Least-squares solutions to the matrix equations \(AX = B\) and \(XC = D\)

DOI10.1016/j.amc.2010.04.002zbMath1193.65046OpenAlexW2115852812MaRDI QIDQ984351

Yongxin Yuan

Publication date: 19 July 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2010.04.002

zbMATH Keywords

numerical examplesspectral decompositionmatrix equationsymmetric solutionmatrix differentiationleast-squares solution

Mathematics Subject Classification ID

Related Items (14)

The Re-nnd and Re-pd solutions to the matrix equationsAX = C,XB = D ⋮ Determinantal representations of solutions to systems of quaternion matrix equations ⋮ The solutions to linear matrix equations \(AX=B\), \(YA=D\) with \(k\)-involutory symmetries ⋮ On the Hermitian structures of the solution to a pair of matrix equations ⋮ Solvability of systems of linear matrix equations subject to a matrix inequality ⋮ Some structures of submatrices in solution to the paire of matrix equations \(AX=C,XB=D\) ⋮ An efficient method for special least squares solution of the complex matrix equation \((AXB,CXD)=(E,F)\) ⋮ Constrained solutions of a system of matrix equations ⋮ (Anti-)Hermitian generalized (anti-)Hamiltonian solution to a system of matrix equations ⋮ The generalized bisymmetric (bi-skew-symmetric) solutions of a class of matrix equations and its least squares problem ⋮ The Hermitian \(\{P,\mathrm k+1\}\)-(anti-)reflexive solutions of a linear matrix equation ⋮ On the generalized bi (skew-) symmetric solutions of a linear matrix equation and its procrust problems ⋮ The least square solution with the least norm to a system of quaternion matrix equations ⋮ The solution of the matrix equation \(AXB=D\) and The system of matrix equations \(AX=C\), \(XB=D\) with \(X^*X=I_p\)

Cites Work

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• The matrix equations \(AX=C\), \(XB=D\)
• Least-squares solution with the minimum-norm for the matrix equation \((A\times B,G\times H) = (C,D)\)
• Symmetric and skew-antisymmetric solutions to systems of real quaternion matrix equations
• The generalized reflexive solution for a class of matrix equations \( (AX=B, XC=D)\)
• Computing the CS decomposition of a partitioned orthonormal matrix
• Singular value and generalized singular value decompositions and the solution of linear matrix equations
• Perturbation analysis of the canonical correlations of matrix pairs
• The reflexive and anti-reflexive solutions of the matrix equation \(AX=B\).
• Positive solutions to the equations \(AX=C\) and \(XB=D\) for Hilbert space operators
• The matrix equations \(AX=B, XC=D\) with \(PX= sXP\) constraint
• Tikhonov regularization for weighted total least squares problems
• Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
• Least squares solutions to the equations \(AX = B, XC = D\) with some constraints
• Towards a Generalized Singular Value Decomposition

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