The solutions of a class of Sylvester-like linear matrix equations and the estimation of the associated measurements of their solutions

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Ill-posedness and regularization problems in numerical linear algebra (65F22) Numerical optimization and variational techniques (65K10) Matrix equations and identities (15A24) Inequalities involving eigenvalues and eigenvectors (15A42) Numerical methods for matrix equations (65F45)

Cites Work

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On the \(\star\)-Sylvester equation \(AX\pm X^{\star} B^{\star} = C\)
Some further notes on the matrix equations \(A^TXB+B^TX^TA=C\) and \(A^TXB+B^TXA=C\)
A lower bound for the product of eigenvalues of solutions to matrix equations
Uniqueness of solution of a generalized \(\star\)-Sylvester matrix equation
The solutions to some operator equations
Least-squares solution with the minimum-norm for the matrix equation \(A^T XB + B^T X^T A = D\) and its applications
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Linear matrix equations from an inverse problem of vibration theory
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Computational Methods for Linear Matrix Equations
Structured Condition Numbers for Invariant Subspaces
A Multigrid Method to Solve Large Scale Sylvester Equations
Principal component analysis in linear systems: Controllability, observability, and model reduction
The Equations A^TX\pm X^TA=B
Generalized Sylvester Equations
Best Approximate Solution of Matrix Equation AXB+CYD=E
Explicit Solutions of Linear Matrix Equations
Matrix theory. Basic results and techniques
Network Flows That Solve Sylvester Matrix Equations

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