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An Iterative Method for the Least Squares Anti-bisymmetric Solution of the Matrix Equation

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Recent Developments in Intelligent Systems and Interactive Applications (IISA 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 541))

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Abstract

In this paper the authors on the basis of Conjugate Gradient Method of solving linear algebraic equations, using special transformation and approximate disposal, proposed an Iterative Method, which can solve the least squares anti-bisymmetric solution of the matrix equation AXB + CXD = F. Using this iterative method, for an arbitrary initial anti-bisymmetric matrix, we can obtain a solution within finite iterative steps in the absence of round off errors. Further this solution with least norm can be obtained by choosing a special initial matrix. In addition, the expression of its optimal approximation solution to a given matrix can be obtained.

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Authors and Affiliations

  1. Science College, Air Force Engineering University, Xi’an, 710051, China

    Li Lin, Yuan Xiujiu, Liu Jing & Su Dongqing

Authors
  1. Li Lin
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  2. Yuan Xiujiu
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  3. Liu Jing
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  4. Su Dongqing
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Corresponding author

Correspondence to Li Lin .

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Editors and Affiliations

  1. Department of Computer Science, Universitat Politècnica de Catalunya, Barcelona, Spain

    Fatos Xhafa

  2. SOA University, Bhubaneswar, Odisha, India

    Srikanta Patnaik

  3. School of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, China

    Zhengtao Yu

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Lin, L., Xiujiu, Y., Jing, L., Dongqing, S. (2017). An Iterative Method for the Least Squares Anti-bisymmetric Solution of the Matrix Equation. In: Xhafa, F., Patnaik, S., Yu, Z. (eds) Recent Developments in Intelligent Systems and Interactive Applications. IISA 2016. Advances in Intelligent Systems and Computing, vol 541. Springer, Cham. https://doi.org/10.1007/978-3-319-49568-2_5

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  • DOI: https://doi.org/10.1007/978-3-319-49568-2_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-49567-5

  • Online ISBN: 978-3-319-49568-2

  • eBook Packages: EngineeringEngineering (R0)

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