An iterative method for symmetric solutions and optimal approximation solution of the system of matrix equations \(A_{1}XB_{1} = C_{1}, A_{2}XB_{2} = C_{2}\)

DOI10.1016/j.amc.2006.05.124zbMath1134.65032OpenAlexW2060899753MaRDI QIDQ865560

Ya-Xin Peng, Lei Zhang, Xi-Yan Hu

Publication date: 19 February 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.05.124

zbMATH Keywords

iterative methodoptimal approximationsymmetric solutionleast-norm solutionsystems of matrix equations

Mathematics Subject Classification ID

Related Items (21)

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Cites Work

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• The matrix equations \(AX=C\), \(XB=D\)
• A pair of simultaneous linear matrix equations \(A_ 1XB_ 1=C_ 1,A_ 2XB_ 2=C_ 2\) and a matrix programming problem
• Augmentability in optimization theory
• Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations
• Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
• On the existence of a common solution \(X\) to the matrix equations \(A_{i} XB_{j}\)=\(C_{ij}\), \((i,j){\in}\Gamma\).
• An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation \(AXB\)=\(C\)
• Methods of conjugate gradients for solving linear systems
• A representation of the general common solution to the matrix equations \(A_1XB_1=C_1\) and \(A_2XB_2=C_2\) with applications

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