1 Dear raphael Couturier,
3 We have received the reports from our advisors on your manuscript, "A scalable multisplitting algorithm to solve large sparse linear systems", which you submitted to Journal of Supercomputing.
5 Based on the advice received, the Editor feels that your manuscript could be accepted for publication should you be prepared to incorporate minor revisions. When preparing your revised manuscript, you are asked to carefully consider the reviewer comments which are attached, and submit a list of responses to the comments. Your list of responses should be uploaded as a file in addition to your revised manuscript.
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20 Springer Journals Editorial Office
21 Journal of Supercomputing
25 COMMENTS FOR THE AUTHOR:
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30 Reviewer #2: This work focus on an better algorithm that solves very large sparse linear systems. The presentation of this paper is clear and within the scope of the journal. However, the paper can be improved in the following ways:
32 |1. It is better to clearly state the major contributions of this paper in the introduction.
34 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.
39 |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
40 |author to provide extensive comparison studies with those approaches. In Section 4 the paper provides some experiments with very limited scope (solving
41 |one simple problem and comparing with one well known problems). This seems not enough. Another way is to provide a qualitative comparison against other
42 |proposed approaches and explain why the proposed approach is better. But this is also not found.
46 |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.
50 |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.
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58 Reviewer #3: In this paper the authors proposed a practical multi-splitting method based on parallel iterative blocks which gives better results than classical GMRES method for the 3D Poisson problem. The paper is well-organized, written smoothly, and provide solid theoretical analysis, detailed algorithm presentation and concrete experiment results.
60 There are three problems/questions the reviewer is concerned with: i) what is the main contribution of this paper, i.e. the key advantage of the new algorithm compared to other multi-splitting methods, why not provide some experiments for comparison between them, rather than with only the classical GMRES?
62 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.
64 iii) In the last line on the page 7, there is apparent error "multi-saplitting".
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71 Reviewer #5: In this paper, the authors have implemented a Krylov multisplitting method to solve sparse linear systems on large-scale computing platforms. The technical approach and analysis of this paper is reasonable and the paper is clear, logical, and understandable. However, the paper does not take into considerate account relevant current and past research on the topic.
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78 Reviewer #6: In this paper it says that the Krylov GMRES method is compared with a new parallel muti-splitting method of the authors. The paper also says that this new method is an adaptation of another method based on references [11] and [9]. It is unclear from the paper whether the analysis includes the a comparison of their new method to the method of reference [9]. Does the new method do better than that one or is it similar or worse.
80 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.
82 Was the method of reference [9] implemented by the authors of [9]? How did they do against GMRES?
