An iterative method for the symmetric and skew symmetric solutions of a linear matrix equation \(AXB+CYD=E\)

DOI10.1016/j.cam.2009.11.052zbMath1190.65071OpenAlexW2148366330MaRDI QIDQ848561

Xingping Sheng, Guo-Liang Chen

Publication date: 4 March 2010

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

Full work available at URL: https://doi.org/10.1016/j.cam.2009.11.052

zbMATH Keywords

algorithmiterative methodsymmetric solutionlinear matrix equationminimum norm solutionleast norm solutionoptimal approximation solutionskew symmetric solution

Mathematics Subject Classification ID

Related Items (18)

Alternating direction method for generalized Sylvester matrix equation \(AXB + CYD = E\) ⋮ Generalized conjugate direction algorithm for solving the general coupled matrix equations over symmetric matrices ⋮ Numerical algorithms for solving the least squares symmetric problem of matrix equation AXB + CXD = E ⋮ Solutions of the generalized Sylvester matrix equation and the application in eigenstructure assignment ⋮ An iterative updating method for undamped structural systems ⋮ Generalized conjugate direction algorithm for solving general coupled Sylvester matrix equations ⋮ An efficient iterative updating method for hysteretic damping models ⋮ An iterative algorithm for the least squares generalized reflexive solutions of the matrix equations \(AXB = E\), \(CXD = F\) ⋮ The solution of a generalized Sylvester quaternion matrix equation and its application ⋮ Finite iterative algorithms for solving generalized coupled Sylvester systems. I: One-sided and generalized coupled Sylvester matrix equations over generalized reflexive solutions ⋮ Least squares solutions of the matrix equation \(AXB+CYD=E\) with the least norm for symmetric arrowhead matrices ⋮ Analytical best approximate Hermitian and generalized skew-Hamiltonian solution of matrix equation \(AXA^{\mathrm{H}}+CYC^{\mathrm{H}}=F\) ⋮ An iterative algorithm for the generalized reflexive solutions of the generalized coupled Sylvester matrix equations ⋮ Least squares Hermitian solution of the complex matrix equation \(AXB+CXD=E\) with the least norm ⋮ An iterative algorithm for solving the generalized Sylvester-conjugate matrix equation ⋮ Computing symmetric solutions of general Sylvester matrix equations via Lanczos version of biconjugate residual algorithm ⋮ Cramer's rule for a system of quaternion matrix equations with applications ⋮ Modified CGLS iterative algorithm for solving the generalized Sylvester-conjugate matrix equation

Cites Work

• Singular value and generalized singular value decompositions and the solution of linear matrix equations
• Computing a nearest symmetric positive semidefinite matrix
• The matrix equation AXB+CYD=E
• On solutions of matrix equation \(AXB+CYD=F\)
• An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation \(AXB\)=\(C\)
• Generalized inverses. Theory and applications.
• A finite iterative method for solving a pair of linear matrix equations \((AXB,CXD)=(E,F)\)
• The inverse problem of bisymmetric matrices with a submatrix constraint
• Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations
• An efficient iterative method for solving the matrix equationAXB +CYD =E
• The Equation $AXB + CYD = E$ over a Principal Ideal Domain
• The matrix equationAXB+CYD=Eover a simple artinian ring
• Best Approximate Solution of Matrix Equation AXB+CYD=E
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