Volume 10, Issue 4
ADMM-Based Methods for Nearness Skew-Symmetric and Symmetric Solutions of Matrix Equation $AXB = C$

East Asian J. Appl. Math., 10 (2020), pp. 698-716.

Published online: 2020-08

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• Abstract

New equivalent forms of a matrix nearness problem are proposed and necessary and sufficient conditions for a skew-symmetric or symmetric matrix $X$ to be a solution of the problem are obtained. In order to find approximate solutions of the problem, we employ two ADMM-based iterative methods and prove their global convergence. Numerical simulations demonstrate the effectiveness of the methods developed.

• Keywords

ADMM, matrix nearness problem, global convergence, preconditioning, iterative method.

15A24, 15A39, 65F30

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@Article{EAJAM-10-698, author = {Dongmei Yu , and Cairong Chen , and Deren Han , }, title = {ADMM-Based Methods for Nearness Skew-Symmetric and Symmetric Solutions of Matrix Equation $AXB = C$}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {4}, pages = {698--716}, abstract = {

New equivalent forms of a matrix nearness problem are proposed and necessary and sufficient conditions for a skew-symmetric or symmetric matrix $X$ to be a solution of the problem are obtained. In order to find approximate solutions of the problem, we employ two ADMM-based iterative methods and prove their global convergence. Numerical simulations demonstrate the effectiveness of the methods developed.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.100719.230320 }, url = {http://global-sci.org/intro/article_detail/eajam/17949.html} }
TY - JOUR T1 - ADMM-Based Methods for Nearness Skew-Symmetric and Symmetric Solutions of Matrix Equation $AXB = C$ AU - Dongmei Yu , AU - Cairong Chen , AU - Deren Han , JO - East Asian Journal on Applied Mathematics VL - 4 SP - 698 EP - 716 PY - 2020 DA - 2020/08 SN - 10 DO - http://doi.org/10.4208/eajam.100719.230320 UR - https://global-sci.org/intro/article_detail/eajam/17949.html KW - ADMM, matrix nearness problem, global convergence, preconditioning, iterative method. AB -

New equivalent forms of a matrix nearness problem are proposed and necessary and sufficient conditions for a skew-symmetric or symmetric matrix $X$ to be a solution of the problem are obtained. In order to find approximate solutions of the problem, we employ two ADMM-based iterative methods and prove their global convergence. Numerical simulations demonstrate the effectiveness of the methods developed.

Dongmei Yu, Cairong Chen & Deren Han. (2020). ADMM-Based Methods for Nearness Skew-Symmetric and Symmetric Solutions of Matrix Equation $AXB = C$. East Asian Journal on Applied Mathematics. 10 (4). 698-716. doi:10.4208/eajam.100719.230320
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