Conjugate Decomposition and Its Applications

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• 作者：Li-Ping Wang (1)
  Jinyun Yuan (2)
  
• 关键词：Singular value decomposition ; Conjugate decomposition ; Generalized inverse ; Least squares solution ; Projection ; Orthogonal projection ; Frequency estimate ; FFT
• 刊名：Journal of the Operations Research Society of China
• 出版年：2013
• 出版时间：June 2013
• 年：2013
• 卷：1
• 期：2
• 页码：199-215
• 全文大小：900KB
• 参考文献：1. Dai, Y.-H.: Private communication (2006)
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• 作者单位：Li-Ping Wang (1)
  Jinyun Yuan (2)
  
  1. Department of Mathematics, College of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P.R. China
  2. Departamento de Matemática -UFPR, Centro Politénico, CP: 19.081, Curitiba, PR, 81531-980, Brazil
  
• ISSN：2194-6698

文摘

The conjugate decomposition (CD), which was given for symmetric and positive definite matrices implicitly based on the conjugate gradient method, is generalized to every m×n matrix. The conjugate decomposition keeps some SVD properties, but loses uniqueness and part of orthogonal projection property. From the computational point of view, the conjugate decomposition is much cheaper than the SVD. To illustrate the feasibility of the CD, some application examples are given. Finally, the application of the conjugate decomposition in frequency estimate is given with comparison of the SVD and FFT. The numerical results are promising.