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 |
Generalized Absolute Value Matrix Equation, Unique Solution, Singular Values
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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
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
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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Download@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}
}
TY - JOUR 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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