Improved Cauchy radius for scalar and matrix polynomials

DOI10.1090/proc/13826zbMath1383.15017arXiv1709.03040OpenAlexW2963788238MaRDI QIDQ4595992

Aaron Melman

Publication date: 8 December 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.03040

zbMATH Keywords

matrix polynomialpolynomial eigenvalue problempolynomial zeroCauchy radiuspolynomial root bound

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Matrices over function rings in one or more variables (15A54)

Related Items (3)

A unifying framework for generalizations of the Eneström-Kakeya theorem ⋮ Matrices whose eigenvalues are those of a quadratic matrix polynomial ⋮ Refinement of Pellet radii for matrix polynomials

Cites Work

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• Bounds for eigenvalues of matrix polynomials with applications to scalar polynomials
• Iterative system solvers for the frequency analysis of linear mechanical systems
• Bounds for eigenvalues of matrix polynomials
• Generalization and variations of Pellet's theorem for matrix polynomials
• Locating the Eigenvalues of Matrix Polynomials

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