|1. It is better to clearly state the major contributions of this paper in the introduction.
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The following paragraph is added 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 blocks 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.
+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 other iterative methods. So our main contribution is to use the multisplitting method which splits the problem to solve into different blocks 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.
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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.
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-In fact, the machine we have used, almost one year ago, is not accessible anymore, it has been reformed. In this paper, we show that, for a very well-known problem, the 3D Poisson problem that is used in many simulations, our method is more efficient than the GMRES method which is a very well-known method.
+In fact, the machine we have used, almost one year ago, is not accessible anymore, it has been reformed. In this paper, we show that, for a very well-known problem, the 3D Poisson problem that is used in many simulations, our method is more efficient than the GMRES method which is a very well-known method.
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+We have added some experimental results obtained on a small cluster comparing the performances of our Krylov multisplitting method with those of the well-known block Jacobi multisplitting method and the GMRES method. These experiments clearly show that our method is better than the other two methods and the classical multisplitting method is the worst one. For this reason in the rest of the work we have compared the performances of our method only to those of the GMRES method.
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RAPH : on peut modifier des trucs pour répondre dans le papier? ca serait bien :-)
+Lilia: J'ai un peu modifié la section 3, mais on peut toujours l'améliorer. As-tu d'autres idées à ajouter, Mr...? :)
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ii) The authors supposed a good scalability of the new algorithm, but the experiment's proof seems not enough, as it just gave the weak scalability comparison, which just could lead to a conclusion of improved execution time, while a strong scalability curve might be more persuasive.
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-As said previously, the machine we have used is reformed and currently we have no access to make other large-scale tests. In fact, we consider that GMRES is quite scalable because its good performances have been proven in many research works and it is used by many other researchers and tools. So we have compared our multisplitting method with it by using weak scaling which allows to have broadly a constant amount of computations on each core.
+As said previously, the machine we have used is reformed and currently we have no access to make other large-scale tests. In fact, we consider that GMRES is quite scalable because its good performances have been proven in many research works and it is used by many other researchers and tools. So we have compared our multisplitting method with it by using weak scaling which allows to have broadly a constant amount of computations on each core.
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+As said previously, we have added some experiments performed on a small cluster comparing our method to the GMRES method and the classical block Jacobi multisplitting method.
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* Reviewer #5 *
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However, the paper does not take into considerate account relevant current and past research on the topic.
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-%Doing many experiments with many cores is not easy and requires to access to a supercomputer with several hours for developing a code and then improving it.-
+Doing many experiments with many cores is not easy and requires to access to a supercomputer with several hours for developing a code and then improving it. This is why in our work we have focused on experiments to solve one well-known sparse linear equations which is the 3D Poisson problem and to compare the performances of our Krylov multisplitting method to the GMRES method which is a very used method. In addition, the machine we have used is not accessible anymore, it has been reformed.
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The paper should be rewritten to clearly explain what is being compared. It seems as if the method in [9] is not included in the comparison.
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+Section 4 is rewritten in order to explain our choice to compare our Krylov multisplitting method with only the GMRES method. We have added in the paper some experimental results obtained on a small cluster which clearly show that our method is more efficient than GMRES and block Jacobi multisplitting methods.
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