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On Symmetric and Skew-Symmetric Solutions to a Procrustes Problem

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Numerical Linear Algebra in Signals, Systems and Control

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 80))

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Abstract

Using the projection theorem in a Hilbert space, the quotient singular value decomposition (QSVD) and the canonical correlation decomposition (CCD) in matrix theory for efficient tools, we obtained the explicit analytical expressions of the optimal approximation solutions for the symmetric and skew-symmetric least-squares problems of the linear matrix equation \(AXB = C\). This can lead to new algorithms to solve such problems.

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Acknowledgments

The author Deng would like to thank the China Scholarship Council for providing the State Scholarship Fund to pursue his research at the University of Minnesota as a visiting scholar. The author Boley would like to acknowledge partial support for this research from NSF grant IIS-0916750.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University Changsha, 410082, Hunan, People’s Republic of China

    Yuan-Bei Deng

  2. Department of Computer Science and Engineering, University of Minnesota Minneapolis, Minneapolis, MN, 55455, USA

    Daniel Boley

Authors
  1. Yuan-Bei Deng
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  2. Daniel Boley
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Corresponding author

Correspondence to Yuan-Bei Deng .

Editor information

Editors and Affiliations

  1. CESAME, Batiment Euler, Universite Catholique de Louvain, 4, avenue Georges Lemaitre, Louvain la Neuve, 1348, Belgium

    Paul Van Dooren

  2. Department of Electrical and Computer, Engineering, Texas A&M University, Zachry Engineering Center, College Station, 77843-3128, Texas, USA

    Shankar P. Bhattacharyya

  3. Dept. Mathematics, Chinese University Hong Kong, Shatin, New Territories, Hong Kong/PR China

    Raymond H. Chan

  4. Dept. Mathematics, University of Connecticut, Auditorium Road 196, Storrs, 06269-3009, Connecticut, USA

    Vadim Olshevsky

  5. , Electrical Engineering, Indian Institute of Technology, Kharagpur, 721302, India

    Aurobinda Routray

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Deng, YB., Boley, D. (2011). On Symmetric and Skew-Symmetric Solutions to a Procrustes Problem. In: Van Dooren, P., Bhattacharyya, S., Chan, R., Olshevsky, V., Routray, A. (eds) Numerical Linear Algebra in Signals, Systems and Control. Lecture Notes in Electrical Engineering, vol 80. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0602-6_11

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  • DOI: https://doi.org/10.1007/978-94-007-0602-6_11

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-0601-9

  • Online ISBN: 978-94-007-0602-6

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