Perturbation analysis for the eigenproblem of periodic matrix pairs

DOI10.1016/S0024-3795(01)00347-0zbMath1013.15004OpenAlexW2047794463WikidataQ127370910 ScholiaQ127370910MaRDI QIDQ5954130

Wen-Wei Lin, Ji-guang Sun

Publication date: 30 January 2002

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0024-3795(01)00347-0

zbMATH Keywords

condition numbersbackward errorseigenvalue pairsperiodic matrix pairsperturbation bounds

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42)

Related Items (17)

Perturbation bounds for the periodic Schur decomposition ⋮ On perturbation bounds of generalized eigenvalues for diagonalizable pairs ⋮ On estimating the separation associated with the periodic continuous Sylvester equation ⋮ A note on the approximation of two-sided Rayleigh quotient to eigenvalues ⋮ On the Hermitian positive definite solutions of nonlinear matrix equation \(X^s + A^\ast X^{-t_1} A + B^\ast X^{-t_2} B = Q\) ⋮ The Rayleigh-Ritz method, refinement and Arnoldi process for periodic matrix pairs ⋮ New bounds for perturbation of the orthogonal projection ⋮ The Maximal Solution and Comparison Theorems for the Periodic Discrete-Time Riccati Equation ⋮ Sensitivity analysis for the generalized singular value decomposition ⋮ Computing periodic deflating subspaces associated with a specified set of eigenvalues ⋮ On condition numbers of the spectral projections associated with periodic eigenproblems ⋮ Backward errors of periodic invariant subspaces for regular periodic matrix pairs ⋮ Structured Eigenvalue Problems ⋮ Perturbation analysis for best approximation and the polar factor by subunitary matrices ⋮ Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem ⋮ Perturbation of eigenvalues for periodic matrix pairs via the Bauer-Fike theorems ⋮ A note on the Hoffman-Wielandt theorem for generalized eigenvalue problems

Uses Software

• mctoolbox

Cites Work

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• The geometric approach for linear periodic discrete-time systems
• Stability theory for linear time-invariant plants with periodic digital controllers
• The difference periodic Ricati equation for the periodic prediction problem
• Structured Backward Error and Condition of Generalized Eigenvalue Problems
• Periodic descriptor systems: solvability and conditionability
• A Theory of Condition

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