Perturbation analysis for the eigenvalue problem of a formal product of matrices

DOI10.1023/A:1021966001542zbMath1003.65032OpenAlexW1508354024MaRDI QIDQ1599133

Peter Benner, Volker Mehrmann, Hong-guo Xu

Publication date: 8 January 2003

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1021966001542

zbMATH Keywords

perturbation theoryeigenvalue problemerror boundsHamiltonian matrixmatrix pencilsdeflating subspaceperiodic \(QZ\) algorithm

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42)

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Perturbation bounds for the periodic Schur decomposition ⋮ Approximation by matrices with simple spectra ⋮ On estimating the separation associated with the periodic continuous Sylvester equation ⋮ A numerical method for computing the Hamiltonian Schur form ⋮ The Rayleigh-Ritz method, refinement and Arnoldi process for periodic matrix pairs ⋮ The Maximal Solution and Comparison Theorems for the Periodic Discrete-Time Riccati Equation ⋮ Computing periodic deflating subspaces associated with a specified set of eigenvalues ⋮ On estimating the separation of two periodic matrix sequences ⋮ On condition numbers of the spectral projections associated with periodic eigenproblems ⋮ Backward errors of periodic invariant subspaces for regular periodic matrix pairs ⋮ Fast and backward stable computation of eigenvalues and eigenvectors of matrix polynomials ⋮ Structured Eigenvalue Problems ⋮ 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

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