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Fast algorithm for parallel solving inversion of large scale small matrices based on GPU

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Abstract

Inverting a matrix is time-consuming, and many works focus on accelerating the inversion of a single large matrix by GPU. However, the problem of parallelizing the inversion of a large number of small matrices has received little attention. These problems are widely applied in computer science, including accelerating cryptographic algorithms and image processing algorithms. In this paper, we propose a Revised In-Place Inversion algorithm for inverting a large number of small matrices on the CUDA platform, which adopts a more refined parallelization scheme and outperforms other algorithms, achieving a speedup of up to 20.9572 times over the batch matrix inverse kernel in CUBLAS. Additionally, we found that there is an upper bound on the input data size for each GPU device, and the performance will degrade if the input data size is too large. Therefore, we propose the Saturation Size Curve based on this finding to divide matrices into batches and improve the algorithm performance. Experimental results show that this strategy increases the algorithm’s performance by 1.75 times and effectively alleviates the problem of performance degradation.

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All data sets this paper used were randomly generated by MATLAB, and there are no specific restrictions on the data sets.

Notes

  1. https://github.com/XFastDataLab/inverse_simple.

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Funding

This paper accepted financial support from the National Natural Science Foundation of China (No. 61673186, No. 61972010), and the Natural Science Foundation of Fujian Province, China (No. 2021J01317), we acknowledge sincerely financial support above.

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Author notes

  1. Chen Yewang, Fan Wentao, Zhang Yong and Du Jixiang have contributed equally to this work.

Authors and Affiliations

  1. The College of Computer Science and Technology, Huaqiao University, Jimei Avenu 668, Xiamen, 361021, Fujian, China

    Jin Xuebin, Chen Yewang, Fan Wentao & Du Jixiang

  2. Fujian Key Laboratory of Big Data Intelligence and Security, Huaqiao University, Jimei Avenu 668, Xiamen, 361021, Fujian, China

    Jin Xuebin, Chen Yewang, Fan Wentao & Du Jixiang

  3. Xiamen Key Laboratory of Computer Vision and Pattern Recognition, Huaqiao University, Jimei Avenu 668, Xiamen, 361021, Fujian, China

    Jin Xuebin, Chen Yewang & Fan Wentao

  4. College of Mechanical Engineering and Automation, Huaqiao University, Jimei Avenu 668, Xiamen, 361021, Fujian, China

    Zhang Yong

Authors
  1. Jin Xuebin
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  2. Chen Yewang
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Contributions

XJ designed the major Algorithm, drafted the manuscript, analyzed and interpretation of experiments, and prepared figures. YC, WF, YZ, and JD revised the manuscript critically for important intellectual content.

Corresponding author

Correspondence to Chen Yewang.

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Xuebin, J., Yewang, C., Wentao, F. et al. Fast algorithm for parallel solving inversion of large scale small matrices based on GPU. J Supercomput 79, 18313–18339 (2023). https://doi.org/10.1007/s11227-023-05336-7

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