Solution of the matrix eigenvalue problem \(VA+A^{*}V=\mu V\) with applications to the study of free linear dynamical systems

DOI10.1016/j.cam.2007.01.001zbMath1142.65036OpenAlexW1974500655MaRDI QIDQ2469617

Ludwig Kohaupt

Publication date: 6 February 2008

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.2007.01.001

zbMATH Keywords

stabilitynumerical examplesmatrix eigenvalue problemdifferential calculus of normsalgebraic Lyapunov equation, linear dynamical system, decoupling and filter effect of weighted semi-normstwo sided bound depending on the initial conditions

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrix equations and identities (15A24) Stability and convergence of numerical methods for ordinary differential equations (65L20) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (8)

Lyapunov type operators for numerical solutions of PDEs ⋮ Spectral properties of the matrix \(C^{-1} B\) with positive definite \(C\) and Hermitian \(B\) as well as applications ⋮ Further spectral properties of the matrix \(C^{-1}B\) with positive definite \(C\) and Hermitian \(B\) applied to wider classes of matrices \(C\) and \(B\) ⋮ Trigonometric spline and spectral bounds for the solution of linear time-periodic systems ⋮ Two-sided bounds on some output-related quantities in linear stochastically excited vibration systems with application of the differential calculus of norms ⋮ On norm equivalence between the displacement and velocity vectors for free linear dynamical systems ⋮ Solution formulas for differential Sylvester and Lyapunov equations ⋮ Two-sided bounds for the asymptotic behaviour of free nonlinear vibration systems with application of the differential calculus of norms

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