YAN Fenggang, WANG Jun, LIU Shuai, JIN Ming, SHEN Yi. SVD-Based Low-Complexity Methods for Computing the Intersection of K ≥ 2 Subspaces[J]. Chinese Journal of Electronics, 2019, 28(2): 430-436. doi: 10.1049/cje.2019.01.013
Citation: YAN Fenggang, WANG Jun, LIU Shuai, JIN Ming, SHEN Yi. SVD-Based Low-Complexity Methods for Computing the Intersection of K ≥ 2 Subspaces[J]. Chinese Journal of Electronics, 2019, 28(2): 430-436. doi: 10.1049/cje.2019.01.013

SVD-Based Low-Complexity Methods for Computing the Intersection of K ≥ 2 Subspaces

doi: 10.1049/cje.2019.01.013
Funds:  This work is supported by the National Natural Science Foundation of China (No.61501142, No.61871149).
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  • Corresponding author: JIN Ming (corresponding author) received the B.E., M.S. and Ph.D. degrees in information and communication engineering from HIT China, in 1990, 1998 and 2004, respectively. From 1998 to 2004, He was with the Department of Electronics Information Engineering, HIT. Since 2006, he became a professor of the School of Information and Electricity Engineering, HIT at Weihai. His current interests include array signal processing and radar polarimetry. (Email:jinming0987@163.com)
  • Received Date: 2017-02-21
  • Rev Recd Date: 2017-10-31
  • Publish Date: 2019-03-10
  • Given the orthogonal basis (or the projections) of no less than two subspaces in finite dimensional spaces, we propose two novel algorithms for computing the intersection of those subspaces. By constructing two matrices using cumulative multiplication and cumulative sum of those projections, respectively, we prove that the intersection equals to the null spaces of the two matrices. Based on such a mathematical fact, we show that the orthogonal basis of the intersection can be efficiently computed by performing singular value decompositions on the two matrices with much lower complexity than most state-of-the-art methods including alternate projection method. Numerical simulations are conducted to verify the correctness and the effectiveness of the proposed methods.
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