On the \(\star\)-Sylvester equation \(AX\pm X^{\star} B^{\star} = C\)

DOI10.1016/j.amc.2012.01.065zbMath1245.15018OpenAlexW2068782821MaRDI QIDQ440722

Eric King-Wah Chu, Chun-Yueh Chiang, Wen-Wei Lin

Publication date: 19 August 2012

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

Full work available at URL: https://doi.org/10.1016/j.amc.2012.01.065

zbMATH Keywords

Lyapunov equationsingular value decompositionsolvabilityQR decompositionSchur decompositionlinear matrix equationgeneralized algebraic Riccati equationpalindromic eigenvalue problem

Mathematics Subject Classification ID

Matrix equations and identities (15A24)

Related Items (19)

On the solvability of generalized Sylvester operator equations ⋮ An extended Hamiltonian algorithm for the general linear matrix equation ⋮ On the solution of the linear matrix equation \(X = Af(X) B + C\) ⋮ On the Sylvester-like matrix equation \(AX+f(X)B=C\) ⋮ On T-Sylvester equations over commutative rings ⋮ Backward errors and small-sample condition estimation for ⋆-Sylveter equations ⋮ A note on Sylvester-type equations ⋮ The solutions of the quaternion matrix equation \(AX^\varepsilon + BX^\delta = 0\) ⋮ Uniqueness of solution of a generalized \(\star\)-Sylvester matrix equation ⋮ Positive definite solutions of the nonlinear matrix equation \(X + A^H\bar{X}^{-1}A = I\) ⋮ Global FOM and GMRES algorithms for a class of complex matrix equations ⋮ Relation between the T-congruence Sylvester equation and the generalized Sylvester equation ⋮ Q-less QR decomposition in inner product spaces ⋮ A flexible global GCRO-DR method for shifted linear systems and general coupled matrix equations ⋮ Projection methods for large-scale T-Sylvester equations ⋮ A note on the \(\top\)-Stein matrix equation ⋮ On a transformation of the ∗-congruence Sylvester equation for the least squares optimization ⋮ SOME ITERATIVE ALGORITHMS FOR POSITIVE DEFINITE SOLUTION TO NONLINEAR MATRIX EQUATIONS ⋮ The solution of the equationAX + BX^⋆ = 0

Uses Software

• Matlab
• mctoolbox

Cites Work

• Iterative algorithms for the minimum-norm solution and the least-squares solution of the linear matrix equations \(A_1XB_1 + C_1X^TD_1 = M_1, A_2XB_2 + C_2 X^TD_2 = M_2\)
• Gradient based and least squares based iterative algorithms for matrix equations \(AXB + CX^{T}D = F\)
• On the matrix function \(AX + X'A'\)
• Iterative algorithms for solving the matrix equation \(AXB + CX^{T}D = E\)
• Vibration of fast trains, palindromic eigenvalue problems and structure-preserving doubling algorithms
• The solution of the matrix equations \(AXB-CXD=E\) and \((YA-DZ,YC- BZ)=(E,F)\)
• A note on the matrix equation \(H=AP+PA**\)
• Structured Condition Numbers for Invariant Subspaces
• Iterative methods for solving linear matrix equation and linear matrix system
• The Equations A^TX\pm X^TA=B
• The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part I
• The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part II
• Accuracy and Stability of Numerical Algorithms
• Backward error, sensitivity, and refinement of computed solutions of algebraic Riccati equations
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