Communications on Applied Mathematics and Computation >

2021 , Vol. 3 >Issue 1: 137 - 156

DOI: https://doi.org/10.1007/s42967-020-00061-x

ORIGINAL PAPER

Randomized Generalized Singular Value Decomposition

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  • 1 College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
    2 College of Jincheng, Nanjing University of Aeronautics and Astronautics, Nanjing 211156, China;
    3 Department of Mathematics, Taizhou University, Taizhou 225300, Zhejiang Province, China

Received date: 2019-09-30

  Revised date: 2020-01-21

  Online published: 2021-03-15

Supported by

The research is supported by the National Natural Science Foundation of China under Grant nos. 11701409 and 11571171, the Natural Science Foundation of Jiangsu Province of China under Grant BK20170591 and the Natural Science Foundation of Jiangsu Higher Education Institutions of China under Grant 17KJB110018.

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Abstract

The generalized singular value decomposition (GSVD) of two matrices with the same number of columns is a very useful tool in many practical applications. However, the GSVD may suffer from heavy computational time and memory requirement when the scale of the matrices is quite large. In this paper, we use random projections to capture the most of the action of the matrices and propose randomized algorithms for computing a low-rank approximation of the GSVD. Serval error bounds of the approximation are also presented for the proposed randomized algorithms. Finally, some experimental results show that the proposed randomized algorithms can achieve a good accuracy with less computational cost and storage requirement.

Key words： Generalized singular value decomposition; Randomized algorithm; Low-rank approximation; Error analysis

Cite this article

Wei Wei, Hui Zhang, Xi Yang, Xiaoping Chen . Randomized Generalized Singular Value Decomposition[J]. Communications on Applied Mathematics and Computation, 2021 , 3(1) : 137 -156 . DOI: 10.1007/s42967-020-00061-x

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