Structured eigenvalue condition numbers and linearizations for matrix polynomials
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Publication:551349
DOI10.1016/j.laa.2011.04.020zbMath1225.65043OpenAlexW2016290153MaRDI QIDQ551349
Daniel Kressner, Bibhas Adhikari, Rafikul Alam
Publication date: 15 July 2011
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2011.04.020
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Hermitian, skew-Hermitian, and related matrices (15B57) Numerical computation of matrix norms, conditioning, scaling (65F35) Matrices over function rings in one or more variables (15A54)
Related Items (11)
A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error ⋮ Wilkinson's bus: weak condition numbers, with an application to singular polynomial eigenproblems ⋮ Singular quadratic eigenvalue problems: linearization and weak condition numbers ⋮ On backward errors of structured polynomial eigenproblems solved by structure preserving linearizations ⋮ Perturbation, extraction and refinement of invariant pairs for matrix polynomials ⋮ Palindromic linearizations of palindromic matrix polynomials of odd degree obtained from Fiedler-like pencils ⋮ Distance Problems for Hermitian Matrix Pencils with Eigenvalues of Definite Type ⋮ Sensitivity Analysis of Nonlinear Eigenproblems ⋮ Implicitly Restarted Refined Generalised Arnoldi Method with Deflation for the Polynomial Eigenvalue Problem ⋮ Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis ⋮ On why using \(\mathbb{DL}(P)\) for the symmetric polynomial eigenvalue problem might need to be reconsidered
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Cites Work
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- Eigenvalues, pseudospectrum and structured perturbations
- Pseudospectra, critical points and multiple eigenvalues of matrix polynomials
- Ellipsoidal calculus for estimation and control
- Error analysis of signal zeros: A projected companion matrix approach
- On the condition of a complex eigenvalue under real perturbations
- Remarks on the perturbation of analytic matrix functions. II
- Perturbation theory for homogeneous polynomial eigenvalue problems
- Backward error and condition of polynomial eigenvalue problems
- Leading coefficients of the eigenvalues of perturbed analytic matrix functions
- Eigenvalue condition numbers: zero-structured versus traditional.
- Structured Pseudospectra and the Condition of a Nonderogatory Eigenvalue
- μ-Values and Spectral Value Sets for Linear Perturbation Classes Defined by a Scalar Product
- Derivatives of Eigenvalues and Eigenvectors of Matrix Functions
- Perturbation of purely imaginary eigenvalues of Hamiltonian matrices under structured perturbations
- Backward Error of Polynomial Eigenproblems Solved by Linearization
- Structured Eigenvalue Condition Number and Backward Error of a Class of Polynomial Eigenvalue Problems
- Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems
- Optimal Scaling of Generalized and Polynomial Eigenvalue Problems
- Structured Backward Error and Condition of Generalized Eigenvalue Problems
- Perturbation of Eigenvalues for Matrix Polynomials via The Bauer--Fike Theorems
- Perturbation Theory for Analytic Matrix Functions: The Semisimple Case
- Normwise Scaling of Second Order Polynomial Matrices
- Accuracy and Stability of Numerical Algorithms
- Structured Hölder Condition Numbers for Multiple Eigenvalues
- Vector Spaces of Linearizations for Matrix Polynomials
- The Conditioning of Linearizations of Matrix Polynomials
- Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
- Structured Eigenvalue Condition Numbers
- Symmetric Linearizations for Matrix Polynomials
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