Bounds for the variation of matrix eigenvalues and polynomial roots

DOI10.1016/0024-3795(94)90432-4zbMath0807.15012OpenAlexW1984968467MaRDI QIDQ1336400

Gerd M. Krause

Publication date: 1 March 1995

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

Full work available at URL: https://doi.org/10.1016/0024-3795(94)90432-4

zbMATH Keywords

numerical resultspolynomial rootsmatrix normsspectral normoptimal matching distancevariation of matrix eigenvalues

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15)

Related Items (9)

Safety neighbournoods for the invariants of the matrix similarity^∗ ⋮ Jordan Structures and Lattices of Invariant Subspaces of Real Matrices ⋮ On the mathematical theory of ensemble (linear-Gaussian) Kalman-Bucy filtering ⋮ Lipschitz properties of structure preserving matrix perturbations ⋮ Explicit stationary distribution of the \((L,1)\)-reflecting random walk on the half line ⋮ Spectral variation bounds in hyperbolic geometry ⋮ Light-tailed behavior of stationary distribution for state-dependent random walks on a strip ⋮ On the stability of matrix-valued Riccati diffusions ⋮ Challenging eigenvalue perturbation problems

Cites Work

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• Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix
• An optimal bound for the spectral variation of two matrices
• Variation of tensor powers and spectrat

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