Bounds for eigenvalues of matrix polynomials with applications to scalar polynomials

DOI10.1016/j.laa.2016.04.005zbMath1338.15028OpenAlexW2337919722MaRDI QIDQ286143

Aaron Melman

Publication date: 20 May 2016

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

Full work available at URL: https://doi.org/10.1016/j.laa.2016.04.005

zbMATH Keywords

boundpolynomial rootpolynomial eigenvalue problemCauchypolynomial zero

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) 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)

Annulus containing all the eigenvalues of a matrix polynomial ⋮ Polynomial eigenvalue estimation: numerical radii versus norms ⋮ Improved Cauchy radius for scalar and matrix polynomials ⋮ An efficient approximation to the Cauchy radius ⋮ Refinement of Pellet radii for matrix polynomials ⋮ Polynomial eigenvalue bounds from companion matrix polynomials ⋮ An alternative proof of Pellet’s theorem for matrix polynomials ⋮ Directional bounds for polynomial zeros and eigenvalues ⋮ Conservation of the numbers of characteristic values of polynomial and entire matrix pencils inside and outside a circle under perturbations

Uses Software

• NLEVP

Cites Work

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• The Quadratic Eigenvalue Problem
• On the Numerical Solution of $(\lambda^2 A + \lambda B + C), x = b$ and Application to Structural Dynamics
• NLEVP
• Analysis of parameterized quadratic eigenvalue problems in computational acoustics with homotopic deviation theory
• Matrix Polynomials
• Locating the Eigenvalues of Matrix Polynomials
• A Generalization of a Theorem of Bôcher

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