Iterative algorithms for the minimum-norm solution and the least-squares solution of the linear matrix equations \(A_1XB_1 + C_1X^TD_1 = M_1, A_2XB_2 + C_2 X^TD_2 = M_2\)

DOI10.1016/j.amc.2011.08.052zbMath1250.65059OpenAlexW2025277247MaRDI QIDQ426323

Kaifu Liang, Jianzhou Liu

Publication date: 11 June 2012

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

Full work available at URL: https://doi.org/10.1016/j.amc.2011.08.052

zbMATH Keywords

conjugate gradient algorithmleast squares solutiongeneralized Sylvester matrix equationsnormal equation

Mathematics Subject Classification ID

Related Items (22)

The iterative algorithm for solving a class of generalized coupled Sylvester-transpose equations over centrosymmetric or anti-centrosymmetric matrix ⋮ The modified conjugate gradient methods for solving a class of generalized coupled Sylvester-transpose matrix equations ⋮ Iterative method to solve the generalized coupled Sylvester-transpose linear matrix equations over reflexive or anti-reflexive matrix ⋮ The MGPBiCG method for solving the generalized coupled Sylvester-conjugate matrix equations ⋮ A property of the eigenvalues of the symmetric positive definite matrix and the iterative algorithm for coupled Sylvester matrix equations ⋮ The solutions of the quaternion matrix equation \(AX^\varepsilon + BX^\delta = 0\) ⋮ HOBi-CGSTAB and HOBi-CRSTAB methods for solving some tensor equations ⋮ On the \(\star\)-Sylvester equation \(AX\pm X^{\star} B^{\star} = C\) ⋮ The BCR algorithms for solving the reflexive or anti-reflexive solutions of generalized coupled Sylvester matrix equations ⋮ Iterative solutions of a set of matrix equations by using the hierarchical identification principle ⋮ The accelerated gradient based iterative algorithm for solving a class of generalized Sylvester-transpose matrix equation ⋮ The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint ⋮ An iterative algorithm for generalized Hamiltonian solution of a class of generalized coupled Sylvester-conjugate matrix equations ⋮ Cyclic and simultaneous iterative methods to matrix equations of the form \(A_iXB_i=F_i\) ⋮ The scaling conjugate gradient iterative method for two types of linear matrix equations ⋮ The matrix iterative methods for solving a class of generalized coupled Sylvester-conjugate linear matrix equations ⋮ A modified CG algorithm for solving generalized coupled Sylvester tensor equations ⋮ Modified conjugate gradient method for obtaining the minimum-norm solution of the generalized coupled Sylvester-conjugate matrix equations ⋮ BCR method for solving generalized coupled Sylvester equations over centrosymmetric or anti-centrosymmetric matrix ⋮ Iterative methods to solve the generalized coupled Sylvester-conjugate matrix equations for obtaining the centrally symmetric (centrally antisymmetric) matrix solutions ⋮ On the relaxed gradient-based iterative methods for the generalized coupled Sylvester-transpose matrix equations ⋮ The solution of the equationAX + BX^⋆ = 0

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• Gradient based and least squares based iterative algorithms for matrix equations \(AXB + CX^{T}D = F\)
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• The matrix equations \(AX=C\), \(XB=D\)
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• Iterative algorithms for solving the matrix equation \(AXB + CX^{T}D = E\)
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• Gradient based iterative solutions for general linear matrix equations
• Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems
• The residual based interactive stochastic gradient algorithms for controlled moving average models
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• 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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