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

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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 projectionCumulative sumCumulative multiplicationSingular value decompositionIntersection

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

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School of Information and Electrical Engineering, Harbin Institute of Technology at Weihai, Weihai 264209, China

School of Astronautics, Harbin Institute of Technology, Harbin 150001, China

This work is supported by the National Natural Science Foundation of ChinaThis work is supported by the National Natural Science Foundation of China

61501142No.61871149

2019

10.1049/cje.2019.01.013

中国电子杂志(英文版)

中国电子杂志(英文版)

CSTPCDCSCDSCIEI
ISSN：1022-4653
年,卷(期)：2019.28(2)
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