On the distance to singularity via low rank perturbations

DOI10.7153/oam-09-44zbMath1342.15006OpenAlexW2310111693MaRDI QIDQ2814819

Christian Mehl, Volker Mehrmann, Michał Wojtylak

Publication date: 23 June 2016

Published in: Operators and Matrices (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/oam-09-44

zbMATH Keywords

Weyl functionlow rank perturbationsingular pencilsdistance to singularity

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) Eigenvalue problems for linear operators (47A75) Matrix pencils (15A22)

Related Items (21)

A Geometric Description of the Sets of Palindromic and Alternating Matrix Pencils with Bounded Rank ⋮ Generic Change of the Partial Multiplicities of Regular Matrix Pencils under Low-Rank Perturbations ⋮ Computation of the nearest structured matrix triplet with common null space ⋮ Rank two perturbations of matrices and operators and operator model for \(\mathbf{t}\)-transformation of probability measures ⋮ Finite rank perturbations of linear relations and matrix pencils ⋮ Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade ⋮ Eigenvalue Placement for Regular Matrix Pencils with Rank One Perturbations ⋮ On the Nearest Singular Matrix Pencil ⋮ Parameter-Dependent Rank-One Perturbations of Singular Hermitian Or Symmetric Pencils ⋮ Bounded rank perturbations of a regular matrix pencil ⋮ Nearest rank deficient matrix polynomials ⋮ Bounded Rank Perturbations of Quasi-Regular Pencils Over Arbitrary Fields ⋮ The gap distance to the set of singular matrix pencils ⋮ A note on an upper and a lower bound on sines between eigenspaces for regular Hermitian matrix pairs ⋮ Distance problems for dissipative Hamiltonian systems and related matrix polynomials ⋮ Global properties of eigenvalues of parametric rank one perturbations for unstructured and structured matrices ⋮ Solving Singular Generalized Eigenvalue Problems by a Rank-Completing Perturbation ⋮ Rank One Perturbations of Matrix Pencils ⋮ Double generalized majorization ⋮ Estimation of Structured Distances to Singularity for Matrix Pencils with Symmetry Structures: A Linear Algebra--Based Approach ⋮ Double generalized majorization and diagrammatics

Uses Software

• Matlab
• Simulink

Cites Work

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• First order spectral perturbation theory of square singular matrix polynomials
• Low rank perturbation of regular matrix polynomials
• Where is the nearest non-regular pencil?
• The characteristic polynomial of a principal subpencil of a Hermitian matrix pencil
• On the Perron roots of principal submatrices of co-order one of irreducible nonnegative matrices
• Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
• Symmetric Linearizations for Matrix Polynomials

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