An algorithm for computing the eigenvalues of block companion matrices

DOI10.1007/s11075-012-9579-5zbMath1260.65024OpenAlexW2171583203MaRDI QIDQ1935391

Marc Van Barel, Katrijn Frederix, Steven Delvaux

Publication date: 15 February 2013

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://lirias.kuleuven.be/handle/123456789/223722

zbMATH Keywords

rootsnumerical exampleseigenvaluescompanion matrixmatrix polynomialQR algorithmHessenberg formrank structured matrixGivens-weight representation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrices over function rings in one or more variables (15A54)

Related Items (6)

Quasiseparable Hessenberg reduction of real diagonal plus low rank matrices and applications ⋮ Block tridiagonal reduction of perturbed normal and rank structured matrices ⋮ Fast and backward stable computation of eigenvalues and eigenvectors of matrix polynomials ⋮ Implicit double shift \(QR\)-algorithm for companion matrices ⋮ A CMV-Based Eigensolver for Companion Matrices ⋮ Fast and Backward Stable Computation of Roots of Polynomials

Cites Work

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• Implicit double shift \(QR\)-algorithm for companion matrices
• A Divide and Conquer method for the symmetric tridiagonal eigenproblem
• On the shifted QR iteration applied to companion matrices
• Relatively robust representations of symmetric tridiagonals
• Eigenvalue computation for unitary rank structured matrices
• A Hessenberg Reduction Algorithm for Rank Structured Matrices
• A Givens-Weight Representation for Rank Structured Matrices
• A QR-Based Solver for Rank Structured Matrices
• A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem
• Polynomial Roots from Companion Matrix Eigenvalues
• Fast QR Eigenvalue Algorithms for Hessenberg Matrices Which Are Rank‐One Perturbations of Unitary Matrices

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