Parameter-Dependent Rank-One Perturbations of Singular Hermitian Or Symmetric Pencils

DOI10.1137/16M1060352zbMath1354.15007MaRDI QIDQ2957680

Michał Wojtylak, Volker Mehrmann, Christian Mehl

Publication date: 27 January 2017

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Hermitian pencilssingular pencilssymmetric pencilsstructured Kronecker canonical formgeneric low-rank perturbations

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Ill-posedness and regularization problems in numerical linear algebra (65F22) Eigenvalues, singular values, and eigenvectors (15A18) Canonical forms, reductions, classification (15A21) Matrix pencils (15A22)

Related Items (14)

Direct and inverse spectral problems for rank-one perturbations of self-adjoint operators ⋮ A Geometric Description of the Sets of Palindromic and Alternating Matrix Pencils with Bounded Rank ⋮ Finite rank perturbations of linear relations and matrix pencils ⋮ Generic symmetric matrix pencils with bounded rank ⋮ Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade ⋮ Miniversal deformations of pairs of symmetric matrices under congruence ⋮ The gap distance to the set of singular matrix pencils ⋮ Spectra of rank-one perturbations of self-adjoint operators ⋮ Global properties of eigenvalues of parametric rank one perturbations for unstructured and structured matrices ⋮ Solving Singular Generalized Eigenvalue Problems by a Rank-Completing Perturbation ⋮ Decompositions and coalescing eigenvalues of symmetric definite pencils depending on parameters ⋮ Estimation of Structured Distances to Singularity for Matrix Pencils with Symmetry Structures: A Linear Algebra--Based Approach ⋮ Spectra of $\mathcal{PT}$-symmetric operators under rank-one perturbations ⋮ Random perturbations of matrix polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the sign characteristics of Hermitian matrix polynomials
• Pencils of complex and real symmetric and skew matrices
• Where is the nearest non-regular pencil?
• The characteristic polynomial of a principal subpencil of a Hermitian matrix pencil
• Anti-triangular and anti-\(m\)-Hessenberg forms for Hermitian matrices and pencils
• Linearization of DAEs along trajectories
• Möbius transformations of matrix polynomials
• On the distance to singularity via low rank perturbations
• Generic Change of the Partial Multiplicities of Regular Matrix Pencils under Low-Rank Perturbations
• A Note on Generic Kronecker Orbits of Matrix Pencils with Fixed Rank
• Low Rank Perturbation of Weierstrass Structure
• Canonical Forms for Hermitian Matrix Pairs under Strict Equivalence and Congruence
• On the Nearest Singular Matrix Pencil
• Low Rank Perturbation of Kronecker Structures without Full Rank
• Coupling of substructures for dynamic analyses.

This page was built for publication: Parameter-Dependent Rank-One Perturbations of Singular Hermitian Or Symmetric Pencils