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On the Unique Solvability of the Generalized Absolute Value Matrix Equation

Received: 13 July 2021     Accepted: 26 July 2021     Published: 2 August 2021
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Abstract

The generalized absolute value matrix equation has application in a variety of optimization problems, its unique solvability is still on the way. In this note, the unique solvability of the generalized absolute value matrix equation is considered. A new unique solvability of generalized absolute value matrix equation is given. The obtained result can be regarded as an extension of the absolute value equation to the generalized absolute value matrix equation. As an application, new convergence of matrix multisplitting Picard-iterative method is presented.

Published in American Journal of Applied Mathematics (Volume 9, Issue 4)
DOI 10.11648/j.ajam.20210904.12
Page(s) 104-107
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Generalized Absolute Value Matrix Equation, Unique Solution, Singular Values

References
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Cite This Article
  • APA Style

    Kai Xie. (2021). On the Unique Solvability of the Generalized Absolute Value Matrix Equation. American Journal of Applied Mathematics, 9(4), 104-107. https://doi.org/10.11648/j.ajam.20210904.12

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    ACS Style

    Kai Xie. On the Unique Solvability of the Generalized Absolute Value Matrix Equation. Am. J. Appl. Math. 2021, 9(4), 104-107. doi: 10.11648/j.ajam.20210904.12

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    AMA Style

    Kai Xie. On the Unique Solvability of the Generalized Absolute Value Matrix Equation. Am J Appl Math. 2021;9(4):104-107. doi: 10.11648/j.ajam.20210904.12

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  • @article{10.11648/j.ajam.20210904.12,
      author = {Kai Xie},
      title = {On the Unique Solvability of the Generalized Absolute Value Matrix Equation},
      journal = {American Journal of Applied Mathematics},
      volume = {9},
      number = {4},
      pages = {104-107},
      doi = {10.11648/j.ajam.20210904.12},
      url = {https://doi.org/10.11648/j.ajam.20210904.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210904.12},
      abstract = {The generalized absolute value matrix equation has application in a variety of optimization problems, its unique solvability is still on the way. In this note, the unique solvability of the generalized absolute value matrix equation is considered. A new unique solvability of generalized absolute value matrix equation is given. The obtained result can be regarded as an extension of the absolute value equation to the generalized absolute value matrix equation. As an application, new convergence of matrix multisplitting Picard-iterative method is presented.},
     year = {2021}
    }
    

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    T1  - On the Unique Solvability of the Generalized Absolute Value Matrix Equation
    AU  - Kai Xie
    Y1  - 2021/08/02
    PY  - 2021
    N1  - https://doi.org/10.11648/j.ajam.20210904.12
    DO  - 10.11648/j.ajam.20210904.12
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 104
    EP  - 107
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20210904.12
    AB  - The generalized absolute value matrix equation has application in a variety of optimization problems, its unique solvability is still on the way. In this note, the unique solvability of the generalized absolute value matrix equation is considered. A new unique solvability of generalized absolute value matrix equation is given. The obtained result can be regarded as an extension of the absolute value equation to the generalized absolute value matrix equation. As an application, new convergence of matrix multisplitting Picard-iterative method is presented.
    VL  - 9
    IS  - 4
    ER  - 

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Author Information
  • College of Mathematics and Statistics, Northwest Normal University, Lanzhou, P. R. China

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