On the Singular “Vectors” of the Lyapunov Operator

DOI10.1137/0608003zbMath0633.65042OpenAlexW1986541128MaRDI QIDQ3771498

Stephen G. Nash, Ralph Byers

Publication date: 1987

Published in: SIAM Journal on Algebraic Discrete Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0608003

zbMATH Keywords

numerical stabilityLyapunov matrix equationsingular vectorsskew-symmetric matrixseparationCounterexamplesnearly optimal matrixreal symmetric minimizer

Mathematics Subject Classification ID

Related Items (14)

Optimal stochastic forcings for sensitivity analysis of linear dynamical systems ⋮ Trace norm bounds for stable Lyapunov operators ⋮ An implicit deflation method for ill-conditioned Sylvester and Lyapunov equations ⋮ A structured condition number for self-adjoint polynomial matrix equations with applications in linear control ⋮ Perturbation analysis of the matrix equation \(X=Q+A^{\text H}(\widehat X-C)^{-1}A\) ⋮ Ralph Byers 1955--2007 ⋮ On the spectral structure of Jordan-Kronecker products of symmetric and skew-symmetric matrices ⋮ A further study on a nonlinear matrix equation ⋮ Solvability and sensitivity analysis of polynomial matrix equation \(X^s + A^TX^tA = Q\) ⋮ Solution formulas for differential Sylvester and Lyapunov equations ⋮ On properties of Sylvester and Lyapunov operators ⋮ Note on “On the Singular “Vectors” of the Lyapunov Operator” by R. Byers and S. Nash ⋮ Sensitivity analysis of the discrete-time algebraic Riccati equation ⋮ Condition numbers of algebraic Riccati equations in the Frobenius norm

Uses Software

• LINPACK

Cites Work

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• A LINPACK-style condition estimator for the equation<tex>AX-XB^{T} = C</tex>
• A Hessenberg-Schur method for the problem AX + XB= C
• On the Separation of Two Matrices
• Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
• An Estimate for the Condition Number of a Matrix
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Explicit Solutions of Linear Matrix Equations
• Solving the Matrix Equation $\sum _{\rho = 1}^r f_\rho (A)Xg_\rho (B) = C$

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