the paper can explain the intuition of multi-splitting. Currently it is more like "Here is what I did" presentation but "why do we do this" is left for the reader to guess.
 `----
+The multisplitting methods are well known to be more adapted to large-scale clusters of processors by minimizing the synchronizations but they suffer from slow convergence. In fact, the larger the number of splitting is, the larger the spectral radius is, thereby slowing the convergence of the multisplitting algorithm. We have used the parallel algorithm of the well known GMRES method to solve locally each block. In addition we have also implemented the outer iteration as a Krylov subspace iteration minimizing some error function which allows to improve the global convergence of the multisplitting algorithm.