Perturbation theorems for the generalized eigenvalue problem

DOI10.1016/0024-3795(82)90120-3zbMath0504.15012OpenAlexW2011906094MaRDI QIDQ1835724

Ji-guang Sun, Ludwig Elsner

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0024-3795(82)90120-3

zbMATH Keywords

generalized eigenvalue problemmatrix pairGrassmann manifoldnormal matrixperturbation of eigenvaluesspectral difference

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (22)

Backward perturbation analysis of certain characteristic subspaces ⋮ Perturbation analysis for the sign functions of regular matrix pairs ⋮ On perturbations of matrix pencils with real spectra, a revisit ⋮ Optimal bounds for the spectral variation of two regular matrix pairs ⋮ A converse to the Bauer-Fike type theorem ⋮ Condition operators, condition numbers, and condition number theorem for the generalized eigenvalue problem ⋮ Generalized eigenvalue for even order tensors via Einstein product and its applications in multilinear control systems ⋮ A sharp version of Bauer-Fike's theorem ⋮ On perturbations of matrix pencils with real spectra. II ⋮ The perturbation bounds for eigenspaces of a definite matrix-pair ⋮ On the variation of the spectra of matrix pencils ⋮ On upper bounds for the spectral variation of two regular matrix pairs ⋮ The nearest definite pair for the Hermitian generalized eigenvalue problem ⋮ Symmetric matrix pencils ⋮ Matrix pencils: Theory, applications, and numerical methods ⋮ On Perturbations of Matrix Pencils with Real Spectra ⋮ PERTURBATION RESULTS RELATED TO PALINDROMIC EIGENVALUE PROBLEMS ⋮ Approximation of PDE eigenvalue problems involving parameter dependent matrices ⋮ Perturbation and interlace theorems for the unitary eigenvalue problem ⋮ An acceleration method for computing the generalized eigenvalue problem on a parallel computer ⋮ Implicit QR algorithms for palindromic and even eigenvalue problems ⋮ Pencils of complex and real symmetric and skew matrices

Cites Work

• Norms and exclusion theorems
• Bounds for iterates, inverses, spectral variation and fields of values of non-normal matrices
• Perturbation bounds for the definite generalized eigenvalue problem
• A note on Stewart's theorem for definite matrix pairs
• The variation of the spectrum of a normal matrix
• Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
• Gershgorin Theory for the Generalized Eigenvalue Problem Ax = λBx
• On the Sensitivity of the Eigenvalue Problem $Ax = \lambda Bx$
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