A generalized companion matrix of a polynomial and some applications

DOI10.1016/0024-3795(83)90164-7zbMath0522.15013OpenAlexW2078782009MaRDI QIDQ1055849

Wilhelm Werner

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0024-3795(83)90164-7

zbMATH Keywords

zeros of polynomialseigenvalue boundsGershgorin's theorembounds for the zerosQR-algorithmcharacteristic equation of a matrixDanilevsky-type algorithmgeneralized companion matrix

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Numerical computation of solutions to single equations (65H05) Canonical forms, reductions, classification (15A21)

Related Items

A note on generalized companion pencils in the monomial basis, Linear construction of companion matrices, A remark on Frank matrices, Inclusion of the roots of a polynomial based on Gerschgorin's theorem

Cites Work

• Matrix methods for polynomials
• On the condition of algebraic equations
• A posteriori error bounds for the zeros of a polynomial
• A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem
• A Generalization of a Theorem of Bôcher
• Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item