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The communication-hiding pipelined BiCGstab method for the parallel solution of large unsymmetric linear systems
Cools S., Vanroose W. Parallel Computing65 1-20,2017.Type:Article
Date Reviewed: Aug 10 2017

In the huge matrices used in high-performance computing (HPC), there exist patterns and relations among the members of the matrix that can be utilized to process the matrices in a more efficient way. Most of the discussions concerned with huge matrices have been focused on the detection of these patterns and their utilization for performant parallel matrix processing.

Iterative and direct method techniques are two main categories for the solutions of matrices in HPC. Iteration-based solutions, which would map the original matrix to a simpler version that can be solved with less time, resource consumption, and gradual relieving of the estimated residual errors, are more common than direct ones. Krylov subspace-based methods are the most salient iterative techniques available for solving large, sparse linear systems. To take advantage of the availability of popular multiprocessor/multicore systems, a crucial problem--the scalability of the algorithm--must be addressed; the pipelined Krylov subspace solver has been invented for higher performance.

Krylov solutions are restricted to sparse and linear systems. Devising methods to mitigate these restrictions has been a research topic for related communities. An extension of the Krylov method, conjugate gradient (CG), and its variants are efforts to extend the functionalities to wider dimensions and less restricted domains. In this regard, the authors of the paper propose a novel and complementary method for huge matrix calculation in HPC, pipelined bi-conjugate gradient stabilized (BiCGstab). They utilize two main features of pipelined techniques in huge matrices: avoiding communication and hiding communication. They draw a new pattern, which relieves the idling due to global synchronization of parallel executing units, and they impose the possible concurrency of communication and computation operations among the involved nodes as an opportunity to expand parallelism. The topic is developed with algorithmic and mathematical discussions in a well-formed and stepwise manner. The numerical results and parallel performance measurements with graphs and tables indicate the efficiency and performance of the proposed mechanism.

Besides its welcome achievements, the paper is a classic sample of a scientific paper, with coherence, smoothness, and structure. It not only contains fruitful discussions concerned with high-performance computing and application of the key topics of linear algebra, but also has gathered plenty of useful references that pave the way for further investigation and research.

Reviewer:  Mohammad Sadegh Kayhani Pirdehi Review #: CR145475 (1710-0661)
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Linear Systems (Direct And Iterative Methods) (G.1.3 ... )
 
 
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