Closed-form algorithms for computing the intersection of two subspaces

作     者：YAN Fenggang LIU Shuai WANG Jun JIN Ming 

作者机构：School of Information Science and EngineeringHarbin Institute of Technology at Weihai 

出 版 物：《Journal of Systems Engineering and Electronics》 (系统工程与电子技术（英文版）)

年 卷 期：2019年第30卷第2期

页      面：245-250页

核心收录：

学科分类：0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 07[理学] 08[工学] 0802[工学-机械工程] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China(61501142 61871149) the project supported by Discipline Construction Guiding Foundation in Harbin Institute of Technology(Weihai)(WH2-0160107) 

主　　题：orthogonal projection singular value decomposition alternate projection method (APM) intersection 

摘      要：Finding the intersection of two subspaces is of great interest in many fields of signal processing. Over several decades,there have been numerous formulas discovered to solve this problem, among which the alternate projection method(APM) is the most popular one. However, APM suffers from high computational complexity, especially for real-time applications. Moreover, APM only gives the projection instead of the orthogonal basis of two given subspaces. This paper presents two alternate algorithms which have a closed form and reduced complexity as compared to the APM technique. Numerical simulations are conducted to verify the correctness and the effectiveness of the proposed methods.