Singular quadratic eigenvalue problems: linearization and weak condition numbers
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Publication:2685122
DOI10.1007/s10543-023-00960-4OpenAlexW4320914435MaRDI QIDQ2685122
Ivana Šain Glibić, Daniel Kressner
Publication date: 19 February 2023
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2204.07424
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18)
Related Items (3)
The \(\mathbb{DL}(P)\) vector space of pencils for singular matrix polynomials ⋮ Solving Singular Generalized Eigenvalue Problems. Part II: Projection and Augmentation ⋮ Invertible bases and root vectors for analytic matrix-valued functions
Uses Software
Cites Work
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- Structured eigenvalue condition numbers and linearizations for matrix polynomials
- The computation of Kronecker's canonical form of a singular pencil
- Wilkinson's bus: weak condition numbers, with an application to singular polynomial eigenproblems
- First order spectral perturbation theory of square singular matrix polynomials
- First order spectral perturbation theory of square singular matrix pencils
- Trimmed linearizations for structured matrix polynomials
- General theory of regular matrix polynomials and band Toeplitz operators
- Kronecker's canonical form and the QZ algorithm
- On the condition of a complex eigenvalue under real perturbations
- The eigenstructure of an arbitrary polynomial matrix: Computational aspects
- Backward error and condition of polynomial eigenvalue problems
- Root polynomials and their role in the theory of matrix polynomials
- The Quadratic Eigenvalue Problem
- A Backward Stable Algorithm for Quadratic Eigenvalue Problems
- Accurate Solutions of Ill-Posed Problems in control theory
- The generalized eigenstructure problem in linear system theory
- Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
- The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part I
- The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part II
- Normwise Scaling of Second Order Polynomial Matrices
- Accuracy and Stability of Numerical Algorithms
- Solving Singular Generalized Eigenvalue Problems by a Rank-Completing Perturbation
- Vector Spaces of Linearizations for Matrix Polynomials
- The Conditioning of Linearizations of Matrix Polynomials
- Perturbation bounds in connection with singular value decomposition
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