ON ADMM-BASED METHODS FOR SOLVING THE NEARNESS SYMMETRIC SOLUTION OF THE SYSTEM OF MATRIX EQUATIONS A1XB1 = C1 AND A2XB2 = C2

Yu-Ning Wu; Min-Li Zeng

doi:10.11948/20190282

2021 Volume 11 Issue 1

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Yu-Ning Wu, Min-Li Zeng. ON ADMM-BASED METHODS FOR SOLVING THE NEARNESS SYMMETRIC SOLUTION OF THE SYSTEM OF MATRIX EQUATIONS A1XB1 = C1 AND A2XB2 = C2[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 227-241. doi: 10.11948/20190282

Citation:

Yu-Ning Wu, Min-Li Zeng. ON ADMM-BASED METHODS FOR SOLVING THE NEARNESS SYMMETRIC SOLUTION OF THE SYSTEM OF MATRIX EQUATIONS A₁XB₁ = C₁ AND A₂XB₂ = C₂[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 227-241. doi: 10.11948/20190282

ON ADMM-BASED METHODS FOR SOLVING THE NEARNESS SYMMETRIC SOLUTION OF THE SYSTEM OF MATRIX EQUATIONS A₁XB₁ = C₁ AND A₂XB₂ = C₂

Yu-Ning Wu^1,2, ,,
Min-Li Zeng³

1.
College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350007, China
2.
School of Basic Education, Putian University, Putian 351100, China
3.
School of Mathematics and Finance, Putian University, Putian 351100, China

Corresponding author: Email address:wuyuning330@163.com(Y. Wu)
Fund Project: The authors were supported by National Natural Science Foundation of China(11901324)

Abstract

Abstract

Two new equivalent forms of the matrix nearness problem are developed. Some sufficient and necessary conditions for a symmetric matrix X? being a solution of the considered problem are presented. Based on the new equivalent forms of the above problem and the idea of the alternating direction method with multipliers (ADMM), we establish two new iterative methods to compute its solution, and analyze the global convergence of the proposed algorithms. Numerical results demonstrate the efficiency of our methods. The development here is an extension of the recent work of Peng, Fang, Xiao and Du [SpringerPlus, 5:1005, 2016] on the nearness symmetric solution of the matrix equation AXB = C.
- Matrix nearness problem /
- symmetric solution /
- ADMM /
- iterative method /
- matrix equations
MSC: 15A06, 15A09

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References

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