SVD-Based Low-Complexity Methods for Computing the Intersection of <i>K</i> ≥ 2 Subspaces

YAN Fenggang; WANG Jun; LIU Shuai; JIN Ming; SHEN Yi

doi:10.1049/cje.2019.01.013

Volume 28 Issue 2

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Article Navigation > Chinese Journal of Electronics > 2019 > 28(2): 430-436

YAN Fenggang, WANG Jun, LIU Shuai, et al., “SVD-Based Low-Complexity Methods for Computing the Intersection of K ≥ 2 Subspaces,” Chinese Journal of Electronics, vol. 28, no. 2, pp. 430-436, 2019, doi: 10.1049/cje.2019.01.013

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YAN Fenggang, WANG Jun, LIU Shuai, et al., “SVD-Based Low-Complexity Methods for Computing the Intersection of K ≥ 2 Subspaces,” Chinese Journal of Electronics, vol. 28, no. 2, pp. 430-436, 2019, doi: 10.1049/cje.2019.01.013

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

doi: 10.1049/cje.2019.01.013

1.
School of Information and Electrical Engineering, Harbin Institute of Technology at Weihai, Weihai 264209, China;
2.
School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

Funds: This work is supported by the National Natural Science Foundation of China (No.61501142, No.61871149).

More Information

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

Abstract

Abstract

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.
- Orthogonal projection,
- Cumulative sum,
- Cumulative multiplication,
- Singular value decomposition,
- Intersection

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References(23)

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