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An improved generalized conjugate residual squared (IGCRS2) algorithm suitable for distributed parallel computing

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Abstract

In this paper, based on generalized conjugate residual squared (GCRS2) algorithm in Zhang et al. (2010 Third International Conference on Information and Computing, pp 326–329, 2010) and the ideas in Gu et al. (Appl Math Comput 186:1243–1253, 2007), we present an improved generalized conjugate residual squared (IGCRS2) algorithm, which is designed for distributed parallel environments. The improved algorithm reduces two global synchronization points to one by changing the computation sequence in the GCRS2 algorithm and all inner products per iteration are independent and communication time required for inner product can be overlapped with useful computation. Theoretical analysis and numerical comparison about isoefficiency analysis show that the IGCRS2 method has better parallelism and scalability than the GCRS2 method and the parallel performance can be improved by a factor of about 2.

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Acknowledgments

The authors would like to thank the referees and Editor for their helpful and detailed suggestions for revising this manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou, 450015, Henan, People’s Republic of China

    Li-Tao Zhang

  2. Foundation Department, Yellow River Conservancy Technical Institute, Kaifeng, 475004, Henan, People’s Republic of China

    Xiao-Na Dong

  3. Laboratory of Computationary Physics, P.O. Box 8009, Beijing, 100088, People’s Republic of China

    Tong-Xiang Gu & Xing-Ping Liu

  4. Institute of Data and Knowledge Engineering, School of Computer and Information Engineering, Henan University, Kaifeng, 475004, Henan, People’s Republic of China

    Xian-Yu Zuo

Authors
  1. Li-Tao Zhang
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  2. Xiao-Na Dong
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  3. Tong-Xiang Gu
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  4. Xian-Yu Zuo
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  5. Xing-Ping Liu
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Corresponding author

Correspondence to Li-Tao Zhang.

Additional information

This research of this author is supported by NSFC Tianyuan Mathematics Youth Fund (11226337), NSFC(11471098,61203179,61202098,61170309,91130024,61272544,61472462 and 11171039), Aeronautical Science Foundation of China (2013ZD55006), Project of Youth Backbone Teachers of Colleges and Universities in Henan Province(2013GGJS-142), ZZIA Innovation team fund (2014TD02), Major project of development foundation of science and technology of CAEP (2012A0202008), Defense Industrial Technology Development Program, Basic and Advanced Technological Research Project of of Henan Province (122300410181,142300410333), China Postdoctoral Science Foundation (2014M552001), Henan Province Postdoctoral Science Foundation (2013031), Natural Science Foundation of Henan Province (13A110399,14A630019,14B110023), Natural Science Foundation of Zhengzhou City (141PQYJS560).

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Zhang, LT., Dong, XN., Gu, TX. et al. An improved generalized conjugate residual squared (IGCRS2) algorithm suitable for distributed parallel computing. Japan J. Indust. Appl. Math. 32, 143–155 (2015). https://doi.org/10.1007/s13160-014-0163-3

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  • DOI: https://doi.org/10.1007/s13160-014-0163-3

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